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.     

A solid state emf study of the pyrrhotite-magnetite equilibrium in the temperature interval 850 to 1275 K

The equilibrium 3/(1 −x)Fe_1−x S(s) + (5 − 2x)/(1 −x)O₂(g) Fe₃O₄(s) + 3/(1 −x)SO₂(g) was studied in the temperature interval 850 to 1275 K by measuring oxygen potentials in a galvanic cell containing calcia stabilized zirconia as solid electrolyte. The SO₂ activity was controlled by equilibrating the solid phases pyrrhotite and magnetite with a continuously flowing SO₂-Ar gas mixture of known composition. Formation of S₂ gas was taken into account and a recently published thermodynamic model for the pyrrhotite phase⁴ was used to derive the Gibbs energy change for the pyrrhotite-magnetite equilibrium and for the formation of Fe_1−x S as a function of the variables temperature and pyrrhotite composition.     

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     

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     

The equilibrium oxygen pressure over the Cr-Y2O3-YCrO3 coexistence measured with the galvanic cell using stabilized ZrO2 solid electrolyte

The equilibrium oxygen pressure over the Cr-Y₂O₃-YCrO₃ coexistence has been measured by the following cells: Cr, Y₂O₃, YCrO₃∥ZrO₂∥Cr, Cr₂O₃ [I] Mn, MnO∥ZrO₂∥Cr, Y₂O₃, YCrO₃ [II] Moreover, the partial electronic conduction parameter,P _e, has been determined simultaneously, as the oxygen partial pressure where then-type electronic and ionic conductivities are equal in the stabilized ZrO₂. The equilibrium oxygen pressure,P _{O 2}, over the Cr-Y₂O₃-YCrO₃ coexistence andP _e are expressed as log (P_{O 2}/atm) = 10.6 − 4.39 × 10⁴1/T ± 0.1 (1385 to 1470 K) log ( P_e/atm = 8.86 − 4.21 x 10₄ 1/T ± 0.3 (1385 to 1470 K) From the equilibrium oxygen pressure and the standard Gibbs energy of formation of Y₂O₃, the standard Gibbs energy of formation of YCrO₃ is calculated as ΔG _o ^f /J mol^™1 = −1.58 x 10⁶ + 2.93 x 10² T ± 7 × 10³ (1385 to 1470 K)     

Determination of the standard gibbs energies of formation of Ba3P2 and Ba3(PO4)2

The standard Gibbs energies of formation of barium phosphide and barium orthophosphate were determined by a chemical equilibration technique yielding the following results: 3Ba(1)+P₂(g)=Ba₃P₂ (s) ΔG°=−732,000+156.1T(±12,800) (J/mol) 3BaO (s)+P₂(g)+5/2O₂(g)=Ba₃(PO₄)₂(s) ΔG°=−2,523,000+580.0T(±16,600) (J/mol) The stability and the thermodynamic behavior of barium compounds as reaction products of dephosphorization of steel were discussed in terms of the oxygen partial pressure and the activity coefficient of Ba_1.5P in molten Ba saturated with CaO. D.J. MIN, formerly Graduate Student, Department of Metallurgy, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan     

Gibbs energies of formation of intermetallic phases in the systems Pt-Mg,Pt-Ca,and Pt-Ba and some applications

