Determination of the standard gibbs energies of formation of Ca3As2, Ca3Sb2, and Ca3Bi2

The standard Gibbs energies of formation of Ca₃As₂, Ca₃Sb₂, and Ca₃Bi₂ were determined by a chemical equilibration technique yielding the following results: 3Ca(1)+2As(1)=Ca₃As₂ (s) ΔG°=−723,800+172.8T (±23,700)(J/mol) 1273 to 1573 K 3Ca(1)+2Sb(1)=Ca₃Sb₂(s) ΔG°=−726,300+159.3T(±24,600) (J/mol) 1273 to 1573K 3Ca(1)+2Bi(1)=Ca₃Bi₂(s) ΔG°=−696,400+195.6T(±23,200) (J/mol) 1148 to 1323 K The thermodynamic data for removal of arsenic, antimony, and bismuth by other experimental investigations were discussed in terms of the activity coefficients of these compounds in slags. The stabilities of these compounds were also discussed by using the critical oxygen partial pressures calculated from the above equations. D.J. MIN, formerly Graduate Student, Department of Metallurgy, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan     

Determination of standard free energies of formation of Ca3P2 and Ca2Sn at high temperatures

The standard free energies of formation of calcium phosphide and calcium stannide were determined by a chemical equilibration technique, yielding the following results: 3Ca(1) + P₂(g) = Ca₃P₂(s) ΔG° = −653,460(±7110) + 144.01(±4.98)T (J/mol)1000 °C to 1300 °C2Ca(1) + Sn(1) = Ca₂Sn(s) ΔG° = −353,970(±1670) + 79.28(±1.26)T (J/mol)1000 °C to 1300 °C 1120 °C The experimental data to express the thermodynamics for removal of phosphorus and tin from molten iron by calcium based slags by other investigators were discussed in terms of the activity co-efficients of Ca₃P₂ and Ca₂Sn in slag melts by using the present results described above.     

Determination of standard free energies of formation of Ca3P2 and Ca2Sn at high temperatures

The standard free energies of formation of calcium phosphide and calcium stannide were determined by a chemical equilibration technique, yielding the following results: 3Ca(1) + P₂(g) = Ca₃P₂(s) ΔG° = −653,460(±7110) + 144.01(±4.98)T (J/mol)1000 °C to 1300 °C2Ca(1) + Sn(1) = Ca₂Sn(s) ΔG° = −353,970(±1670) + 79.28(±1.26)T (J/mol)1000 °C to 1300 °C 1120 °C The experimental data to express the thermodynamics for removal of phosphorus and tin from molten iron by calcium based slags by other investigators were discussed in terms of the activity co-efficients of Ca₃P₂ and Ca₂Sn in slag melts by using the present results described above.     

Thermodynamics of the Ca-S-O,Mg-S-O,and La-S-O systems at high temperatures

High temperature thermodynamic data for equilibria in the Ca-S-O, Mg-S-O, and La-S-0 systems were determined by a galvanic cell technique using calcia stabilized zirconia (CSZ) solid electrolytes. The measured emf data were used to calculate the standard free energy changes of the following reactions: [1] CaO(s) + 1/2S₂(g) → CaS(s) + 1/2O₂(g) 1000 to 1350 K ΔG° = 21906.9 − 0.8T(K)(±400 cal) = 91658 − 3.37 (±1700 J) [2] CaS(s) + 2O₂(g) → CaSO₄(s) 1050 to 1450 K ΔG° = -227530.7 + 80.632T(K) (±400 cal) = -951988.5 + 337.4T (±1700 J) [3] CaO(s) + 3/2O₂(g) + 1/2S₂(g) → CaSO₄(s) 1050 to 1340 K ΔG° = -204892.7 + 79.83T(K)(±400 cal) = -857271.1 + 334.0T (±1700 J) [4] MgO(s) + 1/2S₂(g) → MgS(s) + 5O₂(g) 1000 to 1150 K ΔG° = 45708.6 − 2.897(K)(±500 cal) = 191244.8 − 12.1T (±2100 J) [5] La₂O₃(s) + 1/2S₂(g) → La₂O₂S(s) + 1/2O₂(g) 1080 to 1350 K ΔG° = 17507 − 2.32T(K)(±380 cal) = 73249.3 − 9.7T (±1600 J) [6] La₂O₃S(s) + S₂(g) → La₂S₃(s) + O₂(g) 950 to 1120 K ΔG° = 70940 + 2.25T(K)(±500 cal) = 296812.9 + 9.47 (±2100 J) The ΔG° values of reaction [5] were combined with the literature data for ΔG°_f(La₂O₃) to obtain the standard free energy of formation of La₂O₂S at high temperatures. The values of ΔG°_f thus calculated for La₂O₂S were combined with the ΔG° data for reaction [6] to obtain the standard free energy of formation of La₂S₃ at high temperatures.     

