Thermodynamic Database of the La-Sr-Mn-Cr-O Oxide

1

Diss. ETH No. 18139

Thermodynamic Database of the La-Sr-Mn-Cr-O Oxide

System and Applications to Solid Oxide Fuel Cells

DISSERTATION

for the degree of

DOCTOR OF SCIENCES

of the

SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH

presented by

ERWIN POVODEN-KARADENIZ

Mag. rer. nat.

born on March 18, 1973

Citizen of Austria

accepted on the recommendation of

Prof. Dr. Ludwig J. Gauckler, examiner

Prof. John T.S. Irvine, co-examiner

Dr. Ming Chen, co-examiner

Zurich, 2008

2

Dedicated to my parents

Whatever creates or increases happiness

or some part of happiness,

we ought to do;

whatever destroys or hampers happiness,

or gives rise to its opposite,

we ought not to do.

Aristoteles

3

Acknowledgements

I am deeply grateful to my supervisor Professor Gauckler. He gave me a great chance by

taking me into the boat: a boat that is not only sailed to scientific success. It took me away

from an insecure float wobbling in the surf and approaches a promising future.

Endless gratitude belongs to my wife who stays by my side throughout highs, downs, and

distances, preventing me from losing the way; she is my firm anchor.

I am greatly indebted to Nicholas Grundy for open doors, his patience of a saint, great

teaching, and picky reviewing. He catalyzed my way into the field of thermodynamic

modeling, airing the “modeling is fun” approach at any time.

I would further like to thank Ming Chen for continuing scientific support and advising; he

was often motivating me to spin the wheel of accurate and fast modeling and publishing.

I owe thanks to Franc and Flavia Dugal-Borsari who saved me from an unintentional outdoor

adventure in Zurich during a time when it was extremely difficult to find a new

accommodation. It was a very pleasant time in Zollikon.

I thank Brandon Bürgler and Jennifer Rupp for their pleasing office companionship at the

beginning of my work: they facilitated my jump into the ETH waters.

I would also like to thank Toni Ivas for abiding collegiality, cooperation, and friendship.

I thank the rest of the office crew, Thomas Ryll and Rene Tölke, for always enjoyable

working hours.

Zurich, December 2008

Table of Contents

4

Table of Contents

Summary 7

Zusammenfassung 9

1 Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-

alloy interconnects 11

1.1 Introduction 11

1.1.1 Principles of SOFC 11

1.1.2 The problem of chromium “poisoning” 13

1.2 Volatilization of Cr2O3 14

1.3 Literature survey 17

1.3.1 Degradation of SOFC caused by chromium from the interconnect 17

1.3.2 The role of current load on electrical losses of degraded SOFC 22

1.3.3 Impedance spectroscopy measurements and implications on the

degradation process 24

1.3.4 Microstructures in degraded SOFC 24

1.3.5 Amounts of chromium in SOFC tested with and without current

load 27

1.3.6 Critical assessment of proposed mechanisms of chromium

“poisoning” 28

1.4 Proposed strategies against chromium “poisoning” and their effectiveness 36

1.4.1 Increasing the Cr-tolerance of conventional SOFC with

Cr-interconnects and LSM cathodes 36

1.4.2 New ways – alternative materials 37

2 Aim of study 45

3 Method 46

3.1 Benefits of the thermodynamic La-Sr-Mn-Cr-O oxide database for the

understanding of Cr-poisoning of SOFC 46

3.2 Thermodynamic modeling 47

3.2.1 Stoichiometric solid oxides 47

3.2.2 Solid solution phases – the Compound Energy Formalism (CEF) 48

3.2.3 Vacancies and the concept of reciprocal reactions 49

Table of Contents

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3.2.4 Calculation of defect chemistry using the Calphad approach 51

3.3 Optimization of model parameters 52

4 Thermodynamic assessments 53

4.1 Thermodynamic reassessment of the Cr-O system in the framework of

SOFC research 53

4.1.1 Technology 53

4.1.2 Experimental data 54

4.1.3 Previous assessments of the Cr-O System 58

4.1.4 Thermodynamic modeling 59

4.1.5 Optimization of parameters 66

4.1.6 Results and discussion 67

4.1.7 Conclusions 73

4.2 Thermodynamic assessment of the Mn-Cr-O system for SOFC materials 77

4.2.1 Introduction 77

4.2.2 Experimental 78

4.2.3 Thermodynamic modeling 86

4.2.4 Optimization of parameters 89

4.2.5 Results 93

4.2.6 Discussion 96

4.2.7 Applications on SOFC 97

4.3 Thermodynamic assessment of the La-Cr-O system 101


4.3.2 Literature review of the La-Cr system 103

4.3.3 Literature review of the La-Cr-O system 103

4.3.4 Thermodynamic modeling and optimization 109



4.4 Thermodynamic La-Sr-Mn-Cr-O oxide database for SOFC applications 134


4.4.2 Assessment of data from the literature 135

4.4.3 Modeling and optimization 137



5 Thermodynamic calculations of impacts of chromium on Sr-doped

Table of Contents

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manganite (LSM) cathodes for SOFC 148

5.1 Introduction 149

5.2 Method 150

5.3 Results 152

5.3.1 Thermodynamic calculations of La0.9Sr0.1MnO3-δ contaminated

by chromium 152

5.3.2 Thermodynamic calculations of (La0.8Sr0.2)0.9MnO3-δ contaminated

by chromium 157

5.3.3 Thermodynamic testing of LSM with Mn-deficiency 160

5.3.4 Formation of Cr2O3 162

5.4 Discussion 163

5.5 Conclusions 165

Appendix 170

Thermodynamic La-Cr database 169

Thermodynamic La-Sr-Mn-Cr-O-(H) oxide database 172

Curriculum Vitae 190

Summary

7

Summary

The thermodynamic La-Sr-Mn-Cr-O oxide database is established by assessing oxide

subsystems using the CALPHAD (Calculation of phase diagrams) approach. The new

database is applied to the problem of chromium “poisoning” of Sr-doped lanthanum

manganite cathodes ((La1−xSrx)1-yMnO3-δ or LSM) for Solid Oxide Fuel Cells (SOFC)

stemming from gaseous Cr species from the high-Cr containing alloy of the interconnect. The

chromium is known to deteriorate the electrical performance of the cathodes.

In chapter 1 the basics of planar SOFC are briefly explained, and previous findings of

chromium “poisoning” of SOFC are critically reviewed. Based on the findings from the

literature it gets clear that several questions about the key mechanisms of the chromium

“poisoning” have not been answered yet, and the aim of this study (chapter 2) is to gather a

deeper understanding of these unsolved problems by using thermodynamics. In the third

chapter the reader learns, how thermodynamic calculations can lead to a better understanding

of a system, even if the system is in a thermodynamic non-equilibrium state, and the modeling

approach used in this study is presented. Chapter 4 deals with the construction of the La-Sr-

Mn-Cr-O oxide database based on the assessments of subsystems. The new database is

applied to the problem of chromium “poisoning” of SOFC with Cr-interconnects and LSM

cathodes in chapter 5: a consistent phenomenological description of the process of chromium

“poisoning” of SOFC cathodes is established that is in line with both experimental findings

reported in the literature and thermodynamic calculations using the presented database. It is

shown that chromium “poisoning” of SOFC cathodes is a rather complex process consisting

of several steps, some of them probably occurring simultaneously. Some of these processes

are governed by thermodynamics, and some are kinetically controlled.

A key role is played by the adsorption of gaseous CrO3(g) (g = gaseous) and chromium-

oxyhydroxides stemming from the interconnect on LSM and reaction of chromium with LSM.

The associated chemical changes of the LSM phase, as well as the formation of a new spinel

phase occur under thermodynamic control: decreasing concentrations of vacancies in LSM

that contains chromium are calculated at decreased oxygen partial pressure reflecting SOFC

operation at high current load. This has calamitous consequences for the electrochemical

properties of the cathode. Furthermore spinel blocks pores and thus impedes the oxygen

Summary

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reduction required for the function of the cell. Cr2O3(s) (s = solid) that hampers the diffusion of

oxygen into the electrolyte is a metastable phase in LSM contaminated by chromium.

With this contribution the prevailing question is resolved, which of the phenomena in a

chromium-“poisoned” LSM cathode are governed by thermodynamics. Appropriate measures

can be foreseen preventing the long-term degradation of SOFC cathodes in combination with

high-chromium containing interconnects.

Zusammenfassung

9

Zusammenfassung

Die thermodynamische La-Sr-Mn-Cr-O Oxid-datenbank wird basierend auf dem Assessment

oxidischer Subsysteme mit dem CALPHAD-ansatz (Berechnung von Phasendiagrammen)

aufgebaut. Die neue Datenbank wird auf das Problem der „Chromvergiftung“ von Sr-

dotierten Lanthan-Manganit-kathoden ((La1−xSrx)1−yMnO3-δ oder LSM) für Festoxid-

Brennstoffzellen (SOFC) angewandt, welches von gasförmigen Cr spezies der hochgradig Cr-

führenden Interkonnektor-Legierung herrührt. Es ist bekannt, dass das Crom die elektrische

Leistung der Kathoden verschlechtert.

In Kapitel 1 werden die Grundlagen von planaren SOFC kurz erklärt, und es wird ein

kritischer Überblick über bisherige Erkenntnisse der „Chromvergiftung“ von SOFC gegeben.

Basierend auf den Erkenntnissen aus der Literatur wird klar, dass einige Fragen, welche die

Schlüsselmechanismen der „Chromvergiftung“ betreffen, noch nicht beantwortet wurden. Das

Ziel dieser Studie (Kapitel 2) ist es, unter Verwendung der Thermodynamik ein tieferes

Verständnis dieser ungelösten Probleme zu erlangen. Im dritten Kapitel lernt der Leser, wie

thermodynamische Berechnungen zu einem besseren Verständnis eines Systems führen

können, selbst wenn dieses System sich in einem thermodynamischen

Ungleichgewichtszustand befindet, und der in dieser Studie verwendete Modellansatz wird

vorgestellt. Kapitel 4 beschäftigt sich mit der Konstruktion der La-Sr-Mn-Cr-O Oxid-

Datenbank, basierend auf den Assessments der Subsysteme. In Kapitel 5 wird die neue

Datenbank auf das Problem der „Chromvergiftung“ von SOFC mit Cr-interkonnektoren und

LSM-kathoden angewandt: Eine konsistente phenomenologische Beschreibung des Prozesses

der „Chromvergiftung“ von SOFC-kathoden wird gegeben, welche sowohl im Einklang mit

experimentellen Erkenntnissen in der Literatur als auch mit thermodynamischen

Berechnungen unter Verwendung der präsentierten Datenbank steht. Es wird gezeigt, dass

„Chromvergiftung“ von SOFC-kathoden ein ziemlich komplexer Vorgang mit mehreren,

teilweise gleichzeitig in der Zelle ablaufenden Schritten ist. Manche dieser Prozesse sind

thermodynamisch kontrolliert, und manche laufen unter kinetischer Kontrolle ab.

Eine Schlüsselrolle spielt die Adsorbtion von gasförmigem CrO3(g) (g = gasförmig) und

Chromium-oxyhydroxiden, welche vom Interkonnektor stammen, an LSM und die Reaktion

von Chrom mit LSM. Die damit verbundenen chemischen Änderungen der LSM-phase und

die Bildung einer neuen Spinellphase finden unter thermodynamischer Kontrolle statt. Die

Zusammenfassung

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Berechnungen ergeben abnehmende Konzentrationen der Leerstellen in Cr-hältigem LSM

unter erniedrigtem Sauerstoffpartialdruck, und somit bei Betrieb von SOFC unter hohem

Laststrom . Das hat katastrophale Konsequenzen für die elektrochemischen Eigenschaften der

Kathode. Weiters blockiert Spinell Poren und behindert so die für die Funktion der Zelle

notwendige Sauerstoffreduktion. Cr2O3(s) (s = fest), welches die Diffusion von Sauerstoff in

den Elektrolyt erschwert, ist eine metastabile Phase in Cr-kontaminiertem LSM.

Mit diesem Beitrag werden einige der vorherrschenden Fragen über „Chromvergiftung“ von

SOFC geklärt, und geeignete Maßnahmen zur Verhinderung der Langzeitdegradation von

SOFC-kathoden in Kombination mit hochgradig Chrom-führenden Interkonnektoren können

vorhergesagt werden.

Degradation of planar solid oxide fuel cells (SOFC) with LSM cathodes and Cr-alloy interconnects

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1 Degradation of planar solid oxide fuel cells (SOFC) with

LSM cathodes and Cr-alloy interconnects

E. Povoden and L.J. Gauckler, to be submitted to Int. J. Mater. Rev.

For the use of LSM cathodes in planar SOFC a comprehensive understanding of the

mechanisms of the cell degradation caused by chromium diffusing from the interconnects into

the cell is needed. This “poisoning” has been intensively investigated over the last decade. In

this paper the affects of Cr on the degradation of SOFC with LSM cathodes and Cr-alloy

interconnects are reviewed: the suggested models of chromium “poisoning” of planar SOFC

with chromium-alloy interconnects and (La1-xSrx)1-yMnO3-δ (LSM) cathodes from the

literature are critically assessed. Taking into account all available experimental findings on

the affects of chromium on Sr-doped lanthanum manganite cathodes in planar solid oxide fuel

cells, it can be concluded that several “poisoning” processes contribute to the deterioration of

the cell performance. The review of all available experimental findings on the degradation of

SOFC caused by chromium allows predictions, as to how the extent of degradation caused by

chromium depends on the current load, operation temperature, operation time, as well as the

amount of chromium diffusing from the interconnect.

1.1 Introduction

1.1.1 Principles of SOFC

A fuel cell directly converts chemical energy into electrical energy. A solid oxide fuel cell

consists of two porous electrodes that are separated by a dense, oxygen ion-conducting

electrolyte. A simple schematic of the electrochemical process is shown in Fig. 1.1.1 (next

page).


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Fig. 1.1.1 Scheme of the electrochemical processes in a fuel cell with O2 oxidant and H2 fuel.

White circles symbolize pores. a = anode, c = cathode, e = electrolyte.

The oxygen, supplied at the cathode reacts with electrons from the external electric circuit to

form oxygen ions. These ions migrate through the electrolyte to the anode. At the anode the

oxygen ions react with hydrogen of the fuel to form water and release electrons. The electrons

flow from the anode through the external electric circuit to the cathode. The direct-current

electricity is produced by the electron flow through the external electric circuit.

In an SOFC, cathode and electrolyte consist of refractory solid oxide ceramics, and ceramic-

metal composites are used for the anode. The materials for the cell components need to have a

sufficient chemical and structural stability at rather high temperatures up to 1273 K that occur

during cell production as well as during cell operation. The electrodes are required to have

high reactivity and the electrolyte must allow high oxygen ion diffusion. All the components

of the cell need to be matched in their thermal expansion in order to minimize mechanical

stresses.

A single cell produces a voltage of 0.7 to 1 V and power around 0.5 to 1 W cm-2. Normally

many cells are electrically connected in series by an interconnect, as shown in Fig. 1.1.2 (next

page) for the widely used planar-design SOFC, forming a cell stack to obtain higher voltage

and power.


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Fig. 1.1.2 Planar design of SOFC

The interconnect separates the fuels and oxidants in adjacent cells. It is the most demanding

component in a planar SOFC as it should have a high electronic conductivity, a low ionic

conductivity; stability in both oxidizing and reducing atmospheres at the high cell operating

temperature (from about T = 973 K to 1273 K); low permeability for oxygen and hydrogen to

minimize direct combination of oxidant and fuel during cell operation; a thermal expansion

coefficient close to that of the cathode and the anode; and chemical compatibility (no

reactions) with other cell materials.

1.1.2 The problem of chromium “poisoning”

In the 1990is LaCrO3-based ceramics were intensively investigated for interconnect

applications in SOFC, as the thermal expansions of LaCrO3-based interconnect and

conventional perovskite cathode materials are similar, the electronic conductivity of several

LaCrO3-based ceramics under SOFC operating conditions is high, and their thermal and

redox-stability is satisfying[1]. However high costs of these materials, difficulties in sintering

and manufacturing and low mechanical strength[2] required the development of alternative

interconnect materials. Nowadays the state-of-the-art interconnect is commonly a chromium-

containing metal plate[3-5], as chromium alloys come close to all desired properties. However

high-valent gaseous Cr-oxide and Cr-oxyhydroxides diffuse from the Cr2O3(s) scale covering

the interconnect into the cathode up to the cathode-electrolyte interface and cause the

degradation that results in the strong deterioration of the electrical performance of SOFC.


14

In the last decade a lot of effort was made to elucidate the degradation mechanisms, and it

was suggested that high-valent gaseous Cr-oxide and Cr-oxyhydroxides detrimentally affect

the O2 -adsorbtion, -reduction, and -diffusion processes.

1.2 Volatilization of Cr2O3

Early investigations[6-9] revealed that oxidation of Cr-containing alloys at high temperatures

leads to the redeposition of Cr2O3(s) crystals at cooler parts of the experimental apparatus from

the gas phase. This was a surprising result, as the film of Cr2O3(s) covering the alloy specimen

would have been expected to act as a diffusion barrier preventing the migration of Cr that has

a high vapour pressure from the alloy through the Cr2O3 layer. Furthermore, neither the

vapour pressure of Cr2O3(s) nor its dissociation pressure is high enough to account for the

quantities of deposits observed[10]. Because of the high vapour pressure of Cr it was thus first

considered that the metal itself would diffuse along oxide grain boundaries of the barrier film,

or at discontinuities such as fractures in the film and would then evaporate. But when it was

learned that Cr2O3(s), in the absence of metal, lost weight when heated in oxygen, it became

evident that a volatile Cr-oxide was being formed[10].

Caplan and Cohen[10] investigated the evaporation of Cr2O3(s) by measuring the weight loss

when Cr2O3(s) pellets with 1.2 cm in diameter and height were heated at T = 1273 K in

stagnant air, and at T = 1373 and 1473 K in flowing dry and wet oxygen as well as in dry and

wet argon. Appreciable volatilization occurred in dry oxygen, the weight loss being 0.6 mg at

T = 1373 K and 2.3-2.6 mg at T = 1473 K at a gas flow rate of 200 ml min-1 after 20 h. The

volatilization in wet oxygen was significantly higher after 20 h at the same gas flow rate:

2.1 mg at T = 1373 K and 5.6 mg at T = 1473 K. In stagnant air the volatilization was 0.3 mg

at T = 1273 K after 72 h. Volatilization of Cr2O3(s) was neither observed in dry nor in wet

argon. The observation that no loss of Cr2O3(s) occurs in argon confirms that volatilization

does neither occur by dissociation of the oxide nor as Cr2O3(g) vapor. Since weight loss takes

place under oxidizing conditions, the volatile species must be a higher oxide of chromium. A

known volatile oxide of Cr is CrO3, but its formation by the reaction

2 3(s) 2(g) 3(g)Cr O 3 2O 2CrO+ → (1.2.1)


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is thermodynamically unfavourable at high temperatures[10], Δ°G of Eq. 1.1 is calculated to be

+321 kJ at T = 1273 K using assessed thermodynamic data for Cr2O3(s) from Povoden et

al.[11], data for O2(g) from Dinsdale[12], and for CrO3(g) from Ebbinghaus[13]. As gaseous CrO3(g)

was detected experimentally by mass spectrometry when Cr2O3(s) was heated under oxidizing

conditions, the formation of CrO3(g) occurs under kinetic control[10].

The existence of gaseous Cr-oxyhydroxides as oxidation products (Eqs. 1.2.2 and 1.2.3) in

wet atmosphere was experimentally proven in several studies[14-17]. Their formation by

oxidation of Cr2O3 in wet air reads:

2 3(s) 2(g) 2 (g) 2 2(g)Cr O 1 2O 2H O 2CrO (OH)+ + → (1.2.2)

2 3(s) 2(g) 2 (g) 2 (g)Cr O 1 2O H O 2CrO (OH)+ + → (1.2.3)

Δ°G of reaction 1.2 is calculated to be −158 kJ at T = 1273 K using combined data from Opila

et al.[18] and Ebbinghaus[13], and Δ°G of reaction 1.3 is calculated to be +134 kJ at T = 1273 K

using combined data from Kim and Belton[14] and Ebbinghaus[13]. Ebbinghaus[13] estimated a

significantly higher partial pressure of CrO2(OH)2(g) compared to CrO3(g) in wet atmosphere

up to T = 1600 K based on available thermodynamic data of gaseous Cr-species, and this was

affirmed by thermodynamic modeling[19]. However, in a recent combined experimental and

modeling study[18] these earlier findings are rejected for high temperatures: in wet atmosphere

CrO2(OH)2(g) is predominant in the gas from T ≤ 1173 K, whereas at higher temperatures the

gas phase mainly contains CrO3(g) and CrO2OH(g). This tendency is shown in Fig. 1.2.1 (next

page): the calculated amounts of main Cr-species in the gas phase as a function of temperature

in humid air of 2H Op = 2000 Pa at constant chemical potential of oxygen, μ(O) being −300 J

mol-1 referred to pure oxygen gas result from combined thermodynamic data[11-14,18] cited

above. These findings are supported by the higher volatilization of Cr2O3(s) in wet air.


16

Fig. 1.2.1 Calculated amounts of gas molecules in Cr-gas as a function of temperature for

constant 2H Op = 2000 Pa at μ(O) = −300 J mol-1 referred to 100000 Pa O2(g)

Transpiration experiments of Cr2O3(s) from T = 673 K to 1223 K resulted in the following

partial pressures of Cr at a flow rate of 150 m min-1: pCr = 2.12x10-5 Pa at T = 673 K and

increases as a function of increasing temperature, reaching pCr = 4.57x10-3 Pa at

T = 1223 K[20]. Mass loss of Cr2O3(s) at T = 973 K and 1073 K was measured in air with

different amounts of water, the mass loss being higher at higher water content and higher

temperature: the constant rate of mass loss was 0.6 μg h-1 for 3 mol% H2O in air at T = 973 K,

3.2 μg h-1 for 3 mol% H2O in air at T = 1073 K, and 18.3 μg h-1 for 25 mol% H2O in air at

T = 1073 K.

Cr-vaporization in SOFC:

Konysheva et al.[21] used a transpiration method proposed by Gindorf et al.[20] to measure the

vaporization rate of Cr from Cr5Fe1Y2O3 (Ducrolloy) and Crofer22APU (high-Cr ferritic

steel), two high-chromium alloy interconnects widely used in SOFC, at T = 1073 K for a time

period of about 500 h. The Cr-vaporization rate of Cr5Fe1Y2O3 exceeds that of Crofer22APU

by about a factor of 3 in the temperature range from T = 1023 K to 1173 K, and the


17

vaporization rate increases with increasing temperatures for both alloys. With increasing

humidity the difference in the vaporization rates between the two alloys increases. However,

for an SOFC setup with a Cr5Fe1Y2O3 interconnect plate, an LSM cathode, an yttrium-

stabilized zirconia (YSZ) electrolyte and a Ni-zirconia cermet (ceramic-metallic composite)

anode operated at T = 1173 K and 1273 K, Badwal et al.[22] mentioned significant amounts of

deposited Cr2O3(s) in the air exhaust of the cell; thus quantitative chromium “poisoning” rates

affecting the cathode are difficult to determine. This is in line with the experimental

observation[21] that only a fraction of the chromium deposited at the cathode side contributes

to the strong degradation of SOFC with LSM cathodes and Cr-alloy interconnects that were

tested under a current load of 200 mA cm-2 for 393 h. The amount of Cr in these degraded

cells was 140 μg cm-2 with Cr5Fe1Y2O3, this value being by about a factor of 2.5 higher than

with Crofer22APU.

1.3 Literature survey

1.3.1 Degradation of SOFC caused by chromium from the interconnect

Considering the experimental data from Caplan and Cohen[10], the volatilities of gaseous

CrO3(g) and gaseous Cr-oxyhydroxides are negligible under the low oxygen partial pressure at

the fuel side of the cell, and the chromium problem is restricted to the interconnect-cathode-

electrolyte region of SOFC.

Experimental results[21-29,31,32,34,35] of the degradation of SOFC with LSM cathodes caused by

chromium are listed in Table 1.3.1, pp. 18-21.


18

Table 1.3.1 Results of chromium poisoning of SOFC with and without Cr-containing

interconnects with LSM cathodes collected from the literature


19


20


21

The degrading effect of gaseous chromium species that form at the Cr2O3 scale under

oxidizing conditions and diffuse into the cathode on the cell performance was first reported in

1995 by Taniguchi et al.[23]. These authors measured an increase of cathode polarization and

decrease of cell voltage in an SOFC consisting of an LSM cathode with the compositions

La0.9Sr0.1MnO3-δ, a YSZ electrolyte and a NiO/YSZ anode with a piece of a Ni-Cr-Fe-alloy

(Inconel 600) attached on top of a Pt mesh used as current collector. The cell was

electrochemically tested at T = 1273 K under a current load of 300 mA cm-2 for 400 h. The

cell voltage decreased over this time from initially about 0.7 V to about 0.1 V, and intensity

measurements using electron probe microanalysis showed that Cr was concentrated at the

cathode-electrolyte interface. In a test of the same setup under open circuit conditions for


22

300 h no deterioration of the cell performance was observed, and Cr was randomly distributed

across the cathode. Taniguchi et al.[23] thus linked the cell degradation to the time that the

discharge current was applied, and to chromium deposited at the LSM-YSZ interface filling

pores, hindering the supply of oxygen gas and decreasing the number of reaction sites for the

oxygen reduction. Later these results were confirmed by Badwal et al.[22]: these authors tested

the cell performance of an SOFC with a Cr5Fe1Y2O3 interconnect plate, an LSM cathode, a

YSZ electrolyte and a Ni-zirconia cermet anode at T = 1273 K and a current density of

250 mA cm-2. Experiments without a Cr-based interconnect plate with Pt mesh serving as

current collectors were conducted at T = 1205 K and 188 mA cm-2 current density using the

same electrodes and electrolyte. The cell performance without interconnect plate deteriorated

only little by less than 0.1 V during an operation time of 2500 h. On the other hand the

voltage of the cell with Cr-Fe-alloy interconnect decreased rapidly as a function of operation

time, the voltage drop being 0.4 V after only 16 h. A comparison of measurements of the

overpotentials of SOFC with LSM cathode and high-Cr alloy interconnect with measurements

without interconnect[24-27] or LaCrO3-based interconnect[28] led to the following results: the

overpotentials without interconnects or with LaCrO3-base interconnects consistently became

less negative with time, whereas the opposite was observed for SOFC with Cr-alloy

interconnect. Simner et al.[29] presented cell performance data of an SOFC with LSM cathode,

a Sm2O3-CeO2 interlayer between cathode and electrolyte, a YSZ electrolyte and a Pt counter

electrode (in the following SOFC with Pt counter electrode are denoted as half-cell) with and

without Crofer22APU interconnect at T = 1073 K, holding the cells at 0.7 V: without the

interconnect steel, the cell performance was stable for 110 h, the power density being

0.48 W cm-2. But using a Cr-Fe-alloy interconnect, the cell started to degrade severely after

20 h of testing, its power density decreasing from a maximum of 0.2 W cm-2 to 0.05 W cm-2

after 110 h.

All these experimental studies[22-29] unambiguously proved that chromium stemming from the

alloy interconnect causes the degradation of SOFC.

1.3.2 The role of current load on electrical losses of degraded SOFC

Badwal et al.[22] reported that the degradation rate of SOFC with a Cr5Fe1Y2O3 interconnect

plate, an LSM cathode, a YSZ electrolyte and a Ni-zirconia cermet anode at T = 1173 K and

T = 1273 K was more related to the period of current passage and was less dependent on the

time when no current was flowing through the cell: Badwal et al.[22] ascribed the voltage

decrease to increasing losses of cathodic overpotential, whereas ohmic losses (resistance to


23

flow of electrons through the cathode) increased only insignificantly during the cell tests. The

overpotential losses were higher and the cell deterioration was faster at higher current density.

At the beginning of the cell tests, losses increased sharply and reached their maximum values

after only 15 h of cell operation. Konysheva et al.[21], using a half-cell with a Cr5Fe1Y2O3

interconnect, a La0.65Sr0.3MnO3-δ/LSM+YSZ double layer cathode and a YSZ electrolyte

confirmed the strong dependence of the voltage drop on the current density during 450 h cell

tests at T = 1073 K: at 70 mA cm-1 the voltage decrease was 0.07 V, whereas at 280 mA cm-1

the voltage dropped by 0.6 V. A plateau of degradation was reached after about 400 h of

testing. Konysheva et al.[30] tested the reversibility of degradation in a half-cell setup with Cr-

Fe-alloy interconnect, LSM cathode and YSZ at a current density of 100 mA cm-2 at

T = 1073 K and found that the rapid degradation was reversible and disappeared after

switching off the current load, in agreement with earlier findings[22,23,28,31]. However the cell

degraded rapidly again when the current was switched on again.

Matsuzaki and Yasuda[28] measured an overpotential loss from initially −500 mV to

−2000 mV after 14 h in a half-cell setup with an Inconel 600 interconnect, La0.6Sr0.4MnO3-δ

cathode and a YSZ electrolyte at 300 mA cm-2 current density. Zhen et al.[27] measured a

rapid decrease of cell polarization from initially −350 to −750 mV after only 10 minutes in a

half-cell with Cr-Fe-alloy (RA446) interconnect, LSM cathode and a YSZ electrolyte tested at

T = 1173 K and a current density of 200 mA cm-2. In earlier studies using the same setup a

rapid decrease from −360 to −560 mV after 10 minutes[25,26] was observed. In reference tests

without Cr-Fe-alloy interconnect the results were opposite to the tests with Cr-Fe-alloy

interconnects: the polarization increased from −550 to −300 mV[27] or −420 to −170 mV [24,25]

at 1173 K and a current density of 200 mA cm-2. The polarization behavior of SOFC with Cr-

containing interconnect was explained by the strong inhibiting effect of gaseous Cr-species on

the oxygen reduction in LSM[27], in general agreement with Jiang et al.[24,25,32,33].

Paulson and Birss[34] reported rapid deterioration of the performance of a half-cell setup with

a stainless steel disk containing 15.21 % Cr on top of a (La0.8Sr0.2)0.98MnO3-δ cathode and a

YSZ electrolyte over 5 to 10 h at T = 1073 K applying a −0.5 V potential, with a tendency of

stabilization of the cell performance after this testing period at much lower magnitude of

output current.

The total polarization resistance (Rpol) of a half-cell setup using a Cr-Fe-alloy interconnect, an

LSM/LSM-YSZ cathode double layer and a YSZ electrolyte tested for 400 h was markedly

dependent on the thickness of the LSM-YSZ layer, Rpol being 0.5 Ohm cm2 for a thickness of


24

50 μm, 0.75 Ohm cm2 for 13 μm, and 2 Ohm cm2 for 7 μm[30]. The total polarization

resistance was also higher at higher current load.

Influence of temperature on the degradation:

SOFC with LSM cathodes and high-chromium 430 stainless steel were tested at T = 973 K

and 1073 K for 300 h[35]. The degradation was higher at higher temperatures at 0.7 V; it

deteriorated from 500 mA to 350 mA at T = 1073 K and from 300 mA to 150 mA at

T = 973 K over the testing time of 200 h and then remained constant.

Jiang et al.[32] observed less overpotential losses at lower temperatures in a half-cell with Cr-

Fe-alloy interconnect, LSM cathode and a YSZ electrolyte: they measured an overpotential

change from initially −300 mV to −650 mV after 10 minutes at T = 1173 K, from −900 to

−1200 mV at T = 1073 K, and from −800 to −1120 mV at T = 973 K after 10 minutes.

1.3.3 Impedance spectroscopy measurements and implications on the degradation

process

Badwal et al.[22] observed an increased size of the high frequency arc during the current

passage in half-cell tests using a Cr5Fe1Y2O3 interconnect plate, an LSM cathode and a YSZ

electrolyte as a function of operation time, reflecting increasing cathode resistance. Mazusaki

and Yasuda[28] concluded from the interpretation of impedance spectra of a half-cell with an

Inconel 600 interconnect, a La0.6Sr0.4MnO3-δ cathode and a YSZ electrolyte operated at

T=1073 K and 300 mA cm-2 current load that the degradation in the electrode caused by

chromium was due to the increase in both charge-transfer resistance and surface diffusion

resistance, but not due to the increase in ohmic resistance. Zhen et al.[27] reported the

existence of a high frequency and a low frequency arc in impedance spectra of a half-cell with

Cr-Fe-alloy interconnect, LSM cathode and YSZ electrolyte tested at T = 1173 K and a

current density of 200 mA cm-2. The increase of both arcs over the testing time was ascribed

to the affect of Cr on the oxygen diffusion processes in the LSM cathode and across the LSM-

electrolyte interface and is in line with the interpretations from Jiang[25,33] and Jiang et

al.[24,26,32].

1.3.4 Microstructures in degraded SOFC

Cathodic polarization:

Taniguchi et al.[23] were the first who reported the occurrence of Cr-Mn-spinel in Cr-

“poisoned” SOFC with an LSM cathode by using XRD analysis. This finding was confirmed


25

by Badwal et al.[22] who detected small amounts of Cr-Mn spinel after 100 h of operation of

SOFC with a Cr5Fe1Y2O3 interconnect plate, an LSM cathode, a YSZ electrolyte and a Ni-

zirconia cermet anode at T = 1173 and 1273 K under current load. For the same setup large

quantities of spinel had formed after 2000 to 2500 h of cell operation, in some of the

experiments forming a dense layer of several microns at the cathode-electrolyte interface. In

some cases these authors also observed Cr2O3(s) at the cathode-electrolyte interface;

unfortunately the specific conditions for its formation were not given in more detail. The

amount of spinel at the cathode-electrolyte interface was much larger than within the LSM

cathode particularly after a period of current load. Badwal et al.[22] further observed spinel in

the contact region between interconnect and cathode.

Using a half-cell setup with Inconel 600, LSM cathode and YSZ electrolyte Matsuzaki and

Yasuda[31] reported the formation of a dense layer of Cr-deposit at the LSM-YSZ interface

after a cell test at T = 1073 K and a current density of 300 mA cm-2 over 100 h of polarization.

Zhen et al.[27] observed dense Cr-Mn spinel-deposits exclusively at the LSM-YSZ interface

after a half-cell test of an SOFC with Cr-Fe-alloy interconnect operated for 20 h at

T = 1173 K and a current density of 200 mA cm-2. Using the same setup, Jiang et al.[25,36]

documented spinel formation at the LSM-YSZ interface already after 4 h. The grain size of

spinel was about 0.17 μm after 4 h of cell testing and increased to about 0.7 μm after 50 h.

The zone of these large faceted crystals was followed by a zone of very fine grains (about

0.05 μm) of Cr2O3 towards the cathode-electrolyte interface. The deposition zone broadened

as the polarization time increased from about 60 μm after 50 h to 89 μm after 129 h. Under

the same testing conditions as above, but under anodic polarization very fine grains of Cr2O3

were forming exclusively at the LSM-YSZ interface.

Using the same setup as above, no Cr-deposits formed after 50 h of testing under open circuit

conditions[25,36]. Very small grains of Cr-deposits formed at T = 1373 K under open circuit

conditions, but further details on their spatial distribution and composition were not given.

In a half-cell setup with a Cr-Fe-alloy interconnect, an LSM/LSM-YSZ cathode double layer

and a YSZ electrolyte chromium-deposits were only found in the LSM layer under open

circuit conditions, and the cell-degradation was weak[21]. On the other hand chromium-

deposits were also found in the LSM-YSZ layer and on the surface of the YSZ electrolyte on

increasing the current density up to 280 mA cm-2, and the cell degradation was strong[21]. In

the same setup without LSM-YSZ functional layer no chromium-deposits were detected

without current at T = 1073 K over 393 h. On the other hand Cr-Mn spinel formed already at


26

very low current load of 2 mA cm-2 on the surface of the electrolyte and near the LSM-

electrolyte contact. After 160 h of testing at 100 mA cm-2 current load, large gaps between

YSZ grains formed, and spinel crystals were found on the surface of a thin Cr2O3-layer

adjacent to the electrolyte. Cr2O3 was also found inside YSZ, up to 10 μm away from the

LSM-YSZ interface after 160 h of testing, and 30 μm from the LSM-YSZ contact after 940 h.

Cr2O3 completely filled gaps between YSZ grains. Transmission electron microscopy

analyses revealed the layered structure of the composites: a 0.5 μm thick layer directly

adjacent to the YSZ containing mainly Cr2O3 is covered by a spinel layer.

Paulson and Birss[34] investigated the microstructures in a half-cell setup with a stainless steel

disk containing 15,21 % Cr attached on top of a 4 mm2 square (La0.8Sr0.2)0.98MnO3-δ cathode

that rested on a 144 mm2 square YSZ electrolyte, after the half-cell was tested by a sequence

of 8 chronoamperometry experiments at −0.5 V and T = 1073 K. These authors observed the

formation of a 500 μm broad zone of 8 individual, dense Cr2O3-layers at the edge of LSM on

the YSZ surface. Cr-deposits consisting of Cr2O3 and Cr-Mn-spinel were concentrated in an

about 2 μm broad region at the LSM-YSZ interface. A reference test without polarization did

not lead to these features.

Anodic polarization:

After a half-cell test of an SOFC with Cr-Fe-alloy interconnect operated for 6 h at T = 1173 K

and a current density of 200 mA cm-2, Jiang et al.[36] reported the formation of very fine

particles of Cr2O3, exclusively covering the YSZ surface, and the deposition was less

pronounced at T = 1073 K and 973 K. The morphology of the particles was different than the

morphology of the deposits under cathodic polarization.

No spinel formation was observed in these experiments.

Influence of temperature:

Microstructural changes during half-cell tests of a setup consisting of a Cr-Fe-alloy

interconnect, a La0.72Sr0.18MnO3-δ cathode and a YSZ electrolyte were systematically

investigated as a function of time and temperature at a current load of 200 mA cm-2 by Jiang

et al.[32]. After 5 minutes of testing at T = 1173 K very fine Cr-deposits (< 100 nm) already

formed on the YSZ-surface, and the density and size of deposits increased by time. After 20 h

spinel formation was observed forming a 40 to 50 μm wide band at the LSM-YSZ interface.

In direct contact with YSZ about 500 nm large Cr2O3-grains were detected, almost completely


27

covering the YSZ surface, associated with large grains (about 1 μm) of spinel. The amount of

Cr-deposits was significantly smaller after 20 h of testing and 200 mA cm-2 current load at

T = 973 K: isolated fine particles (about 100 to 200 nm) were detected on the YSZ surface.

The decreasing degradation at lower temperatures was ascribed to slower diffusion and lower

partial pressure of gaseous Cr-species.

1.3.5 Amounts of chromium in SOFC tested with and without current load

Konysheva et al.[21] compared the total amounts of chromium in half-cells with Cr-Fe-alloy

interconnects, a La0.65Sr0.3MnO3-δ/LSM+YSZ double layer cathode and a YSZ electrolyte

after tests without current showing very small degradation, and under 200 mA cm-2 current

density showing strong degradation as a function of testing time at T = 1073 K. The amounts

of chromium in the half-cell operated under a current was 100 μg cm-2 after 150 h and

150 μg cm-2 after 500 h; this is only 15 to 20 % higher than in the cell operated without

current, although the degradation of the polarized cell was remarkably higher. This was

explained by the following: only under current load chromium deposits are concentrated in

the functional region of LSM close to the contact to YSZ where they inhibit oxygen reduction

and diffusion processes.

In SOFC with LSM cathodes and a Cr-Fe-steel interconnect that were tested at T=1073 K for

300 h at 0.7 V, Krumpelt et al.[35] measured about 2.8 wt.% of Cr at 10 μm distance from the

cathode-electrolyte interface. The Cr-content dropped to about 0.5 wt.% at 14 μm distance

from the contact to the electrolyte. It further decreased slightly towards the interconnect-

cathode interface.

In a half-cell with LSM cathode, a Sm2O3-CeO2 interlayer between cathode and electrolyte

and a YSZ electrolyte with a Crofer22APU interconnect operated at T = 1073 K, holding the

cell at 0.7 V for 120 h, Simner et al.[29] measured 5 at.% Cr in the Sm2O3-CeO2 interlayer, but

no Cr in LSM using energy dispersive scanning electron microscopy.

By using molecular dynamics simulation techniques it was stated recently that only 890 ppm

Cr3+ in LSM significantly increase the formation energy of O2- vacancy within about 10 Å

around Cr3+. This may lead to a dramatic drop of the oxygen diffusion coefficient in LSM by

about 60%[36] and pers. comm.


28

1.3.6 Critical assessment of proposed mechanisms of chromium “poisoning”

For the mechanisms of chromium “poisoning” two models have been proposed: 1) Reduction

of gaseous Cr-species under polarization[21-23,30-31,33], and 2) Chemical dissociation of Cr-

species on the LSM surface[24-26,32,33,37]. Both reduction and chemical dissociation processes

reflect non-equilibrium conditions.

1) Several authors[21-23,230,31,33] ascribe the mechanism of chromium “poisoning” to the

reduction of gaseous CrO3(g) and Cr-oxyhydroxides at the cathode-electrolyte interface,

described by inverse Eq. 1.2.1. In an LSM cathode the reduction of CrO3(g) is expected to be

localized at the triple phase boundary (TPB) between LSM, YSZ, and gas, where the reaction

partners for the reduction, electron-donating LSM and oxygen-accepting YSZ are

available[38]. This reduction reaction would compete with the oxygen reduction and would

lead to blocking of the active sites at the TPB and subsequent formation of Cr-Mn spinel by

the reaction of Cr2O3(s) with LSM.

Badwal et al.[22] emphasized that chromium “poisoning” would consist of several processes,

including changes of the chemical composition of the LSM surface, reduction of CrO3(g) at the

cathode-electrode interface competing with the normal oxygen reduction reaction, and

blocking of pores by Cr-Mn spinel and Cr2O3(s). In particular they suggest the tight

intercalation between changes of the chemical composition at the surface of LSM particles

and the oxygen adsorption and surface diffusion kinetics in the early stage of chromium

“poisoning”. Badwal et al.[22] ascribe a key role for the late stages of cell degradation to the

formation of Cr-Mn spinel that would block pores and lead to substantial decrease of the TPB

area. Cr-Mn spinel is interpreted by these authors to form in a solid-solid reaction between

Cr2O3(s) and LSM that may have the simplified form of Eq. 1.3.1 when solid solubility of Cr

in LSM[39] is considered and spinel contains the molar fraction of Cr, X(Cr) = 2X(Mn):

1 3 2 3 1 1 3 2 4(s) 2(g)La Sr MnO 3 2 Cr O La Sr Mn Cr O MnCr O 1 4 O− − − − − + ++ →x x yx x yy y yδ δ (1.3.1)

Eq. 1.3.2 is a possible reaction for the formation of spinel with a higher amount of Mn,

X(Mn)= 2X(Cr):

1 3 2 3 1 1 2 3 2 4(s) 2(g)La Sr MnO 1 2 Cr O La Sr Mn Cr O Mn CrO 5 4 O− − − − − + ++ →x x yx x yy y yδ δ (1.3.2)


29

For equal y in Eqs. 1.3.1 and 1.3.2 less Cr2O3 is needed for the formation of Mn2CrO4, more

oxygen is produced, and LSM gets more deficient in Mn. Oxygen production stems from the

reduction of Mn3+ in perovskite to Mn2+ in spinel. However the formation of spinel can also

be interpreted as a direct solid-gas reaction. Fig. 1.3.1 is a simplified illustration of possible

reaction paths that lead to the end product Cr-Mn spinel.

Fig. 1.3.1 Possible reaction paths for the spinel formation as a function of Gibbs energy.

The true shape of the curves depends on the activation energy Ea and is thus not known.

red = reduction, sp-form = spinel formation.

Which of the possible reaction paths is realized, depends on the activation energy, Ea of the

concerning reaction, and this is not known. The shape of the curves in Fig. 1.3.1 was chosen

based on the consideration that the diffusionless reduction of Cr-gas may have a lower

activation energy than the solid-solid reaction between LSM and Cr2O3(s), and the mobility of

the gas phase is high, thus assuming a lower activation energy for the LSM-Cr-gas reaction.

These assumptions would mean that fast reduction of Cr-gas to Cr2O3(s) occurs as one process,

and the LSM-Cr-gas reaction occurs as a parallel process leading to the formation of spinel.

On the other hand it may last a long time for the Cr2O3(s) that was formed by the reduction

reaction to transform into spinel in the solid-solid reaction with LSM.

