Evidence of residual entropy in the cubic spinel Zn2TiO4

The standard free energies of formation of Zn2Ti04 and ZnTi03 have been determined in the temperature range 930° to i ioo'x from electromotive force measurements on reversible solid oxide galvanic cells;Ag-5at%znll I Pt, + CaO-Zr02 ZnO I II Ag-5at%Zn Y20r Th02 CaO-Zr02 + ,Pt Zn2Ti04+ ZnTi03 and II Ag-5at%Zn CaO-Zr02 + ,Pt ZnTi03+ Ti02 The values may be expressed by the equations,2ZnO (wurtz) + Ti02(rut) -> Zn2Ti04(sp), f:!:.Go = -750-2-46T (±75)cal;ZnO(wurtz) +Ti02(rut) -> ZnTi03(ilmen) ,f:!:.Co = -]600-0·]99T(±50)cal.Combination of the free energy values with the calorimetric heat of formation, and low-temperature and high-temperature heat capacity of Zn2Ti04 reported in literature, suggests a residual entropy of ],9 (±0·6) cal K-1 mol ? for the cubic spinel. Ideal mixing of Zn2+ and Ti4+ ions on the octahedral sites would result in a configurational contribution to the entropy of 2· 75 cal K-1 rnol ".The difference is indicative of short-range ordering of cations on octahedral sites.

Gibbs free energies of formation of ZnAl2O4 and ZnCr2O4

The standard free energies of formation of zinc aluminate and chromite were determined by measuring the oxygen potential over a solid CuZn alloy, containing 10 at.−% Zn, in equilibrium with ZnO, ZnAl2O4+Al2O3(χ) and ZnCr2O4+Cr2O3, in the temperature range 700–900°C. The oxygen potential was monitored by means of a solid oxide galvanic cell in which a Y2O3 ThO2 pellet was sandwiched between a CaOZrO2 crucible and tube. The temperature dependence of the free energies of formation of the interoxidic compounds can be represented by the equations, The heat of formation of the spinels calculated from the measurements by the “Second Law method” is found to be in good agreement with calorimetrically determined values. Using an empirical correlation for the entropy of formation of cubic spinel phases from oxides with rock-salt and corundum structures and the measured high temperature cation distribution in ZnAl2O4, the entropy of transformation of ZnO from wurtzite to rock-salt structure is evaluated.

Thermodynamics and phase equilibria in the system Cu2O CuO ()Ga2O3

The standard Gibbs free energies of formation of CuAlO2 and CuAl2O4 were determined in the range 700° to 1100°C, using emf measurements on the galvanic cells (1) Pt,CuO +] Cu2O/CaO-ZrO2/O2,Pt; (2) Pt,Cu +] CuAlO2+] Al2O3/CaO-ZrO2/ Cu +] Cu2O,Pt; and (3) Pt,CuAl2O4+] CuAlO2+]Al2O3/CaO-ZrO2/O2,Pt. The results are compared with published information on the stability of these compounds. The entropy of transformation of CuO from tenorite to the rock-salt structure is evaluated from the present results and from earlier studies on the entropy of formation of spinels from oxides of the rock-salt and corundum structures. The temperatures corresponding to 3-phase equilibria in the system Cu2O-CuO-Al2O3 at specified O2 pressures calculated from the present results are discussed in reference to available phase diagrams.

Ion exchange equilibria between (Mn,Co)O solid solution and (Mn,Co)Cr2O4 and (Mn,Co)Al2O4 spinel solid solutions at 1100oC

The compositions of the (Mn,Co)O solid solution with rock salt structure in equilibrium with (Mn,Co)Cr2O4 and (Mn,Co)Al2O4 spinel solid solutions have been determined by X-ray diffraction measurements at 1100° C and an oxygen partial pressure of 10–10 atm. The ion exchange equilibria are quantitatively analysed, using values for activities in the (Mn,Co)O solid solution available in the literature, in order to obtain activities in the spinel solid solutions. The MnAl2O4-CoAl2O4 solid solution exhibits negative deviations from Raoult's law, consistent with the estimated cation disorder in the solid solution, while the MnCr2O4-CoCr2O4 solid solution shows slightly positive deviations. The difference in the Gibbs free energy of formation of the two pure chromites and aluminates derived from the results of this study are in good agreement with recent results obtained from solid oxide galvanic cells and gas-equilibrium techniques.

Activities and their relation to cation distribution in NiAl2O4 MgAl2O4 spinel solid solutions

The activity of NiAl2O4 in NiAl2O4MgAl2O4 solid solutions has been measured by using a solid oxide galvanic cell of the type, Pt, Ni + NiAl2O4 + Al2O3(α)/CaOZrO2/Ni + NixMg1−xAl2O4 + Al2O3(α). Pt, in the temperature range 750–1150°C. The activities in the spinel solid solutions show negative deviations from Raoult's law. The cation distribution in the solid solutions has been calculated using site preference energies independent of composition for Ni2+, Mg2+, and Al3+ ions obtained from crystal field theory and measured cation disorder in pure NiAl2O4 and MgAl2O4, and assumi g ideal mixing of cations on the tetrahedral and octahedral positions. The calculated values correctly predict the decrease in the fraction, α, of Ni2+ ions on tetrahedral sites for 1>x>0.25, observed by Porta et al. [J. Solid State Chem.11, 135 (1974)] but do not support their tentative evidence for an increase in α for x < 0.25. The measured excess free energy of mixing can be completely accounted for by using either the calculated or the measured cation distributions. This suggests that the Madelung energy is approximately a linear function of composition in the solid solutions. The composition of NiOMgO solid solutions in equilibrium with NiAl2O4MgAl2O4 solid solutions has been calculated from the results and information available in literature.

