High Temperature Thermodynamic Properties of ZnTe(s)

We have gathered the partial pressure, Knudsen cell, and emf measurements on ZnTe(s) from which the Gibbs energy of formation can be calculated. Published partial pressures of diatomic tellurium have been adjusted to take account of a subsequently published third law analysis of tellurium. The equation used to calculate the total pressure from the rate of mass loss from an extensive set of Knudsen cell measurements has been corrected to give a 5% increase in total pressure and the Gibbs energy of formation has been recalculated. A high temperature heat capacity for ZnTe(s) has been selected from the published data. The Gibbs energies of formation as a function of temperature have then been fit using a third law analysis to give two essentially equally good but extreme fits. In the first, the standard enthalpy of formation agrees with the calorimetric value of −119 kJ/mol but the standard entropy of ZnTe(s) is low by 2-3 J/mol K. In the second, the standard enthalpy of formation is more positive than the calorimetric values by about 3 kJ/mol but the standard entropy of ZnTe(s) is 82 J/mol K and close to the value from low temperature heat capacity measurements. We select values of −119.49 kJ/mol for the standard enthalpy of formation and 78.23 J/mol K for the standard entropy.     

Thermodynamic properties of 1-nutyl-3-methylimidazolium chloride (C<Subscript>4</Subscript>mim[Cl]) ionic liquid

Thermodynamic properties of 1-butyl-3-methylimidazolium chloride (C₄mim[Cl]) ionic liquid were determined using thermogravimetric (TG) differential thermal analysis (DTA). A new method called DTA mass-difference baseline, was used to measure the heat capacity and enthalpy change of phase transformation of ionic liquid from DTA curves. Based on this, the changes in standard enthalpy, entropy, and Gibbs energy were determined. The results show that standard enthalpy and entropy changes of C₄mim[Cl] increase nonlinearly with increasing temperature, while the standard Gibbs energy change decreases nonlinearly with increasing temperature within the temperature range studied (298–453 K). The standard enthalpy of melting and enthalpy of vaporization were determined to be 0.93 and 11.07 kJ/mol, respectively.     

Thermodynamic Evaluation of Yttrium

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第一性原理研究Re的热力学性质

基于准谐Debye-Grüneisen模型,运用第一性原理缀加投影平面波方法研究了Re的热力学性质,拟合了Re的状态方程,计算了Re不同压强下弹性模量、吉布斯自由能、焓、熵、热容和体膨胀系数随温度的变化关系。结果表明:采用八阶Birch-Murnaghan方程拟合得到的Re压强-体积曲线与实验测量结果吻合较好;计算的零压下吉布斯自由能、焓、熵、热容和体膨胀系数随温度的变化均与实验值符合较好;在零压,50、100、150和200GPa压强下,Re的弹性模量和吉布斯自由能随温度升高而减小;焓、熵随温度升高而增加;Re的电子等容热容随温度线性增加,晶格振动等容热容在低温下符合3T幂次规律并随温度增加而迅速增大,且在高温时逐渐接近Dulong-Petit极限;预测的德拜温度约为430K,与实验结果一致。     

Reevaluation of the Fe-Mn phase diagram

New results for the enthalpy of mixing of liquid Fe-Mn alloys, the enthalpy of formation of γ-Fe-Mn solid solutions and the heat capacity of α-Fe-Mn and γ-Fe-Mn alloys obtained by isoperibolic calorimetry and differential thermal analysis (DTA) measurements have been used for the reassessment of the molar Gibbs energy of the various phases of the Fe-Mn system. Experimental information about martensitic transformation temperatures in Fe-Mn alloys published recently was incorporated in the updating of the occurring metastable equilibria. The present reevaluation results in a good fit with all available experimental data and is compared with the results of previous assessments.     