The standard Gibbs energies of formation of platinum-rich intermetallic compounds in the systems Pt-Mg, Pt-Ca, and Pt-Ba have been measured in the temperature range of 950 to 1200 K using solid-state galvanic cells based on MgF2, CaF2, and BaF2 as solid electrolytes. The results are summarized by the following equations: ΔG° (MgPt₇) = −256,100 + 16.5T (±2000) J/mol ΔG° (MgPt₃) = −217,400 + 10.7T (±2000) J/mol ΔG° (CaPt₅) = −297,500 + 13.0T (±5000) J/mol ΔG° (Ca₂Pt₇) = −551,800 + 22.3T (±5000) J/mol ΔG° (CaPt₂) = −245,400 + 9.3T (±5000) J/mol ΔG° (BaPt₅) = −238,700 + 8.1T (±4000) J/mol ΔG° (BaPt₂) = −197,300 + 4.0T (±4000) J/mol where solid platinum and liquid alkaline earth metals are selected as the standard states. The relatively large error estimates reflect the uncertainties in the auxiliary thermodynamic data used in the calculation. Because of the strong interaction between platinum and alkaline earth metals, it is possible to reduce oxides of Group ILA metals by hydrogen at high temperature in the presence of platinum. The alkaline earth metals can be recovered from the resulting intermetallic compounds by distillation, regenerating platinum for recycling. The platinum-slag-gas equilibration technique for the study of the activities of FeO, MnO, or Cr₂O₃ in slags containing MgO, CaO, or BaO is feasible provided oxygen partial pressure in the gas is maintained above that corresponding to the coexistence of Fe and “FeO.” Formerly Professor and Chairman, Department of Metallurgy, Indian Institute of Science Formerly Visiting Scientist, Department of Metallurgy, Indian Institute of Science     

The thermal capacity and enthalpy of gadolinium sesquiselenide over a wide temperature range

Measurements have been made on the thermal capacity of γ-Gd₂Se₃ at 58.88–298.34 K. Values have been obtained for the thermal capacity, entropy, reduced Gibbs energy, and enthalpy under standard conditions: C°_p = 125.87 ± 0.5 J· mole⁻¹ · K⁻¹; S°(298.15 K) = 196.5 · 1.6 J · mole⁻¹ · K⁻¹; Φ°(298.15 K) = 103.6 ± 1.6 J · mole⁻¹ · K⁻¹; H°(298.15 K)-H°(0) = 27681 ± 138 J · mole⁻¹. The enthalpy of Gd₂Se₃ has been measured and the major thermodynamic functions have been calculated for the solid and liquid states over the temperature range 450–2300 K. The temperature dependence of the enthalpy in the ranges 300–1800 K and 2000–2300 K are represented: H°(T)-H°(298.15 K) = = 1.1949 · 10⁻² · T² + 122.38 · T + 347402 · T⁻¹ − 38716 and H°(T)-H°(298.15 K) = 262.81 · T-− 196047, respectively. The calculated temperature, enthalpy, and entropy of melting for Gd₂Se₃ are: T_m = 1925 ± 40 K, Δ_mH° (Gd₂Se₃) = 68.5 kJ · mole^-1, Δ_mS°(Gd₂Se₃) = 35.6 J · mole⁻¹ · K⁻¹. __________ Translated from Poroshkovaya Metallurgiya, Nos. 3–4(448), pp. 56–61, March–April, 2006.     

Thermodynamics of the solid phases in the system Fe−Mn−C

Phase relationships in the Fe−Mn−C system in the temperature range 600 to 1100°C have been studied using metallographic and X-ray methods and the electron microprobe. Isothermal sections of the phase diagram of the system are reported based on the present results and those of earlier investigators. The fcc λ-phase (austenite) containing carbon is stable at all values ofy _Mn=x _Mn/(x _Mn+x _Fe) in the range 890 to 1100°C and in a more restricted composition range at lower temperatures. Its composition under conditions of equilibrium with the carbides (Fe, Mn)₃C, (Fe, Mn)₂₃C₆, ε, and liquid are shown for several temperatures. The free energy of formation of the cementite phase, (Fe, Mn)₃C, at 1000°C, from γ-Fe, γ-Mn (undercooled) and graphite is ΔG ₁₂₇₃=−35,790y _Mn−2760y _Fe+3RT (y _Mn lny _Mn+y _Fe lny _Fe). The data show that the alloyed cementite is essentially and ideal mixture of Fe₃C and Mn₃C,i.e., the metal atoms are distributed at random on the metal sites in the lattice. ROBERT BENZ, formerly of the Research Staff, Massachusetts Institute of Technology, Cambridge, Massachusetts     

