An investigation of high temperature thermodynamic properties in the Pt-Zr and Pt-Hf systems

High-temperature thermodynamic properties of Pt−Zr alloys containing 2 to 25 at. pct Zr and Pt−Hf alloys containing 20 to 25 at. pct Hf have been measured over the temperature range 1100 to 1400 K by a galvanic cell technique using a thoria-based electrolyte. Activities of Zr and Hf show large negative deviations from Raoult's Law; at 1300 K and 23 at. pct Zr of Hf, for instance,a _Zr=6.5×10⁻¹⁶ anda _Hf=7.9×10⁻¹⁷. Correlation of emf results with X-ray phase data enables calculation of standard free energies of formation of the intermetallic compounds ZrPt₅, ZrPt₃, and HfPt₃. At 1300 K ΔG _f ⁰ (ZrPt₅) =−92,680 cal/mole; ΔG _f ⁰ (ZrPt₃)=−91,740 cal/mole; and ΔG _f ⁰ (HfPt₃)=−97,350 cal/mole. The high stabilities of phases in the Pt−Ti, Pt−Zr, and Pt−Hf systems verify the predictions of the Engel-Brewer correlation. The large negative entropies of formation of TiPt₃, ZrPt₃ are discussed. Applications including side reactions in fuel cells and thermocouple systems are mentioned. P. J. MESCHTER, formerly a Graduate Student at the University of Pennsylvania This paper is based upon a dissertation submitted by P. J. Meschter in partial fulfillment of the requirements of the degree of Doctor of Philosophy at the University of Pennsylvania.     

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.     

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.     

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).     

Enthalpies of formation of chromium carbides

Adiabatic oxygen combustion calorimetry has been used to determine the enthalpies of combustion of the chromium carbides Cr₂₃C₆, Cr₇C₃ and Cr₃C₂ to be—15,057.6±12.4 kJ ·mole⁻¹,—4985.3±3.8 kJ ·mole⁻¹ and—2400.5±0.9 kJ ·mole⁻¹ respectively. The products of combustion in all cases were Cr₂O₃ and CO₂. Using standard data for Cr₂O₃ and CO₂, the enthalpies of formation of the carbides have been calculated to be:fΔH ₂₉₈ ^o Cr₂₃C₆=−290.0±27.6 kJ·mole⁻¹ fΔH ₂₉₈ ^o Cr₇C₃=−149.2±8.5 kJ·mole⁻¹ fΔH ₂₉₈ ^o Cr₃C₂=−81.1±2.9 kJ·mole⁻¹     

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     

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.     

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.     

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,     

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.     

The effects of alkaline earth metal ions and halogen ions on the chromium oxide activities in alkaline earth metal oxide-halide-Cr2O3 system fluxes

The solid electrolyte cell — Mo|Cr + Cr₂O₃‖ZrO₂(MgO)‖{Cu-Cr}_alloy + (Cr₂O₃)_fluxes|Mo+ is used at 1673 K to determine Cr₂O₃ activities in MO-MX ₂-Cr₂O₃ (M = Ca²⁺, Ba²⁻, X = F⁻ or Cl⁻) ternary fluxes, which are in equilibrium with the copper-chromium binary alloy. The ternary isothermal phase diagrams of CaO-CaF₂-Cr₂O₃ and BaO-BaCl₂-Cr₂O₃ system fluxes are inferred on the basis of the experimental results and binary phase diagrams. The results indicate that Cr₂O₃ activities in all fluxes always decrease with the increase of the X _MO /X _MX2 ratio. Partial replacement of BaO in BaO-BaF₂-Cr₂O₃ fluxes by CaO is acceptable for economy and efficiency considerations. At the same time, partial substitution of BaO for CaO in CaO-CaF₂-Cr₂O₃ fluxes is advantageous for phosphorus removal and chromium retention as a result of the increased Cr₂O₃ activities, increased basicities, and widening of the liquid zones. Compared to those in BaO-BaF₂-Cr₂O₃ fluxes, Cr₂O₃ activities in CaO-CaF₂-Cr₂O₃ fluxes approximately follow the same curve as the former, although the position and the width of the liquid zones are considerably different, and activities in BaO-BaCl₂-Cr₂O₃ fluxes are higher at the lower Cr₂O₃ content, or vice versa. The activity coefficients of Cr₂O₃ in the fluxes decrease with the increase of the X _MO /X _{MX 2} ratios.     

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 of the Mn-P system

The free energy of mixing in the Mn-P melts in the composition range ofX _p = 0.0 to 0.333 was estimated by coupling the phase boundary information with reliable ΔG° formation for the Mn2P phase. This information was used to obtain the dilute solution properties of P in Mn. P_(l,pure) = P_{(l,Henrian, Mn)} ΔG ^°(Joules) = -203,611.39 + 41.003T The free energy is shown to be more negative than in the Fe system, reflecting a stronger interaction between Mn and P atoms than between Fe and P atoms. Presenting the activity coefficient of P with the expression used by Lupis and Elliott, the first and second interaction coefficients are obtained as follows: ε _P ^P (Mn) = 10.538 + 9728.14/T ρ _P ^P (Mn) = 28.148 + 9101.83/T The Gibbs free energy of formation for Mn₃P was estimated in the temperature range of {dy1233} to {dy1378} K to be 3Mn _l + P_(l = Mn₃P_(s ΔG ^°(Joules) = -241,461.65 + 65.031T     

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     

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.     

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.     

The thermodynamic behavior of sulfur in molten nickel and nickel-base alloys

The thermodynamic properties of dilute solutions of sulfur in pure liquid nickel were investigated at 1500, 1550, and 1575°C for sulfur concentrations up to 0.7 wt pct. Based on the infinitely dilute, wt pct standard state, the equilibrium data obtained for the reaction: H₂(g) + S = H₂S(g) were fitted by the equations: logK = − 1489/T − 1.772, and ΔG° = 6812 + 8.11T, cal/mole. For the solution ofS ₂(g) in pure Ni according to the reaction: 1/2S ₂(g) = S (in Ni), the standard free energy of solution is found to be: ΔG° = - 28,342 + 3.62T, cal/mole. For the very dilute solutions of sulfur normally encountered in nickel-base melting, the activity coefficient of sulfur in pure Ni at 1575°C is given by: log f_S= -0.035 (pct S). The effects of alloying elements normally used in nickel-base alloys on the activity coefficient of sulfur in molten nickel were investigated. The activity coefficient of sulfur is increased by all of the alloying elements studied, as evidenced by the interaction parameters: e_S ^fe = +0.005, e_S ^Cr = +0.030, e_S ^Mo = +0.053, e_S ^Ti = +0.160, and e_S ^A1 = +0.133. Measured values of the activity coefficient of sulfur in the quaternary system Ni-S-Cr-Fe agreed reasonably well with those predicted from binary and ternary data. This work constitutes a portion of the work performed by W. F. VENAL for the Ph.D. degree from the University of Illinois at Chicago Circle. Formerly Professor of Metallurgical Engineering at UICC.     

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.     

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)