Thermodynamic Evaluation of Gadolinium

ＴｈｅｒｍｏｄｙｎａｍｉｃＥｖａｌｕａｔｉｏｎｏｆＧａｄｏｌｉｎｉｕｍＳｈｅｎＨｕａｓｅｎ，ＺｈａｎｇＷｅｉｊｉｎｇ，ＬｉｕＧｕｏｑｕａｎ，ＷａｎｇＲｕｎａｎｄＤｕＺｈｅｎｍｉｎ（沈化森）（张维敬）（刘国权）（王润）（杜振民）（Ｄｅｐａｒｔｍｅｎｔｏ...     

Gibbs Energy of Formation of MnO: Measurement and Assessment

Based on the measurements of Alcock and Zador, Grundy et al. estimated an uncertainty of the order of ±5 kJ mol⁻¹ for the standard Gibbs energy of formation of MnO in a recent assessment. Since the evaluation of thermodynamic data for the higher oxides Mn₃O₄, Mn₂O₃, and MnO₂ depends on values for MnO, a redetermination of its Gibbs energy of formation was undertaken in the temperature range from 875 to 1300 K using a solid-state electrochemical cell incorporating yttria-doped thoria (YDT) as the solid electrolyte and Fe + Fe_1 − δO as the reference electrode. The cell can be presented as

New Contribution to the Thermodynamics of Fe-Cr Alloys as Base for Ferritic Steels

High chromium ferritic-martensitic steels are commonly used for industrial applications requiring high strength at elevated temperature. Such steels typically contain 9-14 at.% Cr and a few percents of minor alloying elements. In recent studies it has been shown that the Cr solubility limit of the standard Fe-Cr phase diagram in that composition range is significantly underestimated. For the purpose of more reliable engineering and out of physical considerations, we reparameterize the Gibbs free energy so that the correct Cr solubility at low temperature (<700 K) is reproduced, while leaving the rest of the phase diagram changed only slightly. The mixing enthalpy and heat capacity resulting from the new parameterization are also compared with experiments and found to be in good agreement.     

Phase Equilibria in the System Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-CaO-CoO and Gibbs Energy of Formation of Ca<Subscript>3</Subscript>CoAl<Subscript>4</Subscript>O<Subscript>10</Subscript>

An isothermal section of the system Al₂O₃-CaO-CoO at 1500 K has been established by equilibrating 22 samples of different compositions at high temperature and phase identification by optical and scanning electron microscopy, X-ray diffraction, and energy dispersive spectroscopy after quenching to room temperature. Only one quaternary oxide, Ca₃CoAl₄O₁₀, was identified inside the ternary triangle. Based on the phase relations, a solid-state electrochemical cell was designed to measure the Gibbs energy of formation of Ca₃CoAl₄O₁₀ in the temperature range from 1150 to 1500 K. Calcia-stabilized zirconia was used as the solid electrolyte and a mixture of Co + CoO as the reference electrode. The cell can be represented as: From the emf of the cell, the standard Gibbs energy change for the Ca₃CoAl₄O₁₀ formation reaction, CoO + 3/5CaAl₂O₄ + 1/5Ca₁₂Al₁₄O₃₃ → Ca₃CoAl₄O₁₀, is obtained as a function of temperature: /J mol⁻¹ (±50) = −2673 + 0.289 (T/K). The standard Gibbs energy of formation of Ca₃CoAl₄O₁₀ from its component binary oxides, Al₂O₃, CaO, and CoO is derived as a function of temperature. The standard entropy and enthalpy of formation of Ca₃CoAl₄O₁₀ at 298.15 K are evaluated. Chemical potential diagrams for the system Al₂O₃-CaO-CoO at 1500 K are presented based on the results of this study and auxiliary information from the literature.     

