Electrical conductivity of molten cryolite-based mixtures obtained with a tube-type cell made of pyrolytic boron nitride

A pyrolytic boron nitride tube-type cell was used to measure the electrical conductivity for molten cryolite, for binary mixtures of cryolite with Al₂O₃, AlF₃, CaF₂, KF, Li₃AlF₆, and MgF2, and for ternary mixtures Na₃AlF₆-Al₂O₃-CaF₂ (MgF₂) and Na₃AlF₆-AlF₃-KF (Li₃AlF₆). The cell constant was about 40 cm^?t. The temperature and concentration dependence of the conductivity in the investigated concentration range was described by the equation $$\begin{gathered} \kappa /S cm^{ - 1} = 7.22 exp\left( { - 1204.3/T} \right) - 2.53\left[ {Al_2 O_3 } \right] - 1.66\left[ {AlF_3 } \right] \hfill \\ - 0.76\left[ {CaF_2 } \right] - 0.206\left[ {KF} \right] + 0.97\left[ {Li_3 AlF_6 } \right] - 1.07\left[ {MgF_2 } \right] \hfill \\ - 1.80\left[ {Al_2 O_3 } \right]\left[ {CaF_2 } \right] - 2.59\left[ {Al_2 O_3 } \right]\left[ {MgF_2 } \right] \hfill \\ - 0.942\left[ {AlF_3 } \right]\left[ {Li_3 AlF_6 } \right] \hfill \\ \end{gathered} $$ whereT represents the temperature in Kelvin and the brackets represent the mole fractions of the additions. The standard deviation was found to be 0.026 S cm^?1 (～1 pct). For practical reasons, it is often desired to express composition in weight percent. In that case, it holds that $$\begin{gathered} \ln \kappa = 1.977 - 0.0200\left[ {Al_2 O_3 } \right] - 0.0131\left[ {AlF_3 } \right] - 0.0060\left[ {CaF_2 } \right] \hfill \\ - 0.0106\left[ {MgF_2 } \right] - 0.0019\left[ {KF} \right] + 0.0121\left[ {LiF} \right] - 1204.3/T \hfill \\ \end{gathered} $$ whereT represents the temperature in Kelvin and the brackets denote the concentration of the additives in weight percent. However, in this case, the maximum relative error of the conductivity equation can reach up to 2.5 pct.     

Alumina solubility in molten salt systems of interest for aluminum electrolysis and related phase diagram data

The solubility of alumina in molten Na₃AlF₆ containing various amounts of AlF₃, CaF₂, and LiF was determined by measuring the weight loss of a rotating sintered corundum disc. The results were fitted to the following empirical expression: 1 $$ [Al_2 O_3 ]_{sat} = A\left( {\frac{t} {{1000}}} \right)^B $$ where 2 $$ \begin{gathered} A = 11.9 - 0.062[AlF_3 ] - 0.003[AlF_3 ]^2 - 0.50[LiF] \hfill \\ - 0.20[CaF_2 ] - 0.30[MgF_2 ] + \frac{{42[LiF] \cdot [AlF_3 ]}} {{2000 + [LiF] \cdot [AlF_3 ]}} \hfill \\ B = 4.8 - 0.048[AlF_3 ] + \frac{{2.2[LiF]^{1.5} }} {{10 + [LiF] + 0.001[AlF_3 ]^3 }} \hfill \\ \end{gathered} $$ where the square brackets denote weight percent of components in the system Na₃AlF₆-Al₂O₃ (sat)-AlF₃-CaF₂-MgF₂-LiF and t is the temperature in degree Celsius. The standard deviation between the equation and the experimental points in the temperature range from 1050 °C to about 850 °C was found to be 0.29 wt pct Al₂O₃. A series of revised phase diagram data of interest for aluminum electrolysis was derived based on the present work and recently published data for primary crystallization of Na₃AlF₆ in the same systems.     