Thermodynamics of the liquid binary iron-titanium by mass spectrometry

At 1545°C (1818 K) the liquid binary system iron-titanium is symmetric and regular with the integral excess Gibbs energy and the integral enthalpy of mixing equal to − 9,700 cal (−40,600 J)x _Fe x _Ti Per g-atom referred to the liquid components. Formerly Postdoctoral Fellow, Department of Metallurgical Engineering, Ohio State University, Columbus, Ohio     

Chemical potentials of oxygen for fayalite-quartz-lron and fayalite-quartz-magnetite equilibria

The oxygen potentials corresponding to fayalite-quartz-iron (FQI) and fayalite-quartz-magnetite (FQM) equilibria have been determined using solid-state galvanic cells: Pt,Fe + Fe₂SiO₄ + SiO₂/(Y₂O₃)ZrO₂/Fe + \r"FeO,\l"Pt and Pt, Fe₃O₄ + Fe₂SiO₄ + SiO₂/(Y₂O₃)ZrO2/Ni + NiO, Pt in the temperature ranges 900 to 1400 K and 1080 to 1340 K, respectively. The cells are written such that the right-hand electrodes are positive. Silica used in this study had the quartz structure. The emf of both cells was found to be reversible and to vary linearly with temperature. From the emf, Gibbs energy changes were deduced for the reactions: 0.106Fe (s) + 2Fe_0.947O (r.s.) + SiO₂ (qz) → Fe₂SiO₄ (ol) δG‡= -39,140+ 15.59T(± 150) J mol^-1 and 3Fe₂SiO₄ (ol) + O₂ (g) → 2Fe₃O₄ (sp) + 3SiO₂ (qz) δG‡ = -471,750 + 160.06 T±} 1100) J mol^-1 The “third-law≓ analysis of fayalite-quartz-wustite and fayalite-quartz-magnetite equilibria gives value for δH‡₂₉₈ as -35.22 (±0.1) and -528.10 (±0.1) kJ mol^-1, respectively, independent of temperature. The Gibbs energy of formation of the spinel form of Fe₂SiO₄ is derived by com-bining the present results on FQI equilibrium with the high-pressure data on olivine to spinel transformation of Fe₂SiO₄.     

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.     

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.     

Enthalpies of formation of liquid and solid (gallium + palladium) alloys

The enthalpies of formation of liquid (Ga + Pd) alloys were determined by direct reaction calorimetry in the temperature range 1322 <T/K < 1761 and the molar fraction range 0 <x _Pd < 0.87. The enthalpies are very negative with a minimum Δ_mix H _m = −70.4 ± 3.0 kJ mol_-1 atx _Pd = 0.6, independent of the temperature. Limiting partial molar enthalpies of palladium and gallium were calculated as Δh _m (Ga liquid in ∞liquid Pd) = −265 ± 10 kJ mol₋₁ and Δh _m (Pd liquid in ∞liquid Ga) = -144 ± 5 kJ mol₋₁. The integral molar enthalpy is given by Δ_mix H _m =x(1-x) (-143.73 -232.47x + 985.77x ²-4457.8.x ³ + 6161.1x ⁴ + 2577.4x ⁵), wherex = x _Pd. Moreover, values for the enthalpies of formation and fusion of PdGa, Pd₂Ga, and the solid solution (withx _Pd = 0.8571) have been proposed. These results have been discussed taking into account the equilibrium phase diagram. Formerly Ph.D. student, Université de Provence     

Standard gibbs energy of formation of Mg<Subscript>48</Subscript>Zn<Subscript>52</Subscript> determined by solution calorimetry and measurement of heat capacity from near absolute zero kelvin

