Oxidation and diffusion in oxides – a progress report

John Ågren

Dept. of Matls. Sci. & Engg.Royal Institute of TechnologyStockholm, 100 44 Sweden

Acknowledgement: Reza Naraghi, Samuel Hallström, Lars Höglund and Malin Selleby

Oxidation and diffusion in oxides – a progress report

NIST Diffusion workshop 2012 Excellence – Relevance - Availability

MGI

ICME

3D-MS

New Research directionsin Materials science and Engineering:


Content

1. Aim of work2. Issues in modelling of oxidation3. Bulk diffusion in oxides

a) Summary and present stageb) Some issues in the diffusion modellingc) Defect structures for oxygen diffusion and

results4. Grain boundary diffusion5. Kirkendall porosity


Predict oxidation:- Sharp-interface methods – DICTRA- Diffuse-interface methods – phase-field

For example: - Oxidation of steels - Degradation of superalloy coatings

We need:- Mathematical expressions for oxidation rate in

terms of diffusional flux as function of gradients in composition or chemical potentials.

- Parameters that characterize a given material

1. Aim of work


2. Issues in modelling of oxidation

Predict:• Rate of oxidation

- External (growth of external layers)- Internal (internal oxide particles)- Grain boundaries in metal and in oxides

• What oxides form?• Porosity

- Kirkendall effect

Jonsson et al. 2006

Giggins and Pettit 1971

Internal oxidation of Mn, Si, Cr etc during carburization (Holm et al. 2010)


External oxidation - generalInward and outward growth

Atmosphere with O2

Metal a Oxide b

Me

OxMe+yO->MexOy

xMe+yO->MexOy

- Oxygen diffusion in the oxide layer gives inward growth- Metal diffusion in the oxide layer gives outward growth


Growth of external layers

Metal a

Oxide bAtmosphere with O2

Oxygen content

Distancexx

Diffusion and flux balances in sharp-interface modelling!


Growth of internal oxide particles• Oxygen must diffuse through external oxide layers and

dissolve in the metallic matrix.• Rate may be controlled by oxygen diffusion, alloy

element diffusion or both.


3. Bulk diffusion in oxides 3.a) Summary and present stage

cLD

xcD

xc

cL

xLJ

:Flux

Kinetic parameters from model.

Darken’s thermodynamic factor, e.g. from Calphad analysis.

Base models on a vacancy mechanism!


Present stage

The models have been implemented in DICTRA.

Data base now contains diffusional mobilities of- Wüstite (Halite)• Fe and O

- Magnetite (Spinel)• Fe Cr O

- Hematite (Corundum)• Fe, Cr, O


3.b) Some issues in the diffusion modelling

• Phase equilibria and driving forces – Calphad thermodynamics

• Defect structures- Vacancies and interstitials- Oxygen substitutional- Fe, Cr etc interstitial

• Diffusing species- Ions- Neutral atoms- Positive holes

• Rate equationsFe-O Calculated from Sundman 1991.


Diffusing species: in ionic systems – two extremes

• Electronic conduction compared to diffusion:- Much faster (charge does not need to be included)- Much slower (ions diffuse as species)If electronic conduction and diffusion are about the same rate (electronic conduction needs to be accounted for)


Fe diffusion in spinel (lattice-fixed frame of reference, Hallström et al. 2011)

(Fe+2,Fe+3)1 (Fe+2,Fe+3,Va)2 (Va,Fe+2)2 (O-2)4

Thermodynamic model (Sundman 1991):

Extra octahedralVaExtra

octahedralFe+2

octahedral fcc tetrahedral

Interstitial sites

1/8*8 sites 4 sites


zV

MyyMyyJ Fe

sFeVaVaFeFeVaFeVaFe

1' '''''''''''''''21

:arguments rate reaction Absolute

Normal octahedral extra octahedral sites sites

)/exp(2 RTGvRTM kk FeL

Fe

FeVaVaFeFeVaFeVaFe uMyyMyyRTD 1'''''''''''''''

21

*


Experimental data on Fe tracer diffusion in spinel - Optimization of Fe mobilities

(Hallström et al. 2011)


Töpfer et.al. 1995

Alloy elements in spinel (lattice fixed frame of reference)

Töpfer et.al. 1995

*

'' '' '' ''' ''' '''

'' '' '' ''' ''' '''

1'

/

CrCr Va Cr CrVa Cr Va CrVa

s

Va Cr CrVa Cr Va CrVa CrCr

μJ y y M y y MV z

D RT y y M y y M u

Cr content of inward growing spinel will inherit Cr content of alloy.


