Correlations between structure and thermodynamic properties of spinels and their applications in technology

Measurements a/the Gibbs' energy enthalpy and entrupy vffarmation oj chromites, vanadites and alumlnat.:s 0/ F", Ni. Co'. Mn, Zn Mg and Cd, using solid oxide galvanic cells over a ternperature range extending approximately lOOO°C, have shown that the '~'Ilir"!,,, J'JrIl/iJ~ tion 0/ cubic 2-3 oxide spinel phases (MX!O,), from component oxide (MO) with rock-salt and X.Os whir c(1f'l/!ldwn st!'llt'lw,·. call b,' represented by a semi-empirical correlalion, ~S~ = --LiS + L'i,SM +~S~:"d(±O.3) cal.deg-1 mol-1 where /',.SM Is the entropy 0/calian mixing oillhe tetrahedral alld octahedral sites o/the spinel and Sr:~ is tlie enfropy associaf,'d Wifh Ih,' randomization a/the lahn-Telier distortions. A review a/the methods/or evaluating the cation distriblltion lfl spille!s suggeJ{j' l/r,l! Ihe most promising scheme is based Oil octahedral site preference energies from the crystal field theory for the Iral1silioll IIIl'f"! IlIIL';. For I/""-Irallsifioll melal cal ions site preference energies are derived relative /0 thol'lt fLI, [ransilion metal ions from measured high tClllP('ftJi ure Cal iUlI disll iiJuriol1 in spine! phases thar contail! one IransilioJl metal and another non-transition metal carion. For 2-3 srinds compulatiorrs b,IS"J Oil i.!c[J;' Temkin mixing on each catioll subialtice predici JistributionJ that are In fair agreement with X-ray and 1I1'IIIrOll ditTraction, /IIdg""!ic dll.! electrical propcrries, and spectroscopic measurements. In 2-4 spineis mixing vI ions do not foliow strictly ideal slllIistli:al Jaws, Th,' OIl/up) associated with the randomizalion 0/the Jllhn-Teller dislOriioll" appear to be significant, only ill spinels witll 3d'. 3d', 3d' (ifld~UI' iOtls in tetrahedral and 3d' and 3d9 ions in octahedral positions. Application 0/this structural model for predicting the thermodynamic proputies ofspinel solid .,olutiofl5 or,' illustrated. F,lr complex systems additional contributions arising from strain fields, redox equilibria and off-center ions have to be qllalllififti. The entropy correlation for spinels provides a method for evaluating structure tran:.jormafiofl entropies in silllple o.\id.-s, ["founlllion on the relative stabilities ofoxides in different crystallCtructures is USe/III for computer ea/culaliof! a/phase dfugrullls ofIlIrer,',,1 III (N.lll1ie5 by method, similar to thost: used by Kaufman and Bernstein for refractory alloy systems. Examples oftechnoiogical appliCation tnclude the predictioll ofdeoxidation equilibria in Fe-Mn-AI-O s),slelll at 1600°C duj ,'Ulllpltfalion 0/phase relutions in Fe-Ni-Cr-S system,

Phase relationships in the system Cr W O and thermodynamic properties of CrWO4 and Cr2WO6

The phase diagram of the Cr-W-O system at 1000° C was established by metallographic and X-ray identification of the phases present after equilibration in evacuated silica capsules. Two ternary oxide phases, CrWO4 and Cr2WO6 were detected. The oxygen potential over the three-phase mixtures, W+Cr2O3 s+CrWO4, WO2.90+CrWO4+Cr2WO6 and Cr2O3+CrWO4+Cr2WO6, were measured by solid state cells incorporating Y2O3 stabilized ZrO2 electrolyte and Ni+NiO reference electrode. The Gibbs' energies of formation of the two ternary phases can be represented by the following equations

A derivation of thermodynamic quantities of liquid alloys from their structure factors

A method of deriving the thermodynamic properties of mixing in liquid alloys Delta G, Delta S and Delta H, from low-Q scattering data has been presented. As an example, the method has been demonstrated with liquid Na-Ga alloys for which both thermodynamic and diffraction data have recently been obtained by the authors.

