Thermodynamics of CoO–MgO solid solutions

Thermodynamics of CoO–MgO solid solutions

Lan Wang a, Alexandra Navrotsky a,*, Rebecca Stevens b,Brian F. Woodfield b, Juliana Boerio-Goates b

a Thermochemistry Facility and NEAT ORU, University of California at Davis, Davis, CA 95616, USAb Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, USA

Received 10 February 2003; accepted 24 March 2003

Abstract

Enthalpies of mixing in CoxMg1�xO solid solutions at T ¼ 298 K have been determined

using high temperature drop solution calorimetry in molten sodium molybdate

(3Na2O � 4MoO3) solvent at T ¼ 973 K. Slightly positive enthalpies of mixing were ob-served, which conform to a regular solution model with interaction parameter

W ¼ ð5:1 � 0:3Þ kJ �mol�1, which is similar to the interaction parameter calculated frompreviously measured activity-composition relations. Standard molar entropies S0m at

T ¼ 298 K calculated from subambient Cp data for CoO, MgO are (52.8� 0.1)J �K�1 �mol�1 and (28.1� 0.1) J �K�1 �mol�1, respectively. Integration of the Cp;m=T of

the Co0:50Mg0:50O mixture yields an entropy of (40.3� 0.1) J �K�1 �mol�1. This value doesnot include configurational entropy from the Co/Mg site disorder. The excess entropy of

Co0:50Mg0:50O is zero within experimental error. Heat capacities were also measured between

T ¼ 298 K and T ¼ 973 K. The enthalpies of mixing do not depend on temperature in thisrange.

� 2003 Elsevier Science Ltd. All rights reserved.

Keywords: CoxMg1�xO solid solution; Enthalpy; Standard entropy; Calorimetry; Interaction parameter

1. Introduction

CoO–MgO is a model system for slightly cation deficient solid solutions

of rocksalt structure [1–4]. It is a randomly diluted magnetic system which

J. Chem. Thermodynamics 35 (2003) 1151–1159

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* Corresponding author. Tel.: +530-752-3292; fax: +530-752-9307.

E-mail address: [email protected] (A. Navrotsky).

0021-9614/03/$ - see front matter � 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0021-9614(03)00083-1

mail to: [email protected]

continues to enjoy considerable interest among theoretical and experimental

physicists [5,6]. Both end-members have the rocksalt structure and offer a rela-

tively simple structural environment in which to access the effect of cation prop-

erties (size, charge and electron configuration) on the thermodynamics. A

number of thermodynamic and kinetic investigations have been performed onthis system [7–14]. Aukrust and Muan [7] determined the activity of CoO in

CoxMg1� xO solid solutions at T ¼ 1473 K by equilibrating with CO2 and CO

or CO2 and H2 gas mixtures. They found ideal behavior within limits of exper-

imental error. Later, Seetharaman and Abraham [9] and Torkar and Inselsb-

acher [12] measured the CoO activity, from emf measurements in solid-state

galvanic cells. Those results showed small positive deviations from ideality and

conformity with a regular solution model. A recent study by Jacob et al. [14]

expressed their activities in terms of a sub-regular model. The experimental re-sults of previous studies utilizing gas equilibration and solid-state galvanic-cell

techniques are listed in table 1.

Enthalpies and entropies of mixing can be calculated from the variation of the ac-

tivities with temperature. However, such determinations can be quite uncertain as a

result of the small temperature range over which equilibrium measurements can

be made and because of errors inherent in defining the temperature dependence of

these data. Thus, independent calorimetric determinations of the heat of mixing is

desirable [15].Previous solution calorimetric results for CoO, MgO and one Co0:5Mg0:5O

sample [13,16–18] are shown in table 2. We utilized improved oxide melt solution

calorimetric techniques, low temperature adiabatic calorimetry and scanning micro-

calorimetry to investigate CoO–MgO solid solutions. The enthalpy of drop solution

was directly measured in molten sodium molybdate (3Na2O � 4MoO3) solvent atT ¼ 973 K. When combined with the available activity-composition data, measure-ments of the enthalpies of mixing of the solid solutions yield the entropy of mix-

ing and provide information concerning the nature of interactions in theCoO–MgO system.