As it is not assured if spinel in fact forms in a solid-solid reaction, reactions of direct

formation of spinel by the interaction between Cr-gas and LSM can be formulated (Eqs. 1.3.3

to 1.3.5) considering the main chromium molecules that interact with LSM for spinel with

X(Cr) = 2X(Mn). Such gas-solid reaction can be split into two reaction steps: formation of


30

Cr2O3(s) from the gas and subsequent spinel formation from Cr2O3 + LSM. The differences of

oxygen contributions to respective reactions stem from the reaction step of Cr2O3(s) formation:

1 3 1 1 3 2 43(g) 2(g)3La Sr MnO CrO La Sr Mn Cr O MnCr O 5 2 O− − − − − + ++ →x x yx x yy y yδ δ (1.3.3)

1 3 2 2(g)

1 1 3 2 4 2 2(g)H

La Sr MnO CrO (OH)La Sr Mn Cr O MnCr O O(g) +5 2 O

33

xx

x yx y

yy y y

δ

δ

− −

− − − +++ →

(1.3.4)

2(g)

1 3 2 (g)

1 1 3 2 4 2H O

La Sr MnO CrO (OH)La Sr Mn Cr O MnCr O 3 2 O(g) +3 4

3xx

x yx y

yy y y

δ

δ

− −

− − − +++ →

(1.3.5)

2) The chemical dissociation of gaseous Cr-species on the LSM surface for the cell

degradation was proposed as the key process for the degradation of SOFC caused by

chromium by another research group[24-27,32,33,37]: Mn2+ on the surface of LSM at reduced

oxygen partial pressure close to the cathode-electrolyte interface would react with gaseous Cr-

species to Cr-Mn-O nuclei, and consequently to Cr-Mn spinel and Cr2O3(s). As Mn2+ is

associated to vacancy formation in LSM that is necessary for the oxygen diffusion,[24-27,32,33,37]

oxygen diffusion is inhibited by the nuclei-formation. It can be seen from Eqs. 1.3.1 to 1.3.5

that oxygen is produced during the formation of spinel. Thus the 2Op at the locations of the

spinel formation is expected to increase. This in turn will also lead to less Mn2+ in LSM[40]

and consequently lower oxygen diffusion in LSM.

The role of the oxygen vacancy diffusion mechanism in an LSM cathode has been considered

controversially: Mogensen and Skaarup[41] concluded from the low oxygen self-diffusion

coefficients of the order of 4×10-14 cm2 s-1 at T = 1173 K[42] that long range bulk migration of

oxygen ions cannot play a significant role for the cathode performance. However they did not

discuss the dependence of oxygen diffusion upon 2Op . Huang et al.[43] confirmed these early

suggestions by evaluating the ionic conductivity of LSM from pure oxygen to 2Op = 300 Pa at

temperatures from 953 K to 1153 K using YSZ as blocking electrode. The ionic conductivity

was lower at lower oxygen partial pressures, opposite to the trend that would be expected

under the control of the vacancy diffusion mechanism. On the other hand the measured

oxygen tracer diffusion coefficient in LSM strongly increases when the oxygen partial

pressure is decreased from pure oxygen to2Op = 200 Pa[44]. Yasuda et al.[44] concluded that


31

oxygen ions in the bulk of LSM diffuse by the vacancy diffusion mechanism. The activation

energy for the diffusion of oxygen for LSM is in the range of 250 to 300 kJ mol-1. This is

close to 270 kJ mol-1 for La0.9Sr0.1CoO3-δ in which oxygen ions are transported by the vacancy

mechanism. This indicates that a vacancy diffusion mechanism also applies to LSM[45]. In an

investigation of active sites for the oxygen reduction at the O2/LSM/YSZ interface[46] for three

different overvoltages of cathode polarization (η = −0.336 V, η = −0.185 V, and

η = −0.090 V) using isotopic oxygen exchange and secondary ion mass spectrometry it was

found that oxygen ions can only diffuse through dense LSM at the high overvoltage of

η= − 0.336 V corresponding to 2Op = 10-4 Pa[46]. The calculated amount of oxygen vacancies

(δ) in La0.8Sr0.2MnO3-δ at 973 K and2Op = 10-4 Pa is δ = 2.4x10-6, compared to δ = 3.94x10-9

in air[23]. This confirms the suggestion that the formation of oxygen vacancies in LSM

contributes to the oxygen diffusion at high current loads[22]. Based on the findings from the

literature it can be summarized that in LSM oxygen diffuses through grain boundaries at high

2Op , as oxygen vacancies are simply not available under these conditions. We believe that the

oxygen vacancy diffusion mechanism contributes to the oxygen diffusion under high current

loads, when the oxygen partial pressure at the cathode-electrolyte interface is decreased

significantly, as it was directly proven by isotopic and tracer diffusion[44] experiments.

Contradictory interpretations[43] from the dependence of the ionic conductivity on2Op need to

be judged with care due to the difficulty of controlling the numerous factors that can influence

the results of the blocking electrode method used.

The electrochemical reduction of CrO3(g) was rejected by the authors favoring the chemical

dissociation approach[24-27,32,33,37]. It is necessary to test the arguments for this claim of

exclusive validity: a strong tendency exists for CrO3(g) to get reduced to Cr2O3(s) at the TPB,

as Δ°G of the reduction being the inversion of reaction Eq. 1.2.1 has a large negative value. It

was also mentioned in the early paper of Caplan and Cohen[10] that substantial precipitation of

Cr2O3(s) from CrO3(g) occurred in the cooler part of the experimental setup. Reduction of

CrO3(g) to Cr2O3(s) was such predominant as to make sampling of gaseous CrO3(g) difficult.

This strong tendency for the precipitation of Cr2O3(s) makes a rejection of the reduction of

CrO3(g) as a possible process contributing to the cell degradation doubtful.

Paulson and Birss[34], as well as Konysheva et al.[21] observed the extension of dense Cr2O3-

layers into YSZ. This phenomenon was well explained by continuous feeding of an initial


32

Cr2O3-layer with CrO3(g), the latter becoming reduced at the new TPB consisting of YSZ and

electron-donating Cr2O3(s)[21,34], whereas an explanation by the chemical dissociation approach

is not satisfying. Thus it is obvious that the explanation of the “poisoning” process by the

chemical dissociation approach alone is not without doubt.

Some indications for two independent chromium poisoning mechanisms can be found in the

work from Jiang et al.[24,26,37]: the two phases formed in the scope of a polarized LSM cathode

exhibit distinctive microstructures: spinel forms large grains, whereas the phase that was most

likely identified as Cr2O3 occurs in fine-grained, partly layered structures. The region of

spinel formation extends several microns from the TPB into the cathode, whereas Cr2O3 is

always located directly at the cathode-electrolyte interface. From the occurrence of fine-

grained Cr2O3 the existence of a large number of nuclei for its formation is concluded, which

does not seem to be the case for the spinel phase. Furthermore, from impedance spectra

analyses it was in fact possible to distinguish two distinctive depositions of Cr-species, one

with a lower rate on the LSM surface, and the second with a higher rate on the YSZ

electrolyte surface. Also two different diffusion processes were distinguished, which both

seemed to be inhibited by chromium poisoning.

If CrO3(g) is electrochemically reduced to Cr2O3(s) in a cell, Cr2O3(s) deposition should also

occur under open-circuit conditions, which was definitively not observed. In this case the

contribution of reduction to the Cr-“poisoning” has to be rejected, and the degradation can be

associated to the dissociation process[24-27,32,33,37] and subsequent formation of spinel.

However the situation changes if the reduction of CrO3(g) is under the main control of the

oxygen partial pressure gradient towards the cathode-electrolyte interface, which is increasing

as a function of increasing polarization. In this case no chromium will be deposited at the

cathode-electrolyte interface under open-circuit conditions, whereas in a polarized cathode the

reduction of CrO3(g) takes place and competes with the oxygen reduction leading to Cr2O3(s)

deposition. This explanation is in line with the microstructural features of tested cells both

under open circuit voltage and under current load, and it is also in line with the observed

temporary reversibility of the cell deterioration[22,23,28,30,31]: by switching off the polarization

the competing reduction of CrO3(g) no longer occurs, and the normal charge transfer can take

place by switching it on again.

But how can one explain the strictly localized deposition of Cr2O3 that also occurs under

anodic polarization[37]? Under oxidizing conditions little Mn2+ is expected to be present in

LSM[40], thus the formation of nuclei by the proposed LSM-Cr interaction won’t occur. This

is in contrast with the complicated mechanism for the formation of Cr2O3(s) under anodic


33

polarization established by Jiang et al.[37] that includes diffusion of Mn3+/Mn2+ driven by the

oxygen evolution reaction at the cathode/electrolyte interface, again with Mn2+ acting as agent

for the formation of Cr-Mn-O nuclei, the number of the latter being less than under cathodic

polarization, and thus lack of spinel formation. Alternatively, the following simple

explanation for strictly localized Cr2O3(s) formation under anodic polarization can be given: in

an LSM cathode the reduction of gaseous Cr-species is expected to be localized at the triple

phase boundary, where the reaction partners for the reduction, electron-donating LSM and

oxygen-accepting yttrium-stabilized zirconia (YSZ) are available[38]. Oxygen deficiency is

negligible in LSM under high2Op [40], and thus under these conditions LSM has no tendency at

all to accept oxygen, contrary to the situation of a strong 2Op gradient under cathodic

polarization. This is a simple and consistent explanation for a strict localization of Cr2O3(s)

formed by reduction of gaseous Cr-species even under anodic conditions.

In cell tests of a polarized platinum electrode using a Cr-containing interconnect no Cr was

observed, contrary to an LSM electrode. This different behavior of Pt and LSM electrodes

under Cr-poisoning was used as an evidence for the exclusive validity of the dissociation

approach, based on an early finding that LSM behaves like a metallic electrode at low

polarization potentials[47] that was not quantified. However this conclusion was not tested in

the light of the oxygen partial pressure gradient towards the electrode-electrolyte interface:

contrary to platinum, vacancies are expected to form in LSM under increasing polarization,

and in LSM a 2Op gradient is expected under polarization, which is indeed not the case in a

platinum cathode. This once again may favor the reduction of CrO3(g) and gaseous Cr-

oxyhydroxide resulting in Cr2O3(s) deposition at the cathode-electrolyte interface in LSM,

opposite to the situation with a platinum cathode.

It was further mentioned that the existence of Cr-containing products away from the TPB

would be in disagreement with the reduction approach. This is indeed true for the case of

CrO3(g) and Cr-oxyhydroxide reduction being the only Cr-poisoning mechanism. However, if

both the chemical dissociation as well as the reduction of gaseous Cr-species is occurring with

different proportions, this apparent antagonism is abolished. In this context experimental

results of a half-cell test with Cr-Fe-alloy (RA446) interconnect, LSM cathode and a YSZ

electrolyte at T = 1173 K and a current density of 200 mA cm-2 from Zhen et al.[27] are

particularly interesting: the slope of the cathode polarization curve (Fig. 4 b[27]) as a function

of time reveals an inflection point after about 6 1/2 h. This is an indication against one unique

“poisoning” mechanism, but several processes may lead to the deterioration of cell


34

performance, and their respective influence on the cell deterioration may vary as a function of

time.

From the considerations in this chapter we conclude that no sustainable arguments exist for

the rejection of the reduction of gaseous Cr-species as one of the controlling mechanisms of

Cr-“poisoning” of SOFC.

The important role of decreased oxygen activity at the LSM-YSZ interface under current load

for the cell degradation was already suggested by Taniguchi et al.[23]. Konysheva et al.[30] give

the following explanation, why the strong oxygen partial pressure gradient in the LSM

cathode under high current densities plays a key role for the degradation: the LSM cathode

has a low electrochemically active area (TPB) near the interface with the electrolyte only.

Under polarization, the oxygen ions formed at this interface are transported from the cathode-

electrolyte interface through the electrolyte. This results in a lower oxygen partial pressure at

the interface as compared to that in air. The higher the current density under SOFC operation,

the lower is the oxygen partial pressure at the contact between LSM and YSZ. The deposition

of chromium followed by its reduction near this interface blocks direct oxygen access to the

electrochemically active sites, thereby still more decreasing the oxygen partial pressure at a

newly formed Cr2O3(s)/electrolyte interface[30]: the TPB between LSM and YSZ diminishes

more and more by the blocking of Cr2O3(s), and oxygen cannot access the TPB. As Cr2O3(s)

has a small electronic conductivity of 0.8 S m-1 at T = 1282 K[48] and 2Op = 1 Pa, the oxygen

ions from this new, weak catalytic reaction diffuse into YSZ, and the chemical activity of the

cell is furthermore deteriorating due to the lack of oxygen supply through the rather dense

Cr2O3 layer to the new TPB. The temporary reversibility of the deterioration by switching the

cell off and on again can also be explained: in contrast to current load operation, under open

circuit the LSM-Cr interactions occur randomly throughout the cathode, thus the remaining

TPB/YSZ active sites are almost unaffected under open current circuit. The small area close

to the new TPB that was strongly depleted of oxygen under current load is filled with air

leaking through remaining pores between LSM and Cr2O3. Applying a current load, the LSM-

Cr interaction is again favored in the region close to YSZ as 2Op decreases at the TPB, even

though the decrease is expected to be less due to less LSM/YSZ active sites caused by the

first degradation. Oxygen is mainly reduced at the new TPB between Cr2O3(s) and YSZ.

Reduction already takes place at higher 2Op at the beginning of the current load operation, as

electronic conductivity of Cr2O3 is significantly higher at higher 2Op (1.8 S m-1 in air[48]).


35

Oxygen ions diffuse into YSZ, but new oxygen is not supplied to the new TPB. Active

LSM/YSZ sites further diminish by ongoing formation of spinel and Cr2O3 deposits, and the

degradation increases as a function of time.

Fig. 1.3.2 is a visualisation of the microstructural consequences of chromium in an LSM

cathode. The reported dependence of structural features of the degraded cell on the operation

temperature, current load, and chromium content is schematized in the picture.

Fig. 1.3.2 Model of chromium poisoning of an SOFC with Cr-interconnect and LSM cathode

based on the findings in the literature. Numbers refer to locations of processes that are

decisive for the degradation

Number 1 in Fig. 1.3.2 denotes the interconnect-cathode interface region where oxidation of

Cr2O3(s) to gaseous Cr-oxides and Cr-oxyhydroxides by Eqs. 1.2.1 to 1.2.3 occurs, followed

by diffusion of the gaseous products into the cathode. Number 2 denotes the region of

interactions between LSM and chromium leading to spinel formation by solid-solid reaction,

Eqs. 1.3.1 to 1.3.2, or gas-solid reaction, Eqs. 1.3.3 to 1.3.5, and number 3 denotes the

reduction of gaseous Cr-species by the reverse of Eq. 1.2.1 leading to the redeposition of

Cr2O3(s) at the cathode-electrolyte interface.


36

1.4 Proposed strategies against chromium “poisoning” and their

effectiveness

1.4.1 Increasing the Cr-tolerance of conventional SOFC with Cr-interconnects and

LSM cathodes

More than ten years ago Badwal et al.[22] proposed that coating of the Cr-interconnect with a

protective electrically conductive dense layer would be an effective strategy against the

diffusion of Cr-species into the cathode. Several promising materials for coating applications

were developed in the following years that act as chromium diffusion barrier and hinder

growth of chromia scale at the alloy surface, thereby improving the electrical conductivity of

the interconnect-cathode interface[49-69]. However, so far volatilization could not be

suppressed completely.

Application of the following coatings upon the interconnect has been shown to considerably

reduce the diffusion of chromium into the cathode thus decreasing the cell degradation:

Electroplated metallic Co[49,50], Co-Mn, or Cu-Mn[51], sputtered Co, Ni, or Cu[52], Mn, La, or

Mn2CrO4[52], Co3O4

[53], MnCo2O4[54-61], Cu1.4Mn1.6O4

[53,54], Ce0.05Mn1.475Co1.475O4[62],

(La,Sr)CoO3[63], La0.67Sr0.33MnO3

[64], La0.65Sr0.3MnO3[58,65], La0.85Sr0.15MnO3-δ

[50],

La0.6Sr0.4Co0.8Fe0.2O3[58], La0.8Sr0.2Mn0.5Co0.5O3-δ

[66], La0.8Sr0.2Mn0.5Co0.5O3[65],

La0.8Sr0.2FeO3-δ[67], two-segment Cr-Al-Y-O nanocomposite and (Mn,Co)3O4

[68], as well as

(Ti,Al)N[69]. However, as Cr in the ppm range significantly influences the oxygen diffusion in

the LSM cathode[36], coating alone does not solve the problems associated to chromium

poisoning completely, but a combination of the quoted strategies is advisable to further

improve the long-time stability of SOFC performance.

The formation of a dense electrically isolating Cr2O3 layer is probably preventable by using

electrolyte materials or a functional layer between LSM cathode and YSZ electrolyte that can

incorporate Cr in solid solution without affecting the electrical conductivity. Furthermore

such a buffer layer may act as a sink for CrO3(g) thus diminishing nuclei formation on LSM. If

the buffer layer contains an ionic conductor, more active sites for the oxygen reduction will

result in a higher Cr-tolerance. This was recently shown for a cell with a YSZ-LSM functional

layer: a functional LSM-YSZ layer adjacent to the YSZ electrolyte led to a lower cell

degradation[30]: increasing the ionic conductivity of the LSM cathode that is predominantly

electronically conducting down to 2Op = 10-7 Pa[70] by admixture of YSZ results in an


37

expanded area of active sites for the oxygen reduction away from the TPB. Thus the number

of active sites is increased, and the cell is more tolerant against chromium[30]. Besides, the

reduction of gaseous chromium will not be restricted to the small area at the TPB due to a

smaller oxygen partial pressure gradient, leading to the formation of more scattered reduction

products instead of a dense layer: thus the block of oxygen diffusion into the electrolyte can

be avoided. The ionic conductivity can be increased by doping the B-site of ABO3 perovskite

with reducible cations. Ideally the selected dopants decrease the mobility of Mn2+ and thus

prevent the formation of nuclei for the adsorption of CrO3(g) without influencing the formation

of vacancies.

1.4.2 New ways – alternative materials

Badwal et al.[22] already considered alternative cathode materials to reduce or stop the

formation of the spinel phase. Matsuzaki and Yasuda[31] concluded from insignificant Cr-

deposits in tested SOFC with Cr-Fe-alloy interconnect, La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF)

cathode and Ce0.8Sm0.2O1.9 electrolyte that the ratio of the reduction of gaseous CrO2(OH)2(g)

to that of O2(g) at the electrode/electrolyte interface is controlled by the electrochemical

properties of the interface. Based on these findings they predicted that highly Cr-tolerant

cathodes can be developed.

In recent time it was found that new cathode materials such as La1-xSrxCo1-yFeyO3-δ (LSCF),

La(Ni,Fe)O3-δ (LNF), and (La,Ba)(Co,Fe)O3-δ (LBCF) are more tolerant against chromium

“poisoning”. LNF and LBCF revealed extraordinary high tolerance against chromium

poisoning. The highest tolerance against the effects of chromium under SOFC operating

conditions combined with high electrical conductivity has been reported recently for

(La,Ni)FeO3-δ [71,72], which makes this material a promising candidate for a steady long-term

SOFC performance. All these perovskites are mixed electronic-ionic conductors; particularly

LSCF and LNF show rather high ionic contributions to the total electrical conductivity.

Effects of Cr upon the degradation of La1-xSrxCo1-yFeyO3-δ (LSCF)[26,71,73], La(Ni,Fe)O3-δ

(LNF)[71,74], and (La,Ba)(Co,Fe)O3-δ (LBCF)[71,75] cathodes were investigated using

impedance spectroscopy. As for LSM these authors concluded that the mechanism of Cr

poisoning can be explained by chemical dissociation of CrO3(g) to the perovskite-structured

materials and nuclei formation in the cases of LSCF and LNF, whereas no proper nuclei were

reported for LBCF. In all these cathodes Cr-deposition was observed throughout the cathode

both under polarization and without polarization, contrary to LSM. The amount of Cr-


38

poisoning of LSCF was considerable. The amount of deposited Cr in LSCF was even larger

without polarization than under polarization, which was explained by a removing effect of

nuclei for the chromium deposition under polarization conditions.

As an alternative to the complicated nuclei mechanism, the following considerations can be

made using the reduction model: For the reduction reaction of CrO3(g) the presence of both an

electron donor and oxygen ion acceptor is necessary, and a typical mixed ionic-electronic

conductor such as LSCF can take over both functions. Thus reduction of CrO3(g) takes place

inside the whole cathode even without being promoted electrochemically by polarization of

the cell. However under strong polarization one can expect that LSCF gets more and more

ionic conducting towards the electrode-electrolyte interface, that is towards lower oxygen

partial pressures, most likely resulting in retarding or inhibiting of the reduction reaction.

Even if the reduction reaction is considered to be the dominant mechanism of chromium

poisoning, nuclei might form in addition, but their influence on the Cr deposition compared to

the reduction of CrO3(g) cannot be decided yet. Opposite to the case of LSM no driving force

for CrO3(g) to migrate to the triple phase boundary exists due to the mixed ionic-electronic

conducting behaviour of the regarding cathodes. The higher the contribution of the ionic

conduction the less complete reduction is expected due to prolonged lack of an electron

donator. Improved inhibition of the reduction of CrO3(g) is predicted for LNF, as this phase

has a particularly high ionic conductivity.

In recent years research activities for LaCrO3-base ceramic interconnector materials were

revitalized by several groups[76-78] to circumvent the problems of chromium “poisoning”.

However, despite rapidly developing processing techniques it is not clear at the moment if the

obstacles of sinterability and low mechanical strength as well as difficult manufacturing

correlated with high costs can be coped.

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Aim of study

45

2 Aim of study

Chromium poisoning of planar SOFC with LSM cathodes and Cr-alloy interconnects is a

complex process consisting of several steps that may occur simultaneously inside the cell.

Mn2+ in LSM plays an important role for the adsorption of gaseous CrO3(g) and Cr-

oxyhydroxide on LSM resulting in blocked oxygen transport from the cathode to the

electrolyte. Reduction of CrO3(g) at the TPB leads to the formation of electrically low

conducting Cr2O3, which further retards the diffusion process of oxygen into the electrolyte.

The causes and consequences of chromium poisoning are clear, and some strategies against

cell degradation caused by chromium have already been successfully applied. However, it

seems that strategies against the cell degradation have been mostly established in a rather

random way so far. For a more systematic and thus more efficient combination of strategies a

strong knowledge about the mechanisms of chromium poisoning of SOFC is required.

Previous experiments have shown that the following factors:

-) High temperature

-) Decrease of oxygen partial pressure at the TPB under current load of SOFC

and processes:

-) Interaction of chromium with LSM leading to Mn-Cr-O nuclei and/or spinel formation

-) Reduction of CrO3(g) to Cr2O3(s) at the TPB

-) Blocking of pores at the TPB by Cr2O3 and/or spinel

govern the degradation of SOFC caused by chromium.

So far it was not possible to define unambiguously, which of these processes play a dominant

role for the degradation and which don’t. In fact it was shown that without sufficient

protection against the diffusion of chromium into the cathode the degradation of SOFC

caused by chromium is not a long-term phenomenon; severe degradation has been observed

after several hours of testing under current load at state-of-the-art SOFC operating

temperatures: from the literature findings it is obvious that the degradation of SOFC caused

by chromium starts immediately after starting SOFC tests under current load. If the process of

chromium “poisoning” were completely governed by thermodynamics, this behaviour would

not be expected, but the effects of chromium would be observed only after thermodynamic

equilibrium is obtained. This means that the kinetic control on the mechanisms of chromium

Aim of study

46

is high, and a degrading cell is in a non-equilibrium state particularly at the early stages of the

degradation.

The following questions have remained unsolved so far:

-) Does spinel form by a solid (LSM)-solid (Cr2O3) reaction or directly in a solid (LSM)-gas

(gaseous Cr) reaction?

-) Can the concentration of deposits at the cathode-electrolyte interface under current load be

explained by thermodynamics?

-) How does the LSM phase chemically change due to the interaction with chromium, and can

this change be explained by thermodynamics?

-) Which of the phases observed in LSM contaminated by chromium form under

thermodynamic control, and what are the conditions that favour their formation?

This work aims to answer these questions by the application of thermodynamic calculations.

Therefore the thermodynamic La-Sr-Mn-Cr-O oxide database needs to be established based

on the assessments of low-order subsystems.

In recent times many materials have been tested for SOFC cathodes. In particular LSM

cathodes have been intensively investigated over the last decade, and several studies can be

found regarding the degradation of LSM cathodes caused by chromium. Thus, and as LSM

cathodes are still considered to serve as promising cathodes due to their high electrical

conductivity and stability at SOFC operating conditions, in this study the author focuses on

the effects of Cr on the degradation of SOFC with LSM cathodes.

3 Method

3.1 Benefits of the thermodynamic La-Sr-Mn-Cr-O oxide database for

the understanding of Cr-poisoning of SOFC

A thermodynamic La-Sr-Mn-Cr-O oxide database is highly desirable to enable fundamental

understanding of the mechanisms of chromium “poisoning” of LSM cathodes for SOFC. As a

degrading cell is in a non-equilibrium state, the obvious question why the results of

thermodynamic calculations should be feasible for a deeper understanding of the mechanisms

Method

47

of chromium “poisoning” needs some explanation: from the conditions of the non-equilibrium

state at the beginning of the degradation process, including the operating temperature,

composition of LSM, and the rate of chromium diffusion the equilibrium state of chromium

“poisoning”, can be calculated using the thermodynamic La-Sr-Mn-Cr-O oxide database:

Cnon -equilibrium (A) equilibrium (B)⎯⎯→ (3.1.1)

By calculating thermodynamic equilibria for a LSM cathode that is affected by chromium (A)

in the relation above, the theoretical final state of chromium poisoning after a very long time

is found by thermodynamic equilibrium calculations (B). For instance, by choosing the

starting conditions composition of LSM and defined amount of Cr at a specific temperature,

using the thermodynamic database one can calculate the expected thermodynamic

equilibrium, for instance under reducing oxygen partial pressures reflecting the situation at the

TPB under current load. Over time the system LSM + Cr will change from its non-

equilibrium state at the beginning of the Cr-“poisoning” process towards the calculated

equilibrium state. C in Eq. 3.1.1 reflects the path the system takes towards its equilibrium

state. From A and B, C can be predicted for changing cathode compositions, temperatures,

and oxygen partial pressures. Hence, taking into account experimental data on the chromium

“poisoning” of SOFC and using a thermodynamic La-Sr-Mn-Cr-O oxide database, one can

draw conclusions on the evolution of the phase chemistry of degraded LSM cathodes.

The presented thermodynamic database of the La-Sr-Mn-Cr-O oxide system is constructed

using the CALPHAD approach[1]. It contains the optimized Gibbs energy functions of solid

oxide phases: for stoichiometric phases as a function of temperature, and for solid solution

phases as a function of temperature and composition. The optimization of model parameters is

based on the accurate assessment of experimental thermodynamic and phase diagram data of

oxide subsystems.

3.2 Thermodynamic modeling

3.2.1 Stoichiometric solid oxides

The stoichiometric ternary phase α, containing m and n moles of two different sorts of

cations, a with the positive electrical charge r and b with the positive electrical charge q,

Method

48

respectively, and p moles of one sort of anions, c with the negative electrical charge s, the

three types of ions sitting in three distinctive crystallographic sublattices, can be described by

the sublattice formula ( ) ( ) ( )qr sm n pa b c . For oxides c = O and charge s = −2. To account for the

charge neutrality criterion, Eq. 3.2.1 is true.

2 0mr nq p+ + = (3.2.1)

The molar Gibbs energy of α, m°Gα at constant pressure is given by

( 1)2 3lnm−° = + + + + +G A BT CT T DT ET FTα (3.2.2)

A, B, C, D, E, and F are model parameters to be optimized by thermodynamic and phase

diagram data. As Cp(α) is defined by

2 22 6 2 −= − − − −pC C DT ET FT (3.2.3)

C, D, E and F are optimized to heat capacity data only. m°Gα can be based on the molar Gibbs

energies of existing binary oxides Ox1: 2-( ) (O )rt ua and Ox2: 2-( ) (O )q

v wb ( , , , N∈t u v w ), if it is

assumed that the heat capacity of the ternary oxide composed by the two binary oxides is

simply the sum of the heat capacities of the composing oxides as shown in Eq. 3.2.4:

22- 2-2-( ) ( ) (O ) ( ) (O )( ) (O ) O (g)

2m m m m m° ° ° ° ° +− −= = + + +

qr qrm n p v wt ua b ba ptv muv nwtm nG G G G G A BTt v tv

α (3.2.4)

m°Gα is the Gibbs energy of formation of the phase α relative to the oxide components. A and B

are optimized by thermodynamic and phase diagram data.

3.2.2 Solid solution phases – the Compound Energy Formalism (CEF)

If in the binary oxide Ox1: 2-( ) (O )rt ua containing cation a with the positive charge r, another

sort of cation with the positive charge q, qb can sit in the same sublattice as a, the sublattice

formula of the resulting solid solution phase β(ss) reads 2-( , ) (O )qrt ua b . Eq. 3.2.5 is the

criterion for charge neutrality:

Method

49

( )2

a bt y q y qu

+= (3.2.5)

Using the Compound Energy Formalism (CEF)[2-4], the molar Gibbs energy of the solid

solution phase contains the Gibbs energies of the compounds. For β(ss) the two compounds

read 2-( ) (O )rt ua and 2-( ) (O )q

t ub . The Gibbs energy of β(ss) at constant pressure reads

( )2-2- ( ) (O )( ) (O ) ln lnqr

t ut ur q r r q r

baa a a ab bG y G y G tRT y y y y Gβ β° = + + + +ss ° ° E ss

m m (3.2.6)

where ray is the site fraction of cation a on the cation sublattice, and qby is the site fraction

cation b on the cation sublattice. R=8.31451 J mol-1 K-1. The second-last term accounts for the

configurational entropy of mixing of t moles of a and b. The last term describes the excess

Gibbs energy of mixing due to interactions of ions in the mixture that can be accounted for by

introducing interaction parameters.

3.2.3 Vacancies and the concept of reciprocal reactions

Let us consider the case of a binary oxide phase (A)2(B)3, A standing for the cation sublattice,

and B denoting the anion sublattice, with only one cation a accepting the charge 3+ or 2+ in

the cation sublattice. If the cation is reduced, the charge neutrality criterion is no longer

obeyed by an anionic sublattice that is completely filled with oxygen. Charge neutrality under

such reducing conditions can be remained by the formation of zero-charged vacancies (Va) in

the anionic sublattice resulting in the phase becoming oxygen-nonstoichiometric. In the

sublattice form the phase can be written as 3 2 2-2 3( , ) (O ,Va)+ +a a . The oxygen nonstoichiometry

is denoted “O3-δ”. The molar Gibbs energy of the phase at constant pressure reads

( ) ( )

3 2 2- 3 2- 2 2- 32 3 2 3 2 3 2 3 2 3

3 2- 2 2- 3

2 3 2 2-2 3 2 3

2 3 3 2 2 2- 2-

A O ( , ) (O ,Va) ( ) (O ) ( ) (O ) ( ) (Va)VaO O

( ) (Va) ( , ) (O ,Va)Va Va VaO O

2 ln ln 3 ln ln

a a a a aa a a

a a aa a a a a

G G y y G y y G y y G

y y G RT y y y y RT y y y y G

δ+ + + + +

−+ + +

+ + +

+ + + + +

° °= = + +

+ + + + + +

° ° °m m m m m

° Em m

(3.2.7)

Once again the molar Gibbs energies of all the 4 endmember compounds 3 2-2 3( ) (O )+a ,

2 2-2 3( ) (O )+a , 3

2 3( ) (Va)+a , and 22 3( ) (Va)+a of the phase are required for the molar Gibbs energy

Method

50

of the phase. However, the only neutral endmember is 3 2-2 3( ) (O )+a . It thus can exist, and its

molar Gibbs energy can be defined by optimization of model parameters by experiments. The

three other endmembers are charged and cannot exist, but a line of neutral compositions

connects 3 2-2 3( ) (O )+a with the reduced compound 2 2-

2 3( ) (2 3O Va)+a , and its Gibbs energy can

be optimized with experiments that are related to the reduction of the phase, for instance

oxygen nonstoichiometry data.

The composition square of the phase can be seen in Fig. 3.2.1 that is redrawn from Hillert[4],

with the neutral line and the reduced compound, denoted with R, included. The 2+ charged

center composition of the square, 3 2 2-2 3( ) (3 2O 3 2Va)+ +a a , denoted with A in Fig. 3.2.1, is

theoretically obtained by mixing equal amounts of either 3 2-

2 3( ) (O )+a and 22 3( ) (Va)+a or 3

2 3( ) (Va)+a and 2 2-2 3( ) (O )+a .

Fig. 3.2.1 The surface of reference for the Gibbs energy of the reciprocal

phase 3 2 2-2 3( , ) (O ,Va)+ +a a approximating its overall Gibbs energy for Δ°Grec > 0 and Δ°Grec = 0,

plotted above the composition square.

A system that obeys this relation is called a reciprocal system, and 3 2 2-2 3( , ) (O ,Va)+ +a a is a

reciprocal phase[4].

For an unambiguous definition of the molar Gibbs energy of the reciprocal phase it is

necessary to give an arbitrary molar Gibbs energy to a reference. As the chosen molar Gibbs

energy of the reference is unlikely the true value, the reference should favorably be a highly

charged compound, thus far off neutral compositions that can really exist. For the example of

the reciprocal solid solution phase 3 2 2-2 3( , ) (O ,Va)+ +a a the 6+ charged compound 3

2 3( ) (Va)+a is

chosen as reference.

Method

51

The surface of reference for the Gibbs energy of the reciprocal phase 3 2 2-2 3( , ) (O ,Va)+ +a a at

very low temperatures (to make the configurational entropic contribution negligible), and

without excess terms for the Gibbs energy is visualized in Fig. 3.2.1 (page 50) and

approximates the whole Gibbs energy of the phase. The morphology of the Gibbs energy

surface depends on Δ°G of the reciprocal reaction 3

2 3( ) (Va)+a + 2 2-2 3( ) (O )+a − 3 2-

2 3( ) (O )+a − 22 3( ) (Va)+a :

3 2 2- 3 2- 2

2 3 2 3 2 3 2 3( ) (Va) ( ) (O ) ( ) (O ) ( ) (Va)rec ° ° °+ + + +° °Δ = + − −a a a aG G G G G (3.2.8)

If Δ°G of the reciprocal reaction, Δ°Grec is positive, the Gibbs energy surface is curved, and

the theoretic compound A will tend to demix to 3 2-2 3( ) (O )+a and 2

2 3( ) (Va)+a by only slightly

oxidizing or reducing it. On the other hand, if Δ°Grec is zero, the Gibbs energy surface is flat

and no tendency of demixing of A exists. In Fig. 3.2.1 (page 50) only the edge of this plane is

seen as bold line. Note that in order to obtain the same Gibbs energy of the reduced

compound R for Δ°Grec > 0 and Δ°Grec = 0, when the Gibbs energies of the endmember 3 2-

2 3( ) (O )+a and the reference 32 3( ) (Va)+a are fixed, the Gibbs energies of the remaining

endmembers are significantly different for Δ°Grec > 0 and Δ°Grec = 0. This is not a problem for

the description of a reciprocal oxide phase, as long as these endmembers are charged and

away from the existing composition range of the phase. Anyway, the true surface shape of a

reciprocal oxide phase with charged endmembers is not known. As no tendency of demixing

was reported for the nonstoichiometric oxide solid solutions that are treated in this study, and

no experiments define a proper value of the reciprocal reaction parameter, it is legitimate to

define Δ°Grec = 0.

3.2.4 Calculation of defect chemistry using the Calphad approach

The Calphad approach is very powerful for the calculation of the defect chemistry of high-

order nonstoichiometric reciprocal solid solution oxide phases[5] such as (A)(B)O3-δ

perovskite with a complex sublattice formula, for instance 3 2 2 3 4 3+ 4+ 2-

3( , ,Va)( , , , , ,Va)(O ,Va)+ + + + +a b c c c d d for a Cr-doped LSM perovskite as a function of

composition, temperature, and oxygen partial pressure. For this purpose model parameters of

the reduced and oxidized compounds are optimized with experimental information on charge

carriers, site fractions and oxygen content.

Method

52

3.3 Optimization of model parameters

The optimization of the thermodynamic parameters was performed using the PARROT

module of the Thermo Calc[6] database system. PARROT can take into account all sorts of

thermodynamic and phase diagram data simultaneously. The program minimizes the sum of

squared errors between calculated and experimentally determined phase diagram and

thermodynamic data. As the use of all the experimental data in a simultaneous least square

calculation often leads to divergence, the authors selectively adjusted the relative weight of

each experimental data point and excluded data that were inconsistent with the majority of the

data points during the optimization procedure. This weighting process is based on the accurate

assessment of experimental thermodynamic and phase diagram data.

References

1. N. Saunders, A.P. Miodownik, Calphad Calculation of Phase Diagrams, Pergamon

Materials Series, Vol. 1. Elsevier Science Ltd., 1998, 479 p.

2. J.-O. Andersson, A.F. Guillermet, M. Hillert, B. Jansson, B. Sundman, A Compound-

Energy Model of Ordering in a Phase with Sites of Different Coordination Numbers, Acta

Metall., 1986, 34, pp. 437-445.

3. M. Hillert, B. Jansson, B. Sundman, Application of the Compound-Energy Model to

Oxide Systems, Z. Metallkd., 1988, 79(2), pp. 81-87.

4. M. Hillert, The Compound Energy Formalism, J. Alloy. Cmpd., 2001, 320, pp. 161-76.

5. A.N. Grundy, E. Povoden, T. Ivas, L.J. Gauckler, Calculation of Defect Chemistry Using

the CALPHAD Approach, Calphad, 2006, 30, pp. 33-41.

6. B. Sundman, B. Jansson, J.O. Andersson, The Thermo-Calc databank system, Calphad,

1985, 9(2), pp. 153-90.

Thermodynamic assessments

53

4 Thermodynamic assessments

4.1 Thermodynamic reassessment of the Cr-O system in the framework

of solid oxide fuel cell (SOFC) research

E. Povoden, A.N. Grundy, and L.J. Gauckler

J. Phase Equilib. Diff., 2006, 27, pp. 353-62.

A comprehensive compilation and evaluation of experimental and thermodynamic data for the

Cr-O system is presented and, by application of the CALPHAD method, a consistent set of

thermodynamic model parameters is optimized based on new experiments. Nonstoichiometry

of eskolaite (Cr2+xO3) is described using the compound energy model, and the liquid is

described using the two-sublattice model for ionic liquids. Cr3O4 is described as a

stoichiometric compound. Also the magnetic transition in Cr2O3 and the oxygen solubility in

Cr are modeled.

4.1.1 Technology

SOFC offers high fuel conversion efficiencies and, due to the high operating temperature

(>1173 K), combined heat- and power-generation capability. For the planar design SOFC,

which offers low fabrication costs, ceramic and metal interconnect materials have been tested

and evaluated over the years. Meanwhile the use of Cr-based alloy interconnect materials has

gained popularity due to their relative ease of fabrication, low manufacturing costs and high

thermal conductivity[1]. Namely a Cr5Fe1Y2O3 oxide dispersion strengthened alloy with the

composition 94 wt.% Cr, 5 wt.% Fe and 1 wt.% Y2O3 developed jointly by Plansee and

Siemens with satisfying material properties has been promoted as a suitable alternative to the

earth alkaline-doped LaCrO3 ceramics interconnect. However, the use of this alloy as an

interconnect material in SOFC leads to the degradation of the fuel cell performance especially

on the cathode side of the fuel cell. Loss of performance caused by the migration of Cr

originating from the alloy interconnect is well documented by several investigators.

Microstructural analyses of the cathode of SOFC show the formation of Cr2O3 and

(CrMn)3O4, which block active sites as well as pores, thus substantially reducing the triple-


54

phase boundary area for the normal oxygen reduction reaction at the cathode/electrolyte

interface.

The influence of Cr from the interconnect alloy on the strontium-doped lanthanum manganite

(LSM) cathode can be modelled in terms of an equilibrium thermodynamic view to contribute

to strategies for reducing the SOFC chromium poisoning process by optimizing SOFC

operating conditions and refining SOFC material compositions.

4.1.2 Experimental data

Phase diagram data:

Experimental investigations of phase diagrams in the Cr-O system were made by Ol’shanskii

and Shlepov[2] and Toker[3]. These authors document the existence of a large miscibility gap

between the metallic and the oxide melt. Eskolaite (Cr2O3) is the dominating stable oxide

phase over a wide temperature range. Results of special points in the Cr-O phase diagram

from several studies are summarized in Table 4.1.1.

Table 4.1.1 Special points in the Cr-O system

Melting of

Cr2O3 in

air, T (K)

Eutectic

T (K)

Eutectic

compo-

sition,

X(O)

Cr3O4

detected

Stability

range

of Cr3O4,

T (K)

Mono-

tectic

T (K) Reference

2257 -- -- -- -- -- Kanolt[4]

experimental

2317 -- -- -- -- -- Wilde and Rees[5]

experimental

2603 -- -- -- -- -- McNally et al.[6]

experimental

2543 ± 25 -- -- -- -- -- Bunting[7]

experimental


55

-- 1933 0.52 no -- 2083 Ol’shanskii and

Shlepov[2], experimental

-- 1918 0.523 no -- 2083 Johnson and Muan[12]

experimental

2571 1941 0.513 yes 1923 –

1978 --

Degterov and Pelton[39]

calculated

-- 1929 0.496 yes 1918 –

1974 2160

Kowalski and Spencer[40]

calculated

-- 1937 0.499 yes 1923 –

1978 2130

Taylor and Dinsdale[41]

calculated

-- 1938 ± 2 0.497 yes 1923 ± 2 –

1978 ± 3 2083

Toker et al.[13]

experimental

2539 1938 0.497 yes 1918 –

1973 2117 This work, calculated

Note: Itallicized data were used for optimization

The melting temperatures of eskolaite in air reported from Kanolt[4] and Wilde and Rees[5] can

be discarded as being too low. Mc Nally[6] measured a melting temperature of 2603 K in air

using an induction furnace. This value significantly deviates from the result of Bunting[7],

who measured T = 2543 ± 25 K also in air. Grube and Knabe[8] found that 1 wt.% Cr2O3

lowers the melting point of metallic Cr from T = 2163 K to between T = 2043 K and 2063 K.

Lam[9] reported the existence of molten chromium with oxygen impurities of 1400 ppm at

T = 2133 K. The monotectic reaction of Cr (bcc) metal and liquid was found at T = 2083 K by

Grube and Knabe[8] and by Ol’shanskii and Shlepov[2]. The question of the existence of a

crystalline Cr3O4 phase was discussed controversially by several authors. Investigations made

by Hilty et al.[10] and Hook and Adair[11] led them to postulate the existence of a crystalline

Cr3O4 phase in the Cr-Fe-O system. Concerning the pure Cr-O system, Ol’shanskii and

Shlepov[2] and Johnson and Muan[12] did not find Cr3O4 up to the eutectic temperature of

chromium oxide, whereas Toker et al.[13] concluded from microstructural observations and a

discontinuity in the slopes of the temperature-oxygen pressure curves for univariant equilibria

involving metallic Cr and various chromium oxide phases that a Cr3O4 phase exists in a

narrow temperature range between T = 1923 K and 1978 K. Microstructures of a quenched


56

chromium melt with maximum oxygen impurities of about 2930 ppm lately investigated by

Lam[9] document an inner Cr3O4 phase and an outer Cr2O3 phase in dispersed oxides in large

chromium grains and grain boundaries. This indicates that the first phase to crystallize on

solidification is Cr3O4 giving strong evidence for the stability of this phase. Thus in this study

the authors accept the findings of Toker et al.[13] and Lam[9].