3.c) Defect structures for oxygen diffusion and resultsWüstite (Halite)

2 3 21 1( , , ) ( )

Sundman's model:Fe Fe Va O

' "

* ' "

1

1

i OO Va O OVa

m

iO Va O OVa

O

μJ y y MV z

D y y Mn

Yamagochi et al. 1982 found that oxygen diffusion rate increases with oxygen potential. Thus oxygen vacancies cannot be the dominating mechanism. We thus postulate that oxygen diffuses on interstitial (cation ) sites:


Oxygen tracer diffusion in Wüstite.

Experiments from Yamaguchi et al 1982


3.c) Defect structures for oxygen diffusion and resultsMagnetite (Spinel)

O tracer diffusion in spinel (lattice-fixed frame of reference)

T= 1150°C

Millot and Niu 1996


At low oxygen potentials it seems reasonable that oxygen diffusion is assisted by anion vacancies. The lower the oxygen potential, the higher fraction of vacancies and rate of diffusion.

(Fe+2,Fe+3)1 (Fe+2,Fe+3,Va)2 (Va,Fe+2)2 (O-2, Va)4

Modification of Sundman’s thermodynamic model:


Interstitial sites

1/8*8 sites 4 sites


(Fe+2,Fe+3)1 (Fe+2,Fe+3,Va)2 (Va,Fe+2,O-2)2 (O-2,Va)4


octahedral tetrahedral

Interstitial sites

1/8*8 sites 4 sites

Alternativ 1

At high oxygen potentials this model predicts very low vacancy fractions . The lower the oxygen potential, the higher fraction of vacancies and rate of diffusion. This is not in agreement with experiments!

fcc


1a a a i i i OO Va O OVa O Va OVa

m

μJ y y M y y M

V z

This may work but gives too a strong increase in vacancy content at high oxygen potentials.It also requires a complete re-assessment of Fe-O!

Schematic diagram

2

12ln / lna

Va Od y d P

2

12ln / lni

O Od y d P

2

16ln / lnO Od D d P

(Millot and Niu 1996)

2

12ln / lnO Od D d P

(Millot and Niu 1996)



Alternativ 2

(Fe+2,Fe+3)1 (Fe+2,Fe+3,Va)2 (Va,Fe+2)2 (O-2, Va)4


Interstitial sites

1/8*8 sites 4 sites

Could the vacancy formation energy be chosen such that:

log aVay


1073 K 1423 K

"

* "

1

1

a a a i OO O Va OVa Va OVa

m

a a a iO O Va OVa Va OVa

O

μJ y y M y MV z

D y RT y M y Mn

At present we have

(Millot and Niu 1996) (Millot and Niu 1996) (Giletti and Hess 1988)


3.c) Defect structures for oxygen diffusion and results Hematite (Corundum)

3 2 3 22 1 3( , ) ( , ) ( , )

Kjellqvist et al. 2008Fe Fe Va Fe O Va

”End members” andplane of electro neutrality


*

1

1

a a a OO Va O OVa

m

a a aO Va O OVa

O

μJ y y MV z

D y y Mn

3 2 3 22 1 3( , ) ( , ) ( , )Fe Fe Va Fe O Va

We postulate


Experiments: Amami et al. 1999


4. Grain boundary diffusion

NiO

5.03.0

/)/1(

aa

:approach Simplified

bulkgb

gbbulkeff

QQ

DdDdD


)()1(

)(1

)(1/1

/'

2

332211

2

22

JVf

f

f

JVVV

JVV

V

VxJJVv

mp

p

p

mmm

mm

m

mOOm

div

div

div

:) fraction (volume porosity Only

:rate Strain porosity No

:change )( density of Rate

atoms of evolume/molmolar

:effect Kirkendall gives flux oxygen of divergence onal,substituti is Oxygen

5. Kirkendall porosity


Maruyama et al. 2004

Voids form as a consequence of a divergence in the oxygen flux.


Schematics of Kirkendall effect in magnetite

μFe

zFe

Distance Distance


Oxyg

en m

obilit

y

DistanceOx

ygen

flux

Distance


zJty OVa //

Distance

Pores Pores


T. Jonsson et al. 2008

FeO

Fe3 O4

Fe2O3


Summary• DICTRA can now handle diffusion in oxides allowing

prediction of oxidation.• Data base now contains diffusional mobilities of

Wüstite (Halite): Fe and OMagnetite (spinel): Fe Cr OHematite (Corundum): Fe, Cr, O

• Grain boundary diffusion is taken into account in a simplified manner.

• Oxygen diffusion may cause Kirkendall effect and porosity.

Oxidation and diffusion in oxides – a progress report

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