The thermodynamic properties of Mg₄₈Zn₅₂ were investigated by calorimetry. The standard entropy of formation at 298 K, Δ_f S ₂₉₈ ^o , was determined from measuring the heat capacity, C _p , from near absolute zero (2 K) to 300 K by the relaxation method. The standard enthalpy of formation at 298 K, Δ_f H ₂₉₈ ^o , was determined by solution calorimetry in hydrochloric acid solution. The standard Gibbs energy of formation at 298 K, Δ_f G ₂₉₈ ^o , was determined from these data. The obtained results were as follows: Δ_f H ₂₉₈ ^o (Mg₄₈Zn₅₂)=(−1214±(300) kJ · mol⁻¹;Δ_fS ₂₉₈ ^o (Mg₄₈Zn₅₂)=(−123±0.36) J · K⁻¹ · mol⁻¹; and Δ_f G ₂₉₈ ^o (Mg₄₈Zn₅₂)=(−1177±(300) kJ · mol⁻¹. The electronic contribution to the heat capacity of Mg₄₈Zn₅₂ was found to be approximately equal to pure magnesium, indicating that the density of states in the vicinity of the Fermi level follows the free electron parabolic law.     

Gaseous complexes formed between trichlorides (A1C13 and FeC13) and dichlorides

It has been found that in general the volatility of dichlorides is much enhanced in the presence of gaseous A1C1₃ and FeCl₃, and the existence of the complexes MA1₂C1₈, MAl₃Cl₁₁, and MFe₂Cl₈ is postulated. ΔH _T, ΔS _T, andT for MCl₂(s) + 2AlCl₃(g) = MAl₂Cl₈(g) are CaCl₂: −17.8 kcal, −25.7 cal K⁻¹ at 900 °K; CoCl₂: −15.2, −19.4 at 750°K; MgCl₂: −13.8, −17.9 at 800°K; MnCl₂: −15.8, −20.9 at 750°K; NiCl₂: −16.3, −24.2 at 750°K. For MCl₂(s) + 3AlCl₃(g) = MAl₃Cl₁₁(g) − CaCl₂: −30.0, −40.5 at 900°K; CoCl₂: −36.6, −47.4 at 700°K; MgCl₂: −42.6, −55.4 at 750°K; MnCl₂: −33.3, −42.0 at 750°K. For MCl₂(s) + 2FeCl₃(g) = MFe₂Cl₈(g) − CdCl₂: −19.4, −20.9 at 700°K: CoCl₂: −16.5, −17.2 at 800°K, MnCl₂: −19.1, −21.2 at 750°K; NiCl₂: −19.7, −24.4 at 800°K. Enhanced volatility was also found for ZnCl₂, PbCl₂, and CuCl, but since the condensed phase was liquid of unknown composition no calculations could be made. Owing to the interplay of the above equilibria with the dimerization equilibria for A1C1₃ and FeCl₃ the effective vapor pressures of the dichlorides in the presence of the trichlorides pass through maxima in the region 600° to 700°C.     

Thermodynamic properties of B2-AlFeNi Alloys. Part I: Investigation by knudsen effusion mass spectrometry

The vaporization of Al-Fe-Ni alloys has been investigated in the temperature range 1180 to 1508 K by Knudsen effusion mass spectrometry (KEMS). Fourteen different compositions were examined in the B2 region: 10 compositions at two fixed Al concentrations,x _Al=0.45 andx _Al=0.50 plus four extra compositions at constantx _Ni/x _Fe=1. For the first time, reliable partial pressures and thermodynamic activities of Al, Fe, and Ni have been evaluated from the measured ion intensities for both the alloy and the pure element. Gibbs energies, partial molar enthalpies, and entropies of formation for all the components have also been obtained. The relative partial molar enthalpies and entropies were found to be nearly temperature independent over the wide temperature ranges investigated. At 1400 K, the Gibbs energy of formation of Al_0.50Fe_0.25Ni_0.25 and Al_0.45Fe_0.275Ni_0.275, with Al(liq), Fe(fcc), and completely paramagnetic Ni(fcc,cpm) as reference states, are −37.9±0.42 kJ/mol and −38.1±0.42 kJ/mol, respectively. At the same temperature, the enthalpies of formation of Al_0.50Fe_0.25Ni_0.25 and Al_0.45Fe_0.275Ni_0.275, with the same reference states, are −51.5±1.7 kJ/mol and −49.2±1.7 kJ/mol, respectively.     

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.