Thermodynamic data:

Oxygen Potentials:

Grube and Flad[14] measured 2Olog( )p values for the Cr-Cr2O3 equilibrium between

T = 1053 K and 1573 K by both oxidizing Cr to Cr2O3 and reducing Cr2O3 to Cr in a flowing

H2-H2O atmosphere. At T ≥ 1573 K they were confronted with the loss of a quarter of Cr in

the case of oxidation; thus at these temperatures 2Olog( )p values were determined solely from

the reduction of Cr2O3. Novokhatskii and Lenev[15] studied the equilibrium of the reduction of

Cr2O3 to Cr with hydrogen from T=1493 K to 1893 K. These authors used a flow method

where thermal diffusion problems were suppressed by inserting corundum bushes into the

reaction tube. Appreciable sublimation of metallic chromium was not observed. Davies and

Smeltzer[16] determined 2Olog( )p values of Cr2O3 at T=1173 K, 1273 K, and 1373 K, using an

electrochemical cell with a calcia-zirconia electrolyte and a Fe/FeO reference electrode. Toker

et al.[13] measured 2

log( )Op values of Cr2O3 by equilibrating Cr and Cr2O3 in H2-CO2 mixtures

of known oxygen potentials at temperatures from T = 1773 K to 2098 K. Pehlke et al.[17] used

two separate series of emf measurements employing the solid oxide electrolyte galvanic cell

technique from T = 1148 K to 1548 K. The reversibility and accuracy of the yttria-doped

thoria electrolyte and the electrode was tested by measurements of a standard iron-chromium

alloy at 1326 K. The independent results of corrected cell potentials of the two measurement

series are excellent. The data are in close agreement with the gas-solid equilibrium

measurements by Jeannin et al.[18]. Disagreement between the emf results from Pehlke et

al.[17], Pugliese and Fitterer[19], and Tretjakow and Schmalzried[20] were assigned to possible

electronic conduction in the zirconia electrolyte used by the latter authors, as well as transport

of oxygen ions from the cathode to the Cr/Cr2O3 anode. Applying the same technique as

Pehlke et al.[17], Holzheid and O’Neill[21] noted a deviation from the well-established trend

from T = 900 K to 1300 K for high-temperature data caused by finite electronic conductivity

at elevated temperatures, causing transfer of oxygen through the cell, as well as the

importance of sufficient time to attain equilibrium, that is, days for T < 1100 K. The obtained


57

dissociation pressures of Cr2O3 are in agreement with average values derived from emf studies

using an yttria-doped thoria electrolyte worked out by Jacob[22] and a very high temperature

gas-mixing study of Toker et al.[13].

Heat Capacities, heat Contents, and entropies:

Anderson’s[23] calorimetric data set of Cp-values lacks detailed documentation of the

experimental procedure. Bruce and Cannell[24] applied a two-dimensional temperature wave

method using a single crystal of Cr2O3 to calculate specific heat in the temperature range

290.68 ≤ T ≤ 323.43 K, and fitted the data to the heat of diffusion equation that considers

some material properties employing a least-mean-squares fit. The accuracy of this study is

evident from excellent data reproduction by performing two runs in the entire temperature

range. Documentation of the experiments, data presentation, and fitting procedure are worked

out very carefully. Resulting Cp data correspond nicely to the most recent calorimetric results

from Klemme et al.[25]. The latter authors measured a consistent data set of heat capacities of

synthetic eskolaite from T = 1.5 K to 340 K with mean increments of 0.56 K. Uncertainties of

0.4 % for Cp (20 K < T < 200 K) and 0.7 % for Cp (T < 20 K) were estimated. For Cp(Cr2O3) =

120.37 J mol-1 K-1 at T = 298.15 K Chase et al.[26] relied on the calculated results from heat

content measurements performed by Kelley et al.[27]. The latter authors fitted their data

measured from T = 400 K to 1800 K by

2 1

298K 2 ° ° −− = + + +TbH H aT T cT d (4.1.1)

yielding

3 2 5 1

298K 28.53 1.10 10 3.736 10 9759° ° − −− = + × + × −TH H T T T (4.1.2)

Temperature derivation of Eq. 4.1.2 results in

3 5 228.53 2.20 10 3.736 10− −= + × − ×pC T T (4.1.3)

For K298° S (Cr2O3) Chase et al.[26] relied on the results from Anderson[23], who calculated

K298° S (Cr2O3) = 81.17 ± 0.84 J K-1mol-1 by a graphical method of plotting the heat capacity

against the logarithm of the temperature and modeling the heat capacity curves with Debye


58

functions. This procedure was critically documented by other authors, for example, Klemme

et al.[25]. Klemme et al.[25] recommend K298° S (Cr2O3) = 83.1 J K-1mol-1 by reevaluating emf

data from Holzheid and O’Neill[21], who calculated K298° S (Cr2O3) = 85.74 ± 1.3 J K-1 mol-1

from their measurements. Dellien et al.[28] adopted their K298° S (Cr2O3) value from Wagman et

al.[29].

Shirokov[30] estimated K298° S of a metastable CrO phase to be 46.86 J K-1 mol-1.

Enthalpies of Formation:

Roth and Wolf[31] found 298Kf,el°Δ H (Cr2O3) = –1125.8 ± 2.5 kJ mol-1 (el=elements) by

applying a calorimetric technique. Mah[32], using a bomb calorimetric combustion technique

at 1323 K and 30 atm oxygen pressure, calculated 298Kf,el°Δ H (Cr2O3) =–1140.98 ± 1.7 kJ mol-1

.

Some difficulty caused by moisture adsorption was encountered in weighing the combustion

products. This was circumvented by heating the combustion products to T = 1323 K. For the

calculation of 298Kf,el°Δ H (Cr2O3) the heat content data given by Kelley et al.[27] were used.

Ramsey et al.[33] used heat capacity and entropy data from tabulations of Coughlin[34] to

obtain 298Kf,el°Δ H (Cr2O3) = –1122.06 kJ mol-1. Navrotsky[35] cited Garrels and Christ[36] for

298Kf,el°Δ H (Cr2O3) = –1128.42 kJ mol-1. Chase et al.[26] evaluated 298Kf,el

°Δ H (Cr2O3) = –1134.7

± 8.4 kJ mol-1 from several earlier studies, while Dellien et al.[28] adopted 298Kf,el°Δ H (Cr2O3) =

–1139.72 kJ mol-1 from Wagman et al.[29]. Klemme et al.[25] recommended 298Kf,el°Δ H (Cr2O3)

= –1128.2 ± 0.4 kJ mol-1 by evaluating emf data from Holzheid and O’Neill[21].

Shirokov[30] estimated 298Kf,el°Δ H (CrO) = –305.4 kJ mol-1 for metastable CrO.

4.1.3 Previous assessments of the Cr-O system

Banik et al.[37] established a phase diagram for the Cr-O system based on a subregular

solution model that is in good agreement with experimental data obtained by Ol’shanskii and

Shlepov[2], thermodynamic data for Cr-Cr2O3 from Fromm and Gebhardt[38], and

thermodynamic estimates for CrO from Shirokov[30]. Degterov and Pelton[39] reassessed the

CrO-Cr2O3 subsystem for the molten slag database using a modified quasi-chemical model for

the liquid phase. Their calculated liquidus temperature of Cr2O3 in air is T = 2571.16 K,

which is in good agreement with an early finding by Bunting[7] who measured T = 2543

± 25 K. Kowalski and Spencer[40] used the associated solution model for the liquid phase

based on the experimental data used by Taylor and Dinsdale[41]. The latter authors proposed a


59

phase diagram in good agreement with the experimental data obtained by Toker[3], using the

same thermodynamic models as the authors use in this work, which are the two-sublattice

ionic model for the liquid and the compound energy model for the Cr2+xO3 phase. Taylor and

Dinsdale[41] fitted Cp data from Anderson[23] close to the antiferromagnetic to paramagnetic

transition and data from Chase et al.[26] at elevated temperatures as a sum of magnetic and

nonmagnetic contributions. Experimental information on phase relations for their assessment

was taken from Ol’shanskii and Shlepov[2], Toker[3], Kelley et al.[27], and Grube and Knabe[8].

The heat capacity of Cr3O4 was taken as 7/5 times the nonmagnetic value for Cr2O3 according

to Neumann and Kopp’s rule. Their calculated values for the enthalpy of formation and the

entropy of Cr3O4 are in agreement with an estimate done by Chipman[42].

Their optimization of one of the charged endpoints in their compound energy model for

eskolaite and the use of six interaction parameters to describe the liquid may lead to problems

on extrapolation to higher-order systems, especially as their miscibility gap does not close on

increasing temperature. The use of six parameters for the description of the Cr3O4 phase is

somewhat incommensurate with the scanty experimental information of this phase.

There is a large uncertainty concerning the exact melting point of Cr2O3, and only few

thermodynamic data of the Cr3O4 phase and the liquid phase exist. This is reflected by

significant variations of the position of the eutectics, the stability field of Cr3O4, and the

temperature of the monotectic reaction of Cr(bcc) and liquid between the assessments of the

Cr-O system.

4.1.4 Thermodynamic modeling

Solid phases:

The crystal structure of eskolaite is α-Al2O3 type, space group R3c . Eskolaite shows an

antiferromagnetic to paramagnetic transition at T = 305.5 K. The magnetic properties of

eskolaite can be described using a magnetic ordering model proposed by Inden[43], and

simplified by Hillert and Jarl[44]. In this model, a magnetic contribution to the Gibbs energy is

added to the nonmagnetic part of the Gibbs energy given as:

MAGmΔ = ln β τ( +1) ( )G RT f (4.1.4)


60

where β is a parameter related to the total magnetic entropy, and τ = T/Tc. Tc is the critical

temperature for magnetic ordering. Tc and β are both dependent on the composition. The

magnetic parameter p equals 0.28.

The defect chemistry of Cr2+xO3 with the sublattice occupation (Cr2+,Cr3+)2 (Cr3+,Va)1 (O2-)3

can be modeled using experimental data from Matsui and Naito[45]. This means that reduction

is accomplished by the formation of interstitial Cr3+ and not by the formation of oxygen

vacancies, which is in agreement with Young et al.[46]. When modeling nonstoichiometry in

an oxide phase, it is important to submit the experimental data to a defect-chemistry analysis.

In the case of Cr2+xO3 modeled with interstitial Cr3+ the defect reaction reads

(g)•••

Cr O Cr O 2'2Cr Va 3O 3 2Cr 1 2Cr 1 4Va 9 4O 3 8O + + → + + + +x x x x x

i i i (4.1.5)

giving the equilibrium constant

3 2 ••• 1 2 1 4 9 4 3 8

Cr O O22 3

Cr O

'[Cr ] [Cr ] [Va ] [O ][Cr ] [Va ][O ]

=x x

i ir x x x

i

pK (4.1.6)

Assuming small defect concentrations all concentrations except Cr'[Cr ]and •••[Cr ]i are ~ 1 and

can be ignored. Due to charge neutrality the relation •••Cri'[Cr ] 3[Cr ]= must hold. Inserting this

into Eq. 4.1.6 gives the proportionalities ••• 3 16Oi 2

[Cr ] −∝ p and 3 16Cr O2'[Cr ] −∝ p . To explain their

experimental results Matsui and Naito[45] proposed a defect reaction that leads to the same

proportionality; however, their equation violates the fundamentals of defect chemistry and

must be rejected in favor of the defect reaction given above (Eqs. 4.1.5 and 4.1.6). The

following other interstitial defects could be assumed: ••Cri giving a slope of 1 4O2

−p , and

••••Cri giving a slope of 3 20O2

−p . Both are unlikely: the former because it is unlikely to get Cr4+

on reduction, the latter because of the large size of Cr2+. Assuming the defect reaction that

describes the formation of oxygen vacancies:

(g)••

Cr O Cr O 2'Cr 1 2O Cr 1 2Va 1 4O+ → + +x x (4.1.7)


61

leads to a proportionality of •• 1 6O O2

[Va ] −∝ P and 1 6Cr O2'[Cr ] −∝ P . This slope does not correspond

to the experimental findings of Matsui and Naito[45]. Also the defects cannot explain the

electrical properties measured by Young et al.[46].

The low nonstoichiometry data from Matsui and Naito[45] show a different slope than their

higher nonstoichiometry data. In contrast to Matsui and Naito[45] who explain this assuming

that neutral Cr forms interstitially, the present authors believe that the different slopes are

caused by a competing defect reaction, for example charge disproportionation,

Cr3+ → Cr2+ + Cr4+, similar to the case of LaMnO3 perovskites[47]. The present authors didn’t

consider this by their defect chemistry model, as it would make the description quite complex.

Fig. 4.1.1 is a graphic representation of the model the authors use to describe the oxygen

nonstoichiometry of eskolaite, where each corner of the composition square represents a °G

parameter.

Fig. 4.1.1 Compound energy model for the Cr2+xO3 phase

The four corner compositions represent all possibilities to express the Cr2+xO3 phase

according to the above formula for the sublattice occupation. The corner Cr3+:Va:O2-

corresponds to stoichiometric Cr2O3. The three other corner compositions present charged

compounds. Only compounds along the neutral line can exist on their own. As the most

reasonable way to model reduction is to use the reduced neutral endpoint


62

(Cr2+)2 (Cr3+2/3Va1/3)1 (O2-)3, labeled A in Fig. 4.1.1, one has to find functions of °G of three

charged corners expressed solely in terms of the neutral compositions. This is done by using

the two equations for the stoichiometric and the reduced endpoints, by choosing an arbitrary

reference, and by defining a reciprocal reaction giving four equations with which all °Gs at the

corners can be expressed.

The function to model the reduction then reads

° ° SER

2+ 3+ 2 Cr O CrCr (Cr Va )(O ) 2 32 2 3 1 3 32 3 (2 3ln 2 3+1 3ln1 3)°

− = + + + +G G G A BT RT (4.1.8)

The last term describes the configurational entropy due to mixing of Cr3+ and Va on the

interstitial site. °G of the 3+ charged endmember (Cr3+)2 (Cr3+)1 (O2-)3 is chosen as reference

and given the value °3+ 3+Cr :Cr

G . Then the reciprocal relation reads

° °

r3+ 3+ 2+ 3+ 2+ 3+Cr :Cr Cr :Va Cr :Va Cr :Cr° °+ = + = ΔG G G G G (4.1.9)

In order to avoid the inevitable formation of miscibility gaps if the energy of the reciprocal

relation is large we set this energy zero, which leads to

° ° ° °

3+ 3+ 2+ 3+ 2+ 3+Cr :Cr Cr :Va Cr :Va Cr :Cr0+ − − =G G G G (4.1.10)

This means that without introducing interaction parameters one gets an ideal description

between Cr2O3 and Cr2+xO3. The expressions for all °Gs at the corners resulting from Eq. 4.1.8

to 4.1.10 are listed in Table 4.1.2, pp.63-64.


63

Table 4.1.2 Thermodynamic description of the

Cr-O System

Element

Element Reference Mass H298 - H0 S298

Cr Cr (bcc_A2) 51.996 4050.0 23.543

O 12 mol O2 15.999 4341.0 102.52

Liquid

2- 2+ 3+

2+ q-

3+ q-

3+ 2-

2+ 2-

2+ 3+ 2- q-p q

VaO Cr Cr

L SER [49]CrCr :Va

L SER [49]CrCr :Va

L SER SERCr OCr :O

L SER SERCr OCr :O

(Cr ,Cr ) (O ,Va )

2 , 2 3

GCR_L

2GCR_L GCR2O3_L 3GCR1O1_L

2 3 GCR2O3_L

2 2 2GCR1O1_

°

°

°

°

= + = +

− =

− = + −

− − =

− − =

p y qy q y y

G H

G H

G H H

G H H

2+ 2- q- 3+ 2- q-0 0

Cr :O ,Va Cr :O ,Va

L

121000= =L L

Solid Cr (bcc_A2)

1 3(Cr) (O,Va) bcc SER [49]Cr:Va Cr

bcc SER SER [49]Cr:O Cr O

0 bccCr:O,Va

GHSERCR

3 GHSERCR + 3GHSEROO + 243

7095420.4 311.5 0.008

°

°

− =

− − =

= −= = − = −c

G H

G H H T

Lp T β

CrO 1 1Cr O SER SER

Cr:O Cr O GCR1O1G H H° − − =

Cr2O3

2 33+ 2-

2 33+3+ 2-

2 33+2+ 2-

2+ 2

2+ 3+ 3+ 2-2 1 3

Cr O° SER SERCr OCr :Va:O

Cr O° SER SER [49]Cr OCr :Cr :O

Cr O° SER SER [49]Cr OCr :Cr :O

°Cr :Va:O

13

(Cr , Cr ) (Cr ,Va) (O )

2 -3 GCR2O3

3 3 GCR2O3 GHSERCR

3 3 GCRO0 GHSERCR 5.2923

− =

− − = +

− − = + −

G H H

G H H

G H H T

G 2 3-

Cr O SER SER [49]Cr O


0.28 308.6 3.0

− − = − −

= = =c

H H T

p T β

Cr3O4

3 4Cr O° SER SERCr:O Cr O3 4 GCR3O4 − − =G H H

Functions


64

-3 2 -1

[49]

[49]

[49]23

GCR2O3 1164542 728.56 119.8 ln4.97 10 1050000

GCR1O1 0.5GCR2O3 0.5GHSEROO 255269 53.82GCR3O4 1.5GCR2O3 0.5GHSEROO 280045 93.76GCRO0 108305 GCR2O3 GHSERCR

GCR2O3_L GCR2O3 4390

= − + −− × +

= − + −= − + −

= + +

= +

T T TT T

TT

[49]

78 169GCR1O1_L 0.5GCR2O3 0.5GHSEROO 339673 121.4

−= − + −

TT

Note: All parameters are in SI units: J, mol, K, Pa: R = 8.31451 J mol-1 K-1.

Parameters for solid Cr, liquid Cr, and gaseous O are from Dinsdale[49]

In contrast to Taylor and Dinsdale[41], who needed 4 parameters to model the Cr2O3 phase and

had to arbitrarily equate the °G of (Cr2+)2 (Va)1 (O2-)3 to stoichiometric Cr2O3, the latter

constraint is not needed in the model, and one can reduce the number of parameters to only

two.

The oxygen solubility in solid Cr(bcc) can be described by an interstitial solution model of the

form (Cr)1(O,Va)3. For the optimization of model parameters, literature data from Caplan and

Fraser[48] are used. It was not possible to model the oxygen solubility using the

endmember °Cr:O G as this endmember turned out to be too stable and CrO3 appeared in the

stability diagram at high oxygen partial pressures. Therefore a large value is given to the

endmember °Cr:O G (in this case 0 was a large number) and the oxygen stability is modeled

with the temperature dependence of °Cr:O G and a regular interaction parameter 0

Cr:O,VaL that

must of course be negative.

The Cr3O4 phase is based on the eskolaite phase. Its heat capacity is given by Neumann and

Kopp’s rule. Metastable CrO is described in the same way.

The descriptions for solid and liquid chromium metal and gaseous O2 are from Dinsdale[49].

Ionic liquid:

The two-sublattice ionic liquid model[50,51] is selected to describe the ionic liquid. As the

experimental data on the liquid phase are scarce, the number of parameters is kept as low as

possible. The sublattice occupation (Cr3+,Cr2+)p(O2-,Vaq-)q is chosen. With this expression one

is able to obtain reasonable results for the liquid phase using the positive interaction

parameters, 2+ 2-0

Cr :O ,VaL and 3+ 2-0

Cr :O ,VaL that are required to give the miscibility gap. Fig. 4.1.2

(next page) is a graphic expression of the model, where each corner of the composition square

represents a °G parameter of the liquid phase.


65

Fig. 4.1.2 Two-sublattice ionic liquid model for the Cr-O system

The four corner compositions represent all possibilities to express the liquid phase according

to the above formula. The liquid composition changes along the hyperbolic curves in Fig.

4.1.2.

A special feature of the Cr-O system is the occurrence of a eutectic very close to the

composition of CrO. The eutectic temperature is mainly determined by the value of the corner

Cr2+:O2-.

One derives the °GL functions of the oxide compositions (Cr3+:O2-) and (Cr2+:O2-) from the

eskolaite phase. The °GL of liquid Cr is taken from Dinsdale[49]. In this model description of

the liquid phase metallic Cr-liquid can be described by both the corners Cr2+:Va and Cr3+:Va.

Cr3+:Va must be metastable compared to Cr2+:Va. One way of doing this would be to simply

say that Cr3+:Va equals Cr2+:Va plus a large positive term, for example +600000 as given

to 2+°

Cu :VaG by Hallstedt et al.[52] in his original assessment of the Cu-O system. This is

however problematic for reciprocal systems. If the reciprocal energy of the system is large

there will be a tendency to form miscibility gaps as pointed out by Hillert and Sundman[53].

Hallstedt and Gauckler[54] recently reoptimized the Cu-O liquid, obtaining the

parameter 2+°

Cu :VaG from the reciprocal relation and giving it a reciprocal energy of 0. This

considerably improved the description of the Cu-O liquid and removed the inverted


66

miscibility gap found at high temperatures in the original assessment[52]. An identical strategy

is employed here. Thus metallic liquid is given by the corner 2+° L

Cr :VaG .The

parameter 3+° L

Cr :VaG is obtained by the reciprocal reaction given as

° L ° L ° L ° L

r r3+ 2+ 3+ 2- 2+ 2-Cr :Va Cr :Va Cr :O Cr :O = 2 + 3 ; 0− + Δ Δ =G G G G G G (4.1.11)

4.1.5 Optimization of parameters

The complete set of optimized thermodynamic parameters describing the Cr-O system is

given in Table 4.1.2 (pp. 63-64).

The optimization of the thermodynamic parameters was performed using the PARROT

module of the Thermo Calc[55] database system. In principle, PARROT can take into account

all sorts of thermodynamic and phase diagram data simultaneously. The program minimizes

the sum of squared errors between the calculated and experimentally determined phase

diagram and thermodynamic data. As the use of all the experimental data in a simultaneous

least square calculation often leads to divergence, the authors selectively adjusted the relative

weight of each experimental data point and excluded data that were inconsistent with the

majority of the data points during the optimization procedure.

The first parameters to be optimized were the Cp-parameters of Cr2O3. These parameters were

then kept fixed during the rest of the optimization. The data used were heat content data from

Kelley et al.[27] and Cp data from Klemme et al.[25] at T = 290 K and from T = 335 K to 338 K

with a low relative weight. The authors optimized Tc and β using Cp data from Klemme et

al.[25] close to the antiferromagnetic to paramagnetic transition temperature. To determine the

parameters describing the enthalpy and entropy of Cr2O3 2Olog( )p data from Jeannin et al.[18]

and Toker et al.[13], high temperature emf data from Holzheid and O’Neill [21], and, with low

relative weight, 298.16f,el°Δ H and 298.16

° S data from Holzheid and O’Neill[21] were used. In the

next step the authors optimized the nonstoichiometry of Cr2+xO3 using data from Matsui and

Naito[45]. They assessed Cr3O4 and the liquid simultaneously, using experimental phase

equilibria data from Toker et al.[13], experimental data on the liquidus at the oxygen poor side

from Toker et al.[13], and experimental data on the liquidus at the oxygen rich side of the

miscibility gap from Ol’shanskii and Shlepov[2]. The melting temperature of eskolaite in air

was taken from Bunting[7]. Finally the solubility of O in solid Cr was optimized using data


67

from Caplan and Fraser[48]. In Table 4.1.1 (p. 54-55) values that were used for our

optimization are written in italic letters.

4.1.6 Results and discussion

Phase diagram:

The calculated phase diagram with oxygen isobars is shown in Fig. 4.1.3.

Fig. 4.1.3 Calculated Cr-O phase diagram with oxygen isobars (Pa, logarithmic) given.

The gas phase was not included in the calculation

An enlargement of the phase diagram close to the CrO composition is presented in Fig. 4.1.4

(next page).


68

Fig. 4.1.4 Enlargement of the calculated Cr-O phase diagram close to the

CrO composition, with experimental data and oxygen isobars (Pa, logarithmic) included

The shape of the liquidus at the oxygen poor side of the miscibility gap resulting from the

authors’ optimization relying on a single experimental datum from Toker et al.[13] and an

earlier experiment from Ol’shanskii and Shlepov[2] is slightly deviating from former

optimizations. The calculated liquidus temperature of eskolaite in air is T = 2539 K, in good

agreement with the measurement from Bunting[7]. For the monotectic temperature of the

reaction of Cr (bcc) and liquid the present authors calculate T = 2117 K, and for the eutectic

one gets T=1938 K at a mole fraction of oxygen of 0.497. Cr3O4 is formed at T = 1918 K by

the eutectoid reaction 2 3 2 3 4Cr O Cr 1 2O Cr O+ + → . At a mole fraction of oxygen > 0.497 it

decomposes in a peritectic reaction at T = 1973 K forming Cr2O3 and liquid. Fig. 4.1.5 (next

page) shows the calculated oxygen potential phase diagram of the Cr-O system with

experimental 2Olog( )p data included.


69

Fig. 4.1.5 Calculated oxygen potential phase diagram of the Cr-O system,

with experimental2Olog( )p data as a function of temperature from different studies

The experimentally determined phase stabilities from Toker et al.[13] are particularly well

reproduced by the authors’ optimization. The shape and size of the miscibility gap is

speculative due to the lack of experimental data. The stability of Cr3O4 is shown in

the2Olog( )p versus temperature diagram in Fig. 4.1.6.

Fig. 4.1.6 Stability of Cr3O4 in the2Olog( )p versus temperature diagram


70

The solubility of oxygen in Cr(bcc) is shown in Fig. 4.1.7.

Fig. 4.1.7 Calculated oxygen solubility in Cr(bcc)

with experimental data and oxygen isobars (Pa, logarithmic) included

For the maximum solubility of oxygen in Cr(bcc) one calculates 0.08 at.% at T=1938 K. If the

commonly used – however grubby – notation “Cr2O3-δ” is applied, the total charge of Cr is

given by 6+2δ. The maximum calculated δ = 0.098 at T = 1918 K. The cation

overstoichiometry resulting from the presented optimization might seem somewhat high, but

it results simply from the extrapolation of experimental data from Matsui and Naito[45] on

excess Cr as a function of 2Op down to the oxygen partial pressure at the Cr-Cr2O3

equilibrium following the proportionality given by the defect chemistry analysis in section

4.1.4. The comparison of the calculated nonstoichiometry in Cr2+xO3 with the experimental

data by Matsui and Naito[45] is given in Fig. 4.1.8 (next page).


71

Fig. 4.1.8 Optimized nonstoichiometry of Cr2+xO3 with the only available experimental data

from Matsui and Naito[45] included. Optimization of a temperature dependence is represented

by dotted lines. Solid lines result from our accepted optimization without considering

temperature dependence. The low nonstoichiometry data show a different slope than the

higher nonstoichiometry data.

The solid lines correspond to the optimization that is accepted in this work. Obviously the

calculated results show a temperature dependence that is significantly stronger compared to

the experiments. Considering a temperature dependence for the reduced neutral endpoint of

the phase Cr2+xO3 gives values of GCRO0 202130 235 GCR2O3 2 3GHSERCR= − + + +T (dotted

lines in Fig. 4.1.8) and leads to the reduced neutral endpoint being too stable at low

temperatures. Therefore, and due to existing data at only three different temperatures from a

single author it was decided not to optimize a temperature dependence giving

GCRO0 108305 GCR2O3 2 3GHSERCR= + + . The data at low oxygen nonstoichiometries were

not used, as the introduction of an additional defect species would be required to reproduce

these.


72

Thermodynamic Data:

The heat capacities, Cp, of the solid Cr2O3 phase (Fig. 4.1.9) are well represented by our

assessment.

Fig. 4.1.9 Comparison of calculated heat capacities of Cr2O3 with experimental data

For the magnetic parameter β we calculate 3.0, and for Tc we get 308.6. For 298Kf,el°Δ H (Cr2O3)

we calculate –1123 kJ mol-1, which is in particularly good agreement with the data from

Ramsey et al.[33], and for 298K° S (Cr2O3) we get 85 J K-1mol-1, which is very close to the

results from Holzheid and O’Neill[21]. For 298Kf,el°Δ H (Cr3O4) we calculate –1402 kJ mol-1, and

for 298K° S (Cr3O4) we get 175 J K-1mol-1. These values for Cr3O4 deviate significantly from the

results of Taylor and Dinsdale[41] who calculated 298Kf°Δ H (Cr3O4) = –1447.685 kJ mol-1, and

298K° S (Cr3O4) = 150.555 J K-1 mol-1. For a metastable CrO phase we calculate

-1298Kf,el 306 kJ mol°Δ = −H , and -1 -1

298K 79 J K mol° = −S based on the estimates of Shirokov[30].


73

4.1.7 Conclusions

With the presented reassessment of the Cr-O system the authors are able to excellently

describe available thermodynamic and phase diagram data with as few optimizing parameters

as possible. However, it must be kept in mind that experimental data on the liquid miscibility

gap are largely missing, and that a large variation of the measured melting points of eskolaite

exists.

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35. A. Navrotsky, Thermochemistry of chromium compounds, especially oxides at high

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p. 410.

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Cr-Cr2O3, Z. Metallkd., 1980, 71(10): pp. 644-45.

38. E. Fromm, E. Gebhardt: Gases and Carbon in Metals, Springer Verlag, Berlin,

Heidelberg, New York, 1976, pp. 521-34 (in German).

39. S. Degterov, A.D. Pelton, Critical evaluation and optimization of the thermodynamic

properties and phase diagrams of the CrO-Cr2O3, CrO-Cr2O3-Al2O3, and CrO-Cr2O3-CaO

systems, J. Phase Equilib., 1996, 17(6), pp. 476-87.


76

40. M. Kowalski, P.J. Spencer, Thermodynamic reevaluation of the Cr-O, Fe-O and Ni-O

systems: Remodelling of the liquid, bcc and fcc phases, Calphad, 1995, 19(3), pp.

229-43.

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systems using the ionic liquid and compound energy models, Z. Metallkd., 1990, 81(5),

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77

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1985, 9(2), pp. 153-90.

4.2 Thermodynamic assessment of the Mn-Cr-O system for SOFC

materials


Int. J. Mater. Res., 2006, 97, pp. 569-78.

By application of the CALPHAD method, a consistent set of thermodynamic model

parameters is optimized for the Cr-Mn-O system based on experimental data. Chromium

manganese spinel MnyCr3-yO4 and its tetragonally distorted polymorph are described using the

compound energy model, and the liquid is described using the two-sublattice model for ionic

liquids. Also solid solutions of the phases (Cr1-yMny)2+xO3, Mn2-yCryO3, and (Mn1-yCry)1-xO are

considered. Relevance for solid oxide fuel cells is discussed.

4.2.1 Introduction

For the planar design of SOFC the use of heat-resistant high chromium alloys has been

promoted as a suitable alternative to earth alkaline doped LaCrO3 ceramic interconnect

materials[1,2]. However, mobilization predominantly via the gas phase[3] of Cr originating from

the alloy interconnect leads to the formation of Cr2+xO3 (eskolaite) and chromium manganese

spinel MnyCr3-yO4 which block catalytically active sites as well as pores, thus substantially

diminishing the triple phase boundary area for the normal oxygen reduction reaction at the

cathode/electrolyte interface[4]. Simner et al.[5] observed that the formation of chromium

manganese spinel layers on top of a Cr2O3 oxide scale on the surface of a Mn-containing

ferritic stainless steel (Crofer22 APU) interconnect with 76.6 wt.% Fe, 22.8 wt.% Cr, and

0.45 wt.% Mn resulted in an improvement of short-term SOFC operation. The processes by

which these protective oxide scales reduce the chromium poisoning and their effect on cell

degradation during long-term SOFC operation are not well known yet. We are contributing to

the understanding of the underlying thermodynamics of these processes by assessing the Mn-

Cr-O system using the CALPHAD approach.

The thermodynamic data of the pure elements are taken from Dinsdale[6], and the data for the

Mn-O, Cr-O, and Mn-Cr binaries from Grundy et al.[7], Povoden et al.[8], and Lee [9]


78

respectively. No new ternary phases are found in the Mn-Cr-O system, however all the binary

oxides except pyrolusite (prl), MnO2, show varying degrees of mutual solid solubility.

The most prominent oxide phase in the Mn-Cr-O system is cubic chromium manganese spinel

with the formula MnyCr3-yO4. Normal spinel is given by the formula [A2+](B3+)2O4, whereas

spinel of the formula [B3+](A2+B3+)O4 with half of B on the tetrahedral sites – marked with

angular brackets in the above formulas – is called inverse spinel. In the case of cubic

MnyCr3-yO4 both the trivalent cations of manganese and chromium show a remarkable

preference to fill the octahedral sites marked with round brackets in above formulas[10]. Spinel

containing a large amount of Mn3+ becomes tetragonally distorted on lowering the

temperature as a consequence of the macroscopic Jahn-Teller effect that is caused by the

distortion of the octahedral sites occupied by Mn3+[11].

In this work we use the following abbreviations: β-spl for cubic chromium manganese spinel

solid solution, α-spl for tetragonally distorted polymorph spinel solid solution, β-hsm (β-

hausmannite) for the cubic and α-hsm (α-hausmannite) for the tetragonally distorted Mn3O4

endmember of the spinel solid solution, bxb for Mn2O3 (bixbyite) with dissolved Cr, esk for

Cr2+xO3 (eskolaite) with dissolved Mn, mgs for Mn1-xO (manganosite) with dissolved Cr, bcc

for chromium manganese alloy with bcc A2 structure, and liq for the liquid phase.

4.2.2 Experimental

Phase diagram data:

Our calculated phase diagram of the MnOx-Cr2O3 system in air is shown in Figs. 4.2.1, 4.2.2

(p. 79), and 4.2.3 (p. 80). Fig. 4.2.4 (p. 80) shows the calculated phase diagram at

2

-4O 1×10 Pa=p .


79

Fig. 4.2.1 Calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 in air. The gas

phase was not included in the calculation.

Fig. 4.2.2 Calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 in air, with

experimental data. The gas phase was not included in the calculation.


80

Fig. 4.2.3 Mn rich part of the calculated pseudo-binary phase diagram

of the system MnOx-Cr2O3 in air, with experimental data.

Fig. 4.2.4 Calculated pseudo-binary phase diagram of the system MnOx-Cr2O3 under strongly

reducing conditions (2

-4O 1×10 Pa=P ), showing the expanded stability field of β-spl + mgs.


81

Speidel and Muan[12] present a phase diagram of the MnOx-Cr2O3 system in air in the

temperature range 873 K to 2253 K resulting from the determination of phase equilibria using

quenching techniques and X-ray and microscopic examination (Fig. 4.2.2, p. 79).

They find β-spl + α-spl + bxb coexisting in equilibrium at T = 1183 ± 5 K, and β-spl + esk +

liq in equilibrium at T = 2243 ± 20 K. They estimate a minimum temperature of T = 773 K for

the stability of β-spl. The Mn solubility in (Cr2-yMny)1+xO3 reported from Speidel and Muan[12]

is significantly higher than it is found by Golikov et al.[13] and Pollert et al.[14].

Golikov et al.[13] studied the MnOx-Cr2O3 system using quenching techniques and high

temperature X-ray diffractometry in air in the temperature range from T = 973 K to 1673 K.

Their resulting phase diagram is in considerable disagreement with the findings of Speidel

and Muan[12]. They report a minimum temperature of β-spl stability of T = 973 K and lower

solubility of Cr in tetragonally distorted MnyCr3-yO4 and of Cr in Mn2-yCryO3. They consider

the solubility limit of Mn in (Cr1-yMny)2+xO3 to be negligible.

Pollert et al.[14,15] studied phase stabilities in the MnOx-Cr2O3 system in the temperature range

from T = 1100 K to 1620 K in air by means of X-ray measurement of annealed samples. Their

data are shown in Figs. 4.2.2, p. 79 and 4.2.3, p. 80.

The solubility limit of Cr in Mn2-yCryO3 is measured by these authors to be y = 0.14 at T =

1105 K in air. This value is in agreement with the result from Geller and Espinosa[16], but it is

lower than the findings from Speidel and Muan[12]. Pollert et al.[14] report a solubility limit of

y = 1.42 at oxygen partial pressure >> 20000 Pa. From the absence of changes of the lattice

parameters of esk in equilibrium with β-spl annealed at T = 1105 K and 1620 K in air

compared to pure Cr2O3 they conclude that the solubility of Mn in (Cr2-yMny)1+xO3 is low and

does not depend significantly on temperature.

Tanahashi et al.[17] investigated the compositions of coexisting β-spl + mgs and β-spl + esk

from 2

-6O 2×10=p to 2 2×10 Pa at T = 1873 K thus determining the range of solid solubility of

β-spl by quenching techniques under controlled CO-CO2 atmosphere (Fig. 4.2.5, next page).


82

Fig. 4.2.5 Cr contents of β-spl in equilibrium with mgs, β-spl in equilibrium with esk, esk in

equilibrium with β-spl, and mgs in equilibrium with β-spl in the pseudo-binary MnOx-Cr2O3

system as a function of oxygen partial pressures at T = 1073 K, 1473 K, and 1873 K.

Experimental data are included.

Phase relations were verified using X-ray diffraction. In order to identify the equilibrium

compositions, each phase in the quenched specimens was subjected to electron probe

microanalysis (EPMA). They found increasing Mn solubility in cubic MnyCr3-yO4 at oxygen

partial pressure higher than -22 10 Pa× , and significantly increasing Cr solubility in cubic

MnyCr3-yO4 with decreasing oxygen partial pressure (Fig. 4.2.5). The compositions of β-spl

are located on a line connecting MnCr2O4 with β-hsm in the ternary plot. From this result

Tanahashi et al.[17] conclude that Mn is dissolved in cubic MnyCr3-yO4 in the form of Mn3O4.

They report small solubility of Mn in (Cr1-yMny)2+xO3 at 2

-6O 2×10=p , which increases slightly

with increasing oxygen partial pressure. They found almost unchanging solubility of Cr in

(Mn1-yCry)1-xO from 2

-6O 2×10=p to 22 10 Pa× at T = 1873 K. As the compositions of mgs

solid solution are located on the line connecting Mn1-xO with CrO in the ternary phase


83

diagram, these authors conclude that chromium oxide dissolves in (Mn1-yCry)1-xO in the form

of CrO.

Bobov et al.[18] investigated the composition changes of the two phase equilibrium β-spl +

mgs at T = 1073 K, 1173 K, and 1273 ± 5 K in the oxygen partial pressure range from 0.1 to

10-13 Pa (Fig. 4.2.5, p. 82).

For the invariant three phase equilibrium mgs + β-spl + bcc Ranganathan and Hajra[19]

measured the Mn content in bcc to be 25.2 cat.% at T = 1323 K performing an isopiestic

experiment (Fig. 4.2.6).

Fig. 4.2.6 Ternary phase diagram of the system Cr-Mn-O with stoichiometric single phase

equilibria (points), single solid solution phase equilibria (heavy lines), two-phase fields and

three-phase fields. Dotted lines are tie lines. Three-phase field boundaries are denoted with

thin solid lines. Also the experimental result on the three phase equilibrium MnO + MnCr2O4

+ bcc from Ranganathan[19] is plotted.

There are no data on oxygen nonstoichiometry of MnyCr3-yO4.


84

Holba et al.[11] investigated the martensitic α-spl → β-spl transition temperatures, enthalpies

and entropies of MnyCr3-yO4 samples annealed at T = 1723 K using X-ray analysis and DTA

measurement. With decreasing Mn-content the temperature for the transition decreases (Fig.

4.2.2, p. 79). Samples with y < 1.8 do not show Jahn–Teller distortion at room temperatures,

and remain β-spl. Giving α-spl the formula [Mn2+](Mn3+,Cr3+)2O4 this corresponds to a

minimum concentration of [Mn3+] = 0.4 for the formation of α-spl.

Thermodynamic data:

Cubic spinel (β-spl):

Only values for the standard Gibbs energy of formation of β-spl of the composition MnCr2O4

are published. Tanahashi et al.[20] derive 2 4

β-splMnCr Of

°Δ G = –958 ± 8 kJ mol-1 from liquid Mn,

solid Cr and oxygen at T = 1873 K in the 2Op range from -62×10 to -4 1.5×10 Pa from the

standard Gibbs free energy changes of the reactions

Mn (in molten Fe) + 2 Cr (in molten Fe) +2 O2(g) = MnCr2O4 (4.2.1)

and

Mn (in molten Cu) + 2 Cr (s) + 2O2(g) = MnCr2O4 (4.2.2)

Using compiled °MnOfΔ G and

2 3

°Cr OfΔ G [21] they calculate

2 4

β-splMnCr Of

°Δ G from its oxides to be

–59 ± 8 kJ mol-1. We recalculate this value using the most recently assessed °MnOfΔ G [7] and

2 3

°Cr OfΔ G [8] values at T = 1873 K giving

2 4

β-splMnCr Of

°Δ G = –66 ± 8 kJ mol-1. Tsai and Muan[22]

experimentally determined compositions of coexisting MnyCr3-yO4 - MnyAl3-yO4 solid

solutions formed from Cr2O3-Al2O3 mixtures at T = 1873 K. From these data and the activities

of CrO1.5 in Mn0.5AlO2 and AlO1.5 in Mn0.5CrO2 obtained from a previous study[23] they derive

ΔG of the reaction

CrO1.5 + Mn0.5AlO2 = AlO1.5 + Mn0.5CrO2 (4.2.3)

to be –10 kJ mol-1 at T = 1873 K, which is equivalent to fΔ G of 2 4 2 4

β-splMnCr Of f MnAl O )1 2(Δ − ΔG G .

This means that the Gibbs energy of formation of β-spl of the composition MnCr2O4 from its


85

oxides using this calculation technique depends on the value of 2 4f MnAl O

°Δ G . Tsai and Muan[22]

chose the value determined by Lenev and Novokhatskiy[24], 2 4f MnAl O

°Δ G = –32.6 kJ mol-1

giving 2 4

β-splMnCr Of

°Δ G = –52.6 kJ mol-1 at T = 1873 K. Using other values for 2 4f MnAl O

°Δ G reported

in the literature[25-27] leads to deviating 2 4

β-splMnCr Of

°Δ G of –34.4 ± 10 kJ mol-1, –46.1 kJ mol-1, and

–36.1 kJ mol-1. Biggers[28] by using the same technique as Tsai and Muan [22] in the CoO-

MnO-Cr2O3 system found 2 4

β-splMnCr Of

°Δ G = –59.0 kJ mol-1 at T=1523 K.

The spread of 2 4

β-splMnCr Of

°Δ G values resulting from different studies and our recalculations is

shown in Fig. 4.2.7.

Fig. 4.2.7 Calculated Gibbs energy of formation of β-spl of the composition MnCr2O4 as a

function of temperature, with experimental data and error bars. Filled symbols correspond to

originally reported literature data, unfilled symbols correspond to recalculated values.

Tetragonally distorted spinel (α-spl):

Pollert et al.[15] present thermodynamic data on the transition of α-spl to β-spl. According to

these authors the transition of pure α-hsm to β-hsm takes place at T=1445 K.

ΔΗ α β = 18810 J mol-1, and ΔS α β = 13 J K-1 mol-1.


86

4.2.3 Thermodynamic modeling

Cubic spinel (β-spl):

There is experimental evidence on the presence of Cr2+ in β-spl as the Cr endmember of β-spl

was found to be a stable phase in a small temperature range[29,30]. As the degree of inversity of

β-spl is very low[10], β-spl can therefore be described by the simple formula

[Mn2+,Cr2+](Cr3+,Mn3+)2O4 using the compound energy model[31–33].

Lu et al.[34] measured the electrical conductivity of β-spl. They propose small polaron hopping

between Mn3+ and Mn4+ on the octahedral sites as mechanism for the electrical conductivity.

To maintain electroneutrality Mn2+ is formed on the octahedral sites resulting in a charge

disproportionation reaction. Considering these findings an alternative description of β-spl

would read [Mn2+,Cr2+](Cr3+,Mn2+,Mn3+,Mn4+)2O4. However there is no experimental data

quantifying the amount of Mn4+ in β-spl, so we stick to the less complex description without

Mn2+ and Mn4+ on the octahedral sites. In our description we further go along with the

presumption that the amount of oxygen vacancies may be neglected.

All endmembers of our model β-spl are neutral. In our CALPHAD assessment the °G values

of all compounds are given relative to the enthalpy of selected reference states for the

elements at T = 298.15 K and p = 105 Pa[6]. This state is denoted SER (Stable Element

Reference). The Gibbs energies of the endmembers [Mn2+](Mn3+)2O4 that corresponds to

β-hsm, and [Cr2+](Cr3+)2O4 that corresponds to Cr3O4 are taken from the assessed binaries[7,8].