TABLE 1

Previous thermodynamics studies of the CoO–MgO system

Lit. Authors T/K aCoOa DmixHm

b SEm Methods

(kJ �mol�1) (J �K�1 �mol�1)

1963 Aukrust et al. [7] 1473 ¼XCoO 0 0 Gas equi.

1971 Bren�zz�yy et al. [8] 1473 ¼XCoO 0 0 Gas equi.

1971 Seetharaman et al. [9] 1073–1273 PXCoO 1.0� 0.6 0 Solid cell

1972 Popov et al. [10] 1123–1423 PXCoO )0.2 – Gas equi.

1974 Rigaud et al. [11] 1273–1473 PXCoO + + Solid cell

1980 Torkar et al. [12] 1100–1300 PXCoO 1.2� 0.6 0 Solid cell

1992 Jacob et al. [14] 1373 PXCoO 1.7 0.7 Solid cell

a aCoO ¼ activity of CoO; X¼mole fraction of CoO.bValues of DmixHm and SEm are at X ¼ 0:5.

1152 L. Wang et al. / J. Chem. Thermodynamics 35 (2003) 1151–1159

2. Experimental methods

2.1. Sample preparation

The CoO was prepared by heating Co3O4 (Alpha-Aesar, Johnson Matthey,

mass fraction 0.997 metals basis, Stock No. 40184, CAS# 1308-06-1) in air at

T ¼ 1123 K for 1 h, and then heating it under argon at T ¼ 1173 K for 24 h.

The sample was then cooled under argon for 6 h. MgO was a commercial samplefrom Alpha-Aesar (Johnson Matthey, mass fraction 0.9999 metals basis, Stock No.

43186, CAS# 1309-48-4). It was heated at T ¼ 973 K for 4 h in a vacuum furnace

before use.

The CoO–MgO solid solutions were synthesized under argon by solid-state reac-

tion of a stoichiometric mixture of the end members at T ¼ 1373 K. After 48 h ofheat treatment with two intermediate grindings, the solid solution was subjected

to a final 48 h treatment under argon at T ¼ 1273 K. The treatments under argonminimized Co3þ content [13].

2.2. Characterization

All samples were examined by X-ray diffraction, using a Scintag PAD V diffrac-

tometer (Cu Ka radiation, 45 kV, 40 mA, and h–2h goniometer geometry), with astep size of 0.02 degree and a collection time of 10 s/step. The diffraction patterns

show all the samples are single phase materials having rocksalt structure. Lattice pa-

rameters were refined by the program Jade 6.0 [19] using all the peaks. These latticeparameters (see table 3), within experimental limits of error, confirm Vegard�s Lawand are in agreement with those reported by Kannan [6], Davies and Navrotsky

[13], and Schnahage et al. [20].

The compositions of CoxMg1� xO were determined by electron microprobe anal-

ysis on a Cameca SX-50 instrument with a beam current of 10.02 A and an acceler-

ating voltage of 20 kV. Pellets (�5 mg) were fixed in a plastic mount with epoxyresin, and polished with diamond paste. Well-polished cobalt oxide and magnesium

TABLE 2

Heats of solution of CoO–MgO system determined by previous studies

Composition Solvent, T/K Heat of solution

(kJ �mol�1)

CoO 3Na2O � 4MoO3 (970 K) [16] )20.51� 0.399PbO � 3CdO � 4B2O (970 K) [16] 23.95� 0.632PbO �B2O3 (986 K) [13] 21.38� 1.262PbO �B2O3 (965 K) [18] 24.81� 0.46

MgO 3Na2O � 4MoO3 (970 K) [16] )37.10� 0.309PbO � 3CdO � 4B2O (970 K) [16] )9.17� 0.662PbO �B2O3 (986 K) [13] 4.88

3Na2O � 4MoO3 (973 K) [17] )37.6� 0.6Co0:5Mg0:5O 2PbO �B2O3 (986 K) [13] 12.78� 0.76

L. Wang et al. / J. Chem. Thermodynamics 35 (2003) 1151–1159 1153

oxide were used as standards. The results (see table 3) show all samples are homo-

geneous and close to the nominal compositions.