The utilization of galvanic cells using Caβ″-Alumina solid electrolytes in a thermodynamic investigation of the CaO- AI2O3 system

Caβ″-alumina solid electrolytes have been used in calcium concentration electrochemical cells to determine the standard free energies of formation of the calcium aluminates, from their constituent oxides, in the temperature ranges specified: (1) CaO(s) + 6Al₂O₃(s) → CaO6Al₂0₃(s) ΔG° =-4270.9 - 9.4r(K)(±200)cal = -17869.4 - 39.3T (±840)J; 1100 to 1500 K. (2) CaO(s) + 2Al₂O₃(s) → CaO.2Al₂O₃(s) ΔG° = -3087.1 - 6.39HK) (±300)cal = -12916.4 -26.74T (±1260)J; 1100 to 1500 K. (3) CaO(s) + Al₂O₃(s)→ CaO-Al₂O₃(s) ΔG° = -3612.1 -4.35T(K) (±200)cal = -15113.0 - 18.2r(±840)J; 1050 to 1500 K. (4) 3CaO(s) + Al₂O₃(s) → 3CaO-Al₂O₃(s) ΔG° = -1868.7 - 7.05T(K)(±200)cal = -7818.6 - 29.57(±840)J; 1050 to 1320 K.     

Activities of oxygen in liquid copper and silver from electrochemical measurements

Modified coulometric titrations on the galvanic cell:O in liquid Cu or Ag / ZrO₂( + CaO) / Air, Pt, were performed to determine precisely the oxygen activities in liquid copper and silver in the range of relatively low oxygen concentration. The present experimental results were remarkably reproducible in comparison with the published data. The standard Gibbs energies of solution of oxygen in liquid copper and liquid silver for 1/2 O₂(l atm) → O(l at. pct) were determined respectively to be ΔG° (in Cu) = −18040 −0.03 T(K) (± 120) cal · g-atom−1 = −75500 −0.12 T(K)(± 500) J · g-atom−1, ΔG°(inAg)= -3860+ 1.56 T(K) (±90) cal · g-atom−1 = −16140 + 6.52 T(K)(±380) J · g-atom−1 where the reference state for dissolved oxygen was an infinitely dilute solution. The present value of the partial entropy of oxygen dissolved in liquid copper differs significantly from that suggested by many investigators. Further, the present equation for liquid copper has been found to be consistent with a correlation proposed previously by the present authors. The equation for liquid silver is in good agreement with the published ones.     

Activities of oxygen in liquid Bi,Sn, and Ge from electrochemical measurements

Modified coulometric titrations on the galvanic cell: O in liquid Bi, Sn or Ge/ZrO₂( + CaO)/Air, Pt, were performed to determine the oxygen activities in liquid bismuth and tin at 973, 1073 and 1173 and in liquid germanium at 1233 and 1373 K. The standard Gibbs energy of solution of oxygen in liquid bismuth, tin and germanium for 1/2 O₂ (1 atm) →O (1 at. pct) were determined respectively to be ΔG° (in Bi) = −24450 + 3.42T (±200), cal· g-atom⁻¹ = − 102310 + 14.29T (±900), J·g-atom⁻¹, ΔG° (in Sn) = −42140 + 4.90T (±350), cal· g-aton⁻¹ = −176300 + 20.52T (± 1500), J-g-atom⁻¹, ΔG° (inGe) = −42310 + 5.31 7 (±300), cal·g-atom⁻¹ = −177020 + 22.21T(± 1300), J· g-atom⁻¹, where the reference state for dissolved oxygen was an infinitely dilute solution. It was reconfirmed that the modified coulometric titration method proposed previously by two of the present authors produced far more reliable results than those reported by other investigators. TOYOKAZU SANO, formerly a Graduate Student, Osaka University     

