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

The standard Gibbs energies of formation of Cr₃C₂, Cr₇C₃, and Cr₂₃C₆ have been determined by electromotive force (emf) measurements using galvanic cells of the type (−) Cr, CrF₂, CaF₂ // CaF₂ // CaF₂, CrF₂, ‘Cr−C’ (+) The measurements have been carried out in the temperature range 1002 to 1176 K. The ΔG° values obtained in the present work are generally in agreement with some of the earlier emf measurements but differ significantly from those obtained by Cr₂O₃−CO equilibrium studies.     

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     

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     

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     

High temperature thermodynamic properties of the chromium carbides Cr7C3 and Cr3C2 determined using a galvanic cell technique

The standard free energies of formation of Cr₇C₃ and Cr₃C₂ have been obtained from emf measurements on the following galvanic cells with BaF₂-BaC₂ solid solutions as the electrolyte: Cr,Cr₂₃C₆∣BaF-BaC₂∣Cr₂₃C₆,Cr₇C₃ (920 to 1250 K) (A) Cr₂₃C₆, Cr₇C₃ ∣BaF₂-BaC₂∣W, WC (900 to 1200 K) (B) WC, W∣BaF₂-BaC₂∣Cr₃C₂, Cr₇C₃ (973 to 1173 K) (C) Combining the results of this study with a previous work¹⁵ and those of Kulkarniet al. and Dawsonet al., the following equations for ΔG _f ^ℴ of Cr₇C₃ and Cr₃C₂ have been determined: from cell (A): ΔG _Cr7C3 ^o (±2300) = −155410(±173) − 35.8(±0.1)T joules; from cell (B): ΔG _Cr7C3 ^o (±2000) = −155585(±385) − 35.8(±0.4)T joules for the reaction 7Cr + 3C = Cr₇C₃; from cell (C): ΔG _Cr3C2 ^o , (±1200) = −92860(±210) − 19.4(±0.2)T joules for the reaction 3Cr + 2C = Cr₃C₂.     

Thermodynamic study of Na2O-SiO2 melts at 1300° and 1400 °C

The vapor pressures of Na above stirred Na₂O-SiO₂ melts in equilibrium with graphite and CO were determined at 1300° and 1400 °C using the transpiration technique. Compositions studied ranged from about 60 mole pct SiO₂ to close to SiO₂ saturation. Activities of components Na₂O and SiO₂ were calculated from the data. Log a_Na2_O (pure liquid as standard state) varies from about −8.7 and −8.5 at silica saturation to −6.3 and −6.1 at 40 mole pct Na₂O at 1300° and 1400 °C, and the molar Gibbs energy of mixing, ΔG _m, at the disilicate composition (X_Na2_O = 0.33) at each of these temperatures is −83.0 and −85.4 kJ, respectively. The Toop and Samis, Yokokawa and Niwa, and Lin and Pelton solution models for binary silicates were applied to the ΔG _m data at 1350 °C and parameters for the models were estimated to give best fits. All three models show good correspondence with the measured ΔG _m curve. The capabilities of the models in predicting activity data in this system have been compared. D. N. Rego, Formerly Graduate Student at Carnegie-Mellon University, G.K. Sigworth, Formerly with Carnegie-Mellon University,     

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     

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.     

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.     

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.     

Thermodynamic properties of complex oxides in the Sm-Ba-Cu-O system

An assembly for performing electromotive force (EMF) measurements using either a CaF₂ single crystal or a MgO partially stabilized zirconia as a solid-state electrolyte has been constructed. Heat capacities of member complex oxides in the Sm-Ba-Cu-O system were measured by an adiabatic scanning calorimeter. From the EMF data, the standard Gibbs energies, standard enthalpies of formation, standard entropies, and decomposition pressures of the complex oxides were calculated. The standard Gibbs energies of reaction of complex oxides from relevant simple oxides Sm₂O₃, BaO, and CuO were derived. It was found that all complex compounds in this system were thermodynamic stable. The tendency of the thermodynamic stability of the solid solution compound Sm_1+x , Ba_2−x Cu₃O _y decreases with the solubility x from 0 to 0.4.     

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

The standard Gibbs energies of formation of Mn₇C₃, Mn₅C₂, Mn₁₅C₄, and Mn₂₃C₆ have been obtained from emf measurements using galvanic cells of the type (-)Mn, MnF₂, CaF₂//CaF₂//CaF₂, MnF₂, ‘Mn-C’(+) The measurements have been carried out in the temperature range 909 to 1247 K. In the case of measurements with Mn-C alloy containing 12.9 wt pct C (Mn₇C₃-C two-phase region at room temperature), the slope change in the emf-temperature curve at 1181 K suggests the formation of a hitherto unidentified phase above this temperature.     

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.     

The activity of calcium in calcium-metal-fluoride fluxes

The standard Gibbs energy of reaction Ca (1) +O (mass pct, in Zr) = CaO (s) has been determined as follows by equilibrating molten calcium with solid zirconium in a CaO crucible: ΔG° = -64,300(±700) + 19.8(±3.5)T J/mol (1373 to 1623 K) The activities of calcium in the CaO_satd-Ca-MF₂ (M: Ca, Ba, Mg) and CaO_satd-Ca-NaF systems were measured as a function of calcium composition at high calcium contents at 1473 K on the basis of the standard Gibbs energy. The activities of calcium increase in the order of CaF₂, BaF₂, and MgF₂ at the same calcium fraction of these fluxes. The observed activities are compared with those estimated by using the Temkin model for ionic solutions. Furthermore, the possibility of the removal of tramp elements such as tin, arsenic, antimony, bismuth, and lead from carbon-saturated iron by using calcium-metal-fluoride fluxes is discussed. Formerly Graduate Student, Department of Metallurgy, The University of Tokyo.     

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.     

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     

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.