Solubility and activity of oxygen in liquid indium and copper indium alloys

The solubility of oxygen in liquid indium in the temperature range 650–820 °C and in liquid copper-indium alloys at 1100 °C in equilibrium with indium sesquioxide has been measured by a phase equilibration technique. The solubility of oxygen in pure indium is given by the relation log(at.% O) = −4726/T + 3.73 (±0.08) Using the recently measured values for the standard free energy of formation of In2O3 and assuming that oxygen obeys Sievert's law up to saturation, the standard free energy of solution of molecular oxygen in liquid indium is calculated as View the MathML sourceΔG°= −51 440 + 8.07 T (±500) cal where the standard state for dissolved oxygen is an infinitely dilute solution in which activity is equal to atomic per cent. The effect of indium additions on the activity coefficient of oxygen dissolved in liquid copper was measured by a solid oxide galvanic cell. The interaction parameter ϵ0In is given by View the MathML source The experimentally determined variation of the activity coefficient of oxygen in dilute solution in Cu-In alloys is in fair agreement with that predicted by a quasichemical model in which each oxygen atom is assumed to be interstitially coordinated to four metal atoms and the nearest neighbour metal atoms are assumed to lose approximately half their metallic cohesive energies.

Activities in the spinel solid solution, phase equilibria and thermodynamic properties of ternary phases in the system Cu Fe O

A review of the structural and thermodynamic information and phase equilibria in the Cu-Fe-O system suggested that a consistent, quantitative description of the system is hampered by lack of data on activities in the spinel solid solution CuFe2O4-Fe3O4. Therefore the activity of Fe3O4 in this solid solution is derived from measurements of the oxygen potentials established at 1000°C by mixtures containing Fe2O3 and spinel solid solutions of known composition. The oxygen pressures were measured manometrically for solid solutions rich in CuFe2O4, while for Fe3O4-rich compositions the oxygen potentials were obtained by an emf technique. The activities show significant negative deviations from Raoult’s law. The compositions of the spinel solid solutions in equilibrium with CuO + CuFeO2 and Cu + CuFeO2 were obtained from chemical analysis of the solid solution after magnetic separation. The oxygen potential of the three-phase mixture Cu + CuFeO2 + Fe3O4(spinel s.s.) was determined by a solid oxide galvanic cell. From these measurements a complete phase diagram and consistent thermodynamic data on the ternary condensed phases, CuFeO2 and CuFeO2O4, were obtained. An analysis of the free energy of mixing of the spinel solid solution furnished information on the distribution of cations and their valencies between the tetrahedral and octahedral sites of the spinel lattice, which is consistent with X-ray diffraction, magnetic and Seebeck coefficient measurements.

Gibbs free energy of formation of magnesium stannate

he thermodynamic properties of the spinel Mg2SnO4 have been determined by emf measurements on the solid oxide galvanic cell,View the MathML source in the temperature range 600 to 1000°C. The Gibbs' free energy of formation of Mg2SnO4 from the component oxides can be expressed as View the MathML source,View the MathML source These values are in good agreement with the information obtained by Jackson et al. [Earth Planet. Sci. Lett.24, 203 (1974)] on the high pressure decomposition of magnesium stannate into component oxides at different temperatures. The thermodynamic data suggest that the spinel phase is entropy stabilized, and would be unstable below 207 (±25)°C at atmospheric pressure. Based on the information obtained in this study and trends in the stability of aluminate and chromite spinels, it can be deduced that the stannates of nickel and copper(II) are unstable.

Electrochemical determination of activities in Cr2O3 Al2O3 solid solutions

The activity of Cr20~ in Cr20~-A12Oa solid solution has been determined in the temperature range 800~176 from electromotive force measurements on the solid oxide galvanic cell Pt,Cr + Cr2OJY~O~-ThO2/Cr + Cr~A12-xO~,Pt The activities of Cr203 and A120~ in the solid solution show both positive and negative deviations from Raoult's law. The heat and entropy of mixing of the solid Solution obtained from the temperature dependence of the emf can be expressed as AH = XCr203XA1203 [31,700Xcrzo3 -}- 37,470XA1203] J mole -I hS = -- 1.8R [Xcr2o3 In Xcr2o3 + XA12o3 In XAaos]The entropy of mixing is 10% lower than that predicted by the Temkin model.The large positive heat of mixing in the Cr2Os-A12Oa solid solution, however, suggests that this apparent: entropy discrepancy originates with the clustering of positive ions on the cation sublattice. The asymmetric miscibility gap exhibited in the CrzOa-A12Oa system below 900~ is consistent with the thermodynamic data trends recorded at the more elevated temperatures.