Thermodynamic approach to quantitative assessment of propensity of metallic melts to amorphization

On thermodynamic grounds, it was found that key properties that control the capacity of molten metallic alloys for transition into an amorphous state are the excess (configurational) entropy and heat capacity of the liquid. Chemical short-range order in liquids exhibiting various ten-dencies to glass formation was analyzed on the basis of the associated solution theory and the results of detailed thermodynamic research on a wide set of alloys. An interrelation was established between the association, characteristics of molten alloys (viscosity η, activation energies of viscous flow, and crystallization) that determine the possibility of amorphization and characteristics of glassy state stability (glass transition point, Gibbs energy, and enthalpy of crystallization). It was demonstrated that the magnitude of the key functions is completely determined by the covalent constituent of chemical interaction between components and depends mainly on the entropy terms of association reactions. The prospects for developing the quantitative criteria of amorphization on the basis of the entropy of association was discussed. It was also shown that the suggested approach based on taking into accoun the specificity of chemical interaction between components can be useful for prediction of physical, chemical, and mechanical properties of solid amorphous metallic materials.     

Vapor pressure of SeO2 (s) and optical density of SeO2 (g)

The optical density of the vapor generated by SeO₂ (s) between about 416 and 505 K has been measured between 400 and 200 nm for optical path lengths of 10.14 and 10.15 cm and temperatures of 533, 733, 1133, and 1420 K. A pressure of oxygen of about 0.7 to 0.9 atm was present in the cells and that of Se₂ was below the minimum detectable of about 0.001 atm. For one cell, complete vaporization occurred at 481.5 K and a vapor pressure of 5.02 × 10⁻³ atm was calculated from the weight of SeO₂ (s), the volume profile of the optical cell, and the temperature distribution along the cell. Assuming Beer’s law is obeyed for a number of vibronic peaks, the vapor pressure is obtained as log₁₀ P (atm)=−5705/T+9.5443 in close agreement with two studies with fused silica Bourdon gauges. Beer’s law constants relating the pressure to the optical density at various wavelengths are obtained for the optical path temperatures listed above. Thermodynamic data previously published for solid and liquid SeO₂ need be changed only slightly to be consistent with the present vapor pressure. We obtain a standard enthalpy of sublimation at 298 K of 112.70 kJ/mol and standard entropies at 298 K of 258.72 and 66.693 J · mol⁻¹ · K⁻¹ for, respectively, gaseous and solid SeO₂.     

Vapor pressure of SeO2 (s) and optical density of SeO2 (g)

The optical density of the vapor generated by SeO₂ (s) between about 416 and 505 K has been measured between 400 and 200 nm for optical path lengths of 10.14 and 10.15 cm and temperatures of 533, 733, 1133, and 1420 K. A pressure of oxygen of about 0.7 to 0.9 atm was present in the cells and that of Se₂ was below the minimum detectable of about 0.001 atm. For one cell, complete vaporization occurred at 481.5 K and a vapor pressure of 5.02 × 10⁻³ atm was calculated from the weight of SeO₂ (s), the volume profile of the optical cell, and the temperature distribution along the cell. Assuming Beer’s law is obeyed for a number of vibronic peaks, the vapor pressure is obtained as log₁₀ P (atm)=−5705/T+9.5443 in close agreement with two studies with fused silica Bourdon gauges. Beer’s law constants relating the pressure to the optical density at various wavelengths are obtained for the optical path temperatures listed above. Thermodynamic data previously published for solid and liquid SeO₂ need be changed only slightly to be consistent with the present vapor pressure. We obtain a standard enthalpy of sublimation at 298 K of 112.70 kJ/mol and standard entropies at 298 K of 258.72 and 66.693 J · mol⁻¹ · K⁻¹ for, respectively, gaseous and solid SeO₂.     