Liquidus temperatures for primary crystallization of cryolite in molten salt systems of interest for aluminum electrolysis

Temperatures for primary crystallization of Na₃AlF₆ in multicomponent electrolyte systems of interest for the aluminum electrolysis process were determined by thermal analysis. The results are presented as binary and quasibinary diagrams and discussed in view of the literature data. An empirical equation describing liquidus temperatures for primary crystallization of Na₃AlF₆ was derived: $$\begin{gathered} t/(^\circ C) = 1011 + 0.50[AlF_3 ] - 0.13[AIF_3 ] - \frac{{3.45[CaF_2 ]}}{{1 + 0.0173[CaF_2 ]}} \hfill \\ + 0.124[CaF_2 ] \cdot [AlF_3 ] - 0.00542([CaF_2 ] \cdot [AlF_3 ])^{1.5} \hfill \\ - \frac{{7.93[Al_2 O_3 ]}}{{1 + 0.0936[Al_2 O_3 ] - 0.0017[Al_2 O_3 ]^2 - 0.0023[AlF_3 ] \cdot [Al_2 O_3 ]}} \hfill \\ - \frac{{8.90[LiF]}}{{1 + 0.0047[LiF] + 0.0010[AlF3]^2 }} - 3.95[MgF_2 ] - 3.95 \hfill \\ \end{gathered} $$ wheret is the temperature in degree Celsius and the square brackets denote the weight percent of components in the system Na₃AlF₆-AlF₃-CaF₂-Al₂O₃-LiF-MgF₂-KF. The composition limitations are [AlF₃] ≈ [CaF₂] ≈ [LiF] < 20 wt pct, [MgF₂] ≈ [KF] < 5 wt pct, and [A1₂O₃] up to saturation.     

Thermodynamic properties of Na2O-SiO2-CaO melts at 1000 to 1100 °C

The thermodynamic properties of Na₂O-SiO₂ and Na₂O-SiO₂-CaO melts have been measured using the galvanic cell Activities of Na₂O were calculated from the reversible emf of the cell. This is possible because the activity of Na₂O in the Na₂O-WO₃ liquid is known from previous work. Data for the binary Na₂O-SiO₂ system were obtained between 1000 and 1100 °C and for compositions ranging from 25 wt pct to 40 wt pct Na₂O. At 1050 °C, Log varied from approximately 10.2 at 25 wt pct Na₂O to approximately −8.3 at 40 wt pct Na₂O, the dependence with respect to composition being nearly linear. The Gibbs-Duhem equation was used to calculate the activities of SiO₂(s), and the integral mixing properties,G ^M, H^M, andS ^M, were derived. At the di-silicate composition,G ^M = −83 kJ/mol,H ^M = −41 kJ mol andS ^M = 33 J/mol K at 1000 °C. (Standard states are pure, liquid Na₂O and pure, solid tridymite.) The activity data are interpreted in terms of the polymeric nature of silicate melts. Activities of Na₂O in the Na₂O-CaO-SiO₂ system were measured for the 25, 30 and 35 wt pct Na₂O binary compositions with up to 10 wt pct CaO added. The addition of CaO caused an increase in the activity of Na₂O at constant . The experimental data agree well with the behavior predicted by Richardson’s ternary mixing model.     

Reactive infiltration of 25 vol pct TiO2/Al composites

The purpose of this investigation was to establish the reaction path during processing of a 25 vol pct TiO₂ preform and molten Al composite by pressure infiltration. Initial preform temperatures between 550° and 850 °C, melt temperatures from 715° to 850 °C, and two postinfiltration cooling rates were considered. The reaction path between molten Al and TiO₂ under the conditions examined involved three steps:

The oxygen potential of the systems Fe+FeCr2O4+Cr2O3 and Fe+FeV2O4+V2O3 in the temperature range 750–1600°C

