Gibbs energies of formation of chromium carbides

The carbon potentials corresponding to the two-phase mixtures Cr + Cr₂₃C₆, Cr₂₃C₆ + Cr₇C₃, and Cr₇C₃ + Cr₃C₂ in the binary system Cr-C were measured in the temperature range 973 to 1173 K by using the methane-hydrogen gas equilibration technique. Special precautions were taken to prevent oxidation of the samples and to minimize thermal segregation in the gas phase. The standard Gibbs energies of formation of Cr₂₃C₆, Cr₇C₃, and Cr₃C₂ were derived from the measured carbon potentials. These values are compared with those reported in the literature. The Gibbs energies obtained in this study agree well with those obtained from solid-state cells incorporating CaF₂ and ThO2(Y₂O₃) as solid electrolytes and sealed capsule isopiestic measurements reported in the literature.     

Gibbs energies of formation of rare earth oxysulfides

The standard Gibbs energy change accompanying the conversion of rare earth oxides to oxysulfides by reaction of rare earth oxides with diatomic sulfur gas has been measured in the temperature range 870 to 1300 K using the solid state cell: Pt/Cu+Cu₂S/R₂O₂S+R₂O₃‖(CaO)ZrO₂‖Ni+NiO, Pt where R=La, Nd, Sm, Gd, Tb, and Dy. The partial pressure of diatomic sulfur over a mixture of rare earth oxide (R₂O₃) and oxysulfide (R₂O₂S) is fixed by the dissociation of Cu₂S to Cu in a closed system. The buffer mixture of Cu+Cu₂S is physically separated from the rare earth oxide and oxysulfide to avoid complications arising from interaction between them. The corresponding equilibrium oxygen partial pressure is measured with an oxide solid electrolyte cell. Gibbs energy change for the conversion of oxide to the corresponding oxysulfide increases monotonically with atomic number of the rare earth element. Second law enthalpy of formation also shows a similar trend. Based on this empirical trend Gibbs energies of formation of oxysulfides of Pr, Eu, Ho, and Er are estimated as a function of temperature.     

Estimation of the viscosities of binary metallic melts using Gibbs energies of mixing

In the present work, information on the integral molar Gibbs energies of mixing is employed to calculate the viscosities of binary substitutional metallic melts. A correlation has been established between the second derivative of the integral molar Gibbs energy of mixing with respect to composition and the corresponding function for the Gibbs energy of activation for viscosity. The viscosities predicted from available thermodynamic data in the case of a number of binary metallic systems using this correlation show satisfactory agreement with the values reported from experimental measurements. The value of this correlation in predicting the viscosities of complex metallic melts is also examined.     

关于标准生成吉布斯自由能的一种计算方法及绘图实例

根据目前国际上流行的数学和工程计算软件IVIATCAB能很好地帮助工程师和科学家解决实际工程和技术问题的特点，针对热力学标准生成吉布斯自由能对材料合成和加工过程中的物质的反应和相变分析具有密切关系的情况，介绍了一种用MATLB软件计算标准生成吉布斯自由能及绘图的简便方法，并通过实例进行了说明。     

Calculation of radioimmunoassay standard curves

A method for calculating radioimmunoassay standard curves, based on the theory of Ekins et al., is described. Because a four-parameter model is used, nonlinear standard curves are the result. The calibration curve is fitted to the measured standard points by means of a weighted least-squares method. The program based on this model can be easily processed on a desk-top calculator. For all 250 runs of six different assays, very good standard curves could be obtained. The mean deviation between the concentrations of the standard points and the corresponding calculated values was about 6%. In 26% of the cases it could be shown that the model we describe gave significantly better results than did two simpler ones.     

Calculation of the surface energies,energies of rupture,and theoretical strengths of cubic monocarbides

Conclusions An analysis is made of several thermodynamic methods of calculation of surface energy and of bond models for cubic monocarbides of transition metals. The specific surface energies of the carbides were calculated taking into account some characteristic features of atomic interactions in these compounds. In addition, the energies of rupture of the carbides are given, together with their estimated theoretical strengths. The variation of these properties with temperature is examined. Calculated results are compared with literature data.Translated from Poroshkovaya Metallurgiya, No. 1(157), pp. 70–74, January, 1976.     

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.     

TiC涂层反应标准吉布斯自由能变化的计算及其绘图

以化学气相沉积法制备TiC涂层的反应为实例,建立了TiC涂层反应的标准吉布斯自由能变化的计算模型,应用所开发的计算和绘图程序,精确地计算和绘制了TiC涂层反应的标准吉布斯自由能变化与温度关系图形.     

Use of solid-electrolyte Galvanic cells to determine the activity of CaO in the CaO-ZrO2 system and the standard Gibbs free energies of formation of CaZrO3 from CaO and ZrO2

The activity of CaO in the CaO-ZrO₂ system has been measured at 1572 to 1877 K with a Galvanic cell composed of 4CaO ? P₂O₅ as the solid electrolyte. The activity ZrO₂ was calculated from the activity of CaO by integrating the Gibbs-Duhem relation. From the activities of CaO and ZrO₂, the standard Gibbs free energy of formation of CaO ? ZrO₂ was determined as follows: ΔG _f ⁰ /J mol^?1 = -25,200 (±150) - 17.58 (±0.085)T (1633 to 1873 K)     

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     

Determination of standard gibbs energies of formation of Cr2N and CrN

The standard Gibbs energies of formation of Cr₂N and CrN have been measured by an equilibration technique and by using thermogravimetry and differential thermal analysis (TG-DTA) at temperatures ranging from 1232 to 1523 K. The results are expressed as follows:

Determination of standard gibbs energies of formation of MgO,SrO, and BaO

The standard Gibbs energy of formation of MgO was determined from the measurement of the ΔG° for the reaction ; by equilibrating Mg and Nb with a magnesia crucible and is expressed as follows: Mg(l)+ l/2O₂(g) = MgO(s) ΔG° = −657,000(±5000) + 141(±13)T [J/mol] (973 to 1323 K) The standard Gibbs energies of formation of SrO and BaO were determined by equilibrating silver and MO(M: Sr, and Ba) in a graphite crucible on the basis of the reactionM(in Ag) + CO (g) = MO (s) + C (s), yielding the following results:

Calculation of the interfacial energies between α and γ iron and equilibrium particle shape

The interfacial energies between α and γ iron were calculated for Kurdjumov-Sachs (K-S), Nishiyama-Wassermann (N-W), and one orientation relationship (OR), which may represent irrational OR, with varying interface orientation. The relaxation of atomic structure in the vicinity of the interface was performed by the Monte Carlo method using an embedded atom method (EAM) potential. Whereas the polar plot of calculated interfacial energies exhibited small and large cusps for the K-S and N-W ORs, an almost equiaxed energy surface with shallow cusps was obtained for the irrational ORs. The equilibrium shape of an α particle, N-W oriented with the γ matrix, was a thick rectangular plate with broad facets containing monatomic ledges. In contrast, the equilibrium shape of a particle, K-S oriented with the γ matrix, was elongated nearly in the closed-packed directions with {112}_y type and another broad facet that achieves relatively good matching. The volume of these shapes in the Wulff space tends to be smaller for K-S than that of the N-W OR. The equilibrium shape of the grain boundary α particle at the γ grain boundary was calculated under the assumption that the α particle has K-S OR with one of the two γ grains using the modified Wulff construction proposed earlier. The variation of the shape of the α particle with γ grain boundaries at an early stage of precipitation may primarily be ascribed to the change in the variant of the smallest nucleation activation energy and less prominently to the change in the γ grain boundary energy. This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occurred during the TMS Winter meeting, March 15–17, 2004, in Charlotte, NC, under the auspices of the TMS Alloy Phases Committee and the co-sponsorship of the TMS-ASM Phase Transformations Committee.     

Calculation of the interfacial energies between α and γ iron and equilibrium particle shape

The interfacial energies between α and γ iron were calculated for Kurdjumov-Sachs (K-S), Nishiyama-Wassermann (N-W), and one orientation relationship (OR), which may represent irrational OR, with varying interface orientation. The relaxation of atomic structure in the vicinity of the interface was performed by the Monte Carlo method using an embedded atom method (EAM) potential. Whereas the polar plot of calculated interfacial energies exhibited small and large cusps for the K-S and N-W ORs, an almost equiaxed energy surface with shallow cusps was obtained for the irrational ORs. The equilibrium shape of an α particle, N-W oriented with the γ matrix, was a thick rectangular plate with broad facets containing monatomic ledges. In contrast, the equilibrium shape of a particle, K-S oriented with the γ matrix, was elongated nearly in the closed-packed directions with {112}_γ type and another broad facet that achieves relatively good matching. The volume of these shapes in the Wulff space tends to be smaller for K-S than that of the N-W OR. The equilibrium shape of the grain boundary α particle at the γ grain boundary was calculated under the assumption that the α particle has K-S OR with one of the two γ grains using the modified Wulff construction proposed earlier. The variation of the shape of the α particle with γ grain boundaries at an early stage of precipitation may primarily be ascribed to the change in the variant of the smallest nucleation activation energy and less prominently to the change in the γ grain boundary energy. This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occurred during the TMS Winter meeting, March 15–17, 2004, in Charlotte, NC, under the auspices of the TMS Alloy Phases Committee and the co-sponsorship of the TMS-ASM Phase Transformations Committee.     

基于自由能最小原理的铜精矿物相组成计算研究

针对铜精矿物相组成分析耗时滞后和在线准确判断实现困难的问题,依据地球化学和成矿动力学理论,提出铜精矿历经漫长成矿过程后已基本达到或接近平衡态的假设,并将铜精矿视为若干化合物的混合体,基于成矿平衡态铜精矿体系吉布斯自由能最小原理,构建了铜精矿物相组成线性规划计算模型。几种典型铜精矿的实例验证表明,该模型能较为准确地计算铜精矿物相组成。     

Calculation of biochemical net reactions and pathways by using matrix operations

Pathways for net biochemical reactions can be calculated by using a computer program that solves systems of linear equations. The coefficients in the linear equations are the stoichiometric numbers in the biochemical equations for the system. The solution of the system of linear equations is a vector of the stoichiometric numbers of the reactions in the pathway for the net reaction; this is referred to as the pathway vector. The pathway vector gives the number of times the various reactions have to occur to produce the desired net reaction. Net reactions may involve unknown numbers of ATP, ADP, and Pi molecules. The numbers of ATP, ADP, and Pi in a desired net reaction can be calculated in a two-step process. In the first step, the pathway is calculated by solving the system of linear equations for an abbreviated stoichiometric number matrix without ATP, ADP, Pi, NADred, and NADox. In the second step, the stoichiometric numbers in the desired net reaction, which includes ATP, ADP, Pi, NADred, and NADox, are obtained by multiplying the full stoichiometric number matrix by the calculated pathway vector.