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.     

High temperature thermodynamic properties of the tungsten carbide WC determined using a galvanic cell technique

The standard free energy of formation of WC has been obtained from emf measurements on the following galvanic cells with BaF₂-BaC₂ solid solutions as the electrolyte: Cr,Cr₂₃C₆ | BaF₂-BaC₂ | W,WC (878 to 1132 K) (A) and Mo,Mo₂C | BaF₂-BaC₂ | W,WC (889 to 1309 K) (B) Combining the results of this study with a previous work¹⁶ and those of Kulkarniet al.,¹⁷ the following equations for ΔG°_f of WC have been determined: from cell (A): ΔG°_f (±950) = -38,000 (±328) -6.6 (±0.3)T joules. From cell (B): ΔG°_f (±1000) = -37,866 (±212) - 6.5 (±0.2)T joules for the reaction W + C = WC.     

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     

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.     

Determination of the standard gibbs energy for the reaction of 3BaO (s) + 2Cr (s) + 3/2O2 (g) = 3Ba0 · Cr2O3 (s)

The standard Gibbs energy of formation of 3BaO · Cr₂O₃ has been measured by a chemical equilibrium technique and is expressed as follows: 3BaO (s) + 2Cr (s) + 3/2 O₂ (g) = 3BaO · Cr₂O₃ (s) ΔG^o = -1,260,000 (±3000) + 282 (±24)r(J/mol) The activity coefficient of chromium in copper, which was needed for the foregoing measurement, may be expressed by the following equation: 5790 log γ _Cr ^{o =5790/T-2.10} The value of standard Gibbs energy at 1573 K was found to be close to that of reaction of formation of CaO · Cr₂O₃ expressed in the similar form. The BaO saturated BaF₂ flux is shown to be far more promising in the oxidative dephosphorization of chromium-containing hot metal in comparison with the CaO-SiO₂-CaF₂ flux doubly saturated with CaO and 3CaO-Cr₂O₃.     

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.     

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.     

Kinetic studies of the reaction between Cr23 C6 particles and Cr2O3 particles

The kinetics of reaction between Cr₂₃C₆ particles and Cr₂O₃ particles which yields metallic chromium was studied. This reaction is one of the basic reactions in the Simplex process and is also related to the carbon reduction of metal oxide. The rate of reaction between these particles in a pellet of the mixture was measured by thermogravimetry in vacuum at 1050, 1075, and 1100°C. The molar ratio of Cr₂₃C₆ to Cr₂O₃ in the pellet was maintained at 1:8. At the earlier stages of the reaction, a rate equation for interfacial reaction control was applied and the rate constant α was observed to be inversely proportional to the reciprocal effective radius of Cr₂₃C₆ particles. The indirect gaseous reactions are predominant: 1/6 Cr₂₃C₆ + CO₂ = 23/6 Cr + 2CO 1/3 Cr₂O₃+ CO = 2/3 Cr + CO₂ The reduction of Cr₂O₃ with CO gas is presumed to proceed so rapidly and the equilibrium is attained instantaneously. The reaction of CO₂ with Cr₂₃C₆ particles occurs in the sequence co₂ (g) +c< ⇋ c(o) + co(g) c(o) → CO(g) +c< The latter reaction was thought to be the rate determining step, and the activation energy of this reaction was estimated to be approximately 60 kcal per mole.     

Structural superplasticity in a fine-grained eutectic intermetallic NiAl−Cr alloy

A rapidly solidified and thermomechanically processed fine-grained eutectic NiAl−Cr alloy of the composition Ni₃₃Al₃₃Cr₃₄ (at, pct) exhibits structural superplasticity in the temperature regime from 900°C to 1000°C at strain rates ranging from 10⁻⁵ to 10⁻³ s⁻¹. The material consists of a B2-ordered intermetallic NiAl(Cr) solid solution matrix containing a fine dispersion of bcc chromium. A high strain-rate-sensitivity exponent of m=0.55 was achieved in strain-rate-change tests at strain rates of about 10⁻⁴ s⁻¹. Maximum uniform elongations up to 350 pct engineering strain were recorded in superplastic strain to failure tests. Activation energy analysis of superplastic flow was performed in order to establish the diffusion-controlled dislocation accommodation process of grain boundary sliding. An activation energy of Q _c=288±15 kJ/mole was determined. This value is comparable with the activation energy of 290 kJ/mole for lattice diffusion of nickel and for ⁶³Ni tracer selfdiffusion in B2-ordered NiAl. The principal deformation mechanism of superplastic flow in this material is grain-boundary sliding accommodated by dislocation climb controlled by lattice diffusion, which is typical for class II solid-solution alloys. Failure in superplastically strained tensile samples of the fine-grained eutectic alloy occurred by cavitation formations along NiAl‖‖Cr interfaces.     