From electromotive force (emf) measurements using solid oxide galvanic cells incorporating ZrO₂-CaO and ThO₂?YO_1.5 electrolytes, the chemical potentials of oxygen over the systems Fe+FeCr₂O₄+Cr₂O₃ and Fe+FeV₂O₄+V₂O₃ were calculated. The values may be represented by the equations: $$\begin{gathered} 2Fe\left( {s,1} \right) + O_2 \left( g \right) + 2Cr_2 O_3 \left( s \right) \to 2FeCr_2 O_4 \left( s \right) \hfill \\ \Delta \mu _{O_2 } = - 151,400 + 34.7T\left( { \pm 300} \right) cal \hfill \\ = - 633,400 + 145.5T\left( { \pm 1250} \right) J \left( {750 to 1536^\circ C} \right) \hfill \\ \Delta \mu _{O_2 } = - 158,000 + 38.4T\left( { \pm 300} \right) cal \hfill \\ = - 661,000 + 160.5T\left( { \pm 1250} \right) J \left( {1536 to 1700^\circ C} \right) \hfill \\ 2Fe\left( {s,1} \right) + O_2 \left( g \right) + 2V_2 O_3 \left( s \right) \to 2FeV_2 O_4 \left( s \right) \hfill \\ \Delta \mu _{O_2 } = - 138,000 + 29.8T\left( { \pm 300} \right) cal \hfill \\ = - 577,500 + 124.7T\left( { \pm 1250} \right) J \left( {750 to 1536^\circ C} \right) \hfill \\ \Delta \mu _{O_2 } = - 144,600 + 33.45T\left( { \pm 300} \right) cal \hfill \\ = - 605,100 + 140.0T\left( { \pm 1250} \right) J \left( {1536 to 1700^\circ C} \right) \hfill \\ \end{gathered} $$ . At the oxygen potentials corresponding to Fe+FeCr₂O₄+Cr₂O₃ equilibria, the electronic contribution to the conductivity of ZrO₂?CaO electrolyte was found to affect the measured emf. Application of a small 60 cycle A.C. voltage with an amplitude of 50 mv across the cell terminals reduced the time required to attain equilibrium at temperatures between 750 to 950°C by approximately a factor of two. The second law entropy of iron chromite obtained in this study is in good agreement with that calculated from thermal data. The entropies of formation of these spinel phases from the component oxides can be correlated to cation distribution and crystal field theory.     

Activities in the system LiF−NaF−AlF3

Measurements have been made of the contents of Na and Li in Al in equilibrium with the molten fluorides at 1020 °C. The theory to calculate the activities of the three constituents is derived. Across the Li₃AlF₆-Na₃AlF₆ section the activity coefficients {ie409-1} are given in terms of mol fractionsN _i by $$ \begin{gathered} \log \gamma _{{\text{AIF}}_{\text{3}} } = - 3.034 + 3.342N_{LiF} - 0.848(N_{LiF} )^2 \hfill \\ \log \gamma _{{\text{NaF}}} = - 0.246 - 1.114N_{LiF} - 0.283(N_{LiF} )^2 \hfill \\ \log \gamma _{LiF} = 0.158 - 0.266N_{LiF} - 0.283(N_{LiF} )^2 \hfill \\ \end{gathered} $$ Across the LiF?Na_2.5AlF_5.5 section the activity coefficients for 0≤N _LiF≤0.45 are nearly constant at log \Gg_LiF \t~ 0.1, log \Gg_NaF \t~ 0.4, and log \Gg_{AIF 3} \t~ -2.6.The vapor over these melts is a mixture of LiAlF₄ and NaAlF₄, the pressures being given byp _{LiAlF 4}/bar=0.78a _LiF·a _{AlF 3} andp _{NaAlF 4}/bar=56.2a _NaF·a _{AlF 3}. Combination of these equations with those for the activity coefficients reproduces the maximum observed in the total pressure in the Li₃AlF₆?Na₃AlF₆ section. The increase in pressure observed when Li₃AlF₆ is added to Na₃AlF₆ is due, not to the appearance of LiAlF₄ in the gas, but to the increased pressure of NaAlF₄ following the rise in AlF₃ activity.     

Thermodynamics of iron-aluminum alloys at 1573 K

The activities of iron (Fe) and aluminum (Al) were measured in Fe-Al alloys at 1573 K using the ion-current-ratio technique in a high-temperature Knudsen cell mass spectrometer. The Fe-Al solutions exhibited negative deviations from ideality over the entire composition range. The activity coefficientsγ _Fe, andγ _A1 are given by the following equations as a function of mole fraction (x _Fe,x _Al): 1 $$\begin{gathered} 0< \chi _{A1}< 0.4 \hfill \\ ln \gamma _{Fe} = - 4.511 ( \pm 0.008)\chi _{A1}^2 \hfill \\ ln \gamma _{A1} = - 4.462 ( \pm 0.029)\chi _{Fe}^2 + 0.325( \pm 0.013) \hfill \\ 0.6< \chi _{A1}< 1.0 \hfill \\ ln \gamma _{Fe} = - 4.065 ( \pm 0.006)\chi _{A1}^2 + 0.099( \pm 0.003) \hfill \\ ln \gamma _{A1} = - 4.092 ( \pm 0.026)\chi _{Fe}^2 + 0.002( \pm 0.001) \hfill \\ \end{gathered} $$ The results showed good agreement with those obtained from previous investigations at other temperatures by extrapolation of the activity data to 1573 K.     

