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.     

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     

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.     

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     

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 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     

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.     

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:

Equilibrium phase relations and thermodynamics of the Cr-0 system in the temperature range of 1500 °C to 1825 °C

Phase relations and thermodynamic properties of the Cr-O system were studied at temperatures from 1500 °C to 1825 °C. In addition to Cr and Cr₂O₂, a third crystalline phase was found to be stable in the temperature range from 1650 °C to 1705 °C. The atomic ratio of oxygen to chromium of this phase, which decomposes upon cooling to form Cr and Cr₂O₃, was determined as 1.33 + 0.02, in good agreement with the formula Cr₃O₄. Temperatures and phase assem blages for invariant equilibria of the Cr-O system were determined as follows: Cr₂O₃ + Cr + Cr₃O₄, 1650 °C ± 2 °C; Cr₃O₄ + Cr + liquid oxide, 1665 °C ± 2 °C; and Cr₃O₄ + Cr₂O₃ + liquid oxide, 1705 °C ± 3 °C. The composition of the liquid oxide phase at the eutectic temperature of 1665 °C was found to be close to CrO. Relations between oxygen pressure and temperature for the univariant equilibria of the Cr-O system were established by equilibrating Cr and/or Cr₂O₃ starting materials in H₂-CO₂ mixtures of known oxygen potentials at temper atures from 1500 ΔC to 1825 °C. From this information, the standard free-energy changes (ΔGΔ) for various reactions were calculated as follows: 2Cr (s) + 3/2O₂ = Cr₂O₃ (s): ΔG ° = -1,092,442 + 237.94T Joules, 1773 to 1923 K; 3Cr (s) + 2O₂ = Cr₂O₄ (s): ΔG ° =-1,355,198 + 264.64T Joules, 1923 to 1938 K; and Cr (s) + l/2O₂ = CrO (1): ΔG ° =-334,218 + 63.81T Joules, 1938 to 2023 K. Formerly Graduate Research Assistant, The Pennsylvania State University Formerly Professor     

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.     

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.     

High-temperature thermodynamic stability of ditantalum carbide (Ta2C)

The CO(g) pressure in equilibrium with a Ta₂C-Ta₂O₅-Ta mixture has been measured at temperatures between 1740 and 1900 K using the torsion-effusion technique. From the equilibrium data, the following equation for ΔG°₂ of Ta₂C has been obtained: ΔG°₂ (±300) = −47,000 (±2200) +.IT From the enthalpy term in the ΔG°f equation, a value of —47.9 (±2.3) kcal/mole has been calculated for ΔH°₂₉₈ of Ta₂C which is in good agreement with several calorimetric results. This paper is based upon a thesis submitted by A. D. KULKARNI in partial fulfillment of the requirements of the degree of Doctor of Philosophy at the University of Pennsylvania.     

Quantitative differential thermal analysis of polymorphic transformations in LaGe1.8 and SmSi2

The possibility of using quantitative differential thermal analysis to investigate phase transformations is examined. The temperature, enthalpy, and entropy of polymorphic transformations in LaGe_1.8 and SmSi₂ are determined: T_tr = 724 K, Δ_trH = 1635 ± 79 J · mole⁻¹, Δ_trS = 2.3 ± 0.1 J · mole⁻¹ · K⁻¹ (LaGe_1.8); T_tr = 658 K, Δ_trH = 1384 ± 69 J · mole⁻¹, Δ_trS = 2.1 ± 0.1 J · mole⁻¹ · K⁻¹ (SmSi₂). __________ Translated from Poroshkovaya Metallurgiya, Vol. 46, No. 3–4 (454), pp. 72–78, 2007.     

High-temperature thermodynamic properties of the chromium carbides determined using the torsion-effusion technique