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)     

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.     

The effect of chromium on the activity coefficient of sulfur in liquid Fe−Cr−S alloys

The effect of chromium on the activity coefficient of sulfur in the ternary system Fe−Cr−S has been determined in the temperature range 1525° to 1755°C for chromium concentrations of up to 40 wt pct, using a levitation melting technique in H₂−H₂S atmospheres. The first order free energy interaction coefficient,e _S ^Cr , which is derived on the assumption that the thermal diffusion error is constant for both binary Fe−S and ternary Fe−Cr−S melts under controlled levitation conditions, is given by the relationship:e _S ^Cr =−94.2/T+0.040 The first order enthalpy and entropy interaction coefficients are found to beh _S ^Cr =−430±70 ands _S ^Cr =−0.183±0.007 respectively. These results are in good agreement with recently published data.     

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)     

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)     

Time-temperature-precipitation characteristics of high-nitrogen austenitic Fe−18Cr−18Mn−2Mo−0.9N steel

The time-temperature-precipitation (TTP) and corresponding mechanical properties in high-nitrogen austenitic Fe−18Cr−18Mn−2Mo−0.9N steel (all in weight percent) were investigated using electron microscopy and ambient tensile testing. The precipitation reactions can be categorized into three stages: (1) high-temperature region (above 950°C)—mainly coarse grain-boundary (intergranular) Cr₂N; (2) nose-temperature region—integranular Cr₂N→cellular Cr₂N→intragranular Cr₂N+ sigma (σ); and (3) low-temperature region (below 750°C)—intergranular Cr₂N→cellular Cr₂N→ intragranular Cr₂N+σ+chi(χ)+M₇C₃ carbide. After cellular Cr₂N precipitation became dominant above 800°C, yield and tensile strength gradually decreased, whereas elongation abruptly deteriorated with aging time. On the contrary, prolonged aging in the low-temperature regime increased tensile strength, caused by the precipitation of fine χ and M₇C₃ within grains. Based on the analyses of selected area diffraction (SAD) patterns, the crystallographic features of the second phases were analyzed.     

Activity of chromic oxide in the CaF2−CaO−Cr2O3 and the CaF2−Al2O3−Cr2O3 systems

The values of the activity of Cr₂O₃ in the slags based on the CaF₂−CaO−Cr₂O₃ and the CaF₂−Al₂O₃−Cr₂O₃ systems which may be used in the electroslag remelting (E.S.R.) process have been determined at 1450, 1500 and 1550°C by equilibrating the slags with Pt−Cr alloys of known chromium activity under known oxygen partial pressure and studying the equilibrium 2[Cr] alloy+3/2 O₂(g)=(Cr₂O₃)_slag. It was found that activity of Cr₂O₃ decreases with the addition of CaO and Al₂O₃ in the respective systems. In slags containing less than about 20 wt pct CaO and in the Al₂O₃ bearing slags, solutions of Cr₂O₃ showed a positive deviation from ideality and in slags containing more than 20 wt pct CaO, they showed a negative deviation. Both the authors were formerly with the Department of Metallurgy, University of Sheffield, England     

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.     

Phase equilibria in the ternary system Sc−Cr−C at subsolidus temperatures

Phase equilibria in the ternary system Sc−Cr−C were investigated by metallography, differential thermal analysis, x-ray diffraction, and electron probe microanalysis. A projection of the solidus surface was constructed for the first time. The nature of phase equilibria in the system is defined by the presence of two thermodynamically stable phases based on the compounds Sc₂CrC₃ (whose existence was confirmed) and ScC_1−x. The melting point of the alloys increases with increasing carbon concentration. Compositions in the 〈Cr〉+〈ScC_1−x〉+〈Sc〉 range have a minimum melting temperature equal to 1018±2°C, and the maximum melting temperature in the system, 1660±2°C, is found in alloys containing 〈Cr₃C₂〉+〈Sc₂CrC₃〉+C. Institute for Materials Science Problems. Ukrainian Academy of Sciences, Kiev. Translated from Poroshkovaya Metallurgiya, Nos. 3–4, pp. 18–26, March–April, 1997.     

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