Enthalpy of mixing of liquid Ni-Zr and Cu-Ni-Zr alloys

The partial (Δ and the integral (ΔH) enthalpies of mixing of liquid Ni-Zr and Cu-Ni-Zr alloys have been determined by high-temperature isoperibolic calorimetry at 1565 ± 5 K. The heat capacity (C _p) of liquid Ni₂₆Zr₇₄ has been measured by adiabatic calorimetry (C _p=53.5±2.2 J mol⁻¹ K⁻¹ at 1261±15 K). The integral enthalpy of mixing changes with composition from a small positive (Cu-Ni, ΔH (x _Ni=0.50, T=1473 to 1750 K)=2.9 kJ mol⁻¹) to a moderate negative (Cu-Zr; ΔH(x _Zr=0.46, T=1485 K)=−16.2 kJ mol⁻¹) and a high negative value (Ni-Zr; ΔH(x _Zr=0.37, T=1565 K)=−45.8 kJ mol⁻¹). Regression analysis of new data, together with the literature data for liquid Ni-Zr alloys, results in the following relationships in kJ mol⁻¹ (standard states: Cu (1), Ni (1), and Zr (1)):for Ni-Zr (1281≤T≤2270 K),

Solubility product of aluminum nitride in 3 percent silicon iron

The solubility product of aluminum nitride in 3 pct silicon iron was determined experimentally from 1273 to 1473 K with results described by the equation $$\begin{gathered} \log [pct \underline {Al} _{\alpha (3Si) } pct \underline N _{\alpha (3Si)} ] \hfill \\ = {\text{--11,900/}}T + 3.56 \hfill \\ \end{gathered} $$ whereT is in kelvins and concentrations are in weight percent. In the experiments the equilibrium distribution of nitrogen between purified gamma iron (fcc) and 3 pct silicon alpha iron (bcc) was determined between 1273 and 1523 K.     

Determination of standard gibbs energies of formation of Fe2Mo3O12, Fe2Mo3O8, Fe2MoO4, and FeMoO4 of the Fe-Mo-O ternary system and μ phase of the Fe-Mo binary system by electromotive force measurement using a Y2O3-stabilized ZrO2 solid electrolyte

The standard Gibbs energies of formation of Fe₂Mo₃O₁₂, Fe₂Mo₃O₈, FeMoO₄, and Fe₂MoO₄ of the Fe-Mo-O ternary system and the μ phase of the Fe-Mo binary system have been determined by measuring electromotive forces of galvanic cells having an Y₂O₃-stabilized ZrO₂ solid electrolyte. The results are as follows: $$\begin{gathered} \Delta _f G^\circ (FeMoO_4 )/kJ \cdot mol^{ - 1} = - 1053.5 + 0.2983(T/K) \pm 0.4 \hfill \\ Temperature range: 1112 to 1339 K \hfill \\ \Delta _f G^\circ (Fe_2 Mo_3 O_8 )/kJ \cdot mol^{ - 1} = - 2347 + 0.6814(T/K) \pm 1 \hfill \\ Temperature range: 1112 to 1339 K \hfill \\ \Delta _f G^\circ (Fe_2 Mo_3 O_{12} )/kJ \cdot mol^{ - 1} = - 2993 + 0.9105(T/K) \pm 2 \hfill \\ Temperature range: 1040 to 1145 K \hfill \\ \Delta _f G^\circ (Fe_{0.58} Mo_{0.42} )/kJ \cdot mol^{ - 1} = - 18.7 + 0.0117(T/K) \pm 0.1 \hfill \\ Temperature range: 1162 to 1223 K \hfill \\ \Delta _f G^\circ (Fe_2 MoO_4 )/kJ \cdot mol^{ - 1} = - 1174 + 0.342(T/K) \pm 1 \hfill \\ Temperature range: 1243 to 1466 K \hfill \\ \end{gathered} $$ where the standard pressure is 1 bar (100 kPa).     