Gibbs free energies of formation of indium (III) oxide and sulphate

Emf measurements on the galvanic cell Pt, Ta, In + In,O, / Tho,-Y,03 / Cu + C+O, Pt were used to obtain the standard free energy of formation of 1%03fr om 600 to 900°C. Differential thermal analysis was used to detect the decomposition of In2(S0,), under controlled SO2 + O2 + Ar mixtures in thqtemperature range 640-8wC. X-ray diffraction analysis indicated that the decomposition product was 1%03 without an oxywlphate intermediate. The following equations were obtained for the variation of the standard free-energy change(Jlmole) with temperature:

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,

Potentiometric determination of the Gibbs energies of formation of lead aluminates

The Gibbs energies of formation of three compounds in the PbO-Al2O3 system—2PbO · Al2O3, PbO · Al2O3, andPbO· 6Al2O3—have been determined from potentiometric measurements on reversible solid-state galvanic cells [dformula Pt, Ir | Pb, alpha-Al[sub 2]O[sub 3], PbO [center-dot] 6Al[sub 2]O[sub 3] | ZrO[sub 2]-CaO | NiO, Ni | Pt] [dformula Pt | NiO, Ni | ZrO[sub 2]-CaO | Pb, PbO [center-dot] 6Al[sub 2]O[sub 3], PbO [center-dot] Al[sub 2]O[sub 3] | Ir, Pt] and [dformula Pt | NiO, Ni | ZrO[sub 2]-CaO | Pb, PbO [center-dot] Al[sub 2]O[sub 3], 2PbO [center-dot] Al[sub 2]O[sub 3] | Ir, Pt] in the temperature range 850–1375 K. The results are discussed in the light of reported phase diagrams for the PbO-Al2O3system. The partial pressures of different lead oxide species, PbnOn, n = 1–6, in the gas phase in equilibrium withthe aluminates are calculated by combining the results of this study with the mass-spectrometric data of Drowart et al.(1) for polymerization equilibria in the gas phase. The concentration of oxygen in lead in equilibrium with the aluminatesare also derived from the results and the literature data on the Gibbs energy of solution of oxygen in liquid lead.

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.

Sulphur potential measurements with a two phase sulphide oxide electrolyte

The open circuit potentials of the galvanic cell,Pt (or Au)¦(Ar + H2S + H2)primeparCaS + ZrO2(CaO)par (Ar + H2S+ H2)Prime£t (or Au) has been measured in the temperature range 1000 to 1660 K and PH2S:PH 2 ratios from 1.73×10–5 to 2.65×10–1. The solid electrolyte consists of a dispersion of calcium sulphide in a matrix of calcia-stabilized zirconia. The surface of the electrolyte is coated with a thin layer of calcium sulphide to prevent the formation of water vapour by reaction of hydrogen sulphide with calcium oxide or zirconia present in the electrolyte. The use of a lsquopoint electrodersquo with a catalytically active tip was necessary to obtain steady emfs. At low temperatures and high sulphur potentials the emfs agreed with the Nernst equation. Deviations were observed at high temperatures and low sulphur potentials, probably due to the onset of significant electronic conduction in the oxide matrix of the electrolyte. The values of oxygen and sulphur potentials at which the electronic conductivity is equal to ionic conductivity in the two-phase electrolyte have been evaluated from the emf response of the cell. The sulphide-oxide electrolyte is unsuitable for sulphur potential measurements in atmospheres with high oxygen potentials, where oxidation of calcium sulphide may be expected.

Gibbs energy of formation of nickel orthosilicate (Ni2SiO4)

Two solid state galvanic cells:Pt, Ni + Ni2Si04 + Si02/(Y203)Zr02/Ni + + NiO, Pt (1) and Pt, Ni + NizSiOj + Si02/CaF2/Ni + + NiO, Pt (11) have been employed for the determination of the Gibbs' energy of formation of nickel orthosilicate(Ni2Si04) from nickel oxide and quartz. The emf of cell (I) was reversible and reproducible in the temperature range 925 to 1375K whereas emf of cell (11) drifted with time and changed polarity. From the results of cell (I), the Gibbs' energy of formation of nickel silicate is obtained as,2Ni0 (r.s.) + Si02 (quartz) + Ni2Si04 (olivine)Gibbs' energy of formation of the spinel form of Ni2Si04 is obtained by combining the data for olivine obtained in this study with high pressure data on olivine to spinel transition reported in the literature. The complex time dependence of the emf of cell (11) can be rationalised on the basis of formation of calcium silicates from calcium oxide, generally present as an impurity in the calcium fluoride electrolyte, and silica. The emf of cell (11) is shown to be the function of the activity of calcium oxide at the electrolyte/ electrode interface. The results provide strong evidence against the recent suggestion of mixed anionic conduction in calcium fluoride.