A Setaram TG-96 thermogravimetric system was employed to examine the defect

concentration in CoO. The sensitivity of this equipment is 0.01 mg. CoO (1.5 g) was

heated to T ¼ 1173 K at 5 K �min�1 in pure nitrogen (99.9997 per cent). The ob-served weight loss was 0.08 mg (0.005 per cent). The weight gain in oxygen at

T ¼ 1123 K was determined to be 7.12 per cent, which is exactly the theoretical

weight change for CoO to Co3O4 conversion. These experimental results indicatethat the CoO sample is stoichiometric CoO and not more oxidized than CoO1:001.

The MgO sample was analyzed by TG/FTIR in order to determine any possible

contamination by MgCO3 and H2O. Thermal analyses (TG/DSC) were performed

on a Netzsch STA 449 apparatus. The heating rate was 10 K �min�1 to T ¼ 1373 Kwith an argon atmosphere. The gas evolved was sampled and analyzed (2 scans �min�1) by Fourier transform infrared spectroscopy (FTIR) using a Bruker Equinox

55 spectrometer. Spectra were recorded in the 400 cm�1 to 4000 cm�1 range with a res-

olution of 4 cm�1. The total weight loss was 0.2 per cent below T ¼ 573 K and noweight loss above this temperature. The total amount of H2O was less than 0.1 per

cent. This would not affect calorimetric results significantly. NoMgCO3 was detected.

2.3. Calorimetry

The high-temperature twin Calvet solution calorimeter and the technique used

have been described previously by Navrotsky [21,22]. In this study, sodium molyb-

date (3Na2O � 4MoO3) was used as solvent. Pellets (�15 mg) of end-members andCoxMg1� xO samples were dropped from room temperature into liquid

3Na2O � 4MoO3 solvent at T ¼ 973 K in the calorimeter. Argon gas was flushed

through the calorimeter at 90 mL �min�1 and bubbled through the solvent at5 mL �min�1. The samples dissolved quickly and no calorimetric difficulties wereencountered. The oxidation state of cobalt in the solvent is Co2þ [23].

High temperature heat capacity measurements were carried out on a Setaram

DSC 111 (a Calvet-type instrument) calorimeter in the temperature range

298 < T=K < 973, with 10 K �min�1 heating rate in an atmosphere of pure nitrogen.

TABLE 3

Lattice parameters of CoO–MgO solid solutions from XRD patterns and compositions from stoichiom-

etry and microprobe analysis

Sample Nominal XCoO AnalyzedaXCoO (Lattice parameters) 1010=m

CMO001 0.90 0.89� 0.01 4.2566� 0.0008CMO002 0.75 0.74� 0.01 4.2505� 0.0010CMO003 0.60 0.58� 0.01 4.2415� 0.0008CMO004 0.50 0.50� 0.01 4.2383� 0.0006CMO005 0.40 0.40� 0.01 4.2344� 0.0006CMO006 0.25 0.26� 0.01 4.2280� 0.0044CMO007 0.10 0.09� 0.004 4.2185� 0.0006aUncertainty is two standard deviations of the mean.


NIST Standard Reference Material (SRM 720) synthetic sapphire (a-Al2O3) wasused as a Cp standard. Samples (�100 mg) were loaded into a boat shaped platinumcrucible. Proper operation of the calorimeter was verified by measuring the heat ca-

pacity of magnesium oxide. The measured data for magnesium oxide deviated from

tabulated Cp [24] by an average of 1 per cent, and we estimate this to represent theoverall accuracy of the measurements.