Surface tension and thermodynamic properties of liquid Ag-Bi solutions

With the maximum bubble pressure method, the density and surface tension were measured for five Ag-Bi liquid alloys (X _Bi=0.05, 0.15, 0.25, 0.5, and 0.75), as well as for pure silver. The experiments were performed in the temperature range 544–1443 K. Linear dependences of both density and surface tension versus temperature were observed, and therefore the experimental data were described by linear equations. The density dependence on concentration and temperature was derived using the polynomial method. A similar dependence of surface tension on temperature and concentration is presented. Next, the Gibbs energy of formation of solid Bi₂O₃, as well as activities of Bi in liquid Ag-Bi alloys, were determined by a solid-state electromotive force (emf) technique using the following galvanic cells: Ni, NiO, Pt/O ⁻²/W, Ag _X Bi _(1−X), Bi ₂ O _3(s). The Gibbs energy of formation of solid Bi₂O₃ from pure elements was derived: =−598 148 + 309.27T [J · mol⁻¹] and =−548 008 + 258.94T [J · mol⁻¹]; the temperature and the heat of the α → δ transformation for this solid oxide were calculated as 996 K and 50.14 J · mol⁻¹. Activities of Bi in the liquid alloys were determined in the temperature range from 860–1075 K, for five Ag-Bi alloys (X _Ag=0.2, 0.35, 0.5, 0.65, 0.8), and a Redlich-Kister polynomial expansion was used to describe the thermodynamic properties of the liquid phase. Using Thermo-Calc software, the Ag-Bi phase diagram was calculated. Finally, thermodynamic data were used to predict surface tension behavior in the Ag-Bi binary system.     

Surface tension and thermodynamic properties of liquid Ag-Bi solutions

With the maximum bubble pressure method, the density and surface tension were measured for five Ag-Bi liquid alloys (X _Bi=0.05, 0.15, 0.25, 0.5, and 0.75), as well as for pure silver. The experiments were performed in the temperature range 544–1443 K. Linear dependences of both density and surface tension versus temperature were observed, and therefore the experimental data were described by linear equations. The density dependence on concentration and temperature was derived using the polynomial method. A similar dependence of surface tension on temperature and concentration is presented. Next, the Gibbs energy of formation of solid Bi₂O₃, as well as activities of Bi in liquid Ag-Bi alloys, were determined by a solid-state electromotive force (emf) technique using the following galvanic cells: Ni, NiO, Pt/O ⁻²/W, Ag _X Bi _(1−X), Bi ₂ O _3(s). The Gibbs energy of formation of solid Bi₂O₃ from pure elements was derived: =−598 148 + 309.27T [J · mol⁻¹] and =−548 008 + 258.94T [J · mol⁻¹]; the temperature and the heat of the α → δ transformation for this solid oxide were calculated as 996 K and 50.14 J · mol⁻¹. Activities of Bi in the liquid alloys were determined in the temperature range from 860–1075 K, for five Ag-Bi alloys (X _Ag=0.2, 0.35, 0.5, 0.65, 0.8), and a Redlich-Kister polynomial expansion was used to describe the thermodynamic properties of the liquid phase. Using Thermo-Calc software, the Ag-Bi phase diagram was calculated. Finally, thermodynamic data were used to predict surface tension behavior in the Ag-Bi binary system.     

Hydrogen absorption properties of Mg−Ni alloys prepared by bulk mechanical alloying

The thermodynamic properties of the hydrides of Mg_2−xNi (x=0–0.5) alloys produced by bulk mechanical alloying (BMA) were determined from pressure-composition (PC) isotherms for absorption over temperatures from 623 to 423 K. The vant Hoff plot for the plateau pressures of isotherms clearly indicated the existence of high and low temperature hydrides with different entropy and enthalpy for hydride formation. It was found that both the entropy and enthalpy values for the high temperature hydride were more negative than for the low temperature hydride. The phase transition temperature was 525 K for Mg_2.0Ni and decreased while increasing the value of x. This allotropic transformation was well confirmed by in-situ XRD observations from RT to 673 K under hydrogen atmosphere or in vacuum. This article based on a presentation made in the symposium “The 2nd KIM-JIM Joint Symposium: Hydrogen Absorbing Materials”, held at Hanyang University, Seoul, Korea, October 27–28, 2000 under the auspices of The Korean Institute of Metals and Materials and The Japan Institute of Metals.     

