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.     

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.     

Thermodynamics and kinetics of δ→ α martensitic transformation in Pu alloys

A regular solution model is fit to experimental equilibrium temperatures(T ₀) and pressures(P ₀) for diffusionlessδ→α transformations in Pu-Ga and Pu-Al alloys, in order to define the chemical free energy change ΔG forδ→ α transformation. Analysis of reported isothermalδ→ αtransformation rate data in terms of nucleation-controlled martensitic kinetics gives a nucleation activation energyQ which is a nonlinear function of ΔG. The activation volumeV _* defined byδQ/δΔG is of the order of 10 to 40 atomic volumes, suggestive of rate control by an interfacial Peierls barrier. The grain size dependence of the transformation-start temperature at a fixed cooling rate of 2.08 × 10_-2 Ks_-1 is measured in a Pu-1.7 at. pct Ga alloy, revealing an inhibition of transformation at fine grain sizes. The overall kinetic behavior is characteristic of a martensitic mechanism.     

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.     

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

Enthalpies of formation of (Pd + In) alloys have been obtained by direct reaction calorimetry using a very high temperature calorimeter between 1425 and 1679 K in the concentration range 0 <x _Pd < 0.66. They are very negative with a minimum Δ_mix H _o ^m, = -59.6 /2.5 kJ · mol^-1 atx _Pd = 0.59 and independent of temperature within the experimental error. The integral molar enthalpy of mixing is given by Δ_mixΔH _m ^o /· mol^-1 =x(1 -x)·- (-126.94 - 92.653x-83.231.x ₂ - 734.49.x ₃ + 949.07x ⁴), wherex = x _Pd. The limiting partial molar enthalpy of palladium in indium was calculated as Δh _m(Pd liquid in ∞ liquid In) = -127 ± 5 kJ·mol^-1. The results are discussed and compared with the enthalpies of formation of solid alloys. The anomalous behavior of the partial enthalpy of Pd is assumed to be due to the charge transfer of, at most, two electrons of In to Pd. Formerly Ph.D. Student, Université de Provence.     

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     

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.     

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)     

An electrochemical investigation of the thermodynamic properties of the NaCl-AlCl3 system at subliquidus temperatures

The phase relations in the NaCl-AlCl₃ system ( ) have been determined in the temperature range from 373 to 623 K by isothermal equilibration, electrical conductivity, and electromotive force measurements. Only one ternary compound, NaAlCl₄, was found to be stable, with a melting point of 426 K. The standard Gibbs energy of formation of NaCl and NaAlCl₄ has been measured in the temperature range from 423 to 623 K by a novel galvanic cell technique involving in-situ electrogenerated chlorine electrode in the Na/β″-alumina/NaCl, NaAlCl₄/Cl₂,C and Al/NaCl, NaAlCl₄/Cl₂,C cells along with the Na/β″-alumina/NaCl,NaAlCl₄/Al cell. The Δ _f G _NaCl(s ^)/o and values have been calculated as −412.4+0.095 T (±1) kJ mol⁻¹ and −1117.5+0.2460 T (±2) kJ mol⁻¹, respectively. The standard entropy of NaAlCl₄ (s) at 298 K, computed from the results of the study and the auxiliary information from the literature (184 J K⁻¹ mol⁻¹), show good agreement with the estimated JANAF value (188.28 J K⁻¹ mol⁻¹). The enthalpy of formation of NaAlCl₄ (l) from NaCl (s) and AlCl₃ (s) at 550 K obtained in the present study (−1850 J mol⁻¹) is in agreement with that computed from the heat-capacity measurements (−1910 J mol⁻¹). The present measurements are unique, as a new electrochemical technique is employed in a cell with low-melting sodium chloroaluminate electrolyte to obtain the thermodynamic properties of NaCl and NaAlCl₄ at significantly low temperatures. The Gibbs energy of formation of NaCl (s) is, thus, measured at temperatures as low as 423 K by an electrochemical technique for the first time, in this work.     

The standard gibbs energy of formation of CeF3 and its activity coefficient in cryolite

Literature data are analyzed to give the activity coefficient (γ_Ce) of Ce in dilute solution in Al as log₁₀γ_Ce = −11 356/T + 4.261 referred to liquid Ce as standard state. Measurements were made in the range of 977 to 1288 K of the equilibrium Al (1) + CeF₃ (s) = AlF₃ (s) + Ce(Al) and give, by a third-law calculation, °G ^o = 183 360 + 19.456T joules, and Δ _{fH 298} ^o of CeF₃ = −1701 kJ mol⁻¹. Values of the partition coefficient of Ce between Al and molten cryolite then give activity coefficients of CeF₃ in solution. These activity coefficients decrease as the NaF/AlF₃ ratio is raised, showing acid behavior of CeF₃. It appears to dissolve mainly in the form of Na₂CeF₅.     

Activities of chromium in molten copper at dilute concentrations by solid-state electrochemical cell

In order to obtain the activities of chromium in molten copper at dilute concentrations (<0.008 chromium mole fractions), liquid copper was brought to equilibrium with molten CaCl₂ + Cr₂O₃ slag saturated with Cr₂O₃ (s), at temperatures between 1423 and 1573 K, and the equilibrium oxygen partial pressures were measured by means of solid-oxide galvanic cells of the type Mo/Mo + MoO₂/ZrO₂(MgO)/(Cu + Cr))alloy + Cr₂O₃ + (CaCl₂ + Cr₂O₃)_slag/Mo. The free energy changes for the dissolution of solid chromium in molten copper at infinite dilution referred to 1 wt pct were determined as Cr (s) = Cr(1 wt pct, in Cu) and ΔG° = + 97,000 + 73.3(T/K) ± 2,000 J mol⁻¹.     