The Gibbs energy of the endmember of the formula [Mn2+](Cr3+)2O4 is given by the

expression

3 4

2+ 3+ 2+ 3+ 2+ 3+2 4 2 4 2 4

Cr Oβ-spl β-hsm β-spl β-spl° ° °[Mn ](Cr ) O [Cr ](Cr ) O [Mn ](Mn ) O= 2 3 1 3+ + +G G G A B T (4.2.4)

This endmember is considerably more stable than the endmember of the formula

[Cr2+](Mn3+)2O4. We define this last endmember using a reciprocal relation

3 4

2+ 3+ 2+ 3+ 2+ 3+ 2+ 3+2 4 2 4 2 4 2 4

Cr Oβ-spl β-hsm β-spl° ° ° °[Cr ](Mn ) O [Cr ](Cr ) O [Mn ](Mn ) O [Mn ](Cr ) O1 3= + −G G G G (4.2.5)

The Gibbs energy of the reciprocal reaction is taken to be zero. Thus the endmember

2+ 3+2 4

β-spl°[Cr ](Mn ) OG becomes less stable the more stable 2+ 3+

2 4

β-spl°[Mn ](Cr ) OG becomes.


87

Tetragonally distorted spinel (α-spl):

The transformation of β-spl to α-spl is due to the Jahn-Teller distortion of the octahedral sites

occupied by trivalent Mn ions leading to the tetragonal structure of α-spl[11,15].

Experiments[11,14,15,34] show that α-spl is stabilized at high Mn contents, and the Cr solubility

in tetragonally distorted MnyCr3-yO4 does not extend beyond MnCr2O4. It is very unlikely that

trivalent cations are incorporated into the tetrahedral sites of α-spl, as the degree of inversity

is increasing with higher temperature, whereas for ordering due to Jahn–Teller distortion the

opposite holds. Due to these considerations we may write [Mn2+](Cr3+,Mn3+)2O4 to describe

α-spl. Hence, the two endmembers of α-spl read [Mn2+](Mn3+)2O4 and [Mn2+](Cr3+)2O4. The

Gibbs energy of [Mn2+](Mn3+)2O4 is equal to α-hsm. The Gibbs energy of [Mn2+](Cr3+)2O4 is

given by

3 4

2+ 3+ 2+ 3+ 2+ 3+2 4 2 4 2 4

Cr Oα-spl α-spl α-spl° ° ° α-hsm[Cr ](Mn ) O [Cr ](Cr ) O [Mn ](Mn ) O= 2 3 1 3+ + +G G G A B T (4.2.6)

Bixbyite (bxb):

Geller and Espinosa[16] postulate the incorporation of Cr into Mn2-yCryO3 by a simple

substitution mechanism between Cr3+ and Mn3+. This is a reasonable assumption as the radii

of these ions are very similar[35]. The incorporation of chromium of valencies other than three

is mentioned nowhere in literature. Thus we may describe bxb as (Mn3+,Cr3+)2(O2-)3. The

Gibbs energy of the endmember (Mn3+)2(O2-)3 is taken from Grundy et al.[7], and the Gibbs

energy of (Cr3+)2(O2-)3 is given by

3+ 3+ 2-2 3 2 1 3

° bxb ° esk bxb(Cr ) O (Cr ) (Va) (O )= +G G A (4.2.7)

The experimental data could be reproduced without the optimization of a temperature

dependent parameter.

Manganosite (mgs):

Based on the proposed incorporation of Cr into (Mn1-yCry)1-xO in the form of CrO[15] we tested

a description of mgs given by (Mn2+,Mn3+,Cr2+,Va)(O2-). Using this description the solubility

of Cr in function of oxygen partial pressure experimentally determined by Tanahashi[17] could

not be reproduced correctly. (Mn2+,Mn3+,Cr3+,Va)(O2-) leads to far more satisfactory


88

reproduction of these data. With this description we are in agreement with O’Keefe and

Valigi[36] who observe a decrease in the lattice parameter of mgs compared to undoped

Mn1-xO providing strong support for the assumption that it is Cr3+ that is substituting the much

larger Mn2+ ion and which is forcing the lattice to contract. These experiments also provide

evidence against Cr being incorporated interstitially. The model description of mgs is shown

in Fig. 4.2.8.

Fig. 4.2.8 Geometrical representation of the mgs phase described

using the compound energy model.

The Gibbs energy of the neutral endpoint ( )3+2/3 1/3Cr Va O is given by

3+ (Va )O(Cr )O 11

mgs mgs° °2 3 + 1 3 (1 3ln1 3 2 3ln 2 3)+ +G G RT and based on the Gibbs energy of 13 mole of

esk. Using O(Va)O 21

mgs° ° Gas12= G G the following expression for the parameter

3+(Cr )O1

mgs°G is obtained

3+ 3+ 2- O2(Cr )O (Cr ) (Va) (O )1 2 1 3

mgs mgs° ° esk ° Gas= 1 2 1 3 3 2 (1 3ln1 3 2 3ln 2 3)− − + +G G G RT A (4.2.8)

The Gibbs energies of the three other endmembers are taken from Grundy et al.[7].

Eskolaite (esk):

Pollert et al.[14] postulate the incorporation of trivalent Mn ions into (Cr1-yMny)2+xO3.

Agreeing with these authors we model the solubility of Mn by

(Cr3+,Cr2+,Mn3+)2(Cr3+,Va)1(O2-)3. The Gibbs energy of (Mn3+)2(Cr3+)1(O2-)3 is given by


89

3+ 3+ 3+ 2-(Mn ) (Cr ) O (Mn ) (O )2 1 3 2 3

° esk ° bxb ° SER eskCr= + +G G G A (4.2.9)

and the Gibbs energy of (Mn3+)2(Va)1(O2-)3 by

3+ 3+ 2-(Mn ) (Va) O (Mn ) (O )2 1 3 2 3

° esk ° bxb esk= +G G A (4.2.10)

We take the Gibbs energies of the other endmembers from Povoden et al.[8].

Cr-Mn alloys:

We describe the oxygen solubility in bcc by an interstitial solution model of the form

(Cr,Mn)1(O,Va)3. Experimental data on the oxygen solubility in pure bcc A2 chromium

metal[37] were used for the description of (Cr)1(O,Va)3[8]. No data are reported for the oxygen

solubility in pure bcc A2 manganese metal. Assuming low oxygen solubility in bcc

manganese metal we give a large value to the endmemberMn:O

° bcc G .

The descriptions of further alloy phases are taken from[9].

Liquid:

We model the liquid phase as (Cr3+,Cr2+, Mn3+,Mn2+)p(O2-,Vaq-)q using the two-sublattice

model for ionic liquids [38,39]. The liquidus temperature is optimized using the interaction

parameter3+ 3+ 2-Cr ,Mn :O

liq0L .The binary interaction parameters are taken from Grundy et al.[7],

Povoden et al.[8], and Lee[9].

4.2.4 Optimization of parameters

The complete set of optimized thermodynamic parameters describing the Mn-Cr-O system is

given in Table 4.2.1 (pp. 90-92).


90

Table 4.2.1 Thermodynamic description of the

Cr-Mn-O system a)

Element

Element Reference Mass H298 - H0 S298

Cr BCC_A2 51.996 4050.0 23.543

Mn CBCC_A12 54.938 4996.0 32.008

O ½ mol O2 15.999 4341.0 102.52

Liquid (liq)

2- 2+ 2+ 3+ 3+

2+ q-

3+ q-

3+ 2-

2+ 3+ 2+ 3+ 2- q-p q

VaO Cr Mn Cr Mn

liq SER [9]CrCr :Va

liq SER [9] [9]CrCr :Va

liq SER SER [9]Cr OCr :O

(Cr ,Cr ,Mn ,Mn ) (O ,Va )

2 , 2 2 3 3

GCR_L

2GCR_L GCR2O3_L 3GCR1O1_L

2 3 GCR2O3_L

°

°

°

°

= + = + + +

− =

− = + −

− − =

p y qy q y y y y

G H

G H

G H H

G 2+ 2-

2+ q-

3+ q-

3+ 2-

2+ 2-

liq SER SER [9]Cr OCr :O

liq SER [7]MnMn :Va

liq SER [7] [8] [8]MnMn :Va

liq SER SER [8]Mn OMn :O

liq SER SERMn OMn :O

2 2 2GCR1O1_L

GMN_L

2GMN_L GMN2O3_L 3GMN1O1_L

2 3 GMN2O3_L

2 2 2GMN1O

°

°

°

°

− − =

− =

− = + −

− − =

− − =

H H

G H

G H

G H H

G H H

2+ 2- q-

2+ 2- q-

2+ 2- q-

2+ 3+ 2- q-

2+ 2+ q-

2+ 2+ q-

3+ 3+

[8]

0 liq [9]Cr :O ,Va

0 liq [8]Mn :O ,Va

1 liq [8]Mn :O ,Va

0 liq [8]Mn ,Mn :O ,Va

0 liqCr ,Mn :Va

1 liqCr ,Mn :Va

0Cr ,Mn

1_L

121000

129519

45459

33859

15009 13.6587

504 0.9479

=

=

= −

= −

= − +

= +

L

L

L

L

L T

L T

L 2-liq

:O188487.6 = −

Bcc A2 alloy (bcc)

1 3(Mn,Cr) (Va,O)


91

bcc SER [7]Cr:Va Crbcc SER [7]Mn:Va Mnbcc SER SER [7] [7]Cr:O Cr Obcc SER SER [7] [7]Mn:O Mn O

0 bcc [10]Cr,Mn:Va

1Cr,Mn

GHSERCR

GHSERMN

3 GHSERCR + 3GHSEROO + 243

3 GHSERMN + 3GHSEROO

20328 18.7339

°

°

°

°

− =

− =

− − =

− − =

= − +

G H

G H

G H H T

G H H

L T

Lbcc [10]:Va

0 bcc [9]Cr:O,Va

bcc 2c Cr Mn Cr Mn Cr Mn

4 6 8 [10]Cr Mn Cr Mn Cr Mn

bccCr Mn Cr Mn

9162 4.4183

7095420.4

311.5 580 [ 1325 1133( )

10294( ) 26706( ) 28.117( ) ]

0.008 0.27 [0.48

= − +

= −=

= − − + − − −

− − + − − −

= − − +

T

LpT y y y y y y

y y y y y y

y y y yβ 2Cr Mn

4 [10]Cr Mn

643 0.72035( )

1.93265( ) ]

− −

− −

y y

y y

Manganosite (mgs)

2+ 2-

3+ 2-

2-3+

2-3+2+

2+ 3+ 3+ 2-1 1

° mgs SER SER [8]Mn OMn :O

° mgs SER SER [9]Cr OCr :O

° mgs SER SER [8]Mn OMn :O

0 mgsMn ,Mn :O

(Mn ,Mn , Cr ,Va) (O )

GMN1O1

0.5GCR2O3 71549.3 7.93845

GMN1O1 21883.5213 22.1853365

42

− − =

− − = + −

− − = − −

= −

G H H

G H H T

G H H T

L

3+2+ 2-

[8]

1 mgs [8]Mn ,Mn :O

104.8766

46513.1533=L

Bixbyite (bxb)

2-3+

3+ 2-

3+ 3+ 2-2 3

° bxb SER SER [8]Mn OMn :O

° bxb SER SER [9]Cr OCr :O

(Mn ,Cr ) (O )

2 3 GMN2O3

2 3 GCR2O3 3459

− − =

− − = +

G H H

G H H

Eskolaite (esk)

3+ 2-

3+3+ 2-

3+2+ 2-

2+

2+ 3+ 3+ 3+ 2-2 1 3

° esk SER SER [9]Cr OCr :Va:O

° esk SER SER [9] [7]Cr OCr :Cr :O

° esk SER SER [9] [7]Cr OCr :Cr :O

°Cr

13

(Cr , Cr ,Mn ) (Cr ,Va) (O )

2 3 GCR2O3

3 3 GCR2O3 GHSERCR


− − =

− − = +

− − = + −

G H H

G H H

G H H T

G 2-

3+ 2-3+

3+ 2-

esk SER SER [9] [7]Cr O:Va:O

° esk SER SER SER [8] [7]Mn Cr OMn :Cr :O

° esk SER SER [8]Mn OMn :Va:O

[9]


2 3 GMN2O3 GHSERCR 39503

2 3 GMN2O3 39503

Magnetic contribution0.28

− − = − −

− − − = + +

− − = +

=

H H T

G H H H

G H H

pT 3+ 3+ 2- 3+ 3+ 2-

3+ 2- 3+ 2-

2+ 3+ 2- 2+ 3+ 2-

2+ 2-

esk esk esk eskc Cr :Cr :O Cr :Cr :Oesk esk esk esk

c Cr :Va:O Cr :Va:O

esk esk esk eskc Cr :Cr :O Cr :Cr :Oesk esk

c Cr :Va:O

308.6 3

308.6 3

308.6 3

308.6

= =

= =

= =

=

y y

T y y

T y y

T y

β

β

β

2+ 2-esk esk

Cr :Va:O 3= yβ

Cubic spinel (β-spl)


92

2-3+2+

3+2+ 2-

3+2+ 2-

3+2+ 2-

2+ 2+ 3+ 3+ 2-1 2 4

° β-spl SER SER SERMn Cr OMn :Cr :O

° β-spl SER SER [9]Cr OCr :Cr :O

° β-spl SER SER [8]Mn OMn :Mn :O

° β-spl SERCrCr :Mn :O

(Mn ,Cr ) (Cr ,Mn ) (O )

2 4 GSPINEL

3 4 GCR3O4

3 4 GMN3O4B

− − − =

− − =

− − =

− −

G H H H

G H H

G H H

G H SER SER [8]Mn O2 4 GCR3O4+GMN3O4B -GSPINEL− =H H

Tetragonally distorted spinel (α-spl)

3+2+ 2-

3+2+ 2-

2+ 3+ 3+ 2-1 2 4

° α-spl SER SER SERMn Cr OMn :Cr :O

° α-spl SER SER [8]Mn OMn :Mn :O

(Mn ) (Cr ,Mn ) (O )

2 4 GTSPINEL

3 4 GMN3O4

− − − =

− − =

G H H H

G H H

Functions [8]

[8]

2 13 3

2 13 3

GSPINEL GCR3O4+ GMN3O4B

210795.5+61.69GTSPINEL GCR3O4+ GMN3O4

200941.9+75.1

=

−=

−

T

T

a) Note: All parameters are in SI units: J, mol, K, Pa: R = 8.31451 J mol-1 K-1.

The optimization of the thermodynamic parameters is performed using the PARROT module

of the Thermo Calc[40] database system. PARROT takes into account all sorts of

thermodynamic and phase diagram data simultaneously. The program minimizes the sum of

squared errors between the experimentally determined phase diagram and thermodynamic

data and the corresponding calculated data. As the use of all the experimental data in a

simultaneous least square calculation often leads to divergence, we selectively adjust the

relative weight of each experimental data point and exclude data that are inconsistent with the

majority of the data points during the optimization procedure.

To optimize the parameters Aβ-spl and Bβ-spl in Eq. 4.2.4 we use the 2 4

β-splMnCr Of

°Δ G value derived

from Tsai and Muan[23] using 2 4f MnAl O

°Δ G from Kim and McLean[25] and the composition of

bcc in equilibrium with β-spl and mgs reported by Ranganathan and Hajra[19]. Further the

melting temperature of β-spl in air found by Speidel and Muan[12] is used to optimize Aβ-spl

and Bβ-spl in Eq. 4.2.4 and 3+ 3+ 2-liq0Cr ,Mn :OL . The temperature found from Speidel and Muan[12] for

the two phase equilibrium of Mn rich β-spl (Mn = 94.7 cat.%) and α-spl is used to optimize

Aβ-spl and Bβ-spl in Eq. 4.2.4 and Aα-spl and Bα-spl in Eq. 4.2.4. All these data are given a high

weight.

Further we use – with lower weights – the temperature of the two phase equilibrium β-spl +

liq at X(Cr) = 0.105 from Speidel and Muan[12] to optimize Aβ-spl and Bβ-spl in Eq. 4.2.4 and

3+ 3+ 2-Cr ,Mn :O

liq0L , and we use data on the solubility of Cr in MnyCr3-yO4 at T=1873 K under varying


93

oxygen partial pressures from Tanahashi et al.[17] shown in Fig. 4.2.5, p. 82, and data from

Pollert et al.[14] on the two phase equilibrium β-spl + bxb in air (Fig. 4.2.3, p. 80) to optimize

Aβ-spl and Bβ-spl in Eq. 4.2.4. Temperature data from Speidel and Muan[12] and Pollert et al.[14]

on the phase equilibria α-spl + β-spl and α-spl + β-spl + bxb are used to optimize Aβ-spl and

Bβ-spl in Eq. 4.2.4, and Aα-spl and Bα-spl in Eq. 4.2.6. We use data from Holba et al.[11] on the

temperature dependence of the diffusionless transformation of α-spl to β-spl shown in Fig.

4.2.2, p. 79 to optimize Aβ-spl and Bβ-spl in Eq. 4.2.4, and Aα-spl and Bα-spl in Eq. 4.2.6. Abxb in

Eq. 4.2.7 is optimized using data on the solubility of Cr in Mn2-yCryO3 from Pollert[14], for

Amgs in Eq. 4.2.8 data on the solubility of Cr in (Mn1-yCry)1-xO from Tanahashi et al.[17] are

used (Fig. 4.2.5, p. 82), and for Aesk in Eq. 4.2.9 and 4.2.10 data on the solubility of Mn in

(Cr1-yMny)2+xO3 from Pollert et al.[14] shown in Fig. 4.2.2, p. 79 and Fig. 4.2.5, p. 82 are used.

4.2.5 Results

Phase diagram data:

The calculated phase diagram of the pseudo-binary system MnOx-Cr2O3 in air is shown in

Figs. 4.2.1 and 4.2.2, p. 79. In Fig. 4.2.3, p. 80 the Mn rich part of the diagram is shown in

detail. β-spl is stable in a large temperature range from T = 513 K to 2243 K and from X(Cr) =

0 to X(Cr) = 0.67 in air. β-spl and esk coexist from X(Cr) = 0.66 to 0.992 at 1203 K in air. The

maximum Mn solubility in (Cr1-yMny)2+xO3 is 0.2 cat.% at 2243 K in air. Single phase α-spl is

stable in a small T–X(Cr) range from T = 1153 K to 1441 K and X(Cr) = 0 to 0.054 in air. α-

spl coexists with β-spl from X(Cr) = 0 at T = 1441 K to X(Cr) = 0.175 at T = 1156 K. The

dotted line in Fig. 4.2.2, p. 79 shows the temperature dependence of the diffusionless

transformation of α-spl to β-spl. bxb is stable from T = 694 K to 1154 K in air. The maximum

Cr solubility in Mn2-yCryO3 is 23 cat.% at T = 668 K in air. The two-phase field bxb + α-spl is

only found in a very small area at about 1150 K. prl coexists with esk at T < 513 K in air.

From T = 513 K to 668 K and maximum X(Cr) = 0.65 prl and β-spl coexist in air. prl + bxb is

stable in a small area from T = 668 K to 694 K and X(Cr) = 0 to 0.23 in air.

mgs is not stable in air. At 2Op = 400 Pa it starts to form in equilibrium with β-spl in a small

area at the Mn-rich side of the MnOx-Cr2O3 system around T = 1840 K. This two-phase field

expands under more reducing conditions which can be seen in the calculated phase diagram of


94

the pseudo-binary MnOx-Cr2O3 system at an oxygen partial pressure of -4 1×10 Pa in Fig. 4.2.4,

p. 80.

In Fig. 4.2.5, p. 82 experimental and calculated solubility data of Cr in mgs + β-spl, and Mn

in esk + β-spl are presented. Experimental data from Tanahashi et al.[17] on the solubility of

Cr in the phases of the two phase equilibria mgs + β-spl and esk + β-spl at 1873 K, and from

Bobov et al.[18] on the solubility of Cr in the phases of the two phase equilibria mgs + β-spl at

T = 1073 K, 1173 K, and 1273 K in function of 2Olog( )p are compared to the calculated

results from this work. The data from Bobov et al.[18] were not used for the optimization.

In the isothermal phase diagram of the Mn-Cr-O system at T = 1323 K of Fig. 4.2.6, p. 83 the

stable alloy phases of the system are plotted in addition to the oxides based on the assessment

of the binary Cr-Mn system from Lee[9].

Isothermal sections of the Cr2O3-MnO-MnO2 system at different temperatures are plotted in

Fig. 4.2.9 (next page).


95

Fig. 4.2.9 Isothermal sections of the ternary system Cr2O3-MnO-MnO2 showing oxide and

liquid evolution as a function of temperature and composition. Stoichiometric single phase

equilibria are points, and single solid solution phase equilibria are heavy lines. Dotted lines

are tielines. Three-phase field boundaries are denoted with thin lines.


96

Thermodynamic data:

The calculated enthalpy, entropy and Gibbs energy of formation of β-spl of the composition

MnCr2O4 from the elements is 2 4

β-splMnCr Of

°Δ H = –1599421 J mol-1, 2 4

β-splMnCr O

°S = 116 J mol-1 K-1, and

2 4

β-splMnCr Of

°Δ G = –1634017 J mol-1 at T = 298.15 K. The calculated temperature dependence of the

Gibbs energy of formation of of β-spl of the composition MnCr2O4 from the oxides MnO and

Cr2O3 is shown in Fig. 4.2.7, p. 85. At T = 1873 K we get 2 4

β-splMnCr Of

°Δ G = –34388 J mol-1. In the

temperature range from 1050 to 1800 K 2 4

β-splMnCr Of

°Δ G from the oxides is given by the term

–89167 + 29.338 T with an error of ± 0.21 %.

For α-spl of the composition MnCr2O4 we calculate α-splf

°Δ H = –1596517 J mol-1,

α-spl°S = 98 J mol-1K-1, and fα-spl°Δ G = –1625681 J mol-1 at T = 298.15 K.

4.2.6 Discussion

Phase diagram data:

Our assessed phase diagram is in rough agreement with the findings from Speidel and

Muan[12]. Large deviations of our calculated phase diagram from the phase diagram presented

by these authors concern the stability of the liquid and phase stabilities at low temperatures.

For both cases Speidel and Muan[12] mention the speculative character of their phase diagram

due to the lack of experimental data.

Our assessed phase diagram is in excellent agreement with the findings of Pollert et al.[14,15]

and Ranganathan et al.[19] as shown in Figs. 4.2.2 (p. 79), 4.2.3 (p. 80), and Fig. 4.2.6 (p. 83).

Our calculated T0 line for the diffusionless transformation of α-spl → β-spl is in perfect

agreement with experiments by Holba et al.[11] (Fig. 4.2.2, p. 79). The calculated dependence

of β-spl solid solubility on oxygen partial pressures shown in Fig. 4.2.5, p. 82 agrees well

with the results from Tanahashi et al.[17]. The results from Bobov et al.[18] on the other hand

cannot be reproduced.

Fig. 4.2.9 (p. 95) represents the phase relations of the oxides and the evolution of liquid

formation. The three-phase regions prl + esk + bxb and bxb + esk + β-spl, and the two-phase

fields prl + bxb, β-spl + bxb, and mgs + β-spl dominate the system in a wide temperature

range from T=1200 K to 1900 K (Figs. 4.2.9 a to c). At T=1700 K α-spl is no longer stable

and the three-phase regions mgs + α-spl + β-spl and bxb + α-spl + β-spl (Fig. 4.2.9 a)

disappear. At this temperature small oxygen nonstoichiometry of esk is apparent. The oxygen

nonstoichiometry of mgs is yet insignificant (Fig. 4.2.9 b), but it increases at elevated


97

temperatures becoming apparent at T = 2000 K (Fig. 4.2.9 d). At T = 1900 K phase relations

become more complex due to incipient melting (Fig. 4.2.9 c). At T = 1900 K liquid is formed

at the Mn-rich side of the system, and the-three phase fields bxb + β-spl + liq and mgs + β-spl

+ liq emerge

(Fig. 4.2.9 c). Even more three phase regions due to increasing liquid formation start to exist

at T = 2000 K (Fig. 4.2.9 d). At T = 2400 K the only remaining stable solid phases are esk and

prl (Fig. 4.2.9 f).

Thermodynamic data:

Our calculated 2 4

β-splMnCr Of

°Δ G value at T = 1873 K is in agreement with the 2 4

β-splMnCr Of

°Δ G value

derived from Tsai and Muan[22] using 2 4

splf MnAl O

°Δ G from Kim and McLean[25].

Our assessed ΔHα β and ΔSα β values for the transition of α-hsm to β-hsm compare

favorably with the values reported by Holba et al.[12]. The calculated ΔHα β and ΔSα β values

for the transformation of α-spl to β-spl are very small, indicating that only very little energy is

needed for the transformation to take place.

4.2.7 Applications on SOFC

Due to the large stability range of β-spl and esk in air it is not realistic to prevent the

formation of these unwanted phases under oxidizing conditions at the cathode side of SOFC

operated with high Cr alloy interconnects and LSM cathode.

The composition of Crofer22 APU alloy is close to the Cr-corner of the Mn-Cr-O phase

diagram. In a thermodynamic view the formation of β-sp with the composition MnCr2O4

(Point A in Fig. 4.2.6, p. 84) on Crofer22 APU alloy is expected under SOFC operating

conditions. Hence, the formation of a protective Cr2O3 single phase layer followed by a

chromium manganese spinel on Mn bearing interconnects as it is observed by Simner et al.[5]

must be kinetically controlled. The occurrence of other Cr-Mn phases in the protective scales

formed during thermal exposure of Crofer 22 APU interconnects is not expected

thermodynamically. This is obvious from Fig. 4.2.6, p. 83.

Recently Qu et al.[42] found that the electrical conductivity of chromium manganese spinel

increases with increasing Mn-content. The problem of the application of synthesized Mn-rich

α-spl on the interconnect for the purpose of combining a decrease of Cr evaporation with

enhanced electrical conductivity is that α-spl will with time tend towards its stable

composition of MnCr2O4, which is at point A in Fig. 4.2.6, p. 83 associated with decreasing


98

electrical conductivity. Also α-spl will then transform to β-spl and on thermal cycling of the

SOFC back to α-spl leading to mechanical stresses that might result in the appearance of

cracks.

4.2.8 Conclusions

Due to the lack of inversity and oxygen nonstoichiometry of spinel we chose a model

description of β-spl and α-spl without the introduction of vacancies into the spinel structure.

All features of the system are well described with the optimization of only 8 additional

optimization parameters.

There is a surprising lack of thermodynamic data on β-spl, and the only available

2 4

β-splMnCr Of

°Δ G values are spread over a range of 31 kJ mol-1. Recalculating old experiments using

new thermodynamic data together with phase diagram data we achieved a description, which

is very close to the experimental findings of several authors, and we present well-founded

Δf°H, °S, and Δf

°G data for β-spl and α-spl.

Our Thermo Calc[40] dataset resulting from the presented CALPHAD modeling of the Mn-Cr-

O system allows the calculation of phase stabilities, compositions and transformations of

unwanted MnxCr3-xO4 spinel solid solution and eskolaite phases in solid oxide fuel cells under

any desired temperature and oxygen partial pressure conditions.

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16. S. Geller, G.P. Espinosa, Magnetic and crystallographic transitions in Sc3+, Cr3+, and Ga3+

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1309-1315.

18. A.P. Bobov, A.G. Zalazinsky, V.F. Balakirev, Y.V. Golikov, G.I. Chufarov, Peculiarities

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20. M. Tanahashi, N. Furuta, T. Taniguchi, C. Yamauchi, T. Fujisawa, Standard Gibbs free

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23. H.T. Tsai, A. Muan, Activity composition relations in refractory oxide solid-solutions at

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101

36. M. O’Keefe, M. Valigi, The electrical properties and defect structure of pure and

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4.3 Thermodynamic assessment of the La-Cr-O system

E. Povoden, M. Chen , A.N. Grundy, T. Ivas, and L.J. Gauckler

J. Phase Equilib. Diff. (accepted)

The La-Cr and the La-Cr-O systems are assessed using the Calphad approach. The calculated

La-Cr phase diagram as well as LaO1.5-CrO1.5 phase diagrams in pure oxygen, air, and under

reducing conditions are presented. Phase equilibria of the La-Cr-O system are calculated at T

= 1273 K as a function of oxygen partial pressure.

In the La-Cr system reported solubility of lanthanum in bcc chromium is considered in the

modeling.

In the La-Cr-O system the Gibbs energy functions of La2CrO6, La2(CrO4)3, and perovskite-

structured LaCrO3 are presented, and oxygen solubilities in bcc and fcc metals are modeled.

Emphasis is placed on a detailed description of the perovskite phase: the orthorhombic to

rhombohedral transformation and the contribution to the Gibbs energy due to a magnetic

order-disorder transition are considered in the model. The following standard data of


102

stoichiometric perovskite are calculated: -13298 Kf,oxides (LaCrO ) 73.7 kJ mol° = −Δ H ,

and -1 -1298 K 3 (LaCrO ) 109.2 J mol K° =S . The Gibbs energy of formation from the

oxides, 3f,oxides (LaCrO )Δ =G –72.403–0.0034 T (kJ mol-1) (T = 1273 K to 2673 K) is calculated.

The decomposition of the perovskite phase by the reaction

3 2 3 21 3LaCrO La O Cr + O (g)2 4

→ + ↑ is calculated as a function of temperature and oxygen partial

pressure: at 1273 K the oxygen partial pressure of the decomposition,2O (decomp)p = 10-20.97 Pa.

Cation nonstoichiometry of

La1-xCrO3 perovskite is described using the compound energy formalism (CEF), and the

model is submitted to a defect chemistry analysis.

The liquid phase is modeled using the two-sublattice model for ionic liquids.

4.3.1 Introduction

In SOFC, the thermodynamic stability of the cathode is particularly important for efficient

long-term operation. Sr-doped lanthanum manganites (LSM) with the perovskite structure are

used as cathode materials in SOFC. Diffusion of chromium from the metallic interconnect

with high chromium content into the cathode leads to the formation of Mn(Cr,Mn)2O4 spinel

and Cr2O3 along with a severe cell voltage decrease[1-4]. As the thermal expansions of

LaCrO3-based interconnect and conventional perovskite cathode materials are similar, and Cr-

diffusion into the cathode from LaCrO3-based interconnects is significantly lower than from

Cr-containing metallic interconnects, recently Sr-, V-doped[5] and Zn-doped[6] La1-xCaxCrO3-δ

have been considered as promising alternative interconnect materials for SOFC. Furthermore

earth alkaline-containing LaCrO3 has been proposed as a cathode material in a recent study by

Jiang et al[7].

The presented thermodynamic assessment of the La-Cr-O system is laying the grounding for

extensions to the thermodynamic La-Sr-Mn-Cr-O oxide database that is required to

understand the thermodynamics of SOFC degradation by chromium. It is also a starting point

for extensions to thermodynamic databases with additional components serving as dopants in

LaCrO3 for SOFC interconnect and cathode applications.

The assessment of the La-Cr-O system using the Calphad approach is based on the recently

reassessed La-O[8] and Cr-O subsystems[9]. The lattice stabilities of elements are adopted from

Dinsdale[10]. All available experimental phase diagram, thermodynamic, and structure-

chemical data are critically assessed, aiming on minimizing the squared errors between


103

experiments and calculation during the optimization of model parameters using the PARROT

module of the Thermocalc[11] software.

4.3.2 Literature review of the La-Cr system

The La-Cr system has a eutectic at T = 1138 K[12,13] and 3.4 at.% Cr[13] and a monotectic at

T = 1983 K[12] or T = 2103 K[14] and 96 at.%[12] or 99.1 at.%[14] Cr, as well as a large liquid-

liquid miscibility gap[12,13]. No intermetallic phases were found in the La-Cr system[12,13].

Berezutskii et al.[15] determined the partial enthalpy of mixing in La-Cr liquid with infinite

dilution of Cr, CrΔH at T = 1700 K using high-temperature calorimetry.

As small additions of rare-earth metals essentially increase the high-temperature corrosion

resistance of chromium[16], modeling of the La-solubility in bcc-structured Cr, denoted as

ssαCr , is of technological interest. Small solubility of La in ssαCr was reported[12,14,17], whereas

Cr is almost insoluble in La[13]. The solubility of La in ssαCr was determined in investigations

by Savitskii et al.[12] from T = 1073 K up to the melting of Cr using metallographic and micro-

hardness techniques to be 2.5 at.% at 1983 K. Svechnikov et al.[14] reported a La solubility of

0.68 at.% at T = 2103 K, and Epstein et al.[17] found La < 0.04 at.% in ssαCr at T = 1533 K. The

solubility of La in ssαCr decreases towards lower temperatures.

4.3.3 Literature review of the La-Cr-O system

In the LaO1.5- CrO1.5 system two eutectics were found at 19 at.% Cr2O3 (T = 2243 K)[18] or 12

at.% Cr2O3 (T = 2323±20 K)[19], and at 84 at.% Cr2O3 (T = 2248 K)[18] or 80 at.% Cr2O3 (T =

2473±20 K)[19] in argon atmosphere on either side of the congruently melting perovskite-

structured lanthanum chromite[18-20] (in this study oxides containing Cr(III) and Cr with

higher valencies than three are denoted as chromite and chromate respectively). The melting

temperature of lanthanum chromite in air, Tm(air) = 2773 K was determined by Foëx[21] and

by Coutures[20] using a thermal analysis technique described in more detail in earlier

publications.[22-24] The melting temperature was measured with optical pyrometers. Tm(argon)

= 2703 K was reported by Tresvjatskiy et al.[18], but in the graphic presentation of the phase

diagram in the same paper Tm(argon) ≈ 2600 K, and the exact value of the oxygen partial

pressure was not specified. Experimentally determined special points in the LaO1.5-CrO1.5

quasibinary system reveal a considerable spread. This is not surprising as experiments are

complicated due to the high investigation temperatures and evaporation of predominantly

Cr[25,26]. Furthermore deviations between the data from Tresvjatskiy et al.[18] and Berjoan[19]


104

may partly originate from differences of the oxygen partial pressure, which in both studies

was not exactly specified. The peritectic phase diagram proposed by Cassedanne[27] is in gross

conflict with the phase diagram data from the other groups.

Experimental oxygen solubilities in pure Cr and La were considered in thermodynamic

assessments by Povoden et al.[9] and Grundy et al. [28], whereas experiments on oxygen

solubilities in ssαCr are missing.

Lanthanum chromates:

The following lanthanum chromates were documented: Berjoan[19] reported that orthorhombic

La2CrO6 forms at T > 923 K. Using differential scanning calorimetry (DSC) he determined

the enthalpy change of the reaction

2 3 2 3 2 62(g)32La O Cr O O 2La CrO2

+ + → (4.3.1)

at T=1055 K and 2Op =83000 Pa to be −151±8 kJ mol-1.

The enthalpy of formation of La2(CrO4)3 from the elements at T = 298 K was proposed by

Tsyrenova et al.[29] to be −3961±11.7 kJ mol-1. La2(CrO4)3 decomposes by

890 1030 K

2 4 3 3 2 3 2(g)La (CrO ) 2LaCrO 0.5Cr O 2.25O−⎯⎯⎯⎯⎯→ + + ↑ (4.3.2)

An enthalpy change of 231 kJ mol-1 was determined for this reaction at the average

temperature of T = 960 K.[30]

LaCrO4 has been interpreted as a mixed-valent intermediate decomposition product of

La2(CrO4)3[30,31].

Stoichiometries and thermal stability ranges of lanthanum chromates with complex formulae

were reported by Berjoan et al.[32]. However these were in significant disagreement with later

results obtained by the same author[19].

The perovskite phase:

Existing experimental data of lanthanum chromite perovskite structure[33-45],

thermodynamics[30,33-35,43,46-53], phase stability[54], and nonstoichiometry[55-56] along with the

investigation techniques used are listed in Table 4.3.1 (next page).


105

Table 4.3.1 Calculated and experimental thermodynamic data of La-Cr oxides

1298

[30]

[30]

Enthalpy increments , (kJmol )1090 K

98.19, this work, calculated94.4 HT (high temperature) - calorimetry

1350 K133.05 this work, calculated139.2 HT - calorimetryActivit

−−=

=

KH HT

T

2 3

2 3

2 3 34

Cr O

4 5[53]Cr O

2 6

2 3 2 3

y of Cr O in LaCrO

2100 1.11 10 this work, calculated

2100 1.1 10 1.1 10 Knudsen mass spectrometry

La CrOEnthalpy of the formation reactionLa O + 0.5Cr O +1.5O

−

− −

= = ×

= = × ± ×

T K a

T K a

298K

298K

298K

2(g) 2 6

1f,oxides

-1 -1

2 4 3

1f,elements

f,ele

La CrO

73.0 kJmol this work, calculated

330 Jmol K this work, calculated

La (CrO )

3845 kJmol this work, calculated

2 6

2 6

42 3

La CrO

La CrO

La (CrO )

° −

°

° −

→

Δ = −

=

Δ = −

Δ

H

S

H

298K

298K

298K

1 [29]ments

1 1

2 3 2 3 2(g) 2 4 3

f,oxides

3961 11.7 kJmol , calculated

516 Jmol K this work, calculated

Enthalpy of the formation reactionLa O +1.5Cr O + 2.25O La (CrO )

42 3

42 3

2

La (CrO )

La (CrO )

La (CrO

° −

° − −

°

= − ±

=

→

Δ

H

S

H

298K

1

2 4 3 3 2 3 2(g)

1[30]

372 kJmol this work, calculated

Enthalpy of the dissociation reactionLa (CrO ) 2LaCrO + 0.5Cr O + 2.25O

231 kJmol and this work, fitted

4 3

42 3

)

La (CrO )

−

−

= −

→

Δ =H

298K

298K

975K

3

-1f,elements

-1f,oxides

-1f,oxides

Rhombohedral LaCrOStandard enthalpy



62.35 kJmol this w

3

3

3

LaCrO

LaCrO

LaCrO

°

°

°

Δ = −

Δ = −

Δ = −

H

H

H

1078K

298K

-1 [46]f,oxides 2 3

-1 -1

ork, calculated

73.06 ± 2.79 kJmol Drop solution calorimetry in 2PbO× B O

Standard entropy

109.2 Jmol K this work, calculated

Gibbs energy of formation by 3 L4

3

3

LaCrO

LaCrO

°

°

Δ = −

=

H

S

2 3 2 3 3

1

1[49]

1[52] 2

1a O Cr O LaCrO 2

1273 K 76.75 kJmol this work, calculated1273 K 30.1 1.5 kJmol solid oxide electrolyte - emf 1273 K 42.29 0.38 kJmol CaF - based emf

° −

° −

° −

+ →

= Δ = −= Δ = − ±= Δ = − ±

=

T GT GT G

T 1

1[53]

1

2100 K 79.52 kJmol this work, calculated2100 K 78.9 1.1 kJmol Knudsen mass spectrometry

72.403 0.0034 (kJmol ), 1273 - 2673 K this work, calculated44.45 0.002115

° −

° −

° −

°

Δ = −= Δ = − ±

Δ = − −Δ = − +

GT G

G TG 1 [50]

21 [51]

2

0.4(kJmol ), 855 -1073 K CaF - based emf

94.758 0.08530 (kJmol ), 700 -885 K CaF - based emf

−

° −

±

Δ = − +

T

G T


106

Crystal and magnetic structure: LaCrO3 is orthorhombic (o-prv) at room temperature and

transforms to rhombohedral structure (r-prv) at higher temperatures[20,33-42]. The temperatures,

enthalpy and entropy changes of this first-order[44] transition taken from the literature are

listed in Table 4.3.2 along with the investigation techniques used.

Table 4.3.2 Calculated and experimental data of the orthorhombic to rhombohedral

transition of LaCrO3

The reported transformation temperatures lie between T = 503 K and 583 K. The determined

enthalpy and entropy changes vary from 277 J mol-1 to 502.08 J mol-1 and 0.5 J mol-1 to

[33]

[34] a)

[35] a)

Transition temperature (K)540, this work, calculated503 583 adiabatic calorimetry544 1 DTA, DSC, thermogravimetry, dilatometry536 adiabatic shield calorimetry, HT - XRD (air and vacuu

−±

[36]

[37]

[38] a)

[38] a)

[39]

[20]

[40] a)

[40] a)

m)563 5 DTA, dilatometry, HT - XRD, HT - microscopy, HT - x - ray photography550 HT - XRD528 533 HT - XRD533 3 DTA543 XRD533 HT - XRD540 2 HT - XRD, DSC533 5 HT - XRD, dilatomet

±

−±

±±

[41]

[41]

[41]

[42] a)

[42] a)

[43]

ry545 heating, DSC535 cooling, DSC550 HT - XRD523 starting transition, simultaneous DSC - XRD541 completed transition, simultaneous DSC - XRD533 estimated from neutron powder d

[44]

1

[33]

[34] a)

[3

iffraction509 DSC, XRD

Enthalpy change of transition (Jmol )340, this work, calculated502.08 41.84 at 503 583 K calculated from adiabatic calorimetry277 at 544 1 K DSC403.25 at 536 K

−

± −±

5] a)

[40] a)

[41]

[44]

-1 1

calculated from adiabatic shield calorimetry340 (10 - 40) at 533 5 DSC380 at 550 K DSC310 at 509 K DSC

Entropy change of transition (Jmol K )0.63, this work, calculated0.96 at 503

−

± ±

− [33]

[34] a)

[35] a)

a) used for optimization

583K calculated from adiabatic calorimetry0.5 calculated from DSC0.75 calculated from adiabatic shield calorimetry


107

0.96 J mol-1 K-1. A transformation from rhombohedral to cubic structure at a temperature close

to T = 1300 K was reported by Ruiz et al.[37] and Momin et al.[41], whereas Coutures et al.[20]

reported T = 1923 K using high-temperature x-ray diffraction (HT-XRD), in agreement with

Berjoan[19] (T = 1923 ± 20 K) using dilatometry. Berjoan[19] further reported prevailing of the

cubic structure at T = 2173 K. On the other hand Geller and Raccah[38] as well as Höfer and

Kock[34] did not observe the rhombohedral to cubic transition up to T = 1873 K and

T = 1823 K respectively using differential thermal analysis (DTA).

A magnetic order-disorder transition was documented to occur at T ≈ 287 K[35], 289 K[45], or

295 K[46].

Enthalpy of formation: Cheng and Navrotsky[47] determined the enthalpy of formation of

LaCrO3 by oxide melt solution calorimetry at T = 1078 K.

Heat capacity and enthalpy increment data: the heat capacities of LaCrO3 were measured by

Korobeinikova and Reznitskii[33] from T = 340 K to 900 K using adiabatic calorimetry, Höfer

and Kock[34] (480 to 610 K) and Satoh et al.[45] (150 to 450 K) using DSC, Satoh et al.[45] (T =

77 K to 280 K) using alternating current calorimetry, Sakai et al.[35] (T=100 K to 1000 K)

using laser-flash calorimetry, and Sakai and Stølen[43] (T = 272 K to 1000 K) using adiabatic

shield calorimetry. Enthalpy increments of LaCrO3 at T = 1090 K and 1350 K were measured

by Suponitskii[30] using a high-temperature heat-conducting calorimeter.

Gibbs energy of formation: in order to obtain the Gibbs energy of formation of LaCrO3, Chen

et al.[49] measured electromotive force (emf) of the solid oxide galvanic cell Pt/Cr, La2O3,

LaCrO3/MgO-stabilized ZrO2/Cr2O3, Cr/Pt at 1273 K. Azad et al.[50], Chen et al.[51], and

Dudek et al.[52] measured emf of Pt, O2/La2O3, LaF3/CaF2/LaF3, LaCrO3, Cr2O3/O2, Pt in pure

oxygen from T = 855 K to 1073 K, T = 700 to 885 K, and T = 1273 K respectively. Peck et

al.[53] derived the Gibbs energy of formation of LaCrO3 from the determination of the

thermodynamic activity of Cr2O3 in LaCrO3 for the Cr2O3-poor phase boundary of LaCrO3 in

the temperature range from T = 1887 K to 2333 K using Knudsen effusion mass spectrometry.

Chemical stability: Nakamura et al.[54] reported no weight loss of lanthanum chromite at

T=1273 K from pure oxygen to 2Op =10-16.1 Pa using thermogravimetry combined with X-ray

diffraction (XRD). This means that the perovskite phase does not decompose within this

oxygen partial pressure range, and its oxgen nonstoichiometry is negligible.

Cation nonstoichiometry and defect chemistry: Maximum excess Cr in single-phase La1-xCrO3

of 0.38 cat.% in furnace-cooled LaCrO3 annealed at T = 1773 K in air was reported from

Khattak and Cox[55]. Single phase lanthanum chromite with 0.76 cat.% to 1.28 cat.% excess


108

Cr was prepared at T = 1773 K in a pure oxygen atmosphere[56]. Iliev et al.[56] observed an

intensity decrease of the high frequency band in a Raman spectrum of lanthanum chromite

measured after annealing the phase in vacuum at T = 1273 K. This feature was assigned to a

reduced number of Cr4+ due to partial removal of oxygen during the annealing of the

originally lanthanum-deficient perovskite phase.

