The thermochemistry of transition metal carbides

A general survey is made of the available data for the standard Gibbs energies of formation of solid carbides of transition metals. The results are plotted as standard Gibbs energy vs. temperature diagrams. The equations and the estimated accuracy when available are given for each substance.     

Thermodynamic evaluation of the Cu-R (R: Ce, Pr, Nd, Sm) binary systems

The phase diagrams and thermodynamic properties of the Cu-R (R: Ce, Pr, Nd, Sm) systems are reevaluated on the basis of all available experimental data, including the enthalpies of mixing reported recently. The Redlich-Kister polynomial with two or three terms is used to describe the excess Gibbs energies of liquid phases in the Cu-R systems. All intermediate phases are treated as stoichiometric, and their Gibbs energies of formation are optimized. Based on the optimized thermodynamic parameters, phase diagrams and thermodynamic properties of the Cu-R systems are calculated and compared with the experimental results. The optimized parameters seem to be in good agreement with the experimental data and might represent the regularity and systematic variation of these systems.     

High Temperature Thermodynamic Data for CdTe(c)

The high temperature heat capacity, Gibbs energy of formation, and standard enthalpy and entropy of formation at 298 K are combined with thermodynamic data for Cd and revised data for Te to provide an internally consistent data set for CdTe(c). Equations are given for the Gibbs energy of formation from Cd(g) and Te₂(g) and from the solid or liquid elements as a function of temperature. These give values similar to those used before. However, the derived enthalpy and entropy of formation are significantly different due to a revised heat capacity for CdTe(c). The standard enthalpy and entropy of formation at 298.15 K from the gases are −293262 J/mol and −200.593 J/mol K, respectively. From the solid elements they are −100270 and −4.5334.     

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 assessment of the Aluminum-Manganese (Al-Mn) binary phase diagram

A thermodynamic calculation of the Al-Mn binary system that takes into account recent experimental results and includes five intermetallic compounds and all the solid-solution phases is presented. The Gibbs energy of the body-centered cubic (bcc) phase has been described on the basis of the two-sublattice model that includes the second-order A2/B2 ordering reaction as well. A consistent set of optimized thermodynamic parameters has been arrived at for describing the Gibbs energy of each phase in this system leading to a better fit between calculation and experiments.     

Thermodynamic assessment of the Aluminum-Manganese (Al-Mn) binary phase diagram

A thermodynamic calculation of the Al-Mn binary system that takes into account recent experimental results and includes five intermetallic compounds and all the solid-solution phases is presented. The Gibbs energy of the body-centered cubic (bcc) phase has been described on the basis of the two-sublattice model that includes the second-order A2/B2 ordering reaction as well. A consistent set of optimized thermodynamic parameters has been arrived at for describing the Gibbs energy of each phase in this system leading to a better fit between calculation and experiments.     

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.     

Nanostructural states in solids

On the basis of the joint approaches of nonequilibrium thermodynamics and physical mesomechanics, there is proposed a thermodynamic criterion of existence of a special class of pretransition two-phase nanostructural states in solids near the zero of their thermodynamic Gibbs potential. Such states determine the high structural instability of nanostructures in the external fields and are the basis of different nanotechnologies based on a “bottom-up” assemblying approach. It is suggested to call the materials characterized by nanostructural states as nanostructured. The shear-resistant materials with a grain size d < 100 nm, but being far from the zero of their thermodynamic Gibbs potential, may conveniently be classified as nanosized.     

Thermodynamic vacancy model of the surface energetic state of solids

Based on the broken-bond concept of metal surface formation, a thermodynamic vacancy model of the surface metal layer (TVM), in which the Gibbs surface energy (ΔG _s ) of a metal is defined as the excess adsorption energy of vacancies (N _V(s)) in the surface layer of the metal ΔG _s = −RTlnN _V(s), is developed. The relation is derived from the Gibbs adsorption equation for a metal, which is treated as a binary system that involves atoms and vacancies. TVM enables one to estimate the concentration of vacancies and adatoms on low-index faces of cubic-lattice metals from the literature surface energies evaluated with the use of the surface physics methods. Examples of the application of TVM in the physical chemistry of surfaces and corrosion of metals are given.     

Computation of metastable phases in tungsten-carbon system

Metastable phase equilibria in the W-C system are presented in the vicinity of the metastable reactions involving W₂C, WC_1−x , and WC. Metastable phase boundaries were obtained by reproducing the stable boundaries using optimized Gibbs energy formulations and extrapolating them into regions of metastability. Four metastable reactions were obtained: a metastable congruent melting reaction of WC at 3106 K, a metastable eutectic reaction between WC_1−x and graphite at 2995 K, a metastable eutectic reaction between W₂C and WC at 2976 K, and a metastable eutectic reaction between W₂C and graphite at 2925 K. The reaction enthalpies and entropies associated with these transitions are also computed using the available Gibbs energy data. Furthermore, possible kinetic paths that could lead to metastability are discussed.     