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.     

Phase relations in the system Cu-Gd-O

The phase relations in the system Cu-Gd-O have been determined at 1273 K by X-ray diffrac- tion, optical microscopy, and electron microprobe analysis of samples equilibrated in quartz ampules and in pure oxygen. Only one ternary compound, CuGd₂O₄, was found to be stable. The Gibbs free energy of formation of this compound has been measured using the solid-state cell Pt, Cu₂O + CuGd₂O₄ + Gd₂O₃ // (Y₂O₃) ZrO₂ // CuO + Cu₂O, Pt in the temperature range of 900 to 1350 K. For the formation of CuGd₂O₄ from its binary component oxides, CuO (s) + Gd₂O₃ (s) → CuGd₂O₄ (s) ΔG° = 8230 - 11.2T (±50) J mol^-1 Since the formation is endothermic, CuGd₂O₄ becomes thermodynamically unstable with respect to CuO and Gd₂O₃ below 735 K. When the oxygen partial pressure over CuGd₂O₄ is lowered, it decomposes according to the reaction 4CuGd₂O₄ (s) → 4Gd₂O₃ (s) + 2Cu₂O (s) + O₂ (g) for which the equilibrium oxygen potential is given by Δμ_{o 2} = −227,970 + 143.2T (±500) J mol⁻¹ An oxygen potential diagram for the system Cu-Gd-O at 1273 K is presented.     

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     

Oxygen potentials in Ni + NiO and Ni + Cr2O3 + NiCr2O4 systems

The chemical potential of O for the coexistence of Ni + NiO and Ni + Cr₂O₃ + NiCr₂O₄ equilibria has been measured employing solid-state galvanic cells, (+) Pt, Cu + Cu₂O // (Y₂O₃)ZrO₂ // Ni + NiO, Pt (-) and (+) Pt, Ni + NiO // (Y₂O₃)ZrO₂ // Ni + Cr₂O₃ + NiCr₂O₄, Pt (-) in the temperature range of 800 to 1300 K and 1100 to 1460 K, respectively. The electromotive force (emf) of both the cells was reversible, reproducible on thermal cycling, and varied linearly with temperature. For the coexistence of the two-phase mixture of Ni + NiO, δΜ_{O 2}(Ni + NiO) = −470,768 + 171.77T (±20) J mol⁻¹ (800 ≤T ≤ 1300 K) and for the coexistence of Ni + Cr₂O₃ + NiCr₂O₄, δΜ_{O 2}(Ni + Cr₂O₃ + NiCr₂O₄) = −523,190 + 191.07T (±100) J mol⁻¹ (1100≤ T≤ 1460 K) The “third-law” analysis of the present results for Ni + NiO gives the value of ‡H ₂₉₈ ^o = -239.8 (±0.05) kJ mol⁻¹, which is independent of temperature, for the formation of one mole of NiO from its elements. This is in excellent agreement with the calorimetric enthalpy of formation of NiO reported in the literature.     

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.     

Gibbs free energies of formation of molybdenum carbide and tungsten carbide from 1173 to 1573 K

The gas equilibrium method of CH₄/H₂ has been widely used for measuring carbon potential. However, it has been reported that this method is not applicable at high temperatures since the equilibrium between CH₄ and H₂ is disturbed by the reaction of CH₄ with moisture in the system. Nevertheless, this method should be applicable theoretically at high temperatures below which CH₄ decomposition can be neglected because the equilibrium between CH₄ and H₂ reaches constant ratio in spite of the reaction. Since the role of moisture is to oxidize the sample during the measurements under the oxygen potential determined byPh ₂ o/ph ₂ ratio, the Gibbs free energies of formation of Mo₂C and WC were successfully measured from 1173 to 1573 K by keeping the moisture level in the system low enough not to oxidize the sample. The experimental results are expressed by the following equations which were derived by least squares treatments of the data: Mo₂C:ΔG = -68270 + 8.23T J mol^-1 WC:ΔG = -52330 + 14.06T J mol^-1 These values were in good agreement with those measured by M. Gleiseret al. for narrow tempareture ranges using the CO/CO₂ gas equilibrium method.     

Stability of chromium (III) sulfate in atmospheres containing oxygen and sulfur

The stability of chromium (III) sulfate in the temperature range from 880 to 1040 K was determined by employing a dynamic gas-solid equilibration technique. The solid chromium sulfate was equilibrated in a gas stream of controlled SO₃ potential. Thermogravimetric and differential thermal analyses were used to follow the decomposition of chromium sulfate. Over the temperature range studied, the change in the Gibbs’ free energy of formation of chromium sulfate Cr₂O₃(s) + 3SO₃(g) → Cr₂(SO₄)₃(s) can be expressed as ΔG⁰ = •143,078 + 129.6T (±300) cal mole^•1 ΔG⁰ = •598,350 + 542T (±1250) J mole^•1. X-ray diffraction analysis indicated that the decomposition product was crystalline Cr₂O₃ and that the mutual solubility between Cr₂(SO₄)₃ and Cr₂O₃ was negligible. Over the temperature range investigated, the decomposition pressures were significantly high so that chromium sulfate is not expected to form on commercial alloys containing chromium when exposed to gaseous environments containing oxygen and sulfur (such as those encountered in coal gasification).     

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