Computation of thermodynamic properties of liquid ferrous alloys from structural measurements

Relation between X-ray scattering intensities, mean square thermal fluctuations and thermodynamic properties. High temperature X-ray diffraction study of liquid Fe-Ni and Fe-Si alloys using reflection and transmission geometries. Calculation of the structure factor as a function of wave vector. Extrapolation to zero wave vector. Calculation of the concentration-concentration correlation function defined by A. B. Bhatia and D. E. Thorton. Computation of thermodynamic quantities of mixing A G, LlH and LlS for the binary alloys. Comparison with direct thermodynamic measurements reported in the literature.

Mass spectrometric and electrochemical studies of thermodynamic properties of liquid and solid phases in the CaO Al2O3 system

The activities of CaO and Al2O3 in lime-alumina melts were studied by Knudsen cell-mass spectrometry at 2060 K. Emf of solid state cells, with CaF2 as the electrolyte, was measured from 923 to 1223 K to obtain the free energies of formation of the interoxide compounds. The results are critically evaluated in the light of data reported in the literature on phase equilibria, activities in melts, and stabilities of compounds. A coherent set of data is presented, including the previously unknown free energy of formation of CaO.6Al2O3 and the temperature dependence of activities in the liquid phase.

Thermodynamic properties of Fe3O4 FeV2O4 and Fe3O4 FeCr2O4 spinel solid solutions

Solid solutions of Fe304-FeV204 and Fe304-FeCr204 were prepared and equilibrated with Pt under controlled streams of CO/CO, gas mixtures at 1673 K. The concentration of Fe in Pt was used to determine the activity of Fe304 in the solid solutions. The activity of the second component was calculated by Gibbshhem integration. From these data, the Gibbs energy of mixing was derived for both systems. The experimental results and theoretical values which are determined from calculated cation distribution compare favorably in the case of vanadite solid solutions but not in the case of chromite solid solutions. The difference is attributed to a heat term arising from lattice distortion due to cation size difference. The positive heat of mixing will give rise to a miscibility gap in the system Fe304-FeCr204 at lower temperatures.

Inter and intra crystalline ion exchange equilibria in the system Fe Cr Al O

The tie lines delineating ion-exchange equilibria between FeCr2O4FeAl2O4 spinel solid solution and Cr2O3Al2O3 solid solution with corundum structure have been determined at 1373 K by electron microprobe and EDAX point count analysis of oxide phases equilibrated with metallic iron. Activities in the spinel solid solution are derived from the tie lines and the thermodynamic data on Cr2O3Al2O3 solid solution available in the literature. The oxygen potentials corresponding to the tie-line composition of oxide phases in equilibrium with metallic iron were measured using solid oxide galvanic cells with CaOZrO2 and Y2O3ThO2 electrolytes. These electrochemical measurements also yield activities in the spinel solid solution, in good agreement with those obtained from tie lines. The activity-composition relationship in the spinel solid solution is analysed in terms of the intra-crystalline ion exchange between the tetrahedral and octahedral sites of the spinel structures. The ion exchange is governed by site-preference energies of the cations and the entropy of cations mixing on each site.

Computation of thermodynamic properties of quaternary and higher order systems from binary data using shortest distance composition paths

Equations for the computation of integral and partial thermodynamic properties of mixing in quarternary systems are derived using data on constituent binary systems and shortest distance composition paths to the binaries. The composition path from a quarternary composition to the i-j binary is characterized by a constant value of (Xi − Xj). The merits of this composition path over others with constant values for View the MathML source or Xi are discussed. Finally the equations are generalized for higher order systems. They are exact for regular solutions, but may be used in a semiempirical mode for non-regular solutions.

The Co Cr S ternary diagram at 1223 K and applications to corrosion

Ternary phase relations in the Co-Cr-S system at 1223 K were determined using microprobe analysis of quenched samples. The results are consistent with the data available on the binary systems. A complete solid solution exists between cobalt monosulfide and chromium monosulfide. The CoCr2S4 thiospinel is the only ternary compound formed. A sulfur potential diagram was constructed for the region involving equilibrium between alloy and monosulfide based on thermodynamic data on the Co-Cr, Co-S, and Cr-S binary systems and the ternary information obtained in this study. The sulfidation behavior of Co-Cr alloys reported in the literature is discussed in light of the sulfur potential diagram.