Thermodynamic assessments of the phase diagrams of the hafnium-vanadium and vanadium-zirconium systems

Thermodynamic assessments have been made for the hafnium-vanadium (Hf-V) and vanadium-zirconium (V-Zr) systems using the Calphad-Thermocalc approach. The Gibbs energies of the liquid, body-centered cubic, and close-packed hexagonal phases were described by a substitution solution model with a Redlich-Kister formalism to express the excess Gibbs energy. The C15-Laves phase was treated first as stoichiometric and then with a composition range. A consistent set of optimized thermodynamic parameters was obtained, and calculated phase equilibria were compared with the experimental data. The enthalpy of formation of the C15-Laves phase was calculated equal to approximately −3 and −5 kJ/mol, respectively, in the Hf-V and V-Zr systems, which is in good agreement with predicted values.     

Partial pressures for several In-Se compositions from optical absorbance of the vapor

The optical absorbance of the vapor phase over various In-Se compositions between 33.3–60.99 at.% Se and 673–1418 K was measured and used to obtain the partial pressures of Se₂(g) and In₂Se(g). The results are in agreement with silica Bourdon gauge measurements for compositions between 50–61 at.%, but significantly higher than those from Knudsen cell and simultaneous Knudsen-torsion cell measurements. It is found that 60.99 at.% Se lies outside the sesquiselenide homogeneity range and 59.98 at.% Se lies inside and is the congruently melting composition. The Gibbs energy of formation of the liquid from its pure liquid elements between 1000–1300 K is essentially independent of temperature and falls between −36 to −38 kJ per g atomic weight for 50 and 56% Se at 1200 and 1300 K.     

Activities and immiscibility in the system Cu-Rh

The thermodynamic activity of rhodium in solid Cu-Rh alloys is measured by the electromotive force method in the temperature range from 1050 to 1325 K with a solid-state cell:

Evaluation of enthalpy and entropy changes for binary alloy solidification process

Analytical expression of the entropy and enthalpy changes and apparent specific heat capacity of binary alloys in the solidification process are derived. The non-equilibrium lever rule is employed in the assessments of the relative concentration of binary alloys during solidification. The effect of the partial ordering of alloys in the liquid state is ignored and the alloy solidification process is divided into steps in the evaluations. Furthermore, experimental data from the available literature for Al−Cu alloys are employed to check the predictions of the current approaches, which indicates the reasonability of the current expressions.     

Thermodynamic Properties of YbRhO<Subscript>3</Subscript> and Phase Relations in the System Yb-Rh-O

Thermodynamic properties of the ternary oxide YbRhO₃ were determined by using a solid-state electrochemical cell incorporating calcia-stabilized zirconia as the solid electrolyte in the temperature range from 900 to 1300 K. The standard Gibbs energy of formation of YbRhO₃ from component binary oxides Yb₂O₃ with C-rare earth type structure and Rh₂O₃ with orthorhombic structure can be represented by the equation,

$$\Delta_{\text{f(ox)}} G^{\text{o}} ( \pm 130)/{\text{J/mol}} = - 43164 + 3.436\,({\text{T/K}}).$$

Standard enthalpy of formation of YbRhO₃ from elements in their normal standard states is ?1153.18(±3) kJ/mol and its standard entropy is 100.93(±0.6) J/K/mol at 298.15 K. The decomposition temperature of YbRhO₃ is 1671(±3) K in pure oxygen, 1566(±3) K in air and 1047(±3) K at an oxygen partial pressure of \(\left( {P_{{{\text{O}}_{2} }} /{\text{P}}^{\text{o}} } \right) = 10^{ - 6}\), where P^o = 0.1 MPa is the standard pressure. Decomposition temperature was confirmed by DTA/TGA. Phase diagrams for the system Yb-Rh-O are computed using the thermodynamic data.