Adiabatic calorimetry was performed with a home-built calorimeter of the We-

strum design, described by Woodfield et al. [25]. The calorimetric accuracy was tested

by Cp measurements of a-Al2O3 (NIST SRM 720) over the region 15 < T=K < 400.The deviations from the recommended Cp values [26] were � 2 per cent near T ¼ 15K; they decreased systematically to � 0.15 per cent at T ¼ 50 K, and were within� 0.15 per cent in the region 50 < T=K < 400 K. The sample used for measurementwas about 10 g. Those data will be presented in detail separately.

3. Results and discussion

3.1. Enthalpy of formation

Solution calorimetric results are given in table 4. The enthalpy of drop solution

(DdsHm) of CoO is in agreement with (15.7� 0.4) kJ �mol�1, which calculated fromthe sum of the enthalpy of solution (DsolHm) [16] and enthalpy increment calculated

from the measured heat capacities. The DdsHm of MgO is in agreement with

()5.6� 0.6) kJ �mol�1 calculated from the previously measured DsolHm [16,17] and

enthalpy increment. The values of DdsHm of CoxMg1� xO are plotted as a function

of composition in figure 1. The system shows slightly positive enthalpies of mixing

(DmixHm), as shown in table 5. The values of DmixHm were determined from the dif-

ference between the ideal DdsHm (a linear combination of the end-member DdsHm)

and the observed DdsHm (see figure 2).

TABLE 4

Enthalpies of drop solution in 3Na2O � 4MoO3 at T ¼ 973 KXCoO DdsHm

(kJ �mol�1)a

1 15.66� 0.59 (8)0.89 12.68� 0.42 (8)0.74 9.17� 0.26 (9)0.58 5.66� 0.18 (8)0.50 3.81� 0.31 (8)0.40 1.77� 0.05 (6)0.26 )0.89� 0.14 (8)0.09 )3.98� 0.15 (7)0 )5.34� 0.26 (8)aUncertainty is two standard deviations of the mean; the number in parentheses is the number of

experiments.


The observed DdsHm can be fitted to a quadratic equation, given by

DdsHm=ðkJ �mol�1Þ ¼ ð5:1� 0:3Þx2 þ ð15:9� 0:6Þx� ð5:4� 0:2Þ;r2 ¼ 0:9999; ð1Þ

with r the correlation coefficient. The fitted curve (figure 1) is symmetric. This rep-

resents regular solution behavior relative to the end-members, with a small positive

DmixHm.

The excess Gibbs free energy of mixing (GEm) was calculated from the activity datareported by Torkar and Inselsbacher [12] at T ¼ 1300 K. They used solid-stategalvanic-cell techniques to measure the CoO activities in the solid solutions.

FIGURE 1. Enthalpy of drop solution (DdsHm) of CoxMg1� xO in sodium molybdate solvent at T ¼ 973K plotted against mole fraction CoO. The solid curve represents the quadratic fit to the experimental data,

given by equation (1) in the text; the dashed line represents ideal mixing.

TABLE 5

Thermodynamic properties of mixing of CoxMg1�xO solid solutions at T ¼ 298 KXCoO XMgO DmixHm GEm

(kJ �mol�1)a (kJ �mol�1)b

1 0

0.89 0.11 0.68� 0.42 0.66

0.74 0.26 1.03� 0.26 1.12

0.58 0.42 1.18� 0.18 1.31

0.50 0.50 1.35� 0.31 1.33

0.40 0.60 1.30� 0.54 1.30

0.26 0.74 1.02� 0.14 1.12

0.09 0.91 0.53� 0.15 0.60

0 0

aUncertainty is the uncertainty of DdsHm.bThe reported error is 0.63 kJ �mol�1 [12].