Free energy of formation of Mo2C and the thermodynamic properties of carbon in solid molybdenum

The activity of C in the two-phase region Mo+Mo₂C has been obtained from the C content of iron rods equilibrated with metal+carbide powder mixtures. From this activity data the free energy of formation of α-Mo₂C has been determined as ΔG _f ^o (α-Mo₂C) (1270 to 1573 K)=−47,530−9.46T±920 J/mol. This is in good agreement with the expression obtained from gas-equilibration studies by Gleiser and Chipman, ΔG _f ^o (α-Mo₂C) (1200 to 1340 K)=−48,770−7.57 J/mol, but both our and Gleiser and Chipman's values are about 10 pct lower than those of Pankratz, Weller and King calculated from ΔH _f,298 ^o andC _p vs T data. With the aid of available data for the solid solubility of C in Mo, the thermodynamic properties of C in the terminal solid solution have been calculated as J/mol, J/mol and , the excess entropy ofC in the solid solution assumingC is in the octahedral interstices =43.4±8.2 J/deg.-mol.     

On the Gibbs energy of formation of wustite

Gibbs energy change for the reactionxFe_(s) + 1/2O_2(g) = Fe _x O_(s) has been redetermined using the galvanic cell (−) Fe_(s), Fe _x O_(s)∥ZrO₂ − CaO∥NiO_(s), Ni_(s)(+) in the temperature range 866 to 1340 K. The results are at variance with earlier works in that they reflect the transformations occurring in the iron phase. The Gibbs energy function is represented by two nonlinear equations,viz., ΔG° (866 to 1184 K) = −251480 − 18.100T + 10.187T lnT ± 210 J/mol and ΔG° (1184 to 1340 K) = −286248 + 181.419T - 13.858T lnT ± 210 J/mol. Formerly Research Assistant at the Department of Theoretical Metallurgy, The Royal Institute of Technology, Stockholm     

Potentiometric determination of the gibbs energies of formation of SrZrO3 and BaZrO3

The Gibbs free energies of formation of strontium and barium zirconates have been determined in the temperature range 960 to 1210 K using electrochemical cells incorporating the respective alkaline-earth fluoride single crystals as solid electrolytes. Pure strontium and barium monoxides were used in the reference electrodes. During measurements on barium zirconate, the oxygen partial pressure in the gas phase over the electrodes was maintained at a low value of 18.7 Pa to minimize the solubility of barium peroxide in the monoxide phase. Strontium zirconate was found to undergo a phase transition from orthorhombic perovskite (o) with space groupCmcm; D _2h ¹⁷ to tetragonal perovskite (t) having the space group 14/mcm;D _4h ¹⁸ at 1123 (/+- 10) K. Barium zirconate does not appear to undergo a phase transition in the temperature range of measurement. It has the cubic perovskite (c) structure. The standard free energies of formation of the zirconates from their component binary oxidesAO (A = Sr, Ba) with rock salt (rs) and ZrO₂ with monoclinic (m) structures can be expressed by the following relations: SrO (rs) + ZrO₂ (m) → SrZrO₃ (o) ΔG° = -74,880 - 14.2T (/+-200) J mol^-1 SrO (rs) + ZrO₂ (m) → SrZrO₃ (t) ΔG° = -73,645 - 15.37T (/+-200) J mol^-1 BaO (rs) + ZrO₂ (m) → BaZrO₄ (c) ΔG° = -127,760-1.79T (/+-250) J mol^-1 The results of this study are in reasonable agreement with calorimetric measurements reported in the literature. Systematic trends in the stability of alkaline-earth zirconates having the stoichiometry AZrO₃ are discussed.     