Mass-spectrometric determination of activities in Fe−Cr and Fe−Cr−Ni alloys

The Knudsen cell-mass spectrometer combination has been used to study the Fe?Cr system and some Fe?Cr?Ni liquid alloys. The Fe?Cr liquid alloys at 1600°C are found to be essentially ideal when referred to pure liquids as standard states. Phase equilibria over a limited composition range for this system are derived from the behavior of the ion-current ratios. The necessary equations are derived to apply the integration technique to the measured ion current ratios in a ternary system and the method is applied to the Fe?Cr?Ni system at 1600°C. The results are represented, within experimental error, by the following equations: forN _Fe≥0.6, $$\begin{gathered} ln \gamma _{Fe} = - 0.08 N_{Ni}^2 \hfill \\ \ln \gamma _{Cr} = 0.09 - 0.08 N_{Ni}^2 \hfill \\ \ln \gamma _{Ni} = - 0.26 - 0.08(1 - N_{Ni} )^2 \hfill \\ \end{gathered} $$ forN _Fe=0.45, $$\begin{gathered} \ln \gamma _{Fe} = - 0.20 N_{Ni}^2 \hfill \\ \ln \gamma _{Cr} = 0.09 - 0.20 N_{Ni}^2 \hfill \\ \ln \gamma _{Ni} = - 0.19 - 0.20(1 - N_{Ni} )^2 \hfill \\ \end{gathered} $$      

Thermodynamic properties of the Cu−Sn and Cu−Au systems by mass spectrometry

The activities and partial molar heats of mixing have been determined in the liquid Cu?Sn system at 1320°C and the liquid Cu?Au system at 1460°C. The experimental technique consisted of the analysis of Knudsen cell effusates with a T.O.F. mass spectrometer. The ion current ratio for the alloy components was measured for each system over a range of temperature and composition and the thermodynamic values calculated by a modified Gibbs-Duhem equation. Both systems exhibited negative deviations from ideal behavior. The results can be partially represented by the equations $$\begin{gathered} \log \gamma _{Cu} = - 0.0175x^2 _{Sn} - 0.302 (0 \leqslant x_{Cu} \leqslant 0.20) \hfill \\ log \gamma _{Sn} = - 0.342x^2 _{Cu} + 1.084(0 \leqslant x_{Sn} \leqslant 0.20) \hfill \\ \end{gathered} $$ for the Cu?Sn system at 1320°C and by $$\begin{gathered} \log \gamma _{Cu} = - 0.703x^2 _{Au} - 0.083(0 \leqslant x_{Cu} \leqslant 0.52) \hfill \\ \log \gamma _{Au} = - 1.057x^2 _{Cu} + 0.098(0 \leqslant x_{Au} \leqslant 0.47) \hfill \\ \end{gathered} $$ for the Cu?Au system at 1460°C.     

Kinetics of formation and dissociation of Na2SiF6

Spontaneous fluoride emissions from high-temperature processes can result in an increased atmospheric fluorine content and environmental contamination. Slags containing SiO₂, Na₂O, and CaF₂ tend to be unstable at high temperatures, and gaseous species such as NaF and SiF₄ evolve simultaneously. Furthermore, a reaction between NaF and SiF₄ can occur to produce Na₂SiF₆ (sodium hexafluorosilicate), the behavior and properties of which are not well established. In a previous study, the diffusivity of NaF in argon, nitrogen, and helium was measured. In this study, the rate of NaF vaporization in a SiF₄-Ar atmosphere was investigated and the rates of formation and dissociation of Na₂SiF₆ were measured. Kinetic analyses were carried out and the rate constants of the formation and dissociation of Na₂SiF₆ were obtained. The rate equation for Na₂SiF₆ formation was expressed as follows:

The thermodynamic properties of liquid Fe−Si alloys

The thermodynamic properties of liquid Fe?Si alloys have been determined electrochemically by use of the following galvanic cells: $$\begin{gathered} Cr - Cr_2 O_3 (s)|ZrO_2 (CaO)|Fe - Si(l), SiO_2 (s) \hfill \\ Cr - Cr_2 O_3 (s)|ThO_2 (Y_2 O_3 )|Fe - Si(l), SiO_2 (s) \hfill \\ \end{gathered} $$ The free energy of formation of SiO₂ was measured and is ?139.0 and ?134.3 kcals per mole at 1500° and 1600°C, respectively. The activity coefficients of iron and silicon for the atom fraction of siliconN _Si<0.35 at 1600° and 1500°C can be represented by the quadratic formalism. $$\begin{gathered} \left. {\begin{array}{*{20}c} {log \gamma _{Fe} = - 2.12 N_{Si}^2 } \\ {log \gamma _{Si} = - 2.12 N_{Fe}^2 - 0.22} \\ \end{array} } \right\}1600^ \circ C (2912^ \circ F) \hfill \\ \left. {\begin{array}{*{20}c} {log \gamma _{Fe} = - 2.50 N_{Si}^2 } \\ {log \gamma _{Si} = - 2.50 N_{Fe}^2 - 0.13} \\ \end{array} } \right\}1500^ \circ C (2732^ \circ F) \hfill \\ \end{gathered} $$ The results indicate that an excess stability peak occurs at about the equimolar composition. Combining the heats of solution determined in this study with previous data indicates that the heats also follow the quadratic formalism. The partial molar heats, \(\bar L_{Si} \) and \(\bar L_{Fe} \) , are represented by $$\begin{gathered} \bar L_{Si} = - 31 N_{Fe}^2 - 4 kcals per mole \hfill \\ \bar L_{Fe} = - 31 N_{Si}^2 kcals per mole \hfill \\ \end{gathered} $$ ForN _Si less than 0.35 and by $$\begin{gathered} \bar L_{Si} = - 22 N_{Fe}^2 \hfill \\ \bar L_{Fe} = - 22 N_{Fe}^2 - 7.0 \hfill \\ \end{gathered} $$ forN _Fe less than 0.35. There is an inflection point in the transition region similar to an excess stability peak for the excess free energies. At 1600°C the ThO₂(Y₂O₃) electrolyte exhibited insignificant electronic conductivity at oxygen partial pressures as low as that in equilibrium with Si?SiO₂ (2×10^?16 atm).     

Thermodynamic properties of the liquid Ge-Cu and Ge-Au systems by mass spectrometry

The activities and partial molar heats of mixing have been determined for the liquid Ge-Cu system at 1525°C and the liquid Ge-Au system at 1400°C. The experimental technique consisted of analyzing Knudsen cell effusates with a TOF mass spectrometer. The ion current ratios for the monomeric vapor species were measured as a function of temperature and composition and the thermodynamic properties calculated using a modified form of the Gibbs-Duhem equations. Both systems exhibited negative deviations from ideal behavior. The results for the Raoultian activity coefficients can be partially represented by $$\begin{gathered} \log \gamma _{Ge} = - 2.521X_{Cu}^2 + 0.948 (0 \leqslant X_{Ge} \leqslant 0.2) \hfill \\ \log \gamma _{Cu} = - 0.048X_{Ge}^2 - 0.466 (0 \leqslant X_{Cu} \leqslant 0.2) \hfill \\ \end{gathered} $$ for the Ge-Cu system at 1525°C and by $$\begin{gathered} \log \gamma _{Ge} = - 2.327X_{Au}^2 + 0.465 (0 \leqslant X_{Ge} \leqslant 0.35) \hfill \\ \log \gamma _{Au} = - 0.510X_{Ge}^2 - 0.489 (0 \leqslant X_{Au} \leqslant 0.30) \hfill \\ \end{gathered} $$ for the Ge-Au system at 1400°C. An experimental technique is presented for determining the contribution of dissociative ionization of polymer species to the measured monomeric ion current ratio . The effect of dissociative ionization of the germanium polymer species present in the Knudsen ceil effusate was determined to be negligible.     

Phase equilibria in the system NiO-CaO-SiO2 and gibbs energy of formation of CaNiSi2O6

Phase relations in the pseudoternary system NiO-CaO-SiO₂ at 1373 K are established. The coexisting phases are identified by X-ray diffraction and energy-dispersive X-ray analysis of equilibrated samples. There is only one quaternary oxide CaNiSi2O6 with clinopyroxene structure. The Gibbs energy of formation of CaNiSi₂O₆ is measured using a solid state galvanic cell incorporating stabilized zirconia as the solid electrolyte in the temperature range of 1000 to 1400 K: From the electromotive force (emf) of the cell, the Gibbs energy of formation of CaNiSi₂O₆ from NiO, SiO₂, and CaSiO₃ is obtained. To derive the Gibbs energy of formation of the quaternary oxide from component binary oxides, the free energy of formation of CaSiO₃ is determined separately using a solid state cell based on single crystal CaF₂ as the electrolyte: The results can be expressed by the following equations:      

Electrochemical determination of gibbs energy of formation of NiTiO3 (ilmenite)

Gibbs energy of formation of NiTiO₃ (ilmenite) relative to its component oxides, NiO (rock salt) and TiO₂ (rutile), has been measured employing the solid-state electrochemical cell,