Computation of metastable phases in tungsten-carbon system

Metastable phase equilibria in the W-C system are presented in the vicinity of the metastable reactions involving W₂C, WC_1−x , and WC. Metastable phase boundaries were obtained by reproducing the stable boundaries using optimized Gibbs energy formulations and extrapolating them into regions of metastability. Four metastable reactions were obtained: a metastable congruent melting reaction of WC at 3106 K, a metastable eutectic reaction between WC_1−x and graphite at 2995 K, a metastable eutectic reaction between W₂C and WC at 2976 K, and a metastable eutectic reaction between W₂C and graphite at 2925 K. The reaction enthalpies and entropies associated with these transitions are also computed using the available Gibbs energy data. Furthermore, possible kinetic paths that could lead to metastability are discussed.     

Thermodynamic Study of Liquid Mg-In-Sn Alloys

Liquid Mg-In-Sn alloys were studied by the emf method using concentration cells with liquid electrolyte. Experiments were performed for 30 alloys along three sections on the Gibbs triangle with constantt = 0.25, 0.50, 0.75 [t = X_Sn/(X_Sn + X_In)] and for magnesium concentration from 0.1 to 0.65 at temperatures from 950 to 1100 K. From the change of the slope of the emf versusT, points on the liquidus surface for sixteen alloys were detected. Calculated partial excess Gibbs energies δG_exMg and partial enthalpies δH_Mg were compared with the results of previous work.     

MgO-B2O3二元系熔渣质量作用浓度计算模型

依据化学中广泛应用的同系线性规律,拟合钙、镁复合化合物标准反应吉布斯自由能之间的线性关系式,然后由3CaO·B2O3和2CaO·B2O3的标准反应吉布斯自由能求得3MgO·B2O3和2MgO·B2O3的标准反应吉布斯自由能,进而基于炉渣结构的共存理论和相图,推导MgO-B2O3二元渣系的热力学计算模型.结果表明:1 460℃时,在浓度为0.45＜x(MgO)＜0.80的范围内,理论计算的MgO-B2O3渣系的作用浓度N(B2O3)的变化规律与实测活度α(B2O3)是相同的,且拟合较好.     

Ca—Tb4O7—Fe体系的热力学研究

计算了Ca还原Tb4O7生成纯金Tb(7Ca Tb4O7=4Tb 7CaO),Tb与Fe反应生成TbFe2(Tb 2Fe=TbFe2)的标准Gibbs自由能变化和Gibbs自由能变化。以及反应达平衡时的Ca分压和体系中Ca的实际蒸气压,通过理论计算及实验证明还原扩散法制取Tb-Fe二元系合金时生成物一定是TbFe2。     

Tie lines and activities in the system NiO-MgO-SiO2 at 1373 K

The isothermal section of the phase diagram for the system NiO-MgO-SiO₂ at 1373 is established. The tie lines between (Ni_xMg_1-x )O solid solution with rock salt structure and orthosilicate solid solution (Ni_yMg_1-y)Si_0.5O₂ and between orthosilicate and metasilicate (Ni_zMg_1-z)SiO₃ crystalline solutions are determined using electron probe microanalysis (EPMA) and lattice parameter measurement on equilibrated samples. Although the monoxides and orthosilicates of Ni and Mg form a continuous range of solid solutions, the metasilicate phase exists only for 0 < Z < 0.096. The activity of NiO in the rock salt solid solution is determined as a function of composition and temperature in the range of 1023 to 1377 using a solid state galvanic cell. The Gibbs energy of mixing of the monoxide solid solution can be expressed by a pseudo-subregular solution model: ΔG^ex = X(l - X)[(-2430 + 0.925T)X + (-5390 + 1.758T)(1 - X)] J/mol. The thermodynamic data for the rock salt phase are combined with information on interphase partitioning of Ni and Mg to generate the mixing properties for the orthosilicate and the metasilicate solid solutions. The regular solution model describes the orthosilicate and the metasilicate solid solutions at 1373 K within experimental uncertainties. The regular solution parameter ΔG^ex/Y(1-Y) is -820 (±70) J/mol for the orthosilicate solid solution. The corresponding value for the metasilicate solid solution is -220 (±150) J/mol. The derived activities for the orthosilicate solid solution are discussed in relation to the intracrystalline ion exchange equilibrium between Ml and M2 sites. The tie line information, in conjunction with the activity data for orthosilicate and metasilicate solid solutions, is used to calculate the Gibbs energy changes for the intercrystalline ion exchange reactions. Combining this with the known data for NiSi_0.5O₂, Gibbs energies of formation of MgSi_0.5O₂, MgSiO₃, and metastable NiSiO₃ are calculated. The Gibbs energy of formation of NiSiO₃, from its component oxides, is equal to 7.67 (±0.6)kJ/mol at 1373K.     

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.     

Calculation of ordered equilibria for the Cadmium-Magnesium system

With excess Gibbs energies of Cd and Mg for disordered solutions, together withC _p values for the ordered α″ phase and some data for the phase boundaries, equations were developed for the Gibbs energies of ordered α′, α″, and α? phases. The equilibria that are compatible with these Gibbs energy functions are in reasonable accord with available experimental data. In addition, the values that are predicted for vapor pressure or emf measurements should be in a tractable range for experimental verification.     

Zinc Electroplating in the Presence of Mixtures of o-Oxyazomethine Derivatives

Variations in the potential and current of zinc electroplating as functions of the nature of substituents in the molecules of mixture of o-oxyazomethine derivatives are described based on the linear of Gibbs energy relation. Polar effect of substituents is estimated from partial polar constants by taking into account the mole fraction of each component of the mixture.