Thermodynamics of the system NaF-Alf3. part ii: The free energies of formation of cryolite (Na3AlF6) and chiolite (Na5Al3F14)

The theory of the solid-electrolyte cells is given, and it is shown that cryolite itself with Ca²⁺ in solid solution is a suitable Na⁺-ion conductor. Experimental electromotive forces for the ranges 570° to 725°C and 570° to 670°C, r − 18,960 cal with a standard deviation of ±36 cal (based on a third-law calculation). For 5NaF(s) + 3AlF₃(s) = Na₅Al₃F₁₄(s), ΔG° = −38,560 − 7.081T with a standard deviation of ±130 cal. Combination of these results with recent values for Al + 3/2 F₂ = A1F₃ and for 6NaF + Al = Na₃AlF₆ + 3Na gives ΔH°_f298(Na₃AlF₆) = −792,400 cal and ΔH°_f298(NaF) = −137,530 cal. The latter is in excellent agreement with the most recent critical assessment.     

Determination of standard gibbs energies of formation of MgO,SrO, and BaO

The standard Gibbs energy of formation of MgO was determined from the measurement of the ΔG° for the reaction ; by equilibrating Mg and Nb with a magnesia crucible and is expressed as follows: Mg(l)+ l/2O₂(g) = MgO(s) ΔG° = −657,000(±5000) + 141(±13)T [J/mol] (973 to 1323 K) The standard Gibbs energies of formation of SrO and BaO were determined by equilibrating silver and MO(M: Sr, and Ba) in a graphite crucible on the basis of the reactionM(in Ag) + CO (g) = MO (s) + C (s), yielding the following results:

Variation of Fe3+/Fe2+ and Cu2+/Cu+ equilibrium with basicity of oxide melts

Oxidation-reduction equilibrium experiments were conducted with Li₂O-CaO-Al₂O₃-ZnO-SiO₂-B₂O₃ melts containing small concentrations of either copper oxide or iron oxide. The results indicated that, for oxide melts containing relatively large proportions of amphoteric oxides, i.e., Al₂O₃ and ZnO, the ratios lcub;(Cu²⁺)/(Cu⁺)P _{O 2} ^1/4rcub; and lcub;(Fe³⁺)/(Fe²⁺)P _{O 2} ^1/4rcub; decreased with an increase in basicity. With further increase in basicity, however, these ratios became independent of basicity. For very basic melts, the ratios increased with an increase in basicity. These variations of lcub;(Cu²⁺)/(Cu⁺)P _{O 2} ^1/4rcub; and lcub;(Fe³⁺)/(Fe²⁺)P _{O 2} ^1/4rcub; can be interpreted in terms of the optical basicity of the oxide melts and are consistent with the following general expressions for the red-ox equilibria within acidic and relatively basic melts, respectively: M ⁿ⁺+(1/4)O₂=M⁽ⁿ⁺¹⁾⁺+(1/2)O²⁻ M ⁿ⁺+(1/4)O₂+(3/2)O²⁻=MO₂ ⁽³⁻ⁿ⁾ and M ⁿ⁺+(1/4)O₂=(3/4)M⁽ⁿ⁺¹⁾⁺+(1/4)MO₂ ⁽³⁻ⁿ⁾     

Standard gibbs energies of formation of the carbides of vanadium by emf measurements

The relative partial molar Gibbs energies of vanadium in the vanadium-carbon system have been determined for the V-C alloys containing 36.7, 41.2, 43.1, 44.8, 45.5, 46.8, 50.5, and 54.0 at. pct carbon by using galvanic cells of the type (−) V, VF₃, CaF₂ // CaF₂ // CaF₂, VF₃, ‘V-C’ (+) The measurements were carried out in the temperature range of 816 to 1008 K. The relative partial molar Gibbs energies of carbon have been calculated in the same composition range. The relative integral molar Gibbs energy in the VC single-phase region can be expressed asG ^M = −98,850 + 72,242X_C + (24.81 −37.23X _C)TJ/mol The standard Gibbs energies of formation of V₄C_3-x and V₂CC can be represented as ΔG° = −67,208 + 9.37T J/mol of V_0.60C_0.40 and ΔGδ = −62,581 + 7.10T J/mol of Va66Co.34 respectively.     