The pressures of carbon monoxide in equilibrium with a Cr₂₃C₆-Cr₂O₃-Cr mixture and with a Cr₇C₃-Cr₂O₃-Cr₂₃C₆ mixture have been measured in the temperature range 1100 to 1300 K using the torsion-effusion technique. From the equilibrium data, the following equation for ΔG^of of Cr₂₃C₆ (in cal per mole) has been calculated: ΔG _f ° (±1200) = −77,000 - 18.3T (1150 to 1300 K) Combining the results of this study at temperatures between 1100 and 1300 K with those of Kelleyet al., ³ at temperatures between 1500 and 1720 K, the following equation for ΔG^of of Cr₇C₃ (in cal per mole) has been determined: ΔG _f ° (±400) = −35,200 - 8.7T (1100 to 1720 K) ) The above equation for ΔG^of of Cr₇C₃ has been used to re-evaluate the equilibrium data of Kelleyet al., ³ and the following equation for ΔG^of of Cr₃C₂ (in cal per mole) has been obtained: ΔG _f ° (±400) = −16,400 - 4.4T (1300 to 1500 K) CHROMIUM reacts with carbon to form three carbides:^1,2 Cr₂₃C₆, Cr₇C₃, and Cr₃C₂. The chromium carbides are of considerable technical importance because of their precipitation behavior in certain high-chromium steels and superalloys. A precise knowledge of their thermodynamic properties is essential for the understanding and the prediction of their chemical behavior in various environments. This paper is based upon a thesis submitted by A. D. KULKARNI in partial fulfillment of the requirements of the degree of Doctor of Philosophy at the University of Pennsylvania.     

Standard molar enthalpies of formation of MeAl (Me = Ru,Rh, Os,Ir)

The standard molar enthalpies of formation of RuAl, RhAl, and IrAl have been determined by the direct combination method using a high-temperature calorimeter operated at (1473 ±2) K. The following values are reported: ΔH _f ^o (RuAl) = −(124.1 ± 3.3) kJ/mol; ΔH _f ^o (RhAl) =-(212.6 ± 3.2) kJ/mol; and ΔH _f ^o (IrAl) = -(185.5 ± 3.5) kJ/mol. For OsAl, an approximate value is −77 kJ/mol. The results are compared with available data for related alloys and with predicted values.     

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.     

The Decomposition equilibria of platinum di- and mono-chlorides by the simultaneous torque-knudsen technique

The decomposition equilibria of platinum dichloride have been found to consist of two decomposition steps, with chlorine molecules being the vapor species for both steps. An intermediate metastable PtCl solid is formed in the first step in addition to platinum metal and chlorine molecules. The platinum dichloride decomposes incongruently, the stepwise decomposition being PtCl₂ → PtCl → Pt. The PtCl₂ decomposition reactions consist of PtCl₂(s) = PtCl (metastables) + 1/2 Cl₂ (g) and PtCl₂(s) = Pt(s) + Cl₂ (g). The sum of the third lawΔH _{D, 298} K for the above two reactions is 214.637 ± 1.963 kJ/mole, in very good agreement with the second law ΔH_{D, 298 K} = 215.107 ± 13.062 kJ/mole. The second decomposition step is given by the reaction 2PtCl (metastables) = 2Pt(s) + Cl₂ (g) with a third law ΔH_{D, 298 K} = 127.356 ± 0.791 kJ/mole, in excellent agreement with the second law ΔH_{D, 298 K} = 127.509 ± 6.154 kJ/mole. The calculated heat of formation of PtCl₂ is -139 ± 2 kJ/mole and that of PtCl is -63 ± 1 kJ/mole. Formerly Graduate Assistant. Formerly Undergraduate Research Helper,     

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 thermodynamic properties of the vanadium carbides V2C and VC0.73 determined using a galvanic cell technique

The standard free energies of formation of V₂C and VC_0.73 have been obtained from electromotive force (emf) measurements on the following galvanic cells with BaF₂-BaC₂ solid solutions as the electrolyte: Ta, Ta₂CBaF₂-BaC₂V, V₂ (850 to 1200K) (D) VC_0.73, V₂C BaF₂-BaC₂ Cr, Cr₂₃C₆ (850 to HOOK) (E) VC_0.73, V₂C BaF₂-BaC₂ Mo, Mo₂C (890 to 1247 K) (F) Combining the results of this study with previous work1151 and those of Kukarniet al., ^[19.25] the following equations for ΔG_f° of V₂C and VC_0.73 have been determined: From cell (D), ΔG_v2c°(±1263) = -152,824(±9200) + 5.45(±0.27)7 Joule for the reaction 2V + C = V₂C. From cell (E), ΔG_{vc 0.73}°(±662) = -96,790.8(±6511.7) + 7.0(±0.3)r Joule/g * atom V From cell (F), ΔG_{vc 0.73}°(±665) = -97,000(±4606) + 6.79(±0.78)J Joule/g * atom V for the reaction V + 0.73C = VC_0.73.