Interpretations of the defect chemistry of the perovskite phase were made from electrical

conductivity measurements: the electrical conduction in lanthanum chromite is almost purely

electronic[37,57], affirming the lack of oxygen vacancies in the structure, in line with the results

from thermogravimetry[54]. Ruiz et al.[37] reported that the ionic transport number in

lanthanum chromite is less than 0.05 % up to T = 1250 K. Akashi et al.[58] measured the

isothermal electrical conductivity of an equilibrated La1-xCrO3-Cr2O3 mixture with 5 vol.%

excess Cr2O3 from T = 1573 K to 1673 K from 2

3O 1.0 10 Pa= ×p to

2

4O 2.0 10 Pa= ×p . They

observed an extraordinarily slow equilibration of the samples: More than four months were

required to measure the electrical conductivity at equilibrium state. The conductivity was

proportional to 2

3 16Op , the same as reported in an earlier study[25]. On the other hand a slope

of 2

1 4Op from T=700 K to 1300 K and purely intrinsic conductivity > 1600 K stated by

Shvaiko-Shvaikovskii et al.[57] is inconsistent with the findings from Akashi et al.[58] Shvaiko-

Shvaikovskii et al.[57] deduced n-type conductivity from measurements of transport number,

resistivity and thermo-emf at 2O 1Pa=p and

2

2O 10 Pap = , the electrical conductivity being

proportional to 2

3 8O

−p . The transition from reduced to stoichiometric chromite was

accompanied by a decrease of about 0.1% in weight, thus the presence of interstitial Cr in

reduced chromite was proposed. However n-type conductivity was not approved by any

further study.

Several groups[58,59] agree that the electrical neutrality is maintained by holes and lanthanum

vacancies, and that the carrier is the hole in lanthanum chromite[25,58-60]. Akashi et al.[58]

reported that concentrations of lanthanum vacancies and holes slightly increase from T = 1550

K to 1700 K. In contrast to the other authors Shvaiko-Shvaikovskii et al.[57] and

Meadowcroft[25] proposed the occurrence of chromium vacancies instead of lanthanum

vacancies.


109

4.3.4 Thermodynamic modeling and optimization

Metal phases:

In order to account for the solubility of La in ssαCr , the zeroth-order, composition-

independent interaction parameter[61] 0 bccCr,La:VaL was given a positive value. We chose the

solubility values from Svechnikov et al.[14] for its optimization, as these data are more

comparable to solubilities in other rare earths-transition elements systems.

Povoden et al.[9] described the solubility of oxygen in Cr(bcc) using the model Cr(Va,O)3. For

the reasons discussed recently[62], we reassess the oxygen-solubility in Cr(bcc) using the

model (Cr)(O,Va)1.5, and ssαCr is then given by the two-sublattice description

(La,Cr)(Va,O)1.5. The Gibbs energy of the end-member (Cr)(O)1.5 is defined as

[10] [10]3 32 41.5 2

gasSER SER(Cr)(O) Cr O Cr(bcc) O

° ° °− − = + + +G H H G G A BT (4.3.3)

SERxH is the standard enthalpy of the stable state of element x at 298.15 K and 105 Pa.[10] A and

B are adjustable parameters; using the PARROT module of the Thermocalc software[11] A was

given the fix value 0 for the reasons discussed in an earlier paper[9], and B and a regular

interaction parameter 0Cr:O,VaL were optimized with the same experimental data[9]. Due to the

lack of experimental data the oxygen solubility in ssαCr was modeled as an ideal extension of

the oxygen solubilities in pure La and Cr.

Solid oxides:

Lanthanum chromates:

The Gibbs energy function of La2CrO6 was based on the sum of the Gibbs energy functions of

La2O3, Cr2O3, and O2 in proper stoichiometries and A + BT parameters that were fitted to the

enthalpy of formation from the oxides, Eq. 4.3.1 as well as thermal stability data. The thermal

stability of La2CrO6 is slightly influenced by the thermodynamics of the intermediate, mixed-

valent chromates mentioned above. In order to refine the model parameters of La2CrO6, it was

thus necessary to consider these mixed-valent chromates in a provisional version of the

thermodynamic La-Cr-O database in spite of their arguable stoichiometries, and to optimize

their model parameters with phase diagram data[19,32]. The formation of chromates that contain

mixed Cr valences may be explained by gradual reduction of Cr6+ in La2CrO6 as the

temperature increases. These chromates can be interpreted as intermediate products in the


110

scope of a sluggish decomposition of La2CrO6, which starts at T = 1153 K[19,32] and is

completed at T = 1473 K[32] or 1523 K[19]. The simplified decomposition reaction reads

2 6 2 3 1- 3 21.5- (1.5 )1+La CrO La O La CrO O (g)

2 2[19,32]mixed-valent chromates⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ + + ↑x

xx (4.3.4)

Slight differences of the oxygen partial pressure during experiments may be reflected by a

variable extent of Cr-reduction, and consequently ambiguous stoichiometries of mixed-valent

intermediate chromates. These lanthanum chromates with conflicting stoichiometries[19,32] are

not included in the presented thermodynamic database.

The Gibbs energy function of La2(CrO4)3 was formulated using the same strategy as for

La2CrO6. The model parameters were fitted to the experimental enthalpy and temperature of

decomposition[30]. The enthalpy of formation from the elements[29] was not used as it is a

calculated value.

We go along with the interpretation of LaCrO4 being an intermediate reaction product during

the decomposition of La2(CrO4)3 by Eq. 4.3.2 and do not include this phase in the modeling.


The following denotations are used in this section: the superscript prv is written if the

regarding Gibbs energy expression is the same for both orthorhombic and rhombohedral

perovskite. The superscripts o-prv and r-prv stand for Gibbs energy expressions that have

different values for orthorhombic and rhombohedral perovskite. GRPRV denotes the Gibbs

energy function for stoichiometric rhombohedral perovskite. GVCR4O and GLCR4O stand

for the Gibbs energy functions of the completely oxidized neutral endmember. GVCR4O and

GLCR4O are set equal for orthorhombic and rhombohedral perovskite.

Stoichiometric perovskite: The Gibbs energy function of stoichiometric rhombohedral

LaCrO3 with the sublattice formula (La3+)(Cr3+)(O2-), 3

r-prvLaCrO

°G is given by

[9] [8]

3 GRPRV1 1 ln2 2

3+ 3+ 23

2 3 2 3

r-prv SER SER SERLaLaCrO Cr O La :Cr :O

magCr O La O

−° °

− − −

° °

= =

= + + + + +

G H H H G

G G G A BT CT T (4.3.5)

The parameters A, B, and C are optimized using the enthalpy of formation from Cheng and

Navrotsky[47], activity-data of Cr2O3 in LaCrO3 from Peck et al.[53], heat capacity-data

obtained by adiabatic calorimetry from Sakai and Stølen,[35] and enthalpy increment-data


111

measured at high temperatures[30]. A phase diagram with congruent melting of lanthanum

chromite and two eutectics[18,19] cannot be reproduced by using the emf-experiments[49-52].

Thus these data were excluded from the optimization.

A+BT parameters of the low-temperature orthorhombic perovskite phase were optimized with

those temperatures[34,35,38,40,42], enthalpies[34,35,40] and entropies[34,35] of transition having been

obtained by combined investigation techniques and being internally most consistent. The

rhombohedral to cubic transformation at high temperatures is not considered in the model, as

there is no existing thermodynamic data for this transition.

Cation-nonstoichiometric perovskite: To choose a proper model for nonstoichiometric

perovskite the following considerations are made: the formation of interstitial Cr in lanthanum

chromite proposed by Shvaiko-Shvaikovskii et al.[57] is unlikely due to the densely-packed

perovskite structure, and oxygen nonstoichiometry can be excluded from thermogravimetry[54]

and electrical conductivity[37,58] measurements. Thus the defects in n-type conducting[57]

lanthanum chromite are ambiguous and were not considered in the model.

B-site vacancies are energetically less favored than A-site vacancies in the perovskite

structure[63,64]. This means that the simplest sublattice model to describe cation

nonstoichiometric La1-xCrO3 reads (La3+,Va)(Cr3+,Cr4+)(O2-)3. While this model results in a

satisfying reproduction of experimental data, irreconcilable trouble is encountered at the

extension to the LaO1.5-MnO1.5-CrO1.5 system required for SOFC applications due to

diversities between the model descriptions of lanthanum chromite and lanthanum

manganite[65]. These are solved by allowing Va on the B-site and the anion sublattice of

lanthanum chromite just like in lanthanum manganite[65] leading to the appropriate sublattice

formula (La3+,Va)(Cr3+,Cr4+,Va)(O2-,Va)3. The optimization of selective model parameters

listed in Table 4.3.3 (pp. 112-114) resulted in negligible concentrations of Va on the B-site

and the anion sublattice, and the perovskite formula essentially remains La1-xCrO3.


112

Table 4.3.3 Model descriptions and Gibbs energy functionsa)

3+ 2+ 3+ 2- q-p q

[8]

[8]

[10]

(La ,Cr ,Cr ) (O ,Va )

2 , 3 2 3

GLALIQ

2 3 GLA2O3LIQ

GCRLIQ

2- 3+ 2+ 3+

q-3+

3+ 2-

q-2+

q-3+

VaO La Cr Crliq SER

LaLa :Valiq SER SER

La OLa :Oliq SER

CrCr :Valiq SER

CrCr :Va

p q°

°

°

°

= + = + +

− =

− − =

− =

−

y qy y y y

G H

G H H

G H

G H

Liquid (liq)

[10] [9] [9]

[9]

[9]

[9]

2GCRLIQ GCR2O3_L 3GCR1O1_L

2 5GCROLIQ 179638 79.923

2 2GCR1O1_L

Interaction terms

121000

3+ 2-

2+ 2-

q- q-2+ 2- 3+ 2-

2+

liq SER SERCr OCr :O

liq SER SERCr OCr :O

liq liqCr :O ,Va Cr :O ,Va

Cr

3

2

°

°

= − −

− − = − +

− − =

= =

G H H T

G H H

L L

L

1.5

[10]

61397 5.23 (65393 23 )( )

101850 39016( )

101850 39016( )

(La,Cr)(Va,O)

GHSERCR

q-3+ 2+ 3+

2+ 3+ 2- 2+ 3+

3+ 3+ 2- 3+ 3+

liq,La :Va Cr La

liqCr ,La :O Cr LaliqCr ,La :O Cr La

bcc SERFeCr:Va

La

°

°

= − + − −

= − − −

= − − −

− =

T T y y

L y y

L y y

G H

G

Bcc A2 phase

[10]

[10] [10]2(g)

[10] [10] [28]2(g)

GLABCC3 3GHSERCR (O ) 113.177552 43 3GLABCC (O ) 855000 142.52 4

355151.422

8350

bcc SER:Va La

bcc SER SERCr:O Cr O

bcc SER SERLaLa:O O

bccCr:Va,ObccCr,La:Va

° °

° °

− =

− − = + +

− − = + − +

= −

=

H

G H H G T

G H H G T

L

L[9]

[9]

[9]

0

0.4

311.5

0.008

bccc Crbcc

Cr

=

= −

= −

p

T y

yβ


113

3+ 4+ 3+ 2-3(La ,Va)(Cr ,Cr ,Va)(O ,Va)

3 GOPRV

3 GRPRV

3 5 6

3+3+ 2-

3+3+ 2-

4+3+ 2-

mag

mag

o-prv SER SER SERLa Cr OLa :Cr :O

r-prv SER SER SERLa Cr OLa :Cr :O

o-prv SER SER SERLa Cr OLa :Cr :O

°

°

°

− − − = +

− − − = +

− − − =

x

G H H H G

G H H H G

G H H H

1- 3La CrO perovskite

[72]

[72] [72]

[72]

[72] [72]

[10]2(g)

GS4O

GOPRV GS3V 1 6GS4V

3 5 6GS4O

GRPRV GS3V 1 6GS4V

GOPRV 1.5 (O )3+ 3+

3+ 3+

4+3+ 2-

mag

mag

o-prvmagLa :Cr :Va

r-pLa :Cr :Va

r-prv SER SER SERLa Cr OLa :Cr :O

SER SERLa Cr

°

° °

°

+ − + +

− − − =

+ − + +

− − = − +

G

G H H H

G

G H H G G

G [10]2(g)

[72] [72] [72]

[10]2(g)

[72] [72] [72]

GRPRV 1.5 (O )

5 6GS4O GS3V 1 6GS4V

GOPRV 1.5 (O )

5 6GS4O GS3V 1 6GS4V

3+ 4+

3+ 4+

rvmag

o-prvLa :Cr :Va

mag

r-prvLa :Cr :Va

SER SERLa CrSER SERLa Cr

SER SERLa Cr

°

°

°

°

− − = − +

− − = − +

+ − +

− − = − +

H H G G

G H H

G G

G H H[10]

2(g)

[65] [10]2(g)

[65]

GRPRV 1.5 (O )

3 GOPRV 1.5GVCR4O

0.5GVVV 2GLCR4O 0.75 (O ) 1.41263

3 GRPRV 1.5GVCR4O

0.5GVVV 2GLCR4O 0.7

3+ 2-

3+ 2-

mag

mag

o-prv SER SERCr OVa:Cr :O

r-prv SER SERCr OVa:Cr :O

°

°

°

°

+ − +

− − = +

+ − + − +

− − = +

+ − +

G G

G H H

G T G

G H H[10]

2(g)

[65] [10]2(g)

[65] [10]2(g)

5 (O ) 1.41263

GOPRV 1.5GVCR4O

0.5GVVV 2GLCR4O 0.75 (O ) 1.41263

GRPRV 1.5GVCR4O

0.5GVVV 2GLCR4O 0.75 (O ) 1

3+

3+

mag

mag

o-prv SERCrVa:Cr :Va

r-prv SERCrVa:Cr :Va

°

°

°

°

°

− +

− = +

+ − − − +

− = +

+ − − −

G T G

G H

G T G

G H

G

[65] [10]2(g)

.41263

3 3

2GVCR4O 1 3GVVV 4 3GLCR4O 0.5 (O ) 4.35056

2GVCR4O 1 3GV

4+ 4+2- 2-

4+ 4+

mag

mag

o-prv SER SER r-prv SER SERCr O Cr OVa:Cr :O Va:Cr :O

o-prv SER r-prv SERCr CrVa:Cr :Va Va:Cr :Va

° °

°

° °

+

− − = − − =

= + − + + +

− = − =

= +

T G

G H H G H H

G T G

G H G H[65] [10]

2(g)

3+

VV 4 3GLCR4O (O ) 4.35056

Interaction term250000

Magnetic contribution 291.35 0.894

= La

3+ 3+ 2- 3+ 4+ 2-

mag

prv prvLa :Cr ,Va:O La :Cr ,Va:O

o-prv r-prv o-prv r-prv prvc c i:j:k i:j:k

i

°− − + +

= =

= = = =

G T G

L L

T T y yβ β

4+ 3+

-2

2 6

3+ 6+ 2-2 6

2 4 3

3+ 6+ 2-2 3 12

,Va= Cr ,Cr= O Va

La CrO

(La ) (Cr )(O )

2 6 GLA2CRO6

La (CrO )

(La ) (Cr ) (O )

2 3 12 GLA2C

2 66+3+ 2-

42 36+3+ 2-

(

La CrO SER SER SERLa Cr OLa :Cr :O

La CrO ) SER SER SERLa Cr OLa :Cr :O

jk ,

°

°

− − − =

− − − =

G H H H

G H H H

La -Chromates

R3O12


114

[8] [9]

[8] [9]

Perovskite

Stoichiometric orthorhombic perovskiteGOPRV 0.5GLA2O3A 0.5GCR2O3 73931 3.01 0.68 lnStoichiometric rhombohedral perovskiteGRPRV 0.5GLA2O3A 0.5GCR2O3 73591 2.38 0.68 ln

= + − + −

= + − + −

T T T

T T

Functions

[72] 2 1

[9] [10]2(g)

[72] 2 1

Neutral nonstoichiometric perovskite endmembersGS4O = 597648 213.38 47.56 ln( ) 0.00307 190000

0.5GCR2O3 0.25 (O )

GS3O = 472704 191.7186 47.56 ln( ) 0.00307 1900000.5GCR

−

°

−

− + − − ++ +

− + − − ++

T

T T T T TG

T T T T T[9]

[9] [10]2(g)

[8] [9] [10]2(g)

[72]

[72] 2 1

2O3GVCR4O = 0.5GCR2O3 0.25 (O ) 291802 250

GLCR4O =1 3GLA2O3A 0.5GCR2O3 0.25 (O ) 200000

Perovskite referenceGS4V 607870 268.9 47.56 ln( ) 0.00307 190000

0.5GCR2O

°

°

−

+ − −

+ + −

= − + − − ++

G T

G

T T T T T[10]

2(g)

2 6[8] [9] [10]

2(g)

2 4 3

[8] [9] [10]2(g)

a) All parameters are in SI units : J,

3 1.25 (O )

La CrO

GLA2CRO6 = GLA2O3A 0.5GCR2O3 0.75 (O ) 72615 4.5

La (CrO )

GLA2CR3O12 = GLA2O3A 1.5GCR2O3 2.25 (O ) 371557 205

°

°

°

−

+ + − −

+ + − +

G

G T

G T

1 1mol, K. = 8.31451 Jmol K− −R

Using the compound energy formalism (CEF)[66-68] the molar Gibbs energy of La1-xCrO3 reads

: : ln ln lnprv ° E prvm m mag

° ⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

= + + + + +∑∑∑ ∑ ∑ ∑i j i i j jk i j k k ki j k i j k

G y y y G RT y y y y y y G G (4.3.6)

where yi is the site fraction of Va and La3+ on the A-sublattice, yj is the site fraction of Cr3+,

Cr4+ and Va on the B-sublattice, and yk is the site fraction of O2- and Va on the anion

sublattice of the perovskite A1-xBO3. R = 8.31451 J mol-1 K-1. The third-last term accounts for

the configurational entropy of mixing. The second-last term describes the excess Gibbs

energy of mixing due to interactions of ions in the mixture. These are accounted for by the


115

optimization of interaction parameters. The last term designates the magnetic contribution to

the Gibbs energy. For the magnetic part of the Gibbs energy a magnetic ordering-model

proposed by Inden[69] and simplified by Hillert and Jarl[70] was used. A short summary of this

model can be found in Chen et al.[71] The magnetic parameters Tc and β were fitted to the pC -

data around the magnetic transition temperature from Sakai and Stølen[35].

Fig. 4.3.1 is a visualization of the Cr-containing part of the model the authors use to describe

the cation nonstoichiometry of lanthanum chromite.

Fig. 4.3.1 Representation of the Cr-containing part of the model for nonstoichiometric

lanthanum chromite. The thin lines margin the neutral plane. The neutral compounds used for

the optimization are marked by the black spots.

The parameters of the compound energy formalism are the Gibbs energies of the not

necessarily neutral 12 end-member compounds : :°

i j kG , with the 8 Cr-containing compounds

being the corners of the cube. Only compounds inside the neutral plane can exist on their

own.

3+ 4+ 2-3

prv(La )(Cr )(O )

°G and 3+ 4+3

prv(La )(Cr )(Va)

°G are given in Table 4.3.3 (pp. 112-114). These endmembers of

nonstoichiometric perovskite have been fixed firmly by a sufficient number of consistent

experiments in the LaO1.5-SrO-CrO1.5 system [72]. Thus the authors

adopted 3+ 4+ 2-3

prv(La )(Cr )(O )

°G and 3+ 4+3

prv(La )(Cr )(Va)

°G from Povoden et al.[72].


116

The neutral Cr4+ -containing endmembers

[9] [10]

2 1 2 2 1 12 3 ln ln3 3 3 3 3 3

1 1GVCR4O2 4

4+4+ 22

2 3 2

prv SER SERVaCrO Cr O Va:Cr :VaVa:Cr :O

gasmagCr O O

−° ° °

− −

° °

⎛ ⎞⎜ ⎟⎝ ⎠

= + + +

= = + + + +

G H H G G RT

G G G A BT (4.3.7)

and

[9] [8] [10]

2 2 1 2 2 1 13 ln ln3 3 3 3 3 3 3

1 1 1GLCR4O2 3 4

3+ 4+ 2 4+ 22 3 3

2 3 2 3 2

prv SER SER SERLaLa CrO Cr O La :Cr :O Va:Cr :O

gasmagCr O La O O

− −° ° °

− − −

° ° °

⎛ ⎞⎜ ⎟⎝ ⎠

= + + +

= = + + + +

G H H H G G RT

G G G G A (4.3.8)

and reciprocal relations which were set zero in analogy to Grundy et al.[65] were used to obtain

3+ 2-3

prv(Va)(Cr )(O )

°G , 4+ 2-3

prv(Va)(Cr )(O )

°G , 3+3

prv(Va)(Cr )(Va)

°G , and 4+3

prv(Va)(Cr )(Va)

°G . The configurational entropy-

term in Eq. 4.3.7 describes random mixing of O2- with Va on the anion sublattice. In Eq. 4.3.8

it describes random mixing of La3+ and Va on the A-site.

The parameters A and B of Eq. 4.3.7 and A of Eq. 4.3.8 are optimized using experimental data

of excess Cr in perovskite[56]. Furthermore the temperature dependence of lanthanum

vancancy and hole concentrations from Akashi et al.[58] was considered in the optimization.

As cation diffusion in La1-xCrO3 is extremely slow even at high temperatures, the Cr-

overstoichiometry in a furnace-cooled specimen reported by Khattak and Cox[55] does most

likely not represent the overstoichiometry at an intermediate temperature and was not used for

the optimization.

3+ 3+3

prv(La )(Cr )(Va)

°G results from a reciprocal relation which was set zero in analogy to Grundy et

al.[65]:

[10]2(g)

3 (O )23+ 3+3 3

o-prv,r-prv SER SER o-prv,r-prvLaLaCrVa Cr LaCrOLa :Cr :Va

° ° °− − = = −G H H G G G (4.3.9)

Using Eqs. 4.3.5 to 4.3.8 and adopting the Gibbs energies of the remaining endmembers

3+ 2-3

prv(La )(Va)(O )

°G , 3+3

prv(La )(Va)(Va)

°G , 2-3

prv(Va)(Va)(O )

°G , and3

prv(Va)(Va)(Va)

°G from Grundy et al.[65], the 12

endmembers of the compound energy formalism of the perovskite phase are defined. The


117

introduction of positive interaction parameters 3+ 3+ 2-prv0La ,Va:Cr :OL and 3+ 4+ 2-

prv0La ,Va:Cr :OL that were given

the same values circumvents too high Cr4+ contents at low temperatures that would be in

conflict with the experiments.

The liquid phase:

The two-sublattice model for ionic liquids[73,74] was used for the description of the liquid

phase of the La-Cr-O system. It was based on the liquid descriptions of the binary

subsystems. The chromium species considered in the liquid are Cr2+ and Cr3+. Higher

oxidation states are unlikely to exist in the liquid at normal oxygen partial pressures. The

liquid is thus given by the model description (La3+,Cr2+,Cr3+)p(O2-,Vaq-)q. The experimentally

determined temperatures and liquid compositions[13,14] at the eutectic and monotectic in the

metallic La-Cr system and the partial enthalpy of mixing of Cr, CrΔH [15] in La-Cr liquid were

used to optimize the temperature-dependent regular 02+ 3+

liqCr ,La :VaL and subregular 1

2+ 3+liqCr ,La :VaL

interaction parameters to account for interactions between La and Cr. Furthermore the two

regular interaction parameters 03+ 3+ 2-

liqCr ,La :OL = 0

2+ 3+ 2-liqCr ,La :OL and the two subregular 1

3+ 3+ 2-liqCr ,La :OL =

12+ 3+ 2-

liqCr ,La :O

L were optimized. It was assumed that the interactions between Cr2+-La3+ and

Cr3+-La3+ are of the same order of magnitude in the oxide melt, thus the two regular

interaction parameters were set equal to each other, as were the two sub-regular interaction

parameters. Using the following data for their optimization led to the lowest error between

experiments and calculation: the composition and temperature of the eutectic at the La-rich

side and the composition of the eutectic at the Cr-rich side in the oxide LaO1.5- CrO1.5 system

from Tresvjatskiy et al.[18], the temperature of the eutectic at the Cr-rich side from Berjoan[19],

and the congruent melting temperature of the perovskite phase from Coutures et al.[20] and

Foëx[21]. Berjoan[32] and Tresvjatskiy et al.[18] did not specify the value of the prevailing

oxygen partial pressure during their phase diagram experiments conducted in an argon

atmosphere. As a value of the oxygen partial pressure is required for the optimization, we

defined 2Op = 1 Pa.

4.3.5 Results and Discussion

The La-Cr system:

The calculated phase diagram of the La-Cr system is presented in Fig. 4.3.2 (next page),

together with experimental phase diagram data[12,13,14,17].


118

Fig. 4.3.2 Calculated phase diagram of the La-Cr system with data

from the literature included (symbols).

The positive value of 0 bccCr,La:VaL used to model the bcc phase results in a large miscibility gap

between the La-rich and Cr-rich metals, which is tantamount to a small solubility of La in

ssαCr in agreement with the experiments[14,17]. The model description of the bcc phase results

in a tiny solubility of Cr in La(bcc), denoted as ssLaγ , of -32 10× at.% at 1134 K, the lowest

temperature of stable ssLaγ , which further decreases as a function of increasing temperature.

The calculated enthalpies of mixing are shown in Fig. 4.3.3 (next page) together with the

experimentally determined value[15] that is well reproduced by the calculation.


119

Fig. 4.3.3 Calculated partial enthalpies of mixing of La and Cr in La-Cr liquid, and integral

enthalpies of mixing as a function of composition, with the experiment from Berezutskii et

al.[15] at T = 1700 K included (symbol with error-bar).

Considerable deviations of the calculated liquidus from experiments at the Cr-rich side of the

system can be ascribed to the problem of two different melting temperatures for Cr cited in

the literature, which are T = 2180 K and 2130 K. The higher value was favored by

Dinsdale[10] and is adopted in this study, whereas the lower melting temperature was chosen

by Savitskii et al.[12] and Svechnikov et al.[14].

A satisfying reproduction of the experimental data was obtained by considering a moderate

temperature dependence of 02+ 3+

liqCr ,La :Va

L and 12+ 3+

liqCr ,La :Va

L . This is unfortunately associated with

an inverse liquid-liquid miscibility gap with a minimum at X(Cr) = 0.25 and T ≈ 5000 K that

is of course unphysical.

The La-Cr-O system:

Phase equilibria:

Calculated LaO1.5- CrO1.5 phase diagrams in pure oxygen at2Op =105 Pa, in air at


120

2Op = 21278 Pa, and under reducing conditions at 2Op = 1 Pa representing the typical oxygen

partial pressure in argon atmosphere are shown in Fig. 4.3.4 together with experimental

data[18-21].

Fig. 4.3.4 Calculated phase diagrams of the LaO1.5-CrO1.5 system in pure oxygen, air

atmosphere, and under reducing conditions representing argon atmosphere at 2Op = 1 Pa with

experimental data included (symbols).

Excess Cr in lanthanum chromite is favored at high oxygen partial pressures. A decrease of

Cr4+ during annealing of an originally lanthanum-deficient perovskite phase under reducing

conditions is predicted by the model, reflected by the disappearance of Cr overstoichiometry.

This is in line with the interpretations of Raman spectra from Iliev et al.[56] Be it that the

reported thermodynamic data of La2CrO6[19] and La2(CrO4)3

[30] are correct, lanthanum

chromite is expected to be metastable at room temperature, and orthorhombic perovskite is

stable only at2Op ≤102 Pa. La2CrO6 is stable within a wide temperature-range in pure oxygen,

whereas it does not form in air and argon atmosphere.

Due to the ambiguous oxygen partial pressure of phase diagram experiments[18,19] and the

conflicting data on the melting temperature of lanthanum chromite in argon atmosphere[18] the

presented liquid description is rather tentative. Under oxidizing conditions Cr3+ is favored

over Cr2+ in the liquid. Analogous to Fe in the La-Fe-O system[62] this oxidation of Cr2+ to

Cr3+ governs shifts of eutectic compositions and temperatures and the increase of the melting

temperature of the perovskite phase on increasing the oxygen partial pressure. On the other

hand a significant amount of Cr3+ in the ionic liquid is reduced to Cr2+ under reducing

conditions, and the liquid stability increases considerably at the Cr-rich part of the system


121

leading to a considerably lowered eutectic temperature. The liquid description using the two-

sublattice model for ionic liquids also resulted in a significantly larger decrease of the melting

temperature of lanthanum chromite at 2Op ≈ 1 Pa than the given values in argon

atmosphere[18]. Despite this discrepancy we did not go for an alternative liquid model for the

sake of consistency with our previously assessed systems.

In Fig. 4.3.5 calculated phase equilibria of the La-Cr-O system at T = 1273 K are shown as a

function of oxygen partial pressure.

Fig. 4.3.5 Calculated phase equilibria of the La-Cr-O system at T = 1273 K

as a function of oxygen partial pressure.

It is obvious that no mutual solubilities of La and Cr in bcc metal in equilibrium with oxides

are expected. The same oxygen solubility in Cr as in the assessment by Povoden et al.[9] was

obtained using the new model description (Cr)(O,Va)1.5. At 2Op = 10-34.04 Pa metallic liquid

forms at the lanthanum-rich side of the phase diagram.

Thermodynamic data:

Calculated thermodynamic data of solid oxides are listed together with experimental data

from the literature in Table 4.3.1 (p. 105). Calculated and experimental data on the

orthorhombic to rhombohedral transition of LaCrO3 are listed in Table 4.3.2 (p. 106). Table

4.3.3 (pp. 105-107) is a compilation of the Gibbs energy functions and model descriptions of

the phases in the La-Cr-O system obtained in this study.


122

Lanthanum chromates: Testing an optimization of model parameters of La2(CrO4)3 by using

all available thermodynamic data[29,31] resulted in gross disagreement between optimized and

reported values. The considerable error might be explained by experimental difficulties to

reach equilibrium at the low investigation temperatures, and/or by significant deviations

between the thermodynamic standard data used for the calculation of the enthalpy of

formation from the elements[29] and assessed values[8-10]. Anyway the model parameters were

fitted to the experimental data[30], whereas the calculated standard enthalpy of formation from

the elements[29] was rejected, bearing in mind the high degree of uncertainty of the resulting

description. The perovskite phase: the calculated heat capacities of LaCrO3 are compared with

experiments from the literature in Fig. 4.3.6.

Fig. 4.3.6 Calculated heat capacities of LaCrO3 (solid curve) as a function of T with

experimental data included (symbols). The dashed line marks the temperature of the o-prv ↔

r-prv transition.

The calculated pC -curve extrapolates well to high temperatures. The use of pC -data from

Sakai and Stølen[35] along with enthalpy increment-data from Suponitskii[30] to optimize the


123

parameter CTlnT of the Gibbs energy of stoichiometric perovskite resulted in the lowest error

between experiments and calculation. As CTlnT was set equal for o-prv and r-prv, their pC is

the same. The experimentally determined pC -peak around 545 K caused by the first-order

transition o-prv ↔ r-prv is in fact a discontinuity which cannot be implemented in the model.

The calculated transition temperature of T = 540 K is shown by the broken line in Fig. 4.3.6.

The calculated pC -peak at T = 290 K reflects the temperature of the magnetic order-disorder

transition, the transition temperature being in agreement with the experiments. Two values for

the magnetic parameter p are possible depending on the crystal structure, p=0.28 and p=0.4,

whereby the proper p-value for structures other than bcc, fcc, and hcp is not available in the

literature. The pC -anomaly is equally well reproduced by the model[69,70] using p = 0.28 or p

= 0.4. For the sake of compatibility with the recent assessment of the La-Fe-O system[62] we

chose p = 0.28. Experimental enthalpy increments[30] are well reproduced by the calculation

(see Table 4.3.1, p. 105). Due to the consistency between both groups of calorimetric

experiments[30,35] the term CTlnT is fixed firmly. A small peak which was found around 855 K

can be explained most likely by the decomposition of an undetected impurity phase[35].

The calculated Gibbs energies of the formation of LaCrO3 from the oxides

2 3 2 3 31 1La O + Cr O LaCrO2 2 → (4.3.10)

are listed as a function of temperature together with data from the literature [49-53] in Table

4.3.1, p. 105. The resulting Gibbs energies of formation from emf-measurements are

remarkably less negative than the Gibbs energies of formation derived from Knudsen mass

spectrometry[53]. Only the use of the latter data for the optimization resulted in the proper

phase diagram with congruent melting of the perovskite phase and two eutectics. It needs to

be clarified why all of the emf-measurements are problematic: Azad et al.[50] stated that the

Gibbs energy of formation of LaCrO3 cannot be studied properly using the solid oxide

electrolyte method due to experimental difficulties in measuring the low oxygen potentials

encountered in a mixture of coexisting LaCrO3-La2O3-Cr. Yet it is obvious that the CaF2-

based emf-technique is neither suitable for the determination of thermodynamic data of

lanthanum chromite, as it unavoidably leads to emf that are too low. A possible explanation is

found in a study by Akila and Jacob[75]: Fine precipitates of CaO can form on the surface of

CaF2 in water- or oxygen-containing atmosphere. In this case the emf depends on the activity


124

of CaO at the electrode/electrolyte interface, and changing activity of CaO at the

electrode/electrolyte interface can alter the chemical potential of fluorine at this electrode and

thus the emf across the electrolyte.

Chemical stability of the perovskite phase:

The calculated oxygen partial pressure for the decomposition of lanthanum chromite by the

reaction

3 2 3 21 3LaCrO La O αCr + O (g)2 4

→ + ↑ (4.3.11)

is2Op = 10-20.97 at 1273 K. The calculated decomposition of the perovskite phase by Eq. 4.3.11

is plotted as a function of temperature and oxygen partial pressure in Fig. 4.3.7.

Fig. 4.3.7 Calculated decomposition of lanthanum chromite

as a function of temperature and oxygen partial pressure.

Defect chemistry of the perovskite phase:


125

Applying a defect chemistry analysis of La1-xCrO3 in equilibrium with Cr2O3 the following

defect reaction for its oxidation can be written in the sublattice form, if Cr[Va ]′′′ and ••O[Va ]are

assumed to be negligible according to Akashi et al.[58]:

3+ 3+ 2- 3+ 4+ 2-3 2 2 3 1 3 3(g)

1(La )(Cr )(O ) O (La Va )(Cr )(O )4

+ → (4.3.12)

Using Kröger-Vink notation this defect reaction reads

x x x x xLa La LaCr O 2 Cr O(g)

1 2 1La +Cr +3O O La + Va + Cr +3O4 3 3

•′′′+ → (4.3.13)

and the equilibrium constant of the oxidation reaction is

2

1 3 x 2 3 x 3La La Cr O

x x x 3 1 4La Cr O

[Va ] [La ] [Cr ][O ]= [La ][Cr ][O ]

•′′′ox

OK

p (4.3.14)

For small oxidation extent xLa[La ] , x

Cr[Cr ] , and xO[O ]can be considered to be ~ 1, and charge

neutrality is maintained by

La1[Va ]=3

′′′ Cr[Cr ]• (4.3.15)

Substituting this into Eq. 4.3.14 gives the proportionalities 3

16La Cr O2

[Va ], [Cr ]•′′′ ∝ P .

The concentrations of the defects , , ,La Va Cr and Crx x La La Cr Cr

•′′′ in La1-xCrO3 correspond to the site

fractions A 3+prv

Lay , Aprv

Vay , B 3+prv

Cry , and B 4+prv

Cry in the compound energy formalism. A 3+prv

Lay , Aprv

Vay , B 3+prv

Cry ,

B 4+prv

Cry and the tiny fractions Bprv

Vay and Oprv

Vay are plotted logarithmically as a function of

2Olog p at T = 1073 K and 1673 K in Fig. 4.3.8 (next page) for lanthanum chromite in

equilibrium with Cr2O3. The line for A 3+prv

Lay at 1073 K cannot be seen as it is very close to 1.


126

Fig. 4.3.8 Calculated site fractions of species in La1-xCrO3 in thermodynamic equilibrium

with Cr2O3 logarithmically plotted at T = 1073 K and 1673 K as a function of 2Op . The slope

of 3/16 of the calculated defect concentrations is indicated in the triangle.

At T=1073 K a constant slope of 3/16 of the defect concentrations La Cr[Va ] and [Cr ]•′′′ shown in

the triangle, is calculated from very high to very low oxygen partial pressures. This slope is

fixed by the defect reaction Eq. 4.3.12. At T = 1673 K the slope of 3/16 of La Cr[Va ] and [Cr ]•′′′ is

reproduced by the calculated slope using the compound energy formalism at 105 Pa >2Op >

10-8 Pa; hence oxidation of LaCrO3 to La1-xCrO3 governs the electrical conductivity of

perovskite with fixed activity of Cr2O3 at unity between2Op = 105 Pa and 10-8 Pa at this

temperature. The calculated slopes of La Cr[Va ] and [Cr ]•′′′ are equal to the slope of the electrical

conductivity from 1573 to 1673 K between 2

3O 1.0 10 Pa= ×p and

2

4O 2.0 10 Pa= ×p determined

by Akashi et al.[58]. The conflicting data from Shvaiko-Shvaikovskii et al.[57] may be

explained by problems of reaching equilibrium due to extraordinarily slow cation diffusion in

lanthanum chromite. In Fig. 4.3.9 (next page) the calculated slopes of Va and Cr La Cr•′′′ are


127

compared with slopes of La Cr[Va ] and [Cr ]•′′′ determined by Akashi et al.[58] as a function of

reciprocal temperatures.

Fig. 4.3.9 Calculated defect concentrations in La1-xCrO3 in thermodynamic equilibrium with

Cr2O3 (solid lines) logarithmically plotted as a function of reciprocal temperature along with

the data from Akashi et al.[58] derived from electrical conductivity measurements (symbols

with error-bars, broken lines).

The calculated concentrations agree well with the data derived from electrical conductivity

measurements[58]. The calculated amount of La Cr[Va ] relative to [Cr ]•′′′ is fixed by the criterion for

charge neutrality, Eq. 4.3.15, as calculated Cr[Va ]′′′ and ••O[Va ] are very small. The calculated

relative defect concentrations are in line with those proposed by Akashi et al.[58].

The presented defect chemistry calculations are still rather tentative, as the temperature and

oxygen partial pressure dependence of excess Cr in La1-xCrO3 has not been investigated

systematically so far.


128

4.3.6 Conclusions

Model parameters of the presented thermodynamic La-Cr-O database were optimized with

assessed thermodynamic and phase diagram data.

The thermodynamic descriptions of lanthanum chromates and the liquid phase are rather

tentative due to humble or sketchy experimental information.

The thermodynamic modeling of lanthanum chromite was based on experimental

thermodynamic data reported by Peck et al.[53] and Cheng and Navrotsky[46], as the use of

these data for the optimization of model parameters resulted in a proper reproduction of the

phase equilibria derived from experiments. The orthorhombic to rhombohedral transition in

lanthanum chromite and the magnetic order-disorder transformation are well reproduced by

the model.

Using the new database the stability limits of lanthanum chromite in function of temperature

and oxygen partial pressure can be quantified.

The proposed existence of lanthanum vacancies and holes to maintain charge neutrality in

lanthanum chromite with excess Cr is reproduced by the model, and the calculated slopes of

defect concentrations in function of oxygen partial pressure and temperature are in line with

the slopes derived from electrical conductivity measurements. However the amounts of excess

Cr in La1-xCrO3 used for the optimization of the cation nonstoichiometry are preliminary, and

further work on the temperature dependence of excess Cr as a function of temperature and

oxygen partial pressure would allow a more accurate quantification of the defect chemistry of

lanthanum chromite.

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4.4 Thermodynamic La-Sr-Mn-Cr-O oxide database for SOFC

applications

E. Povoden, M. Chen, A.N. Grundy, and L.J. Gauckler

to be submitted

The thermodynamic La-Sr-Mn-Cr-O oxide database is obtained as an extension of

thermodynamic assessments of oxide subsystems using the Calphad approach. Gibbs energy

functions of SrCrO4, Sr2.67Cr2O8, Sr2CrO4, and SrCr2O4 are presented. Experimental solid

solubilities and nonstoichiometries in La1-xSrxCrO3-δ and LaMn1-xCrxO3-δ are reproduced by

the model.

4.4.1 Introduction

Sr-doped lanthanum manganite (LSM) with the perovskite structure ABO3-δ is used as

cathode materials in SOFC. However diffusion of chromium from the metallic interconnects

into the cathode leads to a severe cell voltage decrease that was linked to the formation of Cr-

containing phases[1,2]. A thermodynamic La-Sr-Mn-Cr-O oxide database is highly desirable

for the development of endurable SOFC: thermodynamic calculations set an important base

for the optimization of cathodes aiming to avoid long-term degradation due to chromium

poisoning. The database should meet the demand to calculate stable and metastable phase

equilibria, thermodynamic driving forces and activities, as well as defect concentrations of the

cathode contaminated by Cr at different temperatures and oxygen partial pressures. These

requirements are conformed by using the CALPHAD approach. For the construction of the


135

La-Sr-Mn-Cr-O oxide database La-Mn-Cr-O oxide and La-Sr-Cr-O oxide systems are

assessed. Sr-Mn-Cr-O oxide is treated as ideal extension from the subsystems.

4.4.2 Assessment of data from the literature

Previous assessments of the La-O, Cr-O, and La-Cr-O databases are adopted[3-5], and the La-

Sr-Mn-O oxide database is taken from Grundy et al.[6] with a slight modification: Grundy et

al.[6] allowed Mn3+ on the A-site of LSM to reproduce experimental oxygen

nonstoichiometries under low oxygen partial pressures. Due to large differences between the

ionic radii of La3+ and Mn3+ and possible coordination numbers (1.5 Å for 12-fold

coordinated La3+, 0.785 Å for at maximum 6-fold coordinated Mn3+)[7] we omit Mn3+ on the

A-site. Calculation of the oxygen nonstoichiometry of perovskite + MnO instead of

metastable single phase perovskite[6] leads to a good agreement between experimental and

calculated nonstoichiometries.

No quaternary phases or solid solutions were found in the Sr-Mn-Cr-O oxide system[8].

Sr-Cr-O oxide:

Thermodynamic functions for Sr-Cr-oxides in the SSUB database[9] are based on estimates[10].

We propose optimized thermodynamic functions for oxide phases of the Sr-Cr-O oxide

system resulting from the assessment of all available experimental data: agreement exists

between Gibbs energies of formation of SrCrO4 determined by emf technique using a Y2O3

stabilized ZrO2 electrolyte[11,12], whereas emf measurements using CaF2-based emf-

technique[13] led to conflicting results likely caused by competing reactions[14]. Differences

concern the reported stabilities of further compounds[11,12,15-19]: for the stabilities of SrCr2O4

and Sr2CrO4 we trust the accurate study of Jacob[11], which is in agreement with Negas and

Roth[15]. On the other hand the conflicting phase equilibria presented by Kisil[16] lack

experimental details. Sr3Cr2O7[12] was approved as high pressure phase only[17]. The

stoichiometry of a phase defined as Sr3Cr2O8[15] was later corrected to be essentially

Sr2.67Cr2O8 by using microprobe analysis[18], in agreement with Hartl and Braungart[19].