A generalized approach to the flood-knapp structure based model for binary liquid silicates: Application and update for the PbO-SiO2 System

The nonideal activity of a metal oxide in a molten binary silicate system is described by treating the liquid as an ideal solution and by considering the formation of a few complexes. Application of this approach to the binary system PbO-SiO₂ shows that the experimentally determined activity of PbO(l) can be modeled by considering the lead silicate melt as an ideal solution of Pb²⁺ and O²⁻,SiO ₄ ⁴⁻ , Si₂O ₇ ⁶⁻ , Si₁₂O ₃₇ ²⁶⁻ , and Si₄O ₁₀ ⁴⁻ . The calculated Gibbs free energy values for the formation of the anionic complexes from O²⁻ and SiO ₄ ⁴⁻ are: ΔGℴ(Si₂O ₇ ⁶⁻ )/J · mol⁻¹ = 38977 − 30.909(T/K); ΔGℴ(Si₁₂O ₃₇ ²⁶⁻ )/J · mol⁻¹ = 200158 − 121.813(T/K); Δℴ(Si₄O ₁₀ ⁴⁻ )/J · mol⁻¹ = 104627 − 28.094(T/K). Values of Gibbs free energy of formation of the solid phases PbO, Pb₄Si0₆, Pb₂SiO₄, PbSiO₃, and SiO₂ which, together with the melt model data, give the best fit to experimental phase relations in the system PbO-SiO₂ were calculated. These values are all in good agreement with literature data.     

Standard enthalpy of formation of Sc5Si3

The standard enthalpy of formation of Sc₅Si₃ has been determined by solute-solvent drop calorimetry at (1473±2) K. The following value is reported: ΔH _f ^o (mean)=−(719.1±34.0) kJ mol⁻¹. This result is compared with corresponding published values for the enthalpies of formation of Me₅Si₃, with Me=Mn, Cr, V, Ti. This comparison shows regularly increasing negative enthalpies of formation from Mn₅Si₃ to Sc₅Si₃. LETTTIA TOPOR, formerly Senior Research Associate, The James Franck Institute, The University of Chicago,     

Electrical conductivities of M3P2O8 (M = Ca,Ba)

Two-probe conductivity measurements made for M₃P₂O₈ (M = Ca, Ba) suggested that the electrical conduction of these phosphates would primarily be due to the migration of Ca²⁺ and Ba²⁺ ions. At relatively low temperatures and high oxygen partial pressures, in contrast to Ca₃P₂O₈, however, Ba₃P₂O₈ shows partial electronic conduction.     

Standard enthalpies of formation of TiSi2 and VSi2 by high-temperature calorimetry

The standard enthalpies of formation of TiSi₂ and VSi₂ have been measured by a new calorimetric method. The following results are reported: ΔH _f ^° (TiSi₂) = −(170.9 ± 8.3) kJ mol⁻¹ and ΔH _{f ^°} (VSi₂) = −(112.4 ± 6.0) kJ mol⁻¹. These results are compared with experimental, assessed, and predicted values reported in the literature and with our own data for the corresponding borides. Estimates are given for the enthalpies of formation of the silicides of scandium and chromium.     

High temperature thermodynamics of the Cr-Cr2N-N2 system

The high-temperature thermodynamic behavior of the Cr-Cr₂N-N₂ system has been investigated in the temperature range 1450 to 1850 K by measuring the equilibrium pressure of nitrogen gas over pure chromium metal and chromium nitride Cr₂N. From the experimental data, the standard free energy and enthalpy of formation of Cr₂N have been determined to be: ΔH° = −104. ± 10 (KJ. mol⁻¹ Cr₂N) ΔG° = −104. + 0.04987 ± 3.8 (KJ. mol⁻¹ Cr₂N)     

Standard enthalpies of formation of some praseodymium alloys by high-temperature direct synthesis calorimetry

The standard enthalpies of formation of eight Pr alloys were determined by direct synthesis calorimetry at 1473 ± 2 K. The following values of ΔHskƒ/°(kJ/g atom) are reported: PrNi₅, −(25.6 ± 1.0); PrRu₂, −(16.9 ± 1.5); PrRh₂, −(60.4 ± 1.7); PrPd, −(78.8 ± 2.5); PrPd₂, −(82.7 ± 3.1); PrIr₂, −(70.7 ± 2.8); PrPt, −(103.4 ± 2.7); and PrPt₂, − (93.5 ± 2.4). The results are compared with data from available literature for some of the Pr alloys and with predicted values from the model of Miedemaet al.