The analysis of Torkar and Inselsbacher [12] gives

GEm ¼ HEm � TSEm; ð2Þ

with HEm ¼ ð1:2 � 0:6) kJ �mol�1 and SEm is zero within the experimental error.

The activity data of Torkar and Inselsbacher [12] were determined at T ¼ 1300 K,while our calorimetric heats of mixing refer to T ¼ 298 K. Any temperature depen-dence in the heat of mixing would be related to excess heat capacities. This effect is

probably negligibly small, as discussed below. The excess free energies are given intable 5.

The DmixHm can be fitted by a regular model, given by

DmixHm ¼ WXCoOð1� XCoOÞ; ð3Þwhere W is the enthalpy parameter and with mole fraction XCoO. A value of

(5.1� 0.3) kJ �mol�1 was found from our measurements. The quoted standard errorreflects the scatter in the heats of drop solution.W can also be calculated independently from activity measurements by fitting the

expression

RT ln aCoO ¼ ð1� XCoOÞ2W þ RT ln XCoO; ð4Þwhere aCoO is the activity of CoO in a mixture. The value derived form activity-com-

position relations reported by Torkar and Inselsbacher [12], is (4.8� 0.6) kJ �mol�1, isin agreement with the calorimetric value derived above, (5.1� 0.3) kJ �mol�1. Thissuggests that excess entropies of mixing are zero within experimental error.

3.2. Excess entropy

Heat capacities of CoO, MgO and Co0:50Mg0:50O solid solution were measured by

an adiabatic calorimeter at 9 < T=K < 400, and by a continuous microcalorimeter

FIGURE 2. Enthalpies of mixing, DmixHm, plotted against mole fraction CoO in CoxMg1�xO at T ¼ 298K. Error bars shown are two standard deviations of the DdsHm measurements. Curve is calculated using

equation (3).


scan in 300 < T =K < 980. The measured heat capacity data, derived thermodynamicfunctions and an analysis of the magnetic and electronic contributions to the heat

capacity will be discussed in a separate paper.

The standard entropy D298:150 S0m of CoO and MgO calculated from subambient

heat capacities are (52.8� 0.1) J �K�1 �mol�1 and (28.1� 0.1) J �K�1 �mol�1, respec-tively. The integration of the Cp/T curve of Co0:50Mg0:50O from T ¼ 0 to T ¼ 298 Kyielded a value of (40.2� 0.1) J �K�1 �mol�1. This entropy does not include theconfigurational entropy from the Co/Mg site disorder in the solid solution. From

the difference between this quantity and the weighted sum of the entropies of the

end-members, we obtain the excess (non-configurational) entropy, (0.2� 0.2)J �K�1 �mol�1. Thus, the nonconfigurational excess entropy is essentially zero.The D973298Hm, calculated from the experimental heat capacities for CoO, MgO and

Co0:50Mg0:50O, is {(36.6� 0.1), (31.5� 0.1), and (33.9� 0.1)} kJ �mol�1 respectively.Thus, the excess heat content of Co0:50Mg0:50O compared with end-members is

(0.2� 0.2) kJ �mol�1. This suggests the temperature dependence of the heat of mixingis negligible at 2986 T=K6 973, and probably to higher temperature. This result is

certainly reasonable given the structural similarities of the three materials and that

they should all approach the same heat capacity limit at high temperatures.

4. Conclusion

High temperature oxide melt calorimetry determined the enthalpies of mixing of

CoxMg1� xO at T ¼ 298 K. Symmetric slightly positive enthalpies of mixing are con-sistent with regular solution behavior. The enthalpy interaction parameter, W , wasmeasured to be (5.1� 0.3) kJ �mol�1. The excess entropy is zero within the experi-mental errors and the enthalpy of mixing shows negligible temperature dependence.

Acknowledgement

This work was supported by the US Department of Energy (DOE ) under Grant

No. DEFGO301ER1S237.

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Thermodynamics of CoO–MgO solid solutions

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