La-Sr-Cr-O oxide:

In the La-Sr-Cr-O oxide and La-Mn-Cr-O oxide systems no quaternary stoichiometric

compounds were reported. Phase equilibria in the La-Sr-Cr-O oxide system in air at 1223 K

and under vacuum at 1873 K were determined by using solid state technique[18]. Limited

solution of Sr in La1-xSrxCrO3-δ perovskite[18] was confirmed by a later investigation[20]. The


136

existence of several Ruddlesden-Popper phases is restricted to reducing conditions; solely

Sr(La,Sr)CrO4 showed reproducible stoichiometry[18]. In contrast to Peck et al.[18] it was

proposed earlier that Sr(La,Sr)CrO4 were stable in air[10]. The exact temperature and oxygen

partial pressure range of Sr(La,Sr)CrO4 is ambiguous, thermodynamic data are missing, and

the solubility of Cr is unknown. Thus its extension to the quinary database would not be

reliable. As Ruddlesden-Popper phases have not been reported to form during SOFC

operation with LSM cathodes, Sr(La,Sr)CrO4 is omitted in the modeling. Myoshi et al.[20]

investigated the single phase region of La1-xSrxCrO3 with x = 0.1, 0.2, and 0.3 as a function of

temperature and oxygen partial pressure using XRD analysis. Peck et al.[21] determined the

Gibbs energy of formation of La1-xSrxCrO3 with x = 0.1, 0.2, and 0.3 using Knudsen mass

spectrometry. Cheng and Navrotsky[22] measured enthalpies of formation of La1-xSrxCrO3-δ

with x = 0.1, 0.2. and 0.3, and δ = 0, −0.04, −0.09, and −0.11 using drop calorimetry at

T = 1080 K. Positive δ in the perovskite formula reflects oxygen deficiency, whereas negative

δ essentially stands for cation nonstoichiometriy. Nonstoichiometry data for La1-xSrxCrO3-δ

with x=0.1, 0.2. and 0.3 at T = 1273K, 1373 K, 1473K, and 1573 K[23], and La0.8Sr0.2CrO3-δ at

1273 K[24] were measured as a function of oxygen partial pressure using thermogravimetry.

Cr4+ and oxygen vacancies are regarded as the major defects[23,24].

La-Mn-Cr-O oxide:

In the La-Mn-Cr-O oxide system no quaternary stoichiometric compounds were reported. An

isothermal section of the La-Mn-Cr-O oxide system at 1073 K in air and pure oxygen has

been published without further commenting of experimental evidences[25]. Complete solid

solution between the LaMnO3 and the LaCrO3 perovskites was affirmed[8].

δ of LaMn0.9Cr0.1O3-δ was measured using thermogravimetry[26].

La-Sr-Mn-Cr-O oxide:

In the La-Sr-Mn-Cr-O oxide system complete solid solubility of Mn and Cr is reported for

La1-xSrxMn1-yCryO3-δ perovskite[8]. Plint et al.[27] concluded from the similarity between X-ray

absorbtion spectra of Cr K of LaCrO3 and La1-xSrxMn0.5Cr0.5O3-δ with x = 0.2, 0.25, and 0.3 at

T = 1173 K that Cr4+ were absent in the latter. Perovskite+MnCr2O4 spinel equilibrium of a

powdered mixture of La0.8Sr0.2MnO3 and Cr2O3 at 1073 K was reported after 1000 h of heat

treatment in air[28].


137


Magnetic and structural transitions of La1-xSrxCrO3-δ [29−35], LaMn1-xCrxO3-δ [26,36−40], and

La1-xSrxMn1-yCryO3-δ [8,41] were reported. Transitions of LaMn1-xCrxO3-δ are complex as they

depend on temperature, composition and oxygen partial pressure. Consistency among

transition data for La1-xSrxCrO3-δ and LaMn1-xCrxO3-δ prevails, whereas diversities exist

regarding the transitions in La1-xSrxMn1-yCryO3-δ . Thus, in terms of the applicability of the

new database for SOFC the authors omit structural transitions in the modeling. Magnetic

transitions have been well reproduced by an ordering-model[42,43] for LaCrO3[5]. However we

did not obtain satisfying results in higher-order perovskites, most likely due to interactions

that cannot be reproduced by the model. As the magnetic transitions are low temperature

features, their modeling was omitted without consequences for the applicability of the

database for SOFC.

4.4.3 Modeling and optimization

Sr-Cr-O oxide:

The sublattice models (Sr2+)(Cr6+)(O2-)4 and (Sr2+)(Cr3+)2(O2-)4 are employed for the

descriptions of SrCrO4 and SrCr2O4. (Sr2+)8/3(Va)1/3(Cr6+)2/3(O2-)8/3(Cr5+)4/3(O2-)16/3 and

(Sr2+)(O2-)1(Sr2+)(Cr4+)(O2-)3 were chosen for Sr2.67Cr2O8 following the proposed formula[19]

and for the Ruddlesden-Popper phase Sr2CrO4, accounting for the structural feature of

alternating rocksalt- and perovskite layers of the latter. Gibbs energy functions of Sr-Cr-

oxides were formulated as

[44] [4] [45]12

y z 2 3 2

gasSER SER SER(Sr) (Cr) (O) Sr Cr O SrO Cr O O

° ° ° °− − − = + + + +x y z xG H H H x G y G v G A BT (4.4.1)

v = 0.75, 0, 7/6, and 0.25 for SrCrO4, SrCr2O4, Sr2.67Cr2O8, and Sr2CrO4 respectively. SERaH is

the standard enthalpy of the stable state of element a at 298.15 K and 105 Pa[45]. A and B are

adjustable parameters; their optimization with the following experimental phase diagram and

thermodynamic data using the PARROT module of the Thermocalc software[46] resulted in

the lowest error between model and experiments: Gibbs energies of formation of SrCrO4[11,12]

and phase stabilities of SrCr2O4 and Sr2CrO4 investigated by equilibration experiments of

different mixed oxide compositions under controlled atmospheres[11], and the equilibrium

Sr2.67Cr2O8+SrCrO4+Cr2O3 as a function of temperature and oxygen partial pressure[11,12]. All


138

reported phase equilibria[11] are correctly reproduced by the model. Optimized parameters and

calculated and experimental thermodynamic data are listed in Table 4.4.1 and 4.4.2.

Table 4.4.1 Optimized model parameters

SrCrO4 SrCrO4

Sr2CrO4 Sr2CrO4

SrCr2O4 SrCr2O4

Sr2.67Cr2O8 Sr2.67Cr2O8

1 3

Sr - Cr oxides273771 J; 131.6 J145000 J; 50 J

98000 J; 95.5 J508507 J; 219 J

La Sr CrO5 6GS4O GS3V 1 6G3+ 4+La :Cr :Va

− −

°

= − == − == = −

= − =

= − +x x

A BA BA BA B

Gδ

[5] [45]

[5]

S4V GRPRV 1.5

5 6GS4O GS3V 1 6GS4V GRPRV

GS3V 1 6GS4O 1 6GS4V

GS3V 5 6GS4O 5 6GS4V

2

3+ 4+ 2-

2+ 3+ 2-

2+ 3+

gasO

La :Cr :O

Sr :Cr :O

Sr :Cr :Va

°

°

°

°

+ −

= − + +

= + −

= − +

G

G

G

G

Table 4.4.2 Calculated and experimental thermodynamic data

2

2 3 2 4-1

-1 [12]

-1 [10]

2.67 2 8 4 2 3

SrO +1 2Cr O + 3 4O SrCrO

273.774 0.13152 kJmol this work, calc.213.050 0.106904 kJmol ,851 1116 K273.825 0.2 0.13157 kJmol ,950 1280 K

Sr Cr O SrCrO Cr O

265.859

°

°

°

=

Δ = − +Δ = − + −Δ = − ± + −

+ +

Δ = −O

G TG TG T

μ2

2

-1

-1 [11]

-1 [10]

2 3 2 3 2 2 1 3

0.15832 kJmol this work, calc.262.340 0.15553 kJmol ,1073 1473 K276.767 0.166 kJmol ,1080 1380 K

(1 ) 2La O SrO 1 2Cr O 4O 2 La Sr CrO

0.1, 0, 2000 K, 93− −

°

+Δ = − + −Δ = − + −

− + + + − =

= = = Δ = −

O

O

x x

TT

Tx x x O

x T Gδ

μμ

δδ -1

-1[20]

.3 kJmol this work, calc.85.7 kJmol°Δ = −G

-1

-1[20]

-1

0.2, 0, 2000 K, 102.4 kJmol this work, calc. 88.7 kJmol

0.3, 0, 2000 K, 109.4 kJmol this work, calc.

°

°

°

= = = Δ = −Δ = −

= = = Δ = −

x T GG

x T G

δ

δ-1[20]

-1

-1[21]

-1

93.5 kJmol0.1, 0, 298 K, 65.2 kJmol this work, calc.

67.88 kJmol0.1, 0.04, 298 K, 55.1 kJmol this

°

°

°

°

Δ = −= = = Δ = −

Δ = −= = = Δ = −

Gx T H

Hx T H

δ

δ-1[21]

-1

° -1[21]

work, calc. 59.15 kJmol

0.2, 0, 298 K, 56.8 kJmol this work, calc. Δ H = 50.54 kJmol

0.2,

°

°

Δ = −= = = Δ = −

−=

Hx T H

x

δ

δ -1

-1[21]

-1

0.09, 298 K, 34.0 kJmol this work, calc. 34.76 kJmol

0.3, 0, 298 K, 48.3 kJmol this work, calc.

°

°

°

= = Δ = −Δ = −

= = = Δ = −

T HH

x T Hδ-1[21]

-1

-1[21]

36.72 kJmol0.3, 0.11, 298 K, 20.6 kJmol this work, calc.

20.48 kJmol

°

°

°

Δ = −= = = Δ = −

Δ = −

Hx T H

Hδ


139


It is essential for a consistent description of the perovskite phase that defects that occur in the

structure in low-order systems remain on the same sites at the extension to higher order; this

is achieved by using the same model. We adopt the description (A,Va)(B,Va)(O-2,Va)3 with

A, B = cations and Va = vacancies[6] using the compound energy formalism[47]. The molar

Gibbs energy of the perovskite phase then reads

: : ln ln 3 lnprv ° E prvm m

° ⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

= + + + +∑∑∑ ∑ ∑ ∑i j i i j jk i j k k ki j k i j k

G y y y G RT y y y y y y G (4.4.2)

where yi is the site fraction of each cation and Va on the A-sublattice, yj is the site fraction of

each cation and Va on the B-sublattice, and yk is the site fraction of O2- and Va on the anion

sublattice. R = 8.31451 J mol-1 K-1. The second-last term accounts for the configurational

entropy of mixing. The last term describes the excess Gibbs energy of mixing. It can be

accounted for by introducing interaction parameters. The parameters of the compound energy

formalism are the Gibbs energies of the end-member compounds : :°

i j kG . Typical compositions

of Sr-doped lanthanum manganites used for SOFC cathodes, e.g. La0.8Sr0.2MnO3-δ are

rhombohedral at SOFC operating temperatures (T=1073 K to 1273 K), and small amounts of

Cr brought into the cathode unlikely lead to a change of the structure. Thus it is reliable to

take the Gibbs energies of the compounds of rhombohedral perovskite from [5] for the model.

Using the above model and the proposed defect chemistry[22-24] the sublattice formula for

La1-xSrxCrO3-δ reads (La3+,Sr2+,Va)(Cr3+,Cr4+,Va)(O2-,Va)3. The molar Gibbs energy °G of

La1-xSrxCrO3-δ is uniquely defined as follows: °Gs of the endmembers (La3+)(Cr3+)(O2-)3,

(La3+)(Cr3+)(Va)3, (La3+)(Va)(O2-)3, (La3+)(Va)(Va)3, (Sr2+)(Va)(O2-)3, (Sr2+)(Va)(Va)3,

(Va)(Va)(O2-)3, and (Va)(Va)(Va)3 and ternary interaction parameters are adopted[5,6,48],

°G(Sr2+)(Cr4+)(Va)3

[44] [4] [45]:

1 5GS4V2 42+ 4+3 2 3 2

gasSER SERSrCrVa Sr Cr SrO Cr O OSr :Cr Va

° ° ° ° °− − = = = + −G H H G G G G (4.4.3)

is chosen as reference, and A and B parameters of °G of two neutral compounds


140

[44] [4] [45]

3 GS4O1 12 4

2+ 4+ 23

2 3 2

SER SER SERSrCrO Sr Cr O Sr :Cr :O

gasSrO Cr O O

−° °

− − −

° ° °

= =

= + + + +

G H H H G

G G G A BT (4.4.4)

[44] [4]

2.5 GS3V5 1 5 5 1 1 1ln ln6 6 6 6 6 6 2

2.5 0.5

2+ 3+ 2 2+ 3+ 2 3

SER SER SERSrCrO Va Sr Cr O

SrO Cr OSr :Cr :O Sr :Cr :Va−

°− − −

° ° ° °⎛ ⎞⎜ ⎟⎝ ⎠

=

= + + + = + + +

G H H H

G G RT G G A BT (4.4.5)

are optimized with all available experimental data of the perovskite phase. Eq. 4.4.4 denotes

°G (Sr2+)(Cr4+)(O2-)3, with A = 27027 and B = −69.6. A = 136453 and B = −91.2 for

2.5 0.5SrCrO Va°G in Eq. 4.4.5. °Gs of the remaining endmembers (La3+)(Cr4+)(Va)3,

(La3+)(Cr4+)(O2-)3, (Sr2+)(Cr3+)(O2-)3, and (Sr2+)(Cr3+)(Va)3 are obtained by conversions of

reciprocal equations that are set zero[48] and are listed in Table 4.4.1 (p. 138).

Though structure-chemical information of site occupancies in LaMn1-xCrxO3-δ perovskite is

missing, it is reliable to allow Cr4+ on the B-site: as Cr4+ exists in nonstoichiometric

lanthanum chromite perovskite[5], it is expected that it is not removed from the structure if the

phase is doped. Thus for LaMn1-xCrxO3-δ we propose the sublattice formula

(La3+,Va)(Mn2+,Mn3+,Mn4+,Cr3+,Cr4+,Va)(O2-,Va)3. All endmember compounds have been

defined in the assessed subsystems. The regular interaction parameter 0L(La3+:Cr3+,Mn3+:O2-)

accounting for interactions between Cr and Mn cations is fitted to experimental

nonstoichiometries[26]; 0L(La3+:Cr3+,Mn3+:O2-) = +9421 J.

The sublattice formula of the quinary perovskite reads

(La3+,Sr2+,Va)(Mn2+,Mn3+,Mn4+,Cr3+,Cr4+,Va)(O2-,Va)3. All endmembers have been defined in

the assessed subsystems.

4.4.4 Results and discussion

The reproduction of experimentally determined Gibbs energies[21] and enthalpies of

formation[22], solid solubilities[18,20], and nonstoichiometries[23,24] of La1-xSrxCrO3-δ, and phase

equilibria in the La-Sr-Cr-O oxide system by the modeling is satisfying as shown in Table

4.4.2 (p. 138), and in Figs. 4.4.1 and 4.4.2 (next page).


141

Fig. 4.4.1 LaO1.5-SrO-CrO1.5 system calculated at T = 1223 K in air atmosphere (solid lines)

with experimental data[17] included (symbols). prv = La1-xSrxCrO3-δ. Calculated phase

equilibria are the same as in[17]. Filled circles, blank circles, and circles with crosses denote

single phase, two phase, and three phase equilibria.


142

Fig. 4.4.2, p. 141 Calculated (lines) and experimental (symbols)[22,23] nonstoichiometries of

La1-xSrxCrO3-δ at different temperatures for x = 0.1, 0.2, 0.25, and 0.3 as a function of oxygen

partial pressure.

The calculated isothermal section of the La-Mn-Cr-O oxide system at T = 1273 K in air is

presented in Fig. 4.4.3.

Fig. 4.4.3 LaO1.5-MnOx-CrO1.5 system calculated at T = 1273 K in air atmosphere. α-spl =

tetragonally distorted Cr-Mn-spinel, β-spl = cubic Cr-Mn-spinel, prv = LaMn1-xCrxO3-δ.

The calculated nonstoichiometries of La1-xSrxCrO3-δ are in good agreement with the

experimental values at higher temperatures, as shown in Fig. 4.4.4 (next page). However it

was not possible to reproduce the nonstoichiometries at T = 1073 K and 973 K. Deducing

from the change of δ from T = 1273 K to 1173 K the measured increase of δ from T = 1173 K

to

1073 K might be too small, possibly caused by equilibration difficulties due to slow diffusion.


143

Fig. 4.4.4 Calculated (lines) and experimental (symbols)[27] nonstoichiometries of

LaMn0.9Cr0.1O3-δ at different temperatures as a function of oxygen partial pressure.

To approximate the absence of Cr4+[27] in quinary perovskite, it would be necessary to give

large positive values to the regular interaction parameters 0L(Sr2+:Cr3+,Mn3+:O2-) and 0L(Sr2+:Cr4+,Mn3+:O2-). Experimentally determined nonstoichiometry of LaCrO3 indicates the

existence of some Cr4+, and the conclusion of missing Cr4+[27] is not based on a direct

chemical analysis of Cr valencies. We believe that complete removal of Cr4+ from the

perovskite structure is unlikely. Thus we stick to a model without interaction parameters.

Experimental findings[8,28] are in line with our calculations.

4.4.5 Conclusions

The thermodynamic La-Sr-Mn-Cr-O oxide database has been obtained by combining

thermodynamic assessments of oxide subsystems. We propose the model

(La3+,Sr2+,Va)(Mn2+,Mn3+,Mn4+,Cr3+,Cr4+,Va)(O2-,Va)3 for the quinary perovskite phase.

Optimized by experiments in pseudoternary and pseudoquaternary oxide subsystems, this

model allows the quantitative calculation of defects as a function of composition, temperature,

and oxygen partial pressure. The new database is adapted for quantitative calculations of


144

phase equilibria and defect chemistry in a Sr-doped lanthanum manganite SOFC cathode

poisoned by chromium.

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Thermodynamic calculations of impacts of chromium on LSM cathodes

148

5 Thermodynamic calculations of impacts of chromium on Sr-

doped lanthanum manganite (LSM) cathodes for solid oxide

fuel cells (SOFC)

E. Povoden, T. Ivas, M. Chen, and L.J. Gauckler, to be submitted

A new thermodynamic database is used for thermodynamic equilibrium calculations in a Sr-

doped lanthanum manganite cathode (LSM) affected by chromium at typical operation

temperatures of 1073 K and 1273 K as a function of oxygen partial pressure. From the results

of these calculations it is concluded that the processes of chromium poisoning of solid oxide

fuel cells (SOFC) are partly explicable by thermodynamics, and partly they occur under

kinetic control: at the cathode/electrolyte interface of a Cr-“poisoned” cell Cr-Mn spinel

exists in thermodynamic equilibrium with LSM, whereas Cr2O3 is metastable. The spinel

formation goes along with increasing Mn2+ in LSM under decreasing oxygen partial

pressures.

From the thermodynamic calculations structural chemical changes in the cathode perovskite

caused by the interaction with chromium can be predicted: it is shown that the interaction of

chromium with the LSM cathode leads to a change of the defect chemistry of the perovskite

phase. In particular the concentrations of cation and oxygen vacancies are smaller than in an

LSM without chromium under decreased oxygen partial pressure at 1273 K. This has

consequences for the electrochemical properties of the cell: the electronic conductivity of the

cathode will decrease, and the contribution of a vacancy mechanism for the oxygen diffusion

in LSM is thermodynamically hampered in the presence of chromium at high temperature and

high current loads.

Even though the chromium problem cannot be solved satisfactorily by varying the cathode

composition or the SOFC operating conditions, the deterioration of the cell performance is

expected to be less pronounced when the cell is operated at lower temperatures and current

loads. Proper strategies to prevent the problem of chromium “poisoning” are proposed.

Thermodynamic calculations of impacts of Cr on LSM cathodes

149

5.1 Introduction

Chromium-containing metallic interconnects are commonly used in planar-design solid oxide

fuel cells (SOFC) due to their high oxidation resistance, thermal stability, mechanical

strength, good electronic and negligible ionic conductivity, as well as low fabrication costs.

However high-valent gaseous Cr-oxide and chromium-oxyhydroxides can diffuse under fuel-

cell operation conditions from the interconnect into the cathode up to the cathode-electrolyte

interface, where they cause the degradation of the cell by detrimentally affecting the O2-

adsorbtion, -reduction, and -diffusion process[1]. In the last decade a lot of efforts were made

to elucidate the degradation mechanisms, though partly with conflicting results.

Consequences of Cr poisoning have been investigated specifically in (La1-xSrx)MnO3-δ (LSM)

perovskite-structured cathodes. For the mechanism of chromium poisoning two models have

been proposed: 1) reduction of gaseous CrO3(g) in dry atmosphere or chromium

oxyhydroxide(g) in wet atmosphere under polarization[2-6] and 2) chemical dissociation of Cr-

species on the LSM surface[7-14].

Ad 1) In an LSM cathode the reduction of CrO3(g) is expected to be localized at the triple

phase boundary, where the reaction partners for the reduction, electron-donating LSM and

oxygen-accepting yttrium-stabilized zirconia (YSZ) are available[15]. This reduction reaction

would compete with the oxygen reduction and lead to blocking of the active sites at the triple

phase boundary (TPB).

Ad 2) In contrast to 1) it was proposed that gaseous Cr-species would be chemically

dissociated to LSM under the polarization of the cell. This affinity would be linked to the

creation of free Mn2+ on the surface of LSM due to the oxygen partial pressure gradient

caused by the polarization. Mn2+ would serve as agent for the formation of Cr-Mn-O nuclei

that would be able to migrate to the triple phase boundary and further into the electrolyte.

Consequently Cr-Mn spinel and Cr2O3(s) would form, associated to these nuclei. The chemical

dissociation approach is coherently based on the interpretation of a large number of

impedance spectra.

Both groups of researchers agree that without polarization Cr is randomly deposited inside the

cathode, and no Cr2O3(s) is formed. On the other hand the electrochemical reduction of CrO3(g)

was rejected by the authors favoring the chemical dissociation approach.


150

In the critical assessment in chapter 1.3.6 it was concluded that doubtless reasons to reject the

reduction approach do not exist. One critical point concerns the extension of dense Cr2O3-

layers into the YSZ electrolyte[6]: this phenomenon can be explained best by continuous

feeding of an initial Cr2O3-layer with CrO3(g), the latter becoming reduced at a new TPB

consisting of YSZ and electron-donating Cr2O3(s). On the other hand this process cannot be

explained satisfactorily by using the chemical dissociation approach.

Even though particularly the early stages of chromium “poisoning” occur in thermodynamic

non-equilibrium, the system SOFC develops towards thermodynamic equilibrium by time.

This is reflected by a flattening of the curves that reflect the performance deterioration as a

function of time, such as the curves of voltage drop and overpotential loss. Thus

thermodynamic calculations allow interpretations of the phase equilibria that result from the

interactions between LSM and chromium, as well as changes of the phase chemistry that are

associated with the chromium contamination of LSM cathodes.

5.2 Method

The La-Sr-Mn-Cr-O oxide database is used for the following thermodynamic calculations:

phase equilibria in Cr-contaminated LSM (in the following denoted as LSM(Cr)), phase

compositions of LSM(Cr) and Cr-Mn spinel, defect concentrations of LSM(Cr), as well as

driving forces for the formation of Cr2O3 were calculated with the poly-module of the

ThermoCalc software[16].

The following model descriptions were used: for the Cr-contaminated cathode perovskite with

the general formula ABO3 a proper sublattice description reads

(La3+,Sr2+,Va)(Mn4+,Mn3+,Mn2+,Cr4+,Cr3+,Va)(O2-,Va)3, for tetragonally distorted spinel

(Mn2+)(Mn3+,Cr3+)2(O2-)4 was chosen[17], for cubic spinel, AB2O4,

(Mn2+,Cr2+)(Mn3+,Cr3+)2(O2-)4 was used[18], and for Cr2O3 (Cr2+,Cr3+)2(Cr3+,Va)(O2-)3 was

taken[18]. Uptake of Cr in LSM is expected, as a complete solid solubility of Cr in LSM has

been shown experimentally[19].

For proper thermodynamic calculations of phase equilibria thermodynamic conditions need to

be set that reflect the conditions of the chromium contamination of SOFC: the bulk pressure

(room pressure, 101325 Pa), the operation temperature (typically from T = 1073 K to

1273 K), the oxygen partial pressure, the cathode composition, and the amount of chromium.


151

The oxygen partial pressure at the interconnect-cathode interface is air. Under current load it

is expected that the oxygen partial pressure will strongly decrease close to the cathode-

electrolyte interface in the triple phase boundary (TPB) region where the oxygen reduction in

LSM takes place: the oxygen partial pressure at the cathode-electrolyte interface, 2O (i)

p can be

approximated from the measured cell voltage of a Pt/LSM/YSZ/Ni-Cermet/Pt solid oxide cell

and the fuel composition by using the equation for the overall electromotive force E of the

cell:

2

2

O

Oln

4(i)

(an)

=pRTE

F p (5.2.1)

R = 8.31451 J mol-1 K-1, F = 96485.309 C mol-1 and 2O (an)

p is given by the ratio of H2-H2O in

the fuel. From a measured cell voltage of 0.7 V[2] at T = 1173 K (fuel: 97 vol.% H2, 3 vol.%

H2O) and a high current load of 300 mA cm-2 a strong decrease of the oxygen partial pressure

at the oxygen reduction sites is expected, 2O (i)

p ≈ 0.01 Pa. As we are interested in the

influences of chromium throughout a cathode under realistic operation conditions of SOFC,

results of the thermodynamic calculations are presented for 2Op ≤ 21278 Pa ≥ 0.01 Pa.

Several LSM cathode compositions can be found in the literature. Part of them is cation

stoichiometric, and part of them has excess Mn that is known to prevent unwanted formation

of electrochemically isolating zirconate at the cathode/electrolyte interface. In this study two

cathode compositions are used for the thermodynamic calculations:

La0.9Sr0.1MnO3-δ and (La0.8Sr0.2)0.9MnO3-δ. The sublattice model for this perovskite phase[20]

allows the formation of vacancies on each site and changing valencies of Mn as a function of

temperature and oxygen partial pressure.

The amount of chromium in the system is defined by the partial pressure of the Cr-gas phase:

exp⎛ ⎞= ⎜ ⎟⎝ ⎠

CrCr

RTp μ

(5.2.2)

This means that by knowing the partial pressure of the Cr-gas phase in the TPB region, it is

possible to calculate the thermodynamics of the chromium contamination. The problem is that

the definite amount of gas that contributes to the degradation phenomena is not known


152

exactly, as only a fraction of the Cr-gas that evaporates from the Cr2O3 scale on the Cr-alloy

interconnect interacts with LSM or is reduced. Fortunately the amount of deposited Cr in a

degraded LSM cathode has been analyzed as a function of distance from the cathode/YSZ

electrolyte interface[21], and the combined data of X(Cr) and the oxygen partial pressure at the

TPB fix the chemical potential of Cr. The amount of deposited Cr close to the LSM(Cr)/YSZ

interface was about 3 wt.% after a long cell test of 300 h at T = 1073 K. If one assumes that

the 2Op under the test conditions was 1 Pa at the the LSM(Cr)/YSZ interface (normal cell

performance), the chemical potential of the Cr-gas phase can be calculated. Even though it is

clear that the chemical potential of Cr will change if the amount of evaporated Cr from

different interconnect materials is different, the Cr-gas reservoir is assumed to be in a

saturated state due to “unlimited” supply from the interconnect during the cell performance,

and thus its chemical potential is fixed in the thermodynamic calculations. This simplification

is reasonable, as in all investigated cell tests with LSM and Cr-alloy interconnects the

degradation was similar, so that changing chromium amounts due to different interconnect

alloys are obviously not detrimental for the cell degradation.

H2O (operation of SOFC in humid air) is not considered in the calculations, as neither

hydroxides nor solubilities of hydrogen or OH− were included in the La-Sr-Mn-Cr-O oxide

database.

5.3 Results

5.3.1 Thermodynamic calulcations of La0.9Sr0.1MnO3 contaminated by chromium

Fig. 5.3.1 (next page) shows phase fractions in Cr-“poisoned” La0.9Sr0.1MnO3-δ at constant

chemical potential of CrO3, μ(CrO3) = −300000 J mol-1 referred to 100000 Pa of CrO3(g) as a

function of oxygen partial pressure at T = 1273 K and 1073 K, and in Figs. 5.3.2 (next page)

and 5.3.3 (p. 153) phase equilibria are indicated: the cathode remains single phase at 2Op >

102.75 Pa. By decreasing the oxygen partial pressure, tetragonally distorted Mn3O4 spinel

(t-sp), the manganese endmember of the Cr-Mn spinel solid solution phase forms.


153

Fig. 5.3.1 phase fractions in Cr-“poisoned” La0.9Sr0.1MnO3-δ as a function of oxygen partial

pressure at T=1273 K and 1073 K at μ(CrO3) = −300000 J mol-1

Fig. 5.3.2 Phase equilibria in Cr-“poisoned” La0.9Sr0.1MnO3-δ and defect concentrations of

La0.9Sr0.1(Mn,Cr)O3-δ as a function of oxygen partial pressure at T = 1273 K and

μ(CrO3) = −300000 J mol-1. A, B, and C denote sublattices of the perovskite phase, with A

and B standing for the cation sublattices and C standing for the oxygen sublattice. Vertical

lines indicate boundaries between different phase equilibria


154

Fig. 5.3.3 Phase equilibria in Cr-“poisoned” La0.9Sr0.1MnO3-δ and defect concentrations of

La0.9Sr0.1(Mn,Cr)O3-δ as a function of oxygen partial pressure at T = 1073 K and

μ(CrO3)= −300000 J mol-1. The vertical line indicates the boundary between phase equilibria

At T = 1273 K (Figs. 5.3.1, p. 153 and 5.3.2, p. 153), tetragonally distorted spinel remains

stable to 2Op = 10-0.4 Pa. At lower

2Op cubic Mn-Cr spinel forms. At 1073 K (Figs. 5.3.1, p.

152 and 5.3.3), tetragonally distorted spinel remains stable to 2Op = 100.75 Pa, followed by the

formation of cubic spinel at lower 2Op . This means that by decreasing the oxygen partial

pressure from 2Op = 104.3, the pressure of air, to 10-1.5 Pa, the amount of spinel in the

contaminated cell increases. At 1073 K Cr-Mn spinel formation is less pronounced, and Cr-

Mn spinel formation starts at lower 2Op than at 1273 K.

To find out about the structural chemical changes in the cathode perovskite caused by reaction

with chromium, the fractions of species in a specific sublattice (site fractions) are calculated at

T=1273 K and 1073 K (plots in Figs. 5.3.2, p. 152 and 5.3.3) as a function of 2Op . The results

are compared with the calculated site fractions in a cathode with a very small chemical


155

potential of Cr, μ(CrO3) = −106 J mol-1 that means with practically no Cr (Figs. 5.3.4 to

5.3.5).

Fig. 5.3.4 Defect concentrations in La0.9Sr0.1MnO3-δ

as a function of oxygen partial pressure at T=1273 K.

Fig. 5.3.5 Defect concentrations in La0.9Sr0.1MnO3-δ

as a function of oxygen partial pressure at T = 1073 K.


156

In general defect concentrations of the Cr-contaminated LSM differ from the defect

concentrations in LSM without Cr at a high temperature of 1273 K: with Cr the

concentrations of vacancies on the A- and B-sublattices decrease stronger by decreasing the

oxygen partial pressure. The increase of oxygen vacancies by decreasing the oxygen partial

pressure on the other hand is weaker when chromium is present. At T = 1273 K and 2Op =

1 Pa, which is the expected 2Op at the LSM/YSZ interface at 250 mA cm-2 current load, the

site fractions of cation vacancies on the A- and B-sublattices for LSM(Cr) are y(Va)A =

1.98x10-6, y(Va)B=4.3x10-6, whereas in LSM y(Va)A = 3.086x10-6 and y(Va)B = 7.096x10-6 are

calculated. The concentration of oxygen vacancies at 1 Pa and T = 1273 K in LSM(Cr) is

slightly higher than in LSM, y(Va)C = 3.01x10-5 in LSM(Cr),compared to y(Va)C = 2.57x10-5

in LSM. A pronounced drop of cation and oxygen vacancies is calculated at 1273 K and 2Op =

10-1 Pa, the expected oxygen partial pressure at the TPB under a high current load of 300 mA

cm-2: the concentration of oxygen vacancies in LSM(Cr) is y(Va)C = 3.39x10-5, compared to

y(Va)C = 9.48x10-5 in LSM. This means that if the oxygen partial pressure at the LSM/YSZ

interface strongly decreases the vacancy concentrations will drop significantly.

The concentrations of Cr3+ and Cr4+ in LSM(Cr) increase when the temperature increases and

the oxygen partial pressure decreases.

The calculated compositions of tetragonally distorted spinel (Fig. 5.3.6 a, next page) and

cubic spinel (Fig. 5.3.6 b) formed during chromium “poisoning” show a strong dependence

upon the oxygen partial pressure: only under low oxygen partial pressures a significant

amount of chromium is found in the spinel phase, whereas at higher oxygen partial pressures

the spinel phase has a composition close to Mn3O4. At T = 1073 K the spinel phase contains

less chromium than at T = 1273 K.


157

Fig. 5.3.6 Calculated site fractions of ions in cubic spinel (6 a) and tetragonally distorted

spinel (6 b) formed during chromium “poisoning” at T = 1273 K and 1073 K

5.3.2 Thermodynamic calculations of (La0.8Sr0.2)0.9MnO3-δ contaminated by chromium

From Fig. 5.3.7 it is obvious that in this widely used LSM composition Cr-“poisoning” leads

to the formation of additional phases already at high oxygen partial pressures: A small amount

of about 5 mol% of the pure spinel endmember, tetragonally distorted Mn3O4 (t-sp) is

expected to form. At T = 1073 K Mn2O3 is stable in a Cr-contaminated LSM cathode with

excess Mn in air.

Fig. 5.3.7 phase fractions in Cr-“poisoned” (La0.8Sr0.2)0.9MnO3-δ as a function of

oxygen partial pressure at T = 1273 K and 1073 K and μ(CrO3) = −300000 J mol-1


158

In Fig. 5.3.8 the compositional changes of cubic spinel are plotted as a function of oxygen

partial pressure at T = 1273 K. In general, the compositions of the spinel phases formed

during chromium “poisoning” become richer in Cr under more reducing conditions, as in the

case of cation-stoichiometric LSM.

Fig. 5.3.8 Calculated site fractions of ions in cubic spinel formed

during chromium “poisoning” at T = 1273 K

It is interesting whether the consequences of chromium for the concentrations of defects in

LSM(Cr) with excess Mn are more or less pronounced than in cation-stoichiometric

LSM(Cr): Phase equilibria and defect concentrations in a (La0.8Sr0.2)0.9MnO3-δ cathode are

shown in Fig. 5.3.9 (next page).


159

Fig. 5.3.9 Phase equilibria in Cr-“poisoned” (La0.8Sr0.2)0.9(Mn,Cr)O3-δ and defect

concentrations in (La0.8Sr0.2)0.9(Mn,Cr)O3-δ as a function of oxygen partial pressure at T =

1273 and μ(CrO3) = −300000 J mol-1. The vertical line indicates the boundary between

different phase equilibria

Fig. 5.3.10 (next page) is a comparison of defect concentrations of (La0.8Sr0.2)0.9MnO3-δ with

Cr (broken lines in Fig. 5.3.10) and without Cr (solid lines in Fig. 5.3.10) at 1273 K. The

vacancy concentrations on the A-sites and B-sites of the Cr-contaminated perovskite phase

are basically in the middle between these vacancy concentrations in LSM. In LSM(Cr) the

concentrations of these cation vacancies drop strongly at low 2Op . Mn2+ is higher in LSM(Cr)

than in LSM at higher 2Op , and the concentration of oxygen vacancies is lower in LSM(Cr)

than in LSM at relatively high and low 2Op .


160

Fig. 5.3.10 Defect concentrations in (La0.8Sr0.2)0.9(Mn,Cr)O3-δ (dashed lines) and

(La0.8Sr0.2)0.9MnO3-δ (solid lines) as a function of oxygen partial pressure at T = 1273.

Calculated concentrations of all species in LSM(Cr) and tetragonally distorted spinel in

equilibrium are listed in Table 5.3.1.

Table 5.3.1 Compositions of LSM(Cr) and spinel in equilibrium at different T at pO2=1

Pa with and without Cr.

5.3.3 Thermodynamic testing of LSM with Mn-deficiency

Only in a cathode with Mn-deficiency it is possible to push the formation of additional phases

towards a lower oxygen partial pressure: for the case of La0.871Sr0.148Mn0.947O3-δ spinel

formation becomes important only at2Op < 0.1 Pa, as it is illustrated in Fig. 5.3.11, next page.


161

Fig. 5.3.11 Phase fractions in a Cr-“poisoned” Mn-deficient LSM as a function of

oxygen partial pressure at T = 1273 and 1073 K and μ(CrO3) = −300000 J mol-1.

The influence of chromium on defect concentrations in La0.871Sr0.148(Mn,Cr)0.947O3-δ is

illustrated in Fig. 5.3.12, next page: The concentration of oxygen vacancies in

La0.871Sr0.148(Mn,Cr)0.947O3-δ is half of an order of magnitude higher than in

(La0.8Sr0.2)0.9MnO3-δ at high oxygen partial pressures. However, after reaching a plateau at

2Op = 103 Pa, y(Va)C even decrease slightly towards lower 2Op , and the concentration of

oxygen vacancies is almost an order of magnitude lower then in (La0.8Sr0.2)0.9MnO3-δ at 2Op =

10-1 Pa.


162

Fig. 5.3.12 Phase equilibria in Cr-“poisoned” Mn-deficient LSM and defect concentrations in

La0.871Sr0.148(Mn,Cr)0.947O3-δ as a function of oxygen partial pressure at T = 1273 K and

μ(CrO3) = −300000 J mol-1 (solid lines). Dashed lines indicate the defect concentrations in

(La0.8Sr0.2)0.9MnO3 without chromium. Vertical lines indicate boundaries between different

phase equilibria

5.3.4 Formation of Cr2O3

This phase was not found in the thermodynamic calculations, and thus its formation is

kinetically controlled. One can get an idea about the degree of metastability of a phase by

calculating its thermodynamic driving force. This is the amount of energy that is needed to

bring the phase to its stable state. The more negative the driving force, the more energy is

needed to stabilize the phase, and the driving force for the formation of the phase is low. If the

driving force is 0, the phase is thermodynamically stable. In Fig. 5.3.13 (next page) the

driving force of Cr2O3 is plotted as a function of temperature at two different 2Op in a LSM

cathode with excess Mn under Cr-“poisoning”.


163

Fig. 5.3.13 Driving force of Cr2O3 as a function of temperature

at different 2Op at μ(CrO3) = −300000 J mol-1.

The driving force for the formation of Cr2O3 is less negative at higher oxygen partial

pressures.

5.4 Discussion

In the following the results of the thermodynamic calculations are compared to experimental

findings on chromium poisoning from the literature. Interpretations are given, which of the

chromium poisoning mechanisms occur under thermodynamic control.

By carrying out equilibrium calculations of state-of-the-art LSM cathodes with the

compositions La0.9Sr0.1MnO3-δ and (La0.8Sr0.2)0.9MnO3-δ at constant chromium in the gas phase

it was tested if spinel formation would be favored thermodynamically under low oxygen

partial pressure, i.e. close to the electrode-electrolyte interface under polarization conditions.

The calculations showed that this is indeed the case. As the A-sublattice of the spinel is

completely filled by Mn2+ under the cell operation conditions, and the only source for this

species is LSM, it is obvious that spinel formation will be associated with increasing Mn2+ in

LSM. Thus, as Mn2+ in LSM increases as a function of decreasing 2Op , also the amount of


164

spinel formed is higher at low oxygen partial pressure. Cr-gas reveals increasing affinity to

LSM towards the electrode-electrolyte interface: both Cr solid solution in LSM and spinel

formation increase under decreasing the oxygen partial pressure.

From the calculation it is interpreted that the spinel phase that forms under Cr-“poisoning” of

the cathode will contain a high amount of Mn, if the oxygen partial pressure at the

cathode/electrolyte interface is about 1 Pa. Only at lower 2Op significant Cr is incorporated in

the spinel phase, with the stoichiometric MnCr2O4 phase forming at about 2Op = 10-1 Pa.

Though spinel formation is thermodynamically driven in Cr-contaminated SOFC, it seems

that spinel formation per se is not one of the keys of severe cell degradation due to chromium,

but the affinity of Cr-gas to the LSM surface, as even very small Cr contamination in the ppm

range apparently leads to a dramatic decrease of the oxygen diffusion in LSM[22].

From impedance spectroscopy analyses it was consistently concluded that the oxygen

diffusion is severely influenced by chromium. The thermodynamic calculations showed that

Cr interacting with LSM leads to a change of the defect chemistry of the perovskite phase,

and particularly to a decreasing amount of oxygen vacancies at high temperatures and low

oxygen partial pressures. As the formation of oxygen vacancies in LSM is inhibited, oxygen

diffusion to the triple phase boundary is retarded. The results of the thermodynamic defect

chemistry calculations of LSM(Cr) thus indicate that the deterioration of the oxygen diffusion

is higher under at decreased oxygen partial pressures reflecting high current loads.

Cr2O3 is found in degraded SOFC, particularly under high current load. However this phase

was not found in the thermodynamic calculations, and its driving force remains negative

under SOFC operating conditions. This means that its formation is kinetically controlled.

Even though Cr2O3 is not a thermodynamically stable phase in Cr-contaminated SOFC, a

strong tendency exists for CrO3(g) to be reduced to Cr2O3(s) at the TPB, as the reduction

reaction has a large negative ΔG. It was also mentioned earlier that a high tendency for the

precipitation of Cr2O3(s) from CrO3(g) exists[23]. In addition to the adsorption process it is

expected that a great many of Cr-gas molecules are driven further to the energy valley for

their reduction, namely the TPB. Thus it is non-contradictory that coupling of Cr-gas to LSM

and subsequent spinel formation at the LSM surface, and the reduction of CrO3 (g) at the TPB

leading to the metastable reduction product Cr2O3(s) occur simultaneously. An alternative way

to form Cr2O3 was discussed by Konysheva et al.[24]: The kinetic decomposition of the spinel

phase may occur in an oxgen partial pressure gradient due to different mobilities of Mn2+ and

Cr3+.


165

In addition to the inhibiting of oxygen diffusion to the TPB and blocking of active triple phase

boundary sites by the thermodynamically controlled formation of spinel and the kinetically

driven formation of Cr2O3(s) and thus retarded diffusion of oxygen ions into the electrolyte,

further unwanted consequences of chromium poisoning can be ascribed to the low electrical

conductivity of Cr2O3[25]. Also Cr-Mn-spinel and Cr-doped LSM are significantly less

conductive than pure LSM[26-29]. The electrical conductivity of Cr-Mn spinel decreases as its

Cr-content increases. From the thermodynamic calculations it can be predicted that increasing

the current load will lead to the formation of a spinel phase with a low electrical conductivity.

The ohmic resistance of spinel will also increase due to more Cr dissolved in spinel as the

amount of deposits of chromium in the cathode increases as a function of time. Furthermore it

is expected that the electrical conductivity of LSM is influenced by chromium particularly

under high current loads, as chromium leads to decreased concentrations of cation and oxygen

vacancies in LSM(Cr) relative to LSM under such operating conditions of SOFC.

5.5 Conclusions

Thermodynamic calculations of LSM contaminated by chromium showed that the formation

of spinel is thermodynamically driven, whereas Cr2O3 is a metastable phase that forms under

kinetic control in degraded SOFC. The formation of spinel is favored under low oxygen

partial pressures, thus in an SOFC under current load this phase is found predominantly at the

LSM/YSZ interface.

The interaction between chromium and LSM leads to changes of the defect chemistry of the

LSM perovskite phase. Particularly diminished concentration of oxygen vacancies relative to

LSM without chromium may be a reason for the inhibited oxygen diffusion in degraded

SOFC at high temperatures and high current loads . This is also true for Mn-deficient LSM

compositions, though the formation of spinel can be restricted to lower oxygen partial

pressures. Its defect chemistry is particularly problematic at low oxygen partial pressures, the

concentration of oxygen vacancies being strongly diminished relative to LSM with excess

Mn. Anyway the use of a Mn-deficient LSM cathode for SOFC is not recommended due to

the formation of electrically isolating zirconate.


166

By lowering the operation temperature of SOFC additional phases are expected to form at

lower oxygen partial pressures. Thus it is expected that in this case the consequences of Cr-

poisoning will persist particularly at high current loads.

From the thermodynamic point of view it can be summarized that there are neither optimized

SOFC operating conditions nor optimized LSM compositions that eliminate the chromium

problem in SOFC with LSM cathode and Cr-alloy interconnect. Even though the deterioration

of the cell performance due to chromium is expected to be less pronounced when the

operation temperature and current load is decreased, chromium “poisoning” of SOFC with an

LSM cathode and Cr-alloy interconnect can only be prevented by applying effective coatings

that act as diffusion barrier in combination with additional functional layers. Furthermore,

interaction between Mn from LSM with Cr may be cumbered by proper doping of the

perovskite with further B-site cations.