Thermodynamic properties and phase boundaries of Co O solutions

The thermodynamic properties of liquid unsaturated Co--O solutions have been determined by electrochemical measurements using (Y sub 2 O sub 3 )ThO sub 2 as solid electrolyte. The cell can be represented as, Pt. MoO sub 2 + Mo | (Y sub 2 O sub 3 )ThO sub 2 | O sub Co , tungsten, Pt, Emf of the cell was measured as a function of oxygen concentration in liquid Co at 1798, 1873 and 1973K. Least-mean squares regression analysis of the experimental data gives for the free energy of solution of diatomic oxygen in liquid Co Delta G exp 0 sub O(Co) = --84935--7.61 T ( plus/minus 400) J/g-atom and self interaction parameter for oxygen epsilon exp O sub O = --97240/T + 40.52 ( plus/minus 1) where the standard state for O is an infinitely dilute solution in which the activity is equal to atomic percent. The present data are discussed in comparison with those reported in the literature and the phase diagram for the Co--O system. 18 ref.--AA.

Oxygen content of liquid cobalt in equilibrium with CoO.(1+x)Al2O3 and -Al2O3

The oxygen concentration of liquid cobalt in equilibrium with cobalt aluminate and a-alumina has been measured by suction sampling and crucible quenching techniques at temperatures between 1770 and 1975 K. Experiments were made with cobalt of high and low initial oxygen contents, and with and without the addition of cobalt aluminate. The effect of temperature on the equilibrium oxygen content is represented by the equation, log (at.% 0) = -10,4001T(K) + 4.64 (±0.008). The composition of the spinel phase, CoO.(1+x)AI20 3, saturated with alumina, has been determined by electron probe microanalysis. The values of x are 0.22 at 1770 Kand 0.28 at 1975 K. The oxygen potential corresponding to the three-phase equilibrium between cobalt, aluminate and alumina, and the standard Gibbs' energy of formation of nonstoichiometric cobalt aluminate are evaluated by combining the results of this study with recently published data on the activity of oxygen in liquid cobalt. Implications of the present results to aluminium deoxidation of liquid cobalt are discussed.

A galvanic sensor for SO3/SO2 based on CaF2/CaSO4 couple

Measurements on the solid state cell, View the MathML source using single crystal CaF2 as the solid electrolyte and CaSO4 as an auxiliary electrode, indicate that the EMF is in agreement with that predicted by the Nernst equation when equilibrium is assumed in the gas phase near the electrodes. The cell can be used to measure the View the MathML source content of gases at temperatures near 1200 K, where approximately 2 h ate required to obtain a steady EMF, without the use of catalysts to improve the kinetics of exchange reaction in the auxiliary electrode. For most applications, the cell EMF will be affected by the presence of water vapour in the gas phase. The cell is well suited for thermodynamic measurements on sulfates, pyrosulfates and their solid and liquid solutions.

Alloy/Oxide Equilibria in Iron--Vanadium--Oxygen and Iron--Niobium--Oxygen Systems

An experimental characterization of three-phase equilibria in Fe--V--O and Fe--Nb--O systems at 1823, 1873 and 1923K has been carried out using a solid state cell and by analysis of quenched samples. The oxygen potentials corresponding to these three-phase equilibria were monitored by a solid state cell incorporating Y sub 2 O sub 3 doped ThO sub 2 with Cr + Cr sub 2 O sub 3 as reference electrode. Similar measurements were carried out for Fe--Nb--O alloys in equilibrium with a mixture of FeNb sub 2 O sub 6 and NbO sub 2 . These measurements permit evaluation of interaction parameters (e exp V sub O = --6590/T + 2.892 and e exp Nb sub O = --4066/T + 1.502) and activity coefficients of vanadiun and niobium in dilute solution (ln gamma exp O sub V = --35 320/T + 12.68 and ln gamma sub Nb exp O = --12 386/T + 4.34) in liquid iron. The results obtained in this study resolve a number of discrepancies in thermodynamic data reported in the literature, especially regarding the activity coefficients of V and Nb and the stability ranges for V sub 2 O sub 3 and VO sub 1+x . 18 ref.--AA