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spinel phases as potential coatings for SOFC metallic interconnects, J. Power sources,

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27. R. Koc, H.U. Anderson, S.A. Howard, in SOFC-1, S.C. Singhal, Ed., PV 89-11, p. 220,

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29. N.M. Sammes, M.B. Phillips, in SOFC-IV, M. Dokiya, O. Yamamoto, H. Tagawa, S.C.

Singhal, Eds., PV 95-01, p. 472, The Electrochemical Society Proceedings Series,

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Appendix

169

Appendix

La-Cr databasea)

@@ Database La-Cr, Povoden-Karadeniz 2008 @@ GO G ENTER-ELEMENT LA CR VA @@ELEMENT NAME REF. STATE ATOMIC MASS H0 S0 AMEND-ELEMENT LA DOUBLE_HCP(ABAC) 1.3891E+02 6.6651E+03 5.6902E+01,, AMEND-ELEMENT CR BCC_A2 5.1996E+01 4.0500E+03 2.35429E+01,, AMEND-ELEMENT VA VACUUM 0 0 0,, @@ ---------------------------------------------------------- @@ Functions @@ ---------------------------------------------------------- @@ Standard data for elements, Dinsdale 1991 @@ La, double hcp ENTER-SYMBO FUNCTION GHSERLA 298.15 -7968.403+120.284604*T-26.34*T*LN(T)-.001295165*T**2; 550 Y -3381.413+59.06113*T-17.1659411*T*LN(T)-.008371705*T**2 +6.8932E-07*T**3-399448*T**(-1); 2000 Y -15608.882+181.390071*T-34.3088*T*LN(T); 4000 N @@ Cr, bcc ENTER-SYMBO FUNCTION GHSERCR 298.15 -8856.94+157.48*T-26.908*t*LN(T)+0.00189435*T**2 -1.47721E-06*T**3+139250*T**(-1); 2180 Y -34869.344+344.18*T-50.0*T*LN(T)-2.88526E+32*T**(-9); 6000 N @@------------------------------------------------------------------- @@ Solid metals, Dinsdale 1991 @@ La, bcc ENTER-SYMBO FUNCTION GLABCC 298.15 -3952.161+88.072353*T-21.7919*T*LN(T)-0.004045175*T**2 -5.25865E-07*T**3; 800 Y +321682.673-3565.08252*T+513.440708*T*LN(T)-0.387295093*T**2 +4.9547989E-05*T**3-36581228*T**(-1); 1134 Y -16377.894+218.492988*T-39.5388*T*LN(T); 1193 Y -136609.91+1123.34397*T-163.413074*T*LN(T)+0.053968535*T**2 -4.056395E-06*T**3+21167204*T**(-1); 2000 Y -8205.988+174.836315*T-34.3088*T*LN(T); 4000 N @@ La, fcc ENTER-SYMBO FUNCTION GLAFCC 298.15

Appendix

170

-6109.797+89.878761*T-21.7919*T*LN(T)-0.004045175*T**2 -5.25865E-07*T**3; 1134 Y -124598.976+955.878375*T-139.346741*T*LN(T)+0.042032405*T**2 -3.066199E-06*T**3+20994153*T**(-1); 2000 Y -12599.386+178.54399*T-34.3088*T*LN(T); 4000 N @@ ---------------------------------------------------------------------- @@ Liquid metal functions, Dinsdale 1991 @@ La ENTER-SYMBO FUNCTION GLALIQ 298.15 +5332.653+18.23012*T-11.0188191*T*LN(T)-0.020171603*T**2 +2.93775E-06*T**3-133541*T**(-1); 1134 Y -3942.004+171.018431*T-34.3088*T*LN(T); 4000 N @@ Cr ENTER-SYMBO FUNCTION GCR_L 298.15 +15483.015+146.059775*T-26.908*T*LN(T)+.00189435*T**2 -1.47721E-06*T**3+139250*T**(-1)+2.37615E-21*T**7; 2180 Y -16459.984+335.616317*T-50*T*LN(T); 6000 N @@------------------------------------------------------------ @@ Gas functions @@ La gas, from SGTE @@ La(g) ENTER-SYMBO FUNCTION F12026T 298.15 +422273.955-30.3347881*T-22.06299*T*LN(T)-0.005444405*T**2 +4.71447833E-07*T**3+102710.1*T**(-1); 600 Y +426628.905-85.4786162*T-13.83676*T*LN(T)-0.011938995*T**2 +1.33826017E-06*T**3-312130.2*T**(-1); 1300 Y +404460.17+114.016725*T-42.00406*T*LN(T)+0.0037094435*T**2 -2.70261E-07*T**3+2891891*T**(-1); 3200 Y +497751.747-246.085237*T+2.791973*T*LN(T)-0.006002155*T**2 +1.30043383E-07*T**3-34158815*T**(-1); 8200 Y -92343.0441+773.338363*T-111.0188*T*LN(T)+0.0037862445*T**2 -2.82257667E-08*T**3+5.418475E+08*T**(-1); 10000 N @@ Cr gas, from SGTE ENTER-SYMBO FUNCTION F7491T 298.15 +390765.331-31.5192158*T-21.36083*T*LN(T)+7.253215E-04*T**2 -1.588679E-07*T**3+10285.15*T**(-1); 1100 Y +393886.928-44.1074654*T-19.96003*T*LN(T)+.001513089*T**2 -4.23648333E-07*T**3-722515*T**(-1); 6000 N @@ Cr2 gas, from SGTE ENTER-SYMBOL FUNCTION F7763T 298.15 +598511.403+41.5353212*T-40.56798*T*LN(T)+.004961847*T**2 -1.61216717E-06*T**3+154422.85*T**(-1); 800 Y +613345.232-104.207991*T-19.7643*T*LN(T)-.007085085*T**2 -4.69883E-07*T**3-1738066.5*T**(-1); 1400 Y +642608.843-369.28626*T+17.64743*T*LN(T)-.02767321*T**2

Appendix

171

+1.605906E-06*T**3-5831655*T**(-1); 2300 Y +553119.895+159.188555*T-52.07969*T*LN(T)-.004229401*T**2 +1.5939925E-07*T**3+14793625*T**(-1); 3900 Y +347492.34+623.137623*T-105.0428*T*LN(T)+3.9699545E-04*T**2 +1.51783483E-07*T**3+1.4843765E+08*T**(-1); 5800 Y -484185.055+2598.25559*T-334.7145*T*LN(T)+.028597625*T**2 -4.97520167E-07*T**3+7.135805E+08*T**(-1); 6000 N @@ -------------------------------------------------------------------- @@ Phases @@ ------------------------------------------------------------------- @@ Metals @@ La, dhcp ENTER-PHASE LADHCP,, 2 1 0.5 LA ; VA;,,, ENTER-PAR G(LADHCP,LA:VA;0) 298.15 +GHSERLA;,,, @@ La, fcc ENTER-PHASE LAFCC,, 2 1 1 LA; VA;,,, ENTER-PAR G(LAFCC,LA:VA;0) 298.15 +GLAFCC;,,, @@ ----------------------------------------------------------------- @@ Alloys @@ BCC_A2 ALLOY ENTER-PHASE BCC,, 2 1 3 LA CR; VA;,,, AMEND-PHASE-DESC BCC MAGN -1 0.4 ENTER-PAR TC(BCC,CR:VA;0) 298.15 -311.5;,,, ENTER-PAR BMAGN(BCC,CR:VA;0) 298.15 -0.008;,,, ENTER-PAR G(BCC,LA:VA;0) 298.15 +GLABCC;,,, ENTER-PAR G(BCC,CR:VA;0) 298.15 +GHSERCR;,,, ENTER-PAR L(BCC,LA,CR:VA;0) 298.15 83500;,,, @@ -------------------------------------------------------------------------- @@ Liquid, ideal extension from lower-order systems ENTER-PHASE LIQ,, 2 1 1 LA CR; VA;,,, AMEND-PHASE LIQ COMP 2,,,,,,,, ENTER-PAR G(LIQ,LA:VA;0) 298.15 +GLALIQ;,,, ENTER-PAR G(LIQ,CR:VA;0) 298.15 +GCR_L;,,, @@ Interaction parameters from binaries ENTER-PAR L(LIQ,LA,CR:VA;0) 298.15 60713-5.49*t;,,, ENTER-PAR L(LIQ,LA,CR:VA;1) 298.15 64573-23*t;,,, @@------------------------------------------------------------ @@ Gas ENTER-PHASE GAS G 1 LA CR CR2;,,, ENTER-PAR G(GAS,LA;0) 298.15 +F12026T+RTLNP;,,, ENTER-PAR G(GAS,CR;0) 298.15 +F7491T+RTLNP;,,,, ENTER-PAR G(GAS,CR2;0) 298.15 +F7763T+RTLNP;,,, @@ GO PAR SET-OUT-LEVEL,,,,, N,, set-interactive

a)databases scripts can be used in Thermocalc with the extension .tcm

Appendix

172

La-Sr-Mn-Cr-O-(H) oxide database

@@ LA-SR-Mn-CR-O-(H) oxide, Povoden-Karadeniz @@ @@ Database La-Sr-Mn-Cr-O-(H), first version: Feb2006 by Povoden. @@ Actual version: Dec2008 by Povoden-Karadeniz @@ @@ COMMENTS @@ @@ Sr-Cr-O liquid: simple description; associate at composition SrCrO4 can @@ help for better fit to experiments – future work @@ @@ No data exist for Sr-Mn-Cr-O. Solubility of Cr in SrMnO3 not known @@ --> Subsystem Sr-Mn-Cr-O is a purely ideal extention @@ @@ no oxygen solubility in La-oxide description (taken from Zinkevich et @@ al.) considered @@ @@ Quinary Ruddlesden popper phase is very tentative, as only few phase @@ diagram data exist! @@ -------------------------------------------------------------------- GO G ENTER-ELEMENT LA SR MN CR O VA H @@ELEMENT NAME REF. STATE ATOMIC MASS H0 S0 AMEND-ELEMENT LA DOUBLE_HCP(ABAC) 1.3891E+02 6.6651E+03 5.6902E+01,, AMEND-ELEMENT SR SR_FCC_A1 8.7620E+01 6.5680E+03 5.5694E+01,, AMEND-ELEMENT MN CBCC_A12 5.4938E+01 4.9960E+03 3.2008E+01,, AMEND-ELEMENT CR BCC_A2 5.1996E+01 4.0500E+03 2.35429E+01,, AMEND-ELEMENT O 1/2_MOLE_O2(G) 1.5999E+01 4.3410E+03 1.0252E+02,, AMEND-ELEMENT H 1/2_MOLE_H2(G) 0.1008E+01 0 0.65340E+02,, AMEND-ELEMENT VA VACUUM 0 0 0,, @@ @@ -------------------------------------------------------------------- @@ Species @@ -------------------------------------------------------------------- ENTER-SPECIES LA+2 LA/+2 ENTER-SPECIES LA+3 LA/+3 ENTER-SPECIES SR+2 SR/+2 ENTER-SPECIES MN+2 MN/+2 ENTER-SPECIES MN+3 MN/+3 ENTER-SPECIES MN+4 MN/+4 ENTER-SPECIES O2 O2 ENTER-SPECIES O3 O3 ENTER-SPECIES O-2 O/-2 ENTER-SPECIES SRO SRO ENTER-SPECIES SRO2 SRO2 ENTER-SPECIES CR+2 CR/+2 ENTER-SPECIES CR+3 CR/+3 ENTER-SPECIES CR+4 CR/+4 ENTER-SPECIES CR+6 CR/+6 ENTER-SPECIES CR1O1 CR1O1 ENTER-SPECIES CR1O2 CR1O2 ENTER-SPECIES CR1O3 CR1O3

Appendix

173

ENTER-SPECIES CR2O3 CR2O3 ENTER-SPECIES CR3O4 CR3O4 ENTER-SPECIES CRH1 CRH1 ENTER-SPECIES CRH1O1 CRH1O1 ENTER-SPECIES CRH1O2 CRH1O2 ENTER-SPECIES CRH1O3 CRH1O3 ENTER-SPECIES CRH2O2 CRH2O2 ENTER-SPECIES CRH2O3 CRH2O3 ENTER-SPECIES CRH2O4 CRH2O4 ENTER-SPECIES CRH3O3 CRH3O3 ENTER-SPECIES CRH3O4 CRH3O4 ENTER-SPECIES CRH4O4 CRH4O4 ENTER-SPECIES CRH4O5 CRH4O5 ENTER-SPECIES CRH5O5 CRH5O5 ENTER-SPECIES CRH6O6 CRH6O6 ENTER-SPECIES H2 H2 ENTER-SPECIES H2O1 H2O1 ENTER-SPECIES H1O1 H1O1 ENTER-SPECIES H1O2 H1O2 ENTER-SPECIES H2O2 H2O2 @@ @@ ---------------------------------------------------------- @@ Functions @@ ---------------------------------------------------------- @@ SER Lattice stabilities, Dinsdale 1991 @@ La, double hcp ENTER-SYMBO FUNCTION GHSERLA 298.15 -7968.403+120.284604*T-26.34*T*LN(T)-.001295165*T**2; 550 Y -3381.413+59.06113*T-17.1659411*T*LN(T)-.008371705*T**2 +6.8932E-07*T**3-399448*T**(-1); 2000 Y -15608.882+181.390071*T-34.3088*T*LN(T); 4000 N @@ Sr, fcc ENTER-SYMBO FUNCTION GHSERSR 298.15 -7532.367+107.183879*T-23.905*T*LN(T)-4.61225E-3*T**2 -1.67477E-07*T**3-2055*T**(-1); 820 Y -13380.102+153.196104*T-30.0905432*T*LN(T)-3.251266E-3*T**2 +1.84189E-07*T**3+850134*T**(-1); 3000 N @@ Mn, cbcca12 ENTER-SYMBO FUNCTION GHSERMN 298.15 -8115.27966+130.059572*T-23.4582*T*LN(T)-0.00734768*T**2 +69827.1*T**(-1); 1519 Y -28733.41+312.2648*T-48*T*LN(T)+1.656847E30*T**(-9); 2000 N @@ Cr, bcc ENTER-SYMBO FUNCTION GHSERCR 298.15 -8856.94+157.48*T-26.908*t*LN(T)+0.00189435*T**2 -1.47721E-06*T**3+139250*T**(-1); 2180 Y -34869.344+344.18*T-50.0*T*LN(T)-2.88526E+32*T**(-9); 6000 N @@ O1, (1/2 O2) ENTER-SYMBO FUNCTION GHSEROO 298.15 -3480.872255-25.5028601*T-11.1355068*T*LN(T)-0.005098873*T**2 +6.6184604E-07*T**3-38364.8742*T**(-1); 1000 Y

Appendix

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-6568.76015+12.66000166*T-16.8138015*T*LN(T)-5.9579637E-04*T**2 +6.78055555E-09*T**3+262904.778*T**(-1); 3300 Y -13986.728+31.259625*T-18.9536*T*LN(T)-4.25243E-04*T**2 +1.0721E-08*T**3+4383200*T**(-1); 6000 N @@------------------------------------------------------------ @@ Binary oxides, optimized @@ La-oxides, Zinkevich 2006 ENTER-SYMBO FUNCTION GLA2O3D 298.15 -1833257+692.9664*T-120.629*T*LN(T)-0.006854*T**2 +808000*T**(-1)-1E7*T**(-2);,,, ENTER-SYMBO FUNCTION GLA2O3H 298.15 32350-13.986*T+GLA2O3D;,,, ENTER-SYMBO FUNCTION GLA2O3X 298.15 43192-18.555*T+GLA2O3D;,,, @@ Sr-oxides, Risold 1996 @@ SrO ENTER-SYMBO FUNCTION GSROSOL 298.15 -607870+268.9*T-47.56*T*LN(T)-0.00307*T**2 +190000*T**(-1);,,, @@ SrO2 ENTER-SYMBO FUNCTION GSRO2SOL 298.15 +GSROSOL+GHSEROO-43740+70*T;,,, @@ Mn-oxides, Grundy 2003 @@ MANGANOSITE, MNO ENTER-SYMBO FUNCTION GMN1O1 298.15 -4.02477557E+05+2.59355626E+02*T-4.68352649E+01*T*LN(T) -3.85001409E-03*T**2+2.12922234E+05*T**(-1);,,, @@ PYROLYSITE, MN1O2 ENTER-SYMBO FUNCTION GMN1O2 298.15 -5.45091278E+05+3.95379396E+02*T-6.52766201E+01*T*LN(T) -7.80284521E-03*T**2+6.64955386E+05*T**(-1);,,, @@ @@ MN2O3-FUNCTION, MODIFIED, Grundy 2006 ENTER-SYMBO FUNCTION GMN2O3 298.15 -9.96393E+05+5.6846E+02*T-9.911E+01*T*LN(T)-2.056E-02*T**2 +6.0822E+05*T**(-1);,,, @@ ALPHA-HAUSMANNITE, ALPHA-MN3O4 (DISTORTED) ENTER-SYMBO FUNCTION GTMN3O4 298.15 -1.43703676E+06+8.89567858E+02*T-1.54747566E+02*T*LN(T) -1.74079033E-02*T**2+9.86138663E+05*T**(-1);,,, @@ BETA-HAUSMANNITE, BETA-MN3O4 (CUBIC) ENTER-SYMBO FUNCTION GCMN3O4 298.15 -1.41618912E+06+8.75120338E+02*T-1.54747566E+02*T*LN(T) -1.74079033E-02*T**2+9.86138663E+05*T**(-1);,,, @@ Cr-O oxides, Povoden 2005 @@ METASTABLE CRO ENTER-SYMBO FUNCTION GCR1O1 298.15 +0.5*GCR2O3-0.5*GHSEROO+255269-53.82*T;,,, @@ ESKOLAITE, Cr2O3 ENTER-SYMBO FUNCTION GCR2O3 298.15 -1.164542E+06+7.2856E+02*T-119.8*T*LN(T)-4.97E-03*T**2 +1.05E+06*T**(-1);,,, @@ reduced neutral endmember of CR2O3 ENTER-SYMBO FUNCTION GCRO0 298.15 +108305+GCR2O3+0.66666666667*GHSERCR;,,, @@ CR-SPINEL CR3O4 ENTER-SYMBO FUNCTION GCR3O4 298.15 +1.5*GCR2O3-0.5*GHSEROO+280045-93.76*T;,,, @@ --------------------------------------------------------------

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175

@@ Ternary oxides, optimized (except perovskite functions) @@ @@ Functions of the La-Sr-O system, Grundy 2004 ENTER-SYMBO FUNCTION SR_ALPHA 298.15 +2*GSROSOL+2.5E+04;,,, ENTER-SYMBO FUNCTION SRH_ALPH 298.15 +2*GSROSOL+2.5E+04;,,, ENTER-SYMBO FUNCTION SRX_ALPH 298.15 +2*GSROSOL+2.5E+04;,,, ENTER-SYMBO FUNCTION LA_BETA 298.15 +GLA2O3D+2.158E+04;,,, ENTER-SYMBO FUNCTION RE_ALPHA 298.15 0;,,, ENTER-SYMBO FUNCTION RE_BETA 298.15 0;,,, @@ @@ Functions of the La-Mn-O system, Grundy et al. 2005 ENTER-SYMBO FUNCTION GL2MNO4 298.15 +GLA2O3D+GMN1O1+6.26029731E+04-3.71704891E+01*T;,,, @@ @@ Functions of the La-Cr-O system, Povoden 2008 @@ LA2CRO6 ENTER-SYMBO FUNCTION GLA2CRO6 298.15 GLA2O3D+0.5*GCR2O3+1.5*GHSEROO-73045-4.14*T;,,, @@ intermediate La-chromates @@ LA16 @@ ENTER-SYMBO FUNCTION GLA16 298.15 @@ 8*GLA2O3D+3.5*GCR2O3+9.5*GHSEROO-540404-9.55*T;,,, @@ LA7 @@ ENTER-SYMBO FUNCTION GLA7 298.15 @@ 3.5*GLA2O3D+GCR2O3+2.5*GHSEROO-154101-2.799*T;,,, @@ LA2CR3O12 ENTER-SYMBO FUNCTION GLA2CR3 298.15 GLA2O3D+1.5*GCR2O3+4.5*GHSEROO-371557+205*T;,,, @@ @@ Functions of the Sr-Mn-O system, Grundy 2004 @@ HEX Phase ENTER-SYMBO FUNCTION GSM4_HEX 298.15 +GSROSOL+GMN1O2-1.11300000E+05;,,, ENTER-SYMBO FUNCTION GSM3_HEX 298.15 +GSROSOL+0.5*GMN2O3-7.73000000E+03 -1.70000000E+01*T;,,, @@ SrMn3Oz as SrMnO3_Mn2O3 ENTER-SYMBO FUNCTION GSM4OZ 298.15 +GMN2O3+GSM4_HEX-8.79100000E+03;,,, ENTER-SYMBO FUNCTION GSM3OZ 298.15 +GMN2O3+GSM3_HEX-2.19200000E+04;,,, @@ RP1 ENTER-SYMBO FUNCTION GS4O_RP1 298.15 +2*GSROSOL+GMN1O2-1.32830000E+05;,,, ENTER-SYMBO FUNCTION GL3O_RP1 298.15 +GSROSOL+0.5*GLA2O3D+0.5*GMN2O3-68300;,,, @@ RP2 ENTER-SYMBO FUNCTION GS4O_RP2 298.15 +3*GSROSOL+2*GMN1O2-8.99100000E+04-90*T;,,, ENTER-SYMBO FUNCTION GL3O_RP2 298.15 +GSROSOL+GLA2O3D+GMN2O3-137400;,,, @@ RP3 ENTER-SYMBO FUNCTION GSM4_RP3 298.15 +4*GSROSOL+3*GMN1O2-3.78500000E+05;,,, @@ Sr7Mn4O1

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ENTER-SYMBO FUNCTION GS7M4 298.15 +7*GSROSOL+4*GMN1O2-6.12450000E+05+50*T;,,, @@ @@ Functions of the Sr-Cr-O system, Povoden 2008 @@ SRCR2O4 ENTER-SYMBO FUNCTION GSC2O4 298.15 +GSROSOL+GCR2O3+98000-95.5*T;,,, @@ SR2CRO4 ENTER-SYMBO FUNCTION GS2CO4 298.15 2*GSROSOL+0.5*GCR2O3+0.5*GHSEROO-145000+50*T;,,, @@ SR3CR2O8 ENTER-SYMBO FUNCTION GS3C2O8 298.15 +2.66666667*GSROSOL+GCR2O3+2.333333333333*GHSEROO -508507+219*T;,,, @@ SRCRO4 ENTER-SYMBO FUNCTION GSCO4 298.15 +GSROSOL+0.5*GCR2O3+1.5*GHSEROO-273771 +131.6*T;,,, @@ SRCR2O7 ENTER-SYMBO FUNCTION GSC2O7 298.15 +GSROSOL+GCR2O3+3*GHSEROO-325047+196*T;,,, @@ @@ Functions of the Mn-Cr-O system, Povoden 2005 @@ CUBIC SPINEL ENTER-SYMBO FUNCTION GSPINEL 298.15 0.666666667*GCR3O4+.33333333334*GCMN3O4-210795.3+61.69*T;,,, @@ TETRAGONALLY DISTORTED SPINEL ENTER-SYMBO FUNCTION GTSPINEL 298.15 0.666666667*GCR3O4+.33333333334*GTMN3O4-200942+75.1*T;,,, @@ @@ Functions of the La-Sr-Cr-O oxide system, Povoden 2008 @@ Ruddlesden Popper phase ENTER-SYMBO FUNCTION GREFRP 298.15 +2*GSROSOL+0.5*GCR2O3+0.5*GHSEROO;,,, ENTER-SYMBO FUNCTION GLCR3O_RP1 298.15 +GLACRO3+GSROSOL+7000-25*t;,,, @@ ---------------------------------------------------------------- @@ Perovskite functions @@ Grundy 2005 @@ Charge compensated by Mn+4 (correct) ENTER-SYMBO FUNCTION GL3O 298.15 +0.5*GLA2O3D+0.5*GMN2O3-63367+51.77*T-7.19*T*LN(T) +232934*T**(-1);,,, @@ ENTER-SYMBO FUNCTION GL3OL 298.15 +0.5*GLA2O3D+0.5*GMN2O3-63367+51.77*T-7.19*T*LN(T) +232934*T**(-1)-3429+4.72*t;,,, @@ ENTER-SYMBO FUNCTION GL3OR 298.15 +0.5*GLA2O3D+0.5*GMN2O3-63367+51.77*T-7.19*T*LN(T) +232934*T**(-1)+400-0.4*t;,,, ENTER-SYMBO FUNCTION GL2O 298.15 +0.5*GLA2O3D+GMN1O1+27672;,,, ENTER-SYMBO FUNCTION GL4O 298.15 +0.5*GLA2O3D+0.75*GMN1O2-91857+20.31*T;,,, ENTER-SYMBO FUNCTION GV4O 298.15 +0.333333*GLA2O3D+GMN1O2-53760;,,, ENTER-SYMBO FUNCTION GVVV 298.15 +6*GL2O+4*GL4O+3*GV4O-12*GL3O-254212;,,, ENTER-SYMBO FUNCTION GMS3O 298.15 +GSROSOL+0.5*GMN2O3-7.73000000E+03-1.44550000E+04

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-1.70000000E+01*T;,,, ENTER-SYMBO FUNCTION GMS4O 298.15 +GSROSOL+GMN1O2-1.11300000E+05+2.26500000E+04 -7.69000000E+00*T;,,, ENTER-SYMBO FUNCTION ANTI 298.15 +547422;,,, @@ Reciprocals: all 0!!!!! @@ @@ Povoden 2008 @@ LaCrO3-PEROVSKITE ENTER-SYMBO FUNCTION GLACRO3 298.15 0.5*GLA2O3D+0.5*GCR2O3-73591+2.38*T-0.68*T* LN(T);,,, ENTER-SYMBO FUNCTION GALACRO3 298.15 +GLACRO3-340+0.63*t;,,, @@ (LaSr)CrO3+/-delta-Perovskite @@ Reference SrCrVa3 ENTER-SYMBO FUNCTION GS4V 298.15 GSROSOL+0.5*GCR2O3-2.5*GHSEROO;,,, @@ Function for neutral endmember SrCrO3 ENTER-SYMBO FUNCTION GS4O 298.15 GSROSOL+0.5*GCR2O3+0.5*GHSEROO+10222-55.52*t;,,, @@ Function for neutral endmember SR(CR+3,VA)O3 ENTER-SYMBO FUNCTION GN 298.15 +GSROSOL+0.5*GCR2O3+11.2386*T+135166-88.42*t;,,, @@ Functions for defect chemistry ENTER-SYMBO FUNCTION GVCR4O 298.15 0.5*GCR2O3+0.5*GHSEROO-291802-250*t;,,, ENTER-SYMBO FUNCTION GLACR4O 298.15 0.33333*GLA2O3D+.5*GCR2O3+0.5*GHSEROO-200000;,,, @@ ---------------------------------------------------------------------- @@ LIQUID FUNCTIONS @@ ---------------------------------------------------------------------- @@ Liquid metal functions, Dinsdale 1991 @@ La ENTER-SYMBO FUNCTION GLALIQ 298.15 +5332.653+18.23012*T-11.0188191*T*LN(T)-0.020171603*T**2 +2.93775E-06*T**3-133541*T**(-1); 1134 Y -3942.004+171.018431*T-34.3088*T*LN(T); 4000 N @@ Sr ENTER-SYMBO FUNCTION GSRLIQ 298.15 +2194.997-10.118994*T-5.0668978*T*LN(T)-3.1840595E-2*T**2 +4.981237E-06*T**3-265559*T**(-1); 1050 Y -10855.29+213.406219*T-39.463*T*LN(T); 3000 N @@ Mn ENTER-SYMBO FUNCTION GMN_L 298.15 +GHSERMN+17859.91-12.6208*T-4.41929E-21*T**7; 1519 Y +GHSERMN+18739.51-13.2288*T-1.656847E30*T**(-9); 3000 N @@ Cr ENTER-SYMBO FUNCTION GCR_L 298.15 +15483.015+146.059775*T-26.908*T*LN(T)+.00189435*T**2 -1.47721E-06*T**3+139250*T**(-1)+2.37615E-21*T**7; 2180 Y -16459.984+335.616317*T-50*T*LN(T); 6000 N @@ ---------------------------------------------------------------------

Appendix

178

@@ Liquid oxide functions, optimized @@ liquid La2O3, Zinkevich 2006 ENTER-SYMBO FUNCTION GLA2O3LIQ 298.15 -1833257+692.9664*T-120.629*T*LN(T)-0.006854*T**2 +808000*T**(-1)-1E7*T**(-2)+141329-56.6220*T;,,, @@ liquid SrO, Risold ENTER-SYMBO FUNCTION GSROLIQ 298.15 -566346+449*T-73.1*T*LN(T);,,, @@ liquid Mn oxides, Grundy ENTER-SYMBO FUNCTION GMN1O1_L 298.15 GMN1O1+4.39465890E+04-2.06284295E+01*T;,,, ENTER-SYMBO FUNCTION GMN2O3_L 298.15 +2*GMN1O1+GHSEROO-6.49525609E+04+4.31437957E+01*T;,,, @@ liquid Cr oxides, Povoden ENTER-SYMBO FUNCTION GCR1O1_L 298.15 0.5*GCR2O3-0.5*GHSEROO+339673-121.4*T;,,, ENTER-SYMBO FUNCTION GCR2O3_L 298.15 GCR2O3+439078-169*T;,,, @@------------------------------------------------------------------- @@ LIQUID WATER, from T.C.R.A.S. Class: 4 ENTER-SYMBO FUNCTION GH2O_L 298.15 -332319.671+1078.59563*T-186.8669*T*LN(T) +.2320948*T**2-9.14296167E-05*T**3+978019*T**(-1); 500 Y -62418.8788-3288.18729*T+495.1304*T*LN(T) -.504926*T**2+4.917665E-05*T**3-18523425*T**(-1); 540 Y -8528143.9+142414.45*T-22596.19*T*LN(T) +27.48508*T**2-.00631160667*T**3+5.63356E+08*T**(-1); 600 Y -331037.282+741.178604*T-117.41*T*LN(T); 601 N @@ ------------------------------------------------------------------------ @@ GAS FUNCTIONS @@ --------------------CHROMIUM GAS---------------------------------------- @@ CR Gas: SGTE v 3.0 (1998), source: Thermocenter of russian academy @@ of science (T.C.R.A.S), Class: 4 @@ SGTE=scientific group thermodata Europe @@ ENTER-SYMBO FUNCTION F7491T 298.15 +390765.331-31.5192158*T-21.36083*T* LN(T) +7.253215E-04*T**2-1.588679E-07*T**3+10285.15*T**(-1); 1100 Y +393886.928-44.1074654*T-19.96003*T*LN(T)+.001513089*T**2 -4.23648333E-07*T**3-722515*T**(-1); 6000 N @@ CR1O1 Gas (SGTE 1998; from T.C.R.A.S Class: 5) ENTER-SYMBO FUNCTION F7705T 298.15 +176483.869-31.9513659*T-30.2897*T*LN(T)-.00607059*T**2 +9.229905E-07*T**3+35263.135*T**(-1); 900 Y +170853.62+32.1684007*T-39.74749*T*LN(T)+.00119977*T**2 -1.52515733E-07*T**3+682877*T**(-1); 4000 Y +307209.502-414.237405*T+14.48744*T*LN(T)-.008463125*T**2 +1.722975E-07*T**3-64209900*T**(-1); 8400 Y -403765.708+805.224944*T-121.5329*T*LN(T)+.003139382*T**2 -1.36845867E-08*T**3+6.35563E+08*T**(-1); 10000 N @@ CR1O1 Gas, REASSESSED BY MING CHEN (2006) BASED ON EBBINGHAUS (1993) ENTER-SYMBO FUNCTION GCR1O1_G 298.15 +173449.4-33.083*T-30.097*T*LN(T)-0.0063*T**2 +31300*T**(-1)+9.5567E-7*T**3; 1000 Y +167489.3+37.31*T-40.555*T*LN(T)+0.00148*T**2 +873600*T**(-1)+1.69E-7*T**3;

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179

3000 N @@ CR1O2 Gas, reassessment Chen 2006, based on Ebbinghaus 1993 ENTER-SYMBO FUNCTION GCR1O2_G 298.15 -109942.78+10.59*T-39.526*T*LN(T)-0.0155*T**2 +245800*T**(-1)+2.43E-6*T**3; 1000 Y -118120+123.81*T-56.696*T*LN(T)-0.00012*T**2 +932050*T**(-1)-8.01667E-8*T**3; 3000 N @@ CR1O3 Gas, reassessed by Ming Chen 2006, based on Ebbinghaus 1993 ENTER-SYMBO FUNCTION GCR1O3_G 298.15 -341231.99+130.61*T-57.2*T*LN(T)-.0216*T**2 +428900*T**(-1)+3.401E-6*T**3; 1000 Y -354716.09+299.89*T-82.569*T*LN(T)-0.00016*T**2 +1814700*T**(-1)+7.33E-9*T**3; 3000 N @@-------------------OXYGEN GAS------------------------------------- @@ O Gas (JANAF 1982, assessment dated 3/77 from SGTE) ENTER-SYMBO FUNCTION F13349T 298.15 +243206.494-20.8612582*T-21.01555*T*LN(T)+1.2687055E-04*T**2 -1.23131283E-08*T**3-42897.09*T**(-1); 2950 Y +252301.423-52.0847281*T-17.21188*T*LN(T)-5.413565E-04*T**2 +7.64520667E-09*T**3-3973170.5*T**(-1); 6000 N @@ O3 Gas (SGTE 1998; from T.C.R.A.S Class: 4) ENTER-SYMBO FUNCTION F14021T 298.15 +130696.944-37.9096643*T-27.58118*T*LN(T)-.02763076*T**2 +4.60539333E-06*T**3+99530.45*T**(-1); 700 Y +114760.623+176.626737*T-60.10286*T*LN(T)+.00206456*T**2 -5.17486667E-07*T**3+1572175*T**(-1); 1300 Y +49468.3956+710.09482*T-134.3696*T*LN(T)+.039707355*T**2 -4.10457667E-06*T**3+12362250*T**(-1); 2100 Y +866367.075-3566.80563*T+421.2001*T*LN(T)-.1284109*T**2 +5.44768833E-06*T**3-2.1304835E+08*T**(-1); 2800 Y +409416.383-1950.70834*T+223.4437*T*LN(T)-.0922361*T**2 +4.306855E-06*T**3-21589870*T**(-1); 3500 Y -1866338.6+6101.13383*T-764.8435*T*LN(T)+.09852775*T**2 -2.59784667E-06*T**3+9.610855E+08*T**(-1); 4900 Y +97590.043+890.798361*T-149.9608*T*LN(T)+.01283575*T**2 -3.555105E-07*T**3-2.1699975E+08*T**(-1); 6000 N @@ -------------O-H GAS----------------------------------- @@ H2 Gas (JANAF THERMOCHEMICAL TABLES SGTE) ENTER-SYMBO FUNCTION H2GAS 298.15 -9522.97393+78.5273873*T-31.35707*T*LN(T)+0.0027589925*T**2 -7.46390667E-07*T**3+56582.3*T**(-1); 1000 Y +180.108664-15.6128262*T-17.84857*T*LN(T)-0.00584168*T**2 +3.14618667E-07*T**3-1280036*T**(-1); 2100 Y -18840.1663+92.3120249*T-32.05082*T*LN(T)-0.0010728235*T**2 +1.14281783E-08*T**3+3561002.5*T**(-1); 6000 N @@ H Gas (JANAF 1982, assessment dated 3/77 from SGTE) ENTER-SYMBO FUNCTION HGAS 298.15 +211801.621+24.4989821*T-20.78611*T*LN(T); 6000 N @@ H2O1 Gas (SGTE 1998; from T.C.R.A.S Class: 4) ENTER-SYMBO FUNCTION F10963T 298.15 -250423.434+4.45470312*T-28.40916*T*LN(T) -.00623741*T**2-6.01526167E-08*T**3-64163.45*T**(-1); 1100 Y -256145.879+30.1894682*T-31.43044*T*LN(T) -.007055445*T**2+3.05535833E-07*T**3+1246309.5*T**(-1); 2800 Y

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180

-268423.418+116.690197*T-42.96842*T*LN(T) -.003069987*T**2+6.97594167E-08*T**3+2458230.5*T**(-1); 8400 Y -489068.882+553.259882*T-92.4077*T*LN(T) +.0016703495*T**2-1.32333233E-08*T**3+1.765625E+08*T**(-1); 18000 Y -165728.771+239.645643*T-59.77872*T*LN(T) +2.213599E-04*T**2-1.2921095E-09*T**3-4.1931655E+08*T**(-1); 20000 N @@ H1O1 Gas (SGTE 1998; from T.C.R.A.S Class: 1) ENTER-SYMBO FUNCTION F10666T 298.15 +30698.6898+15.9096451*T-29.97699*T*LN(T) +.001713168*T**2-6.799205E-07*T**3-25503.82*T**(-1); 3000 Y +31735.5127-12.686636*T-25.42186*T*LN(T) -.003149545*T**2+1.34404917E-07*T**3+116618.65*T**(-1); 8600 Y +41016.0783-20.7343256*T-24.94216*T*LN(T) -.0023107985*T**2+5.91863E-08*T**3-6415210*T**(-1); 18000 Y -154907.953+370.326117*T-69.24542*T*LN(T) +.0019361405*T**2-1.47539017E-08*T**3+1.4391015E+08*T**(-1); +326722.277-65.0792741*T-24.2768*T*LN(T) +6.42189E-05*T**2-1.30298483E-10*T**3-8.292415E+08*T**(-1); 20000 N @@ H1O2 Gas (SGTE 1998; from T.C.R.A.S Class: 4) ENTER-SYMBO FUNCTION F10729T 298.15 +1075.64106-55.242048*T-24.45435*T*LN(T) -.018507875*T**2+2.36297E-06*T**3-29469.05*T**(-1); 800 Y -7932.99164+54.2016233*T-40.775*T*LN(T) -.00501027*T**2+2.122915E-07*T**3+925845*T**(-1); 3600 Y -67875.8961+275.406716*T-68.1173*T*LN(T) +6.12331E-04*T**2-6.573855E-09*T**3+26048030*T**(-1); 6000 N @@ H2O2 Gas (JANAF SECOND EDIT SGTE) ENTER-SYMBO FUNCTION F10983T 298.15 -147258.971-37.1497212*T-26.10636*T*LN(T) -.036948065*T**2+6.659505E-06*T**3+65357.65*T**(-1); 700 Y -156470.505+120.191295*T-50.94271*T*LN(T) -.007931945*T**2+4.29733833E-07*T**3+684985.5*T**(-1); 1500 N @@-------------------CR-O-H GAS---------------------------------------- @@ CR(OH)1 Gas REASSESSED BY MING CHEN (2006) BASED ON EBBINGHAUS (1993) ENTER-SYMBO FUNCTION GCRH1O1_G 298.15 +68260+52.87*T-46.257*T*LN(T) -0.002*T**2+185600*T**(-1)-1.51E-7*T**3; 1000 Y 56684+136.53*T-57.551*T*LN(T) +0.0018*T**2+2218000*T**(-1)-2.75E-7*T**3; 3000 N @@ CRO(OH)1 Gas REASSESSED BY MING CHEN (2006) BASED ON EBBINGHAUS (1993) ENTER-SYMBO FUNCTION GCRH1O2_G 298.15 -274384.32+190.52*T-74.175*T*LN(T) +0.0031*T**2+266750*T**(-1)-9.135E-7*T**3; 1000 Y -276268.52+180.7*T-72.053*T*LN(T) -0.0015*T**2+938850*T**(-1)+5.15E-8*T**3; 3000 N @@ CRO2(OH) Gas, combined assessment Chen 2006 @@ based on Ebbinghaus 1995 @@ and from Povoden based on Kim and Belton 1974 @@ (data suggested by Opila 2007) ENTER-SYMBO FUNCTION GCRH1O3_G 298.15 -497678+273.77*T-83.724*T*LN(T) -0.0146*T**2+715900*T**(-1)+2.39E-6*T**3; 1000 Y -492562+351.47*T-96.9*T*LN(T) -.0018*T**2+1338300*T**(-1)+9.334E-8*T**3; 3000 N @@ CR(OH)2 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH2O2_G 298.15 -351288.4+195.86*T-75.927*T*LN(T) -0.0007*T**2+243850*T**(-1)-9.2E-7*T**3; 1000 Y

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-359644+228.97*T-79.455*T*LN(T) -0.004*T**2+2094950*T**(-1)+1.91E-7*T**3; 3000 N @@ CRO(OH)2 Gas, assessment Chen 2006 based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH2O3_G 298.15 -578683+391.2*T-109.525*T*LN(T) -0.00056*T**2+663150*T**(-1)-5.67833E-07*T**3; 1000 Y -582354+394.6*T-109.25*T*LN(T) -0.004*T**2+1.8967E-07*T**3+1688150*T**(-1); 3000 N @@ CRO2(OH)2 Gas, combined assessment Chen 2006 @@ based on Ebbinghaus 1995 @@ and from Povoden-Karadeniz based on Opila 2007 ENTER-SYMBO FUNCTION GCRH2O4_G 298.15 -787712+400*T-107.819*T*LN(T) -0.019*T**2+513600*T**(-1)+1.9958E-06*T**3; 1000 Y -806262+567*T-131.457*T*LN(T) -0.0049*T**2+3311450*T**(-1)+2.545E-7*T**3; 3000 N @@ CR(OH)3 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH3O3_G 298.15 -650064.7+464.37*T-125.5*T*LN(T) +0.006*T**2+498450*T**(-1)-2.378E-6*T**3; 1000 Y -656538+448.3*T-121.16*T*LN(T) -0.006*T**2+2525450*T**(-1)+2.93E-7*T**3; 3000 N @@ CRO(OH)3 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH3O4_G 298.15 -851590.83+534.3*T-137.098*T*LN(T) -0.0099*T**2+770750*T**(-1)+5.8867E-7*T**3; 1000 Y -861477.76+600.74*T-146.002*T*LN(T) -0.0065*T**2+2669300*T**(-1)+3.35E-7*T**3; 3000 N @@ CR(OH)4 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH4O4_G 298.15 -902751.6+712.5*T-163*T*LN(T) +0.004*T**2+785800*T**(-1)-2.355E-6*T**3; 1000 Y -909897.86+694.973194012145*T-158.41*T*LN(T) -0.0086*T**2+3058600*T**(-1)+4.3E-7*T**3; 3000 N @@ CR(OH)5 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH5O5_G 298.15 -978211.05+820.9*T-190.524*T*LN(T) -0.0054*T**2+1023500*T**(-1)-1.11767E-6*T**3; 1000 Y -991549.1+867.6*T-195.2*T*LN(T) -0.01*T**2+4151100*T**(-1)+5.7467E-7*T**3; 3000 N @@ CR(OH)6 Gas, assessment Chen 2006, based on Ebbinghaus 1995 ENTER-SYMBO FUNCTION GCRH6O6_G 298.15 -1029121.12+967.89*T-216.86*T*LN(T) -0.008*T**2+840600*T**(-1)-1.77E-6*T**3; 1000 Y -1053466+1080.45*T-229.874*T*LN(T) -0.014*T**2+6008850*T**(-1)+7.34E-7*T**3; 3000 N @@ CRO(OH)4 Gas, assessment Chen 2006, based on Ebbinghaus 1993 ENTER-SYMBO FUNCTION G_CRH4O5 298.15 -976204+672.6*T-162.049*T*LN(T) -0.014*T**2+1.35E-07*T**3+665100*T**(-1); 1000 Y -997791.8+813.97*T-180.65*T*LN(T) -0.0096*T**2+4.945E-07*T**3+4671850*T**(-1); 3000 N @@ CRH1 Gas (SGTE 1998; from T.C.R.A.S Class: 4) ENTER-SYMBO FUNCTION F7586T 298.15 +432449.026-56.386334*T-22.37019*T*LN(T) -.00994042*T**2+1.18913267E-06*T**3-77266.05*T**(-1); 1000 Y +421602.4+51.9865812*T-37.99681*T*LN(T) +3.349852E-04*T**2-1.13133917E-07*T**3+1368173*T**(-1); 3500 Y +587860.713-424.36214*T+18.6022*T*LN(T) -.007723995*T**2+7.99444833E-08*T**3-86705500*T**(-1); 5500 Y +1270342.46-2142.60191*T+219.9391*T*LN(T)

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-.034109635*T**2+7.277845E-07*T**3-5.20451E+08*T**(-1); 6000 N @@ @@ @@ -------------------------------------------------------------------- @@ Phases @@ ------------------------------------------------------------------- @@ Binary oxides @@ @@ Sr oxides, Risold @@ ENTER-PHASE SRO2,, 1 SRO2;,,, ENTER-PAR G(SRO2,SRO2;0) 298.15 +GSRO2SOL;,,, @@ @@ Mn oxides, Grundy @@ @@ STOICHIOMETRIC PYROLYSITE, MN1O2 ENTER-PHASE MN1O2,, 2 1 2 MN; O;,,, ENTER-PAR G(MN1O2,MN:O;0) 298.15 +GMN1O2;,,, @@ ---------------------------------------------------------------------- @@ Ternary oxides @@ @@ LA-SR-O, Grundy, Chen @@ ENTER-PHASE LA2O3SS,, 2 2 3 LA+2 LA+3 SR+2; O-2 VA;,,, ENTER-PAR G(LA2O3SS,LA+2:O-2;0) 298.15 +GLAO;,,, ENTER-PAR G(LA2O3SS,LA+2:VA;0),, +GLAO-GHSEROO;,,, ENTER-PAR G(LA2O3SS,LA+3:O-2;0) 298.15 +GLA2O3D;,,, ENTER-PAR G(LA2O3SS,LA+3:VA;0),, +GLA2O3D-3*GHSEROO;,,, ENTER-PAR G(LA2O3SS,SR+2:O-2;0),, +SR_ALPHA+GHSEROO +15.87691*T;,,, ENTER-PAR G(LA2O3SS,SR+2:VA;0),, +SR_ALPHA-2*GHSEROO +15.87691*T;,,, ENTER-PAR L(LA2O3SS,LA+3,SR+2:O-2;0) 298.15 +2.149E+05-7.81E+01*T;,,, ENTER-PAR L(LA2O3SS,LA+3,SR+2:VA;0) 298.15 +2.149E+05-7.81E+01*T;,,, @@ ENTER-PHASE LA2O3_HEXSS,, 2 2 3 LA+3 SR+2; O-2 VA;,,, ENTER-PAR G(LA2O3_HEXSS,LA+3:O-2;0),, +GLA2O3H;,,, ENTER-PAR G(LA2O3_HEXSS,LA+3:VA;0),, +GLA2O3H-3*GHSEROO;,,, ENTER-PAR G(LA2O3_HEXSS,SR+2:O-2;0),, +SRH_ALPH+GHSEROO+15.87691*T;,,, ENTER-PAR G(LA2O3_HEXSS,SR+2:VA;0),, +SRH_ALPH-2*GHSEROO

+15.87691*T;,,, ENTER-PAR L(LA2O3_HEXSS,LA+3,SR+2:O-2;0) 298.15 +193600-78.1*T;,,, ENTER-PAR L(LA2O3_HEXSS,LA+3,SR+2:VA;0) 298.15 +193600-78.1*T;,,, @@ ENTER-PHASE LA2O3_CUBSS,, 2 2 3 LA+3 SR+2; O-2 VA;,,, ENTER-PAR G(LA2O3_CUBSS,LA+3:O-2;0),, +GLA2O3X;,,, ENTER-PAR G(LA2O3_CUBSS,LA+3:VA;0),, +GLA2O3X-3*GHSEROO;,,, ENTER-PAR G(LA2O3_CUBSS,SR+2:O-2;0),, +SRX_ALPH+GHSEROO+15.87691*T;,,, ENTER-PAR G(LA2O3_CUBSS,SR+2:VA;0),, +SRX_ALPH-2*GHSEROO+15.87691*T;,,, ENTER-PAR L(LA2O3_CUBSS,LA+3,SR+2:O-2;0) 298.15 +168700-78.1*T;,,, ENTER-PAR L(LA2O3_CUBSS,LA+3,SR+2:O-2;1) 298.15 -20000;,,, ENTER-PAR L(LA2O3_CUBSS,LA+3,SR+2:VA;0) 298.15 +168700-78.1*T;,,, ENTER-PAR L(LA2O3_CUBSS,LA+3,SR+2:VA;1) 298.15 -20000;,,, @@ La4SrO7 as BETA phase ENTER-PHASE BETA,, 2 2 3 LA+3 SR+2; O-2 VA;,,, ENTER-PAR G(BETA,LA+3:O-2;0),, +LA_BETA;,,, ENTER-PAR G(BETA,LA+3:VA;0),, +LA_BETA-3*GHSEROO;,,, ENTER-PAR G(BETA,SR+2:O-2;0),, +SR_ALPHA+416100+GHSEROO -0.33333333*RE_BETA

+15.87691*T;,,,

Appendix

183

ENTER-PAR G(BETA,SR+2:VA;0),, +SR_ALPHA+416100-2*GHSEROO +0.66666667*RE_BETA+15.87691*T;,,, ENTER-PAR L(BETA,LA+3,SR+2:O-2;0) 298.15 -121000-237.8*T;,,, ENTER-PAR L(BETA,LA+3,SR+2:VA;0) 298.15 -121000-237.8*T;,,, @@ La4Sr3O9, Stoichiometric ENTER-PHASE LA4SR3O9,, 3 4 3 9 LA+3; SR+2; O-2;,,, ENTER-PAR G(LA4SR3O9,LA+3:SR+2:O-2;0),, +2*GLA2O3D+3*GSROSOL+229800 -136.75*T;,,, @@ SrO Solid Solution ENTER-PHASE SRO,, 2 1 1 LA+3 SR+2 VA; O-2;,,, ENTER-PAR G(SRO,LA+3:O-2;0),, +0.5*GLA2O3D+113700;,,, ENTER-PAR G(SRO,SR+2:O-2;0),, +GSROSOL;,,, ENTER-PAR G(SRO,VA:O-2;0),, 0;,,, @@ @@ LA-MN-O, Grundy @@ ENTER-PHASE L2MNO4,, 3 2 1 4 LA+3; MN+2; O-2;,,, ENTER-PAR G(L2MNO4,LA+3:MN+2:O-2;0) 298.15 +GL2MNO4;,,, @@ ENTER-PHASE LMN2O5,, 4 1 1 1 5 LA+3; MN+3; MN+4; O-2;,,, ENTER-PAR G(LMN2O5,LA+3:MN+3:MN+4:O-2;0) 298.15 +GLMN2O5;,,, @@ @@ LA-CR-O, Povoden @@ @@ STOICHIOMETRIC LA2CRO6 ENTER-PHASE LA2CRO6,, 3 2 1 6 LA+3; CR+6; O-2;,,, ENTER-PAR G(LA2CRO6,LA+3:CR+6:O-2;0) 298.15 +GLA2CRO6;,,, @@ intermediate La-chromates @@ STOICHIOMETRIC LA16 @@ ENTER-PHASE LA16,, 3 16 7 44 LA; CR; O;,,, @@ ENTER-PAR G(LA16,LA:CR:O;0) 298.15 +GLA16;,,, @@ STOICHIOMETRIC LA7 @@ ENTER-PHASE LA7,, 3 7 2 16 LA; CR; O;,,, @@ ENTER-PAR G(LA7,LA:CR:O;0) 298.15 +GLA7;,,, @@ @@ STOICHIOMETRIC LA2CR3O12 ENTER-PHASE LA2CR3,, 3 2 3 12 LA+3; CR+6; O-2;,,, ENTER-PAR G(LA2CR3,LA+3:CR+6:O-2;0) 298.15 +GLA2CR3;,,, @@ @@ SR-MN-O, Grundy @@ ENTER-PHASE SR7MN4O15,, 3 7 4 15 SR+2; MN+4; O-2;,,, ENTER-PAR G(SR7MN4O15,SR+2:MN+4:O-2;0),, +GS7M4;,,, @@ ENTER-PHASE SRMN3O6,, 5 1 2 3 1 3 SR+2; MN+3; O-2; MN+3 MN+4; O-2 VA;,,, ENTER-PAR G(SRMN3O6,SR+2:MN+3:O-2:MN+3:O-2;0),, +GSM3OZ+0.5*GHSEROO +11.23859*T;,,, ENTER-PAR G(SRMN3O6,SR+2:MN+3:O-2:MN+3:VA;0),, +GSM3OZ-2.5*GHSEROO +11.23859*T;,,, ENTER-PAR G(SRMN3O6,SR+2:MN+3:O-2:MN+4:O-2;0),, +GSM4OZ;,,, ENTER-PAR G(SRMN3O6,SR+2:MN+3:O-2:MN+4:VA;0),, +GSM4OZ-3*GHSEROO;,,, @@ ENTER-PHASE SR4MN3O10,, 3 4 3 10 SR+2; MN+4; O-2;,,, ENTER-PAR G(SR4MN3O10,SR+2:MN+4:O-2;0),, +GSM4_RP3;,,, @@ ENTER-PHASE SRMNO3_HEX,, 3 1 1 3 SR+2; MN+3 MN+4; O-2 VA;,,, ENTER-PAR G(SRMNO3_HEX,SR+2:MN+3:O-2;0),, +GSM3_HEX+0.5*GHSEROO

+11.23859*T;,,, ENTER-PAR G(SRMNO3_HEX,SR+2:MN+3:VA;0),, +GSM3_HEX-2.5*GHSEROO

+11.23859*T;,,,

Appendix

184

ENTER-PAR G(SRMNO3_HEX,SR+2:MN+4:O-2;0),, +GSM4_HEX;,,, ENTER-PAR G(SRMNO3_HEX,SR+2:MN+4:VA;0),, +GSM4_HEX-3*GHSEROO;,,, @@ @@ RP2, Grundy modified it in LSM modeling ENTER-PHASE RP2,, 4 1 2 2 7 SR+2; SR+2; MN+3 MN+4; O-2;,,, ENTER-PAR G(RP2,SR+2:SR+2:MN+3:O-2;0) 298.15 +3*GSROSOL+GMN2O3+GHSEROO;,,, ENTER-PAR G(RP2,SR+2:SR+2:MN+4:O-2;0) 298.15 +GS4O_RP2;,,, @@ @@ SR-CR-O, Povoden @@ @@ SRCR2O4 ENTER-PHASE SC2O4,, 3 1 2 4 SR+2; CR+3; O-2;,,, ENTER-PAR G(SC2O4,SR+2:CR+3:O-2;0) 298.15 +GSC2O4;,,, @@ SR2CRO4 ENTER-PHASE S2CO4,, 3 2 1 4 SR+2; CR+4; O-2;,,, ENTER-PAR G(S2CO4,SR+2:CR+4:O-2;0) 298.15 +GS2CO4;,,, @@ @@ SR2.67CR2O8 ENTER-PHASE S3C2N,, 3 2.666667 2 8 SR; CR; O;,,, ENTER-PAR G(S3C2N,SR:CR:O;0) 298.15 +GS3C2O8;,,, @@ SRCRO4, Povoden-Karadeniz ENTER-PHASE SCO4,, 3 1 1 4 SR+2; CR+6; O-2;,,, ENTER-PAR G(SCO4,SR+2:CR+6:O-2;0) 298.15 +GSCO4;,,, @@ SRCR2O7, doubtful phase @@ ENTER-PHASE SC2O7,, 3 1 2 7 SR+2; CR+6; O-2;,,, @@ ENTER-PAR G(SC2O7,SR+2:CR+6:O-2;0) 298.15 +GSC2O7;,,, @@ @@ CR-MN-O, Povoden @@ @@ NONSTOICHIOMETRIC MANGANOSITE (MNO) SOLID SOLUTION, Grundy, Povoden-K. ENTER-PHASE MNO_HALIT,, 2 1 1 MN+2 MN+3 CR+3 VA; O-2;,,, ENTER-PAR G(MNO_HALIT,MN+2:O-2;0) 298.15 +GMN1O1;,,, ENTER-PAR G(MNO_HALIT,MN+3:O-2;0) 298.15 +GMN1O1-21883.5213 -22.1853365*T;,,, ENTER-PAR G(MNO_HALIT,CR+3:O-2;0) 298.15 +0.5*GCR2O3-7.93845*T +71549.3;,,, ENTER-PAR G(MNO_HALIT,VA:O-2;0) 298.15 0;,,, ENTER-PAR L(MNO_HALIT,MN+2,MN+3:O-2;0) 298.15 -4.21048766E+04;,,, ENTER-PAR L(MNO_HALIT,MN+2,MN+3:O-2;1) 298.15 +4.65131533E+04;,,, @@ @@ Mn2O3 (Compatible with C-Y2O3, Grundy, Chen, Povoden-Karadeniz) ENTER-PHASE MN2O3,, 3 2 3 1 MN+3 CR+3; O-2 VA; O-2 VA;,,, AMEND-PHASE MN2O3 MAGN,, .28 ENTER-PAR TC(MN2O3,MN+3:O-2:VA;0) 298.15 +309;,,, ENTER-PAR TC(MN2O3,CR+3:O-2:VA;0) 298.15 +308.6;,,, ENTER-PAR BMAGN(MN2O3,MN+3:O-2:VA;0) 298.15 +0.59;,,, ENTER-PAR BMAGN(MN2O3,CR+3:O-2:VA;0) 298.15 +3;,,, ENTER-PAR G(MN2O3,MN+3:O-2:VA;0) 298.15 +GMN2O3;,,, ENTER-PAR G(MN2O3,MN+3:O-2:O-2;0) 298.15 +GMN2O3+GHSEROO +100000+15.87691*T;,,, ENTER-PAR G(MN2O3,MN+3:VA:O-2;0) 298.15 +GMN2O3-2*GHSEROO +100000+15.87691*T;,,, ENTER-PAR G(MN2O3,MN+3:VA:VA;0) 298.15 +GMN2O3-3*GHSEROO;,,, ENTER-PAR G(MN2O3,CR+3:O-2:VA;0) 298.15 +GCR2O3+3459;,,, ENTER-PAR G(MN2O3,CR+3:O-2:O-2;0) 298.15 +GCR2O3+GHSEROO +100000+15.87691*T;,,, ENTER-PAR G(MN2O3,CR+3:VA:O-2;0) 298.15 +GCR2O3-2*GHSEROO +100000+15.87691*T;,,, ENTER-PAR G(MN2O3,CR+3:VA:VA;0) 298.15 +GCR2O3-3*GHSEROO;,,, @@ @@ ESKOLAITE, NONSTOICHIOMETRIC CR2O3 SOLID SOLUTION, Povoden-Karadeniz

Appendix

185

ENTER-PHASE CR2O3,, 3 2 1 3 MN+3 CR+2 CR+3; CR+3 VA; O-2;,,, AMEND-PHASE CR2O3 MAGN,, .28 ENTER-PAR TC(CR2O3,MN+3:CR+3:O-2;0) 298.15 +309;,,, ENTER-PAR TC(CR2O3,MN+3:VA:O-2;0) 298.15 +309;,,, ENTER-PAR TC(CR2O3,CR+2:CR+3:O-2;0) 298.15 +308.6;,,, ENTER-PAR TC(CR2O3,CR+2:VA:O-2;0) 298.15 +308.6;,,, ENTER-PAR TC(CR2O3,CR+3:CR+3:O-2;0) 298.15 +308.6;,,, ENTER-PAR TC(CR2O3,CR+3:VA:O-2;0) 298.15 +308.6;,,, ENTER-PAR BMAGN(CR2O3,MN+3:CR+3:O-2;0) 298.15 +0.59;,,, ENTER-PAR BMAGN(CR2O3,MN+3:VA:O-2;0) 298.15 +0.59;,,, ENTER-PAR BMAGN(CR2O3,CR+2:CR+3:O-2;0) 298.15 +3;,,, ENTER-PAR BMAGN(CR2O3,CR+2:VA:O-2;0) 298.15 +3;,,, ENTER-PAR BMAGN(CR2O3,CR+3:CR+3:O-2;0) 298.15 +3;,,, ENTER-PAR BMAGN(CR2O3,CR+3:VA:O-2;0) 298.15 +3;,,, ENTER-PAR G(CR2O3,MN+3:CR+3:O-2;0) 298.15 +GMN2O3+GSERCR+39503;,,, ENTER-PAR G(CR2O3,MN+3:VA:O-2;0) 298.15 +GMN2O3+39503;,,, ENTER-PAR G(CR2O3,CR+2:CR+3:O-2;0) 298.15 +GCRO0 +.33333333334*GHSERCR -5.2923*T;,,, ENTER-PAR G(CR2O3,CR+2:VA:O-2;0) 298.15 +GCRO0 -0.666666666667*GHSERCR -5.2923*T;,,, ENTER-PAR G(CR2O3,CR+3:CR+3:O-2;0) 298.15 +GCR2O3+GHSERCR;,,, ENTER-PAR G(CR2O3,CR+3:VA:O-2;0) 298.15 +GCR2O3;,,, @@ @@ CUBIC SPINEL, Grundy, Povoden-Karadeniz ENTER-PHASE CMNCR2O4,, 3 1 2 4 MN+2 CR+2; MN+3 CR+3; O-2;,,, ENTER-PAR G(CMNCR2O4,MN+2:CR+3:O-2;0) 298.15 +GSPINEL;,,, ENTER-PAR G(CMNCR2O4,CR+2:CR+3:O-2;0) 298.15 +GCR3O4;,,, ENTER-PAR G(CMNCR2O4,MN+2:MN+3:O-2;0) 298.15 +GCMN3O4;,,, ENTER-PAR G(CMNCR2O4,CR+2:MN+3:O-2;0) 298.15 +GCR3O4+GCMN3O4-GSPINEL;,,, @@ DISTORTED_SPINEL, Grundy, Povoden-Karadeniz ENTER-PHASE TMNCR2O4,, 3 1 2 4 MN+2; MN+3 CR+3; O-2;,,, ENTER-PAR G(TMNCR2O4,MN+2:MN+3:O-2;0) 298.15 +GTMN3O4;,,, ENTER-PAR G(TMNCR2O4,MN+2:CR+3:O-2;0) 298.15 +GTSPINEL;,,, @@ ------------------------------------------------------------------------ @@ Quaternary oxides @@ @@ La-Sr-Mn-O, Grundy @@ ENTER-PHASE LS3MN2O7,, 4 1 2 2 7 SR+2; LA+3 SR+2; MN+3 MN+4; O-2;,,, ENTER-PAR G(LS3MN2O7,SR+2:LA+3:MN+3:O-2;0) 298.15 +GL3O_RP2;,,, ENTER-PAR G(LS3MN2O7,SR+2:LA+3:MN+4:O-2;0) 298.15 +GL3O_RP2+GS4O_RP2

-3*GSROSOL -GMN2O3-GHSEROO-R_RP2;,,, ENTER-PAR G(LS3MN2O7,SR+2:SR+2:MN+3:O-2;0) 298.15 +3*GSROSOL+GMN2O3

+GHSEROO;,,, ENTER-PAR G(LS3MN2O7,SR+2:SR+2:MN+4:O-2;0) 298.15 +GS4O_RP2;,,, @@ ------------------------------------------------------------------------ @@ Quinary phases, ideal extensions from lower-order systems @@ @@ high temperature rhombohedral perovskite, Grundy, Povoden-Karadeniz ENTER-PHASE RPEROV,, 3 1 1 3 LA+3 SR+2 VA; MN+2 MN+3 MN+4 CR+3 CR+4 VA; O-2 VA;,,, @@ ENTER-PAR G(RPEROV,SR+2:MN+2:O-2;0),, +GMS3O+GL2O-GL3OR+GHSEROO

+22.47717*T;,,, ENTER-PAR G(RPEROV,SR+2:MN+3:O-2;0),, +GMS3O+0.5*GHSEROO+11.23859*T;,,, ENTER-PAR G(RPEROV,SR+2:MN+4:O-2;0),, +GMS4O;,,, ENTER-PAR G(RPEROV,SR+2:MN+2:VA;0),, +GMS3O+GL2O-GL3OR-2*GHSEROO+22.47717*T;,,,

Appendix

186

ENTER-PAR G(RPEROV,SR+2:MN+3:VA;0),, +GMS3O-2.5*GHSEROO+11.23859*T;,,, ENTER-PAR G(RPEROV,SR+2:MN+4:VA;0),, +GMS4O-3*GHSEROO;,,, ENTER-PAR G(RPEROV,SR+2:CR+3:O-2;0),, +GN+0.1666667*GS4O

-0.16666667*GS4V;,,, ENTER-PAR G(RPEROV,SR+2:CR+3:VA;0),, +GN-0.8333333*GS4O

+0.8333333*GS4V;,,, ENTER-PAR G(RPEROV,SR+2:VA:O-2;0),, +GMS3O-GL3OR+2*GL4O

-1.5*GV4O+0.5*GVVV +2*GHSEROO+12.62121*T;,,, ENTER-PAR G(RPEROV,SR+2:VA:VA;0),, +GMS3O+2*GL4O-1.5*GV4O

+0.5*GVVV-GL3OR -GHSEROO+12.62121*T;,,, ENTER-PAR G(RPEROV,LA+3:MN+2:O-2;0),, +GL2O+0.5*GHSEROO+11.2386*T;,,, ENTER-PAR G(RPEROV,LA+3:MN+2:VA;0),, +GL2O-2.5*GHSEROO+11.2386*T;,,, ENTER-PAR G(RPEROV,LA+3:MN+3:O-2;0),, +GL3OR;,,, ENTER-PAR G(RPEROV,LA+3:MN+3:VA;0),, +GL3OR-3*GHSEROO;,,, ENTER-PAR G(RPEROV,LA+3:MN+4:O-2;0),, +0.66667*GL4O+0.5*GV4O

-0.166667*GVVV -0.5*GHSEROO+5.76318*T;,,, ENTER-PAR G(RPEROV,LA+3:MN+4:VA;0),, +0.66667*GL4O+0.5*GV4O

-0.166667*GVVV -3.5*GHSEROO+5.76318*T;,,, ENTER-PAR G(RPEROV,LA+3:VA:O-2;0),, +2*GL4O-1.5*GV4O+0.5*GVVV

+1.5*GHSEROO +1.41263*T;,,, ENTER-PAR G(RPEROV,LA+3:VA:VA;0),, +2*GL4O+0.5*GVVV-1.5*GV4O

-1.5*GHSEROO+1.41263*T;,,, ENTER-PAR G(RPEROV,VA:MN+3:O-2;0),, +GL3OR+1.5*GV4O+0.5*GVVV-2*GL4O +1.5*GHSEROO-1.41263*T;,,, ENTER-PAR G(RPEROV,VA:MN+4:O-2;0),, +2*GV4O+0.33333*GVVV-1.33333*GL4O +GHSEROO+4.35056*T;,,, ENTER-PAR G(RPEROV,VA:MN+2:VA;0),, +GL2O+1.5*GV4O+0.5*GVVV-2*GL4O -GHSEROO+9.82596*T;,,, ENTER-PAR G(RPEROV,VA:MN+3:VA;0),, +GL3OR+1.5*GV4O+0.5*GVVV-2*GL4O -1.5*GHSEROO-1.41263*T;,,, ENTER-PAR G(RPEROV,VA:MN+4:VA;0),, +2*GV4O+0.3333*GVVV-1.333*GL4O -2*GHSEROO+4.35057*T;,,, ENTER-PAR G(RPEROV,VA:VA:O-2;0),, +GVVV+3*GHSEROO;,,, ENTER-PAR G(RPEROV,VA:VA:VA;0),, +GVVV;,,, ENTER-PAR G(RPEROV,LA+3:CR+3:O-2;0),, +GLACRO3;,,, ENTER-PAR G(RPEROV,LA+3:CR+3:VA;0),, +GLACRO3-3*GHSEROO;,,, ENTER-PAR G(RPEROV,VA:CR+3:O-2;0),, +GLACRO3+1.5*GVCR4O+0.5*GVVV

-2*GLACR4O+1.5*GHSEROO -1.41263*T;,,,

ENTER-PAR G(RPEROV,VA:CR+3:VA;0),, +GLACRO3+1.5*GVCR4O+0.5*GVVV -2*GLACR4O-1.5*GHSEROO -1.41263*T;,,,

ENTER-PAR G(RPEROV,LA+3:CR+4:VA;0),, GS4O-GN-0.1666667*GS4O +0.16666667*GS4V+GLACRO3

-3*GHSEROO;,,, ENTER-PAR G(RPEROV,LA+3:CR+4:O-2;0),, GS4O+GLACRO3-GN-0.1666667*GS4O +0.16666667*GS4V;,,, ENTER-PAR G(RPEROV,SR+2:CR+4:O-2;0),, +GS4O;,,, ENTER-PAR G(RPEROV,SR+2:CR+4:VA;0),, +GS4V;,,, ENTER-PAR G(RPEROV,VA:CR+4:O-2;0),, +2*GVCR4O+0.33333*GVVV

-1.33333*GLACR4O +GHSEROO+4.35056*T;,,, ENTER-PAR G(RPEROV,VA:CR+4:VA;0),, +2*GVCR4O+0.3333*GVVV

-1.333*GLACR4O -2*GHSEROO+4.35057*T;,,, @@ Optimized interactions

Appendix

187

ENTER-PAR L(RPEROV,LA+3,SR+2:MN+2:VA;1),, -136600;,,, ENTER-PAR L(RPEROV,LA+3,SR+2:MN+2:O-2;1),, -136600;,,, ENTER-PAR L(RPEROV,LA+3,SR+2:MN+4:VA;1),, -117000;,,, ENTER-PAR L(RPEROV,LA+3,SR+2:MN+4:O-2;1),, -117000;,,, ENTER-PAR L(RPEROV,LA+3:CR+3,MN+3:O-2;0),, 9248.6;,,, ENTER-PAR L(RPEROV,LA+3,SR+2:MN+3:O-2;0) 298.15 -1.5*t;,,, ENTER-PAR L(RPEROV,LA+3:CR+4,VA:O-2;0),, 250000;,,, ENTER-PAR L(RPEROV,LA+3:CR+3,VA:O-2;0),, 250000;,,, ENTER-PAR L(RPEROV,LA+3:MN+4,MN+3:O-2;1) 298.15 185;,,, ENTER-PAR L(RPEROV,LA+3:MN+4,VA:O-2;0),, -2;,,, ENTER-PAR L(RPEROV,LA+3,VA:MN+4:O-2;0),, 20;,,, ENTER-PAR L(RPEROV,LA+3:CR+3,MN+3:O-2;0) 298.15 3766;,,, ENTER-PAR L(RPEROV,LA+3:CR+3,MN+3:O-2;1) 298.15 -1297;,,, @@ next two interaction parameters can be used to fit @@ Cr4+ amount in perovskite ENTER-PAR L(RPEROV,SR+2:CR+4,MN+3:O-2;0) 298.15 0;,,, ENTER-PAR L(RPEROV,SR+2:CR+4,MN+4:O-2;0) 298.15 0;,,, @@ @@ Ruddlesden-Popper phase, preliminary, scarce experimental data @@ ENTER-PHASE RP,, 5 1 1 1 3 1 SR+2; LA+3 SR+2; MN+3 MN+4 CR+3 CR+4; O-2; @@ O-2;,,, @@ ENTER-PAR G(RP,SR+2:SR+2:CR+4:O-2:O-2;0) 298.15 GS2CO4;,,, @@ ENTER-PAR G(RP,SR+2:LA+3:CR+3:O-2:O-2;0) 298.15 +GLCR3O_RP1;,,, @@ ENTER-PAR G(RP,SR+2:LA+3:CR+4:O-2:O-2;0) 298.15 GS2CO4+GLCR3O_RP1 @@ -GREFRP;,,, @@ ENTER-PAR G(RP,SR+2:SR+2:CR+3:O-2:O-2;0) 298.15 GREFRP;,,, @@ ENTER-PAR L(RP,SR+2:SR+2,LA+3:CR+3:O-2:O-2;0) 298.15 100000;,,, @@ ENTER-PAR L(RP,SR+2:SR+2,LA+3:CR+4:O-2:O-2;0) 298.15 100000;,,, @@ ENTER-PAR G(RP,SR+2:SR+2:MN+3:O-2:O-2;0) 298.15 +2*GSROSOL+0.5*GMN2O3 @@ +0.5*GHSEROO;,,, @@ ENTER-PAR G(RP,SR+2:SR+2:MN+4:O-2:O-2;0) 298.15 +GS4O_RP1;,,, @@ ENTER-PAR G(RP,SR+2:LA+3:MN+3:O-2:O-2;0) 298.15 +GL3O_RP1;,,, @@ ENTER-PAR G(RP,SR+2:LA+3:MN+4:O-2:O-2;0) 298.15 +GL3O_RP1+GS4O_RP1 @@ -2*GSROSOL-0.5*GMN2O3 @@ -0.5*GHSEROO;,,, @@ ------------------------------------------------------------------------ @@ Liquid, ideal extension from lower-order systems, Povoden-Karadeniz ENTER-PHASE IONIC_LIQUID Y LA+3 SR+2 MN+2 MN+3 CR+2 CR+3; O-2 VA;,,, AMEND-PHASE IONIC_LIQUID COMP 2,,,,,,,, ENTER-PAR G(ION,LA+3:O-2;0) 298.15 +GLA2O3LIQ;,,, ENTER-PAR G(ION,LA+3:VA;0) 298.15 +GLALIQ;,,, ENTER-PAR G(ION,SR+2:O-2;0) 298.15 +2*GSROLIQ;,,, ENTER-PAR G(ION,SR+2:VA;0) 298.15 +GSRLIQ;,,, ENTER-PAR G(ION,MN+2:O-2;0) 298.15 +2*GMN1O1_L;,,, ENTER-PAR G(ION,MN+2:VA;0) 298.15 +GMN_L;,,, ENTER-PAR G(ION,MN+3:O-2;0) 298.15 +GMN2O3_L;,,, ENTER-PAR G(ION,MN+3:VA;0) 298.15 +2*GMN_L+GMN2O3_L-3*GMN1O1_L;,,, ENTER-PAR G(ION,CR+2:O-2;0) 298.15 2*GCR1O1_L;,,, ENTER-PAR G(ION,CR+2:VA;0) 298.15 +GCR_L;,,, ENTER-PAR G(ION,CR+3:O-2;0) 298.15 +GCR2O3_L;,,, ENTER-PAR G(ION,CR+3:VA;0) 298.15 +2*GCR_L+GCR2O3_L-3*GCR1O1_L;,,, @@ Interaction parameters from binaries ENTER-PAR L(ION,MN+2:O-2,VA;0) 298.15 1.29519000E+05;,,, ENTER-PAR L(ION,MN+2:O-2,VA;1) 298.15 -4.54590000E+04;,,, ENTER-PAR L(ION,MN+2,MN+3:O-2;0) 298.15 -3.38590000E+04;,,, ENTER-PAR L(ION,CR+2:O-2,VA;0) 298.15 +121000;,,, ENTER-PAR L(ION,CR+3:O-2,VA;0) 298.15 +121000;,,, @@ Interaction parameters from ternaries ENTER-PAR L(ION,LA+3,MN+2:O-2;0) 298.15 -119062;,,, ENTER-PAR L(ION,LA+3,MN+2:VA;0) 298.15 +11368;,,, ENTER-PAR L(ION,LA+3,MN+2:VA;1) 298.15 -11316.4;,,,

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ENTER-PAR L(ION,LA+3,MN+2:VA;4) 298.15 -9111;,,, ENTER-PAR L(ION,LA+3,MN+3:O-2;0) 298.15 -119062;,,, ENTER-PAR L(ION,SR+2,MN+2:O-2;0) 298.15 -176300;,,, ENTER-PAR L(ION,SR+2,MN+2:VA;0) 298.15 +46000;,,, ENTER-PAR L(ION,SR+2,MN+3:O-2;0) 298.15 -176300;,,, ENTER-PAR L(ION,MN+2,CR+2:VA;0) 298.15 -15009+13.6587*T;,,, ENTER-PAR L(ION,MN+2,CR+2:VA;1) 298.15 +504+0.9479*T;,,, ENTER-PAR L(ION,MN+3,CR+3:O-2;0) 298.15 -188487.7;,,, ENTER-PAR L(IONIC,LA+3,CR+2:O-2;0) 298.15 -101850;,,, ENTER-PAR L(IONIC,LA+3,CR+3:O-2;0) 298.15 -101850;,,, ENTER-PAR L(IONIC,LA+3,CR+2:O-2;1) 298.15 -39016;,,, ENTER-PAR L(IONIC,LA+3,CR+3:O-2;1) 298.15 -39016;,,, ENTER-PAR L(IONIC,LA+3,CR+2:VA;0) 298.15 +60713-5.49*T;,,, ENTER-PAR L(IONIC,LA+3,CR+2:VA;1) 298.15 +64573-23*T;,,, ENTER-PAR L(ION,SR+2,CR+2:VA;0) 298.15 200000;,,, ENTER-PAR L(ION,SR+2,CR+3:O-2;0) 298.15 -619869;,,, ENTER-PAR L(ION,SR+2,CR+3:O-2;1) 298.15 -179575;,,, ENTER-PAR L(ION,SR+2,CR+2:O-2;0) 298.15 -619869;,,, ENTER-PAR L(ION,SR+2,CR+2:O-2;1) 298.15 -179575;,,, @@------------------------------------------------------------ @@ Cr-GAS, SGTE and reassessments by Chen, Povoden-Karadeniz ENTER-PHASE GAS G 1 CR CR1O1 CR1O2 CR1O3 O O2 O3 H2 H H2O1 H1O1 H1O2 H2O2 CRH1 CRH1O1 CRH1O2 CRH1O3 CRH2O2 CRH2O3 CRH2O4 CRH3O3 CRH3O4 CRH4O4 CRH4O5 CRH5O5 CRH6O6;,,, ENTER-PAR G(GAS,CR1O1;0) 298.15 +GCR1O1_G+RTLNP;,,, ENTER-PAR G(GAS,CR1O2;0) 298.15 +GCR1O2_G+RTLNP;,,, ENTER-PAR G(GAS,CR1O3;0) 298.15 +GCR1O3_G+RTLNP;,,, ENTER-PAR G(GAS,O;0) 298.15 +F13349T+RTLNP; 6000 N ENTER-PAR G(GAS,O2;0) 298.15 +F13704T+RTLNP; 20000 N ENTER-PAR G(GAS,O3;0) 298.15 +F14021T+RTLNP; 6000 N ENTER-PAR G(GAS,H2;0) 298.15 +H2GAS+RTLNP; 6000 N ENTER-PAR G(GAS,H;0) 298.15 +HGAS+RTLNP; 6000 N ENTER-PAR G(GAS,H2O1;0) 298.15 +F10963T+RTLNP; 20000 N ENTER-PAR G(GAS,H1O1;0) 298.15 +F10666T+RTLNP; 20000 N ENTER-PAR G(GAS,H1O2;0) 298.15 +F10729T+RTLNP; 6000 N ENTER-PAR G(GAS,H2O2;0) 298.15 +F10983T+RTLNP; 1500 N ENTER-PAR G(GAS,CRH1;0) 298.15 +F7586T+RTLNP; 6000 N ENTER-PAR G(GAS,CRH1O1;0) 298.15 +GCRH1O1_G+RTLNP;,,, ENTER-PAR G(GAS,CRH1O2;0) 298.15 +GCRH1O2_G+RTLNP;,,, ENTER-PAR G(GAS,CRH1O3;0) 298.15 +GCRH1O3_G+RTLNP;,,, ENTER-PAR G(GAS,CRH2O2;0) 298.15 +GCRH2O2_G+RTLNP;,,, ENTER-PAR G(GAS,CRH2O3;0) 298.15 +GCRH2O3_G+RTLNP;,,, ENTER-PAR G(GAS,CRH2O4;0) 298.15 +GCRH2O4_G+RTLNP;,,, ENTER-PAR G(GAS,CRH3O3;0) 298.15 +GCRH3O3_G+RTLNP;,,, ENTER-PAR G(GAS,CRH3O4;0) 298.15 +GCRH3O4_G+RTLNP;,,, ENTER-PAR G(GAS,CRH4O4;0) 298.15 +GCRH4O4_G+RTLNP;,,, ENTER-PAR G(GAS,CRH5O5;0) 298.15 +GCRH5O5_G+RTLNP;,,, ENTER-PAR G(GAS,CRH6O6;0) 298.15 +GCRH6O6_G+RTLNP;,,, ENTER-PAR G(GAS,CRH4O5;0) 298.15 +GCRH4O5_G+RTLNP;,,, @@ @@ CRO3 reference gas ENTER-PHASE CRGAS,, 1 CR1O3;,,, ENTER-PAR G(CRGAS,CR1O3;0) 298.15 +GCR1O3_G+RTLNP;,,, @@ @@ H2O reference gas ENTER-PHASE STEAM,, 1 H2O1;,,, ENTER-PAR G(STEAM,H2O1;0) 298.15 +F10963T+RTLNP; 20000 N @@ @@ O2 reference gas ENTER-PHASE O2GAS,, 1 O2;,,,

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ENTER-PAR G(O2GAS,O2;0) 298.15 +2*GHSEROO+RTLNP;,,, @@ GO PAR @@ SET-OUT-LEVEL,,,,, N,, set-interactive

Curriculum vitae

190

Curriculum Vitae

Personal data

Povoden-Karadeniz, Erwin

Date and place of birth: March 18, 1973, Graz, Austria

Education

01/2005 – 12/2008

Ph. D. thesis: „ Thermodynamic Database of the La-Sr-Mn-Cr-O Oxide System and

Applications to Solid Oxide Fuel Cells“, Nonmetallic Inorganic Materials, Prof. Dr. Ludwig

J. Gauckler, Department of Materials, ETH Zurich, Switzerland.

1992-1999

Geoscience Studies, Karl-Franzens University Graz

Master thesis: „Kontaktmetamorphose und Fluid-Gestein-Interaktion in der östlichen

Monzoni Kontaktaureole“, Prof. Dr. Georg Hoinkes and Prof. Dr. Rainer Abart

1983-1991

Realistisches Gymnasium, Pestalozzistrasse 5, Graz

1979-1983

Elementary School, Berliner Ring, Graz

Publications

R. Abart, N. Badertscher, M. Burkhard, and E. Povoden, Oxygen, carbon and strontium

isotope systematics in two profiles across the Glarus thrust: implications for fluid flow, Contr.

Miner. Petrol., 2002, 143, pp. 192-208.

Curriculum vitae

191

E. Povoden, M. Horacek, and R. Abart, Contact metamorphism of siliceous dolomite and

impure limestones from the Werfen formation in the eastern Monzoni contact aureole, Miner.

Petrol., 2002, 76, pp. 99-120.

A.N. Grundy, E. Povoden, T. Ivas, and L.J. Gauckler, Calculation of defect chemistry using

the CALPHAD approach, Calphad, 2006, 30, pp. 33-41.

E. Povoden, A.N. Grundy, and L.J. Gauckler, Thermodynamic assessment of the Mn-Cr-O

system for solid oxide fuel cell (SOFC) materials, Int. J. Mater. Res., 2006, 97, pp. 569-78.

E. Povoden, A.N. Grundy, and L.J. Gauckler, Thermodynamic reassessment of the Cr-O


2006, 27, pp. 353-62.

E. Povoden, A.N. Grundy, M. Chen, and L.J. Gauckler, Thermodynamic assessment of the

La-Cr-O system, J. Phase Equilib.Diff., 2009, 1, pp. 12-27.

E. Povoden-Karadeniz, A.N. Grundy, M. Chen, T. Ivas, and L.J. Gauckler, Thermodynamic

assessment of the La-Fe-O system, J. Phase Equilib. Diff. (accepted)

E. Povoden, M. Chen, A.N. Grundy, and L.J. Gauckler, Thermodynamic La-Sr-Mn-Cr-O

oxide database for solid oxide fuel cell applications, to be submitted.

E. Povoden, T. Ivas, M. Chen, and L.J. Gauckler, Thermodynamic calculations of impacts of

chromium on Sr-doped Lanthanum manganite (LSM) cathodes for solid oxide fuel cells

(SOFC), to be submitted.

E. Povoden, T. Ivas, and L.J. Gauckler, Degradation of planar solid oxide fuel cells with

(La1-xSrx)1-yMnO3 cathodes and Cr-alloy interconnects, to be submitted.

Presentations

Assessment of the Cr-O system in the frame of SOFC research


Curriculum vitae

192

Poster Presentation

CALPHAD XXXIV, Maastricht, Netherlands, May 06th -11th, 2005

Thermodynamic assessment of the Cr-Mn-O system for solid oxide fuel cell (SOFC)

materials

E. Povoden

Oral Presentation

1st EMPA symposium for Ph.D. students, EMPA Dübendorf, Switzerland, October 20th, 2005

Thermodynamic Assessment of the Cr-Mn-O System for Solid Oxide Fuel Cell (SOFC)

Materials


Oral Presentation

3rd Fuel Cell Research Symposium, EMPA Dübendorf, Switzerland, March 16th, 2006

Thermodynamic assessment of the La-Mn-Cr-O system for applications on solid oxide fuel

cell (SOFC) materials using the CALPHAD approach


Oral Presentation

Thermo 2006, Boulder, Colorado, USA, August 4th, 2006

Thermodynamic assessment of the La-Mn-Cr-O system for applications on solid oxide fel cell

(SOFC) materials


Oral Presentation

HTMC XII, Vienna, Austria, September 18th – 22nd, 2006

The BiO3/2-SbO3/2-ZnO Phase Diagram at 1115°C in air

E. Povoden, Z. Peng, and L.J. Gauckler

Poster Presentation

CALPHAD XXXVI, Pennsylvania State University, Pennsylvania, USA, May 6th – 11th,

2007

Thermodynamic assessment of the La-Cr-O and LaO3/2-MnOx-CrO3/2 Systems

Curriculum vitae

193


Oral Presentation

CALPHAD XXXVI, Pennsylvania State University, Pennsylvania, USA, May 6th – 11th,

2007

Thermodynamic modeling for solid oxide fuel cell research - The La-Sr-Mn-Cr-O system

E. Povoden

Oral Presentation

2nd MRC Graduate Symposium , ETH Zurich, June 27th, 2007

The thermodynamic LaO1.5-SrO-MnO1.5-CrO1.5 and LaO1.5-SrO-FeO1.5-CrO1.5 databases for

SOFC applications using the CALPHAD approach

E. Povoden

Oral Presentation

Guest Talk, Lehrstuhl für physikalische Chemie, Monatnuniversität Leoben, March 28th, 2008

Thermodynamic LaO1.5-SrO-MnO1.5-CrO1.5 and LaO1.5-SrO-FeO1.5-CrO1.5 databases for solid

oxide fuel cells (SOFC) applications

E. Povoden, M. Chen, A.N. Grundy, and L.J. Gauckler

Oral Presentation

CALPHAD XXXVII, Saariselkä, Finland, June 16th – 21st, 2008

Erratum, p. 109, lines 7-14 and Table 4.3.3, p. 112

According to the latest discussion by B. Hallstedt et al., Calphad, 2007, 31(1), p 28-

37 the correct model is (La,Cr)(O,Va)3 and not (La,Cr)(O,Va)1.5: “…in case there is

information of the ordering of element X between different vacant positions in bcc

described by (Me)1(Va)1(Va)1(Va)1 this is taken into account, otherwise the

disordered model for interstitials in bcc, (Me)1(Va,X)3 is to be used…” Thus the

model was also corrected in the thermodynamic assessment of the La-Fe-O system,

Povoden-Karadeniz et al., J. Phase Equilib. Diff., accepted.

The following argumentation for modeling of the oxygen solubility in bcc using

(physically wrong!) Me(O,Va)1.5 was given in a preliminary manuscript of the La-Fe-

O system and is repeated here for the sake of clarification:

“…as there are three octahedral interstitial sites per metal atom in the bcc unit cell

located on the cube faces and cube edges Me(Va,O)3 is undoubtedly a reasonable

model description for the oxygen solubility in bcc. In previous papers the authors have

proposed the model Me(Va,O)1.5 based on the argument, that it is energetically very

unfavorable to simultaneously occupy both the octahedral interstitial sites on the cube

faces and cube edges as these lie very close to each other. A further reason why we

use this description is that for SOFC applications we are primarily interested in the

oxide portion of the phase diagram and we have found that the endmember Me(O)3

used to describe oxygen solubility in the metallic phase can inadvertently appear in

the oxide portion of the phase diagram. For these reasons, and in order to keep this

assessment compatible with our previous assessments we reassess the oxygen

solubility in bcc Fe using the model (Fe)(O,Va)1.5….”

Thermodynamic Database of the La-Sr-Mn-Cr-O Oxide

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