An interactive computer program for calculating ternary phase diagrams

A computer program is described which calculates ternary phase diagrams from the thermodynamic properties of the phases. Sample calculations are given for the molten salt system KClCaCl₂NaCI, the alloy system 7nSnBi, the super-alloy system CrNlFe, and the organic system acetone-chloroform-methyl isobutyl ketone. A computational strategy known as the base phase method is used. This results in a simplification of the algorithms and a large Increase in efficiency. The program, which is highly Interactive with very flexible input and graphical output, is available on-line to North American and European users.     

GEMINI — DiagPlot: 2D & 3D ternary phase diagrams

GEMINI is the Gibbs Energy Minimizer of ThermoSuite, a package of chemoinformatics devoted to thermodynamics. In the last years a special effort was made to develop specific procedures to plot 2D & 3D ternary phase diagrams. The Diphasic Domain Approach Method allows us to plot 2D isobarothermic sections in ternary systems with efficiency and robustness. The technique of regular meshing applied to the extremities of the conodes of a set of such isobarothermic ternary sections allows us to go for a trip in the third dimension, giving a deeper understanding of ternary phase diagrams by adding a visual 3D approach.     

Dualization of boolean functions using ternary decision diagrams

Dualization of Boolean functions is a fundamental problem that appears in various fields such as artificial intelligence, logic, data mining, etc. For monotone Boolean functions, many empirical researches that focus on practical efficiency have recently been done. We extend our previous work for monotone dualization and present a novel method for dualization that allows us to handle any Boolean function, including non-monotone Boolean functions. We furthermore present a variant of this method in cooperation with all solutions solver. By experiments we evaluate efficiency and characteristics of our methods.     

Origin和MATLAB软件对MgCl_2-H_2O-C_4H_8O_2三元体系相图的可视化应用

以MgCl_2-H_2O-C_4H_8O_2三元体系在不同温度下的溶解度相图为对象,采用Origin 9.1和MATLAB软件对该三元体系进行了相图可视化研究。Origin 9.1和MATLAB均可实现对该体系的三元立体渐变曲面相图和三元投影相图的绘制。其中,Origin 9.1版内嵌了绘制三元立体渐变曲面相图和三元投影相图的模块,简单的人机交互界面方便了科学工作者对三元相图的可视化呈现。采用MATLAB编程,在前人工作的基础上,实现了三元相图三角坐标的呈现。同时,Origin 9.1和MATLAB也可对三元相图数据进行差值和拟合。拟合结果可用于绘制光滑的曲面,并得出某一特定组成下的溶解温度。     

Calculation of phase diagrams of the iron-copper and cobalt-copper systems

Synthesis of phase diagrams has been made on Fe-Cu and Co-Cu systems using thermodynamic parameters obtained by analysis of data on phase boundaries and thermodynamic properties. An anomaly in solubility of copper due to the magnetic transition was confirmed to occur in αFe as well as γCo. It was also detected that the solidus curves in both the systems exhibit remarkable retrograde solubility.     

Calculation of the Ti-C,W-C and Ti-W-C phase diagrams

The two binary W-C and Ti-C systems were analysed in thermodynamic terms by using a thermodynamic model which allows for the use of sublattices. Those carbides, which show some variation in their Me/C-ratios, such as the TiC-carbide were treated as solution phases using this model. As a result of this analysis the two binary W-C and Ti-C phase diagrams could be calculated. By combining these results with the analysis of the Ti-W system presented by Murray (1) a number of isothermal sections of the ternary Ti-W-C system were calculated. These are in close agreement with the experimental data according to Rudy et al (2).     

Calculated phase diagrams of Cu-W, Ag-W and Au-W binary systems

Phase diagrams for Cu-W, Au-W systems have been calculated based on available thermodynamic data. It was assumed that there is no mutual solid solubility in all the cases. Liquid phase equilibria were calculated on the basis of sub-regular solution model using Miedema's interaction parameters. Vapour phase boundaries have also been determined.     

Thermodynamically calculated phase diagrams for the Co-Cr-Ta and Co-Cr-Nb systems

Phase diagrams for the Co-Cr-Ta and Co-Cr-Nb systems have been calculated from thermodynamic data for the binary systems involved. Eleven isothermal sections for temperatures between 2200 and 1500 K are given. The calculations are in good agreement with the limited available experimental phase diagram data for these systems.     

Thermodynamic assessments of binary phase diagrams in organic and polymeric systems

The Sanchez–Lacombe (SL) model and the Flory–Huggins model were used for the calculation of binary phase diagrams in organic and polymer systems, respectively. The thermodynamic parameters of the liquid and gas phases in acetone–carbon disulfide (CS₂), butane–heptane, cyclohexane–aniline systems, and liquid phases in polystyrene–polybutadiene and polystyrene–bisphenol A poly-carbonate systems were optimized, based on the experimental data. The calculated results with various pressures are in good agreement with the experimental data. It is hoped that this method will be widely applied in the prediction of binary phase diagrams in organic and polymer systems.     

A new field of phase diagrams of stationary nonequilibrium states

Diamond is a metastable phase, while graphite is the stable phase in low pressure equilibrium phase diagrams of carbon. There seemed to be no way to get diamond from graphite under low pressures. However, a new activated low pressure diamond deposition process has emerged. A new concept of phase diagrams of stationary nonequilibrium states on the basis of nonequilibrium thermodynamics can be used for explanation of the “thermodynamic paradox” that the diamond growth with graphite etching takes place under activated low pressure. The agreement between CALPHAD prediction and experiments is excellent.     

Ortho-equilibrium and para-equilibrium phase diagrams for interstitial / substitutional iron alloys

A mathematical model for the evaluation of compositionally constrained thermodynamic equilibrium has recently been implemented into the computer program MatCalc. This model is applied to the calculation of para-equilibrium phase diagrams for some ternary model iron alloy systems Fe---X---C, with X = Mn, Ni, Cr and Mo. The results are compared to the corresponding full equilibrium (ortho-equilibrium) phase diagrams and the impact of each element on the austenite / ferrite / carbide transformation in steels is analyzed. The para-equilibrium phase diagrams are considerably more simple than the potentially complex ortho-equilibrium phase diagrams, showing cementite formation as the only stable carbide under para-equilibrium conditions. The driving forces for precipitation of cementite and the complex chromium carbides in the Fe---Cr---C system are evaluated as a function of the precipitate composition. The evaluation of the driving forces under para-equilibrium conditions predicts carbide precipitation behavior that agrees with experimental findings.     

Coupled phase diagrams and thermochemical data for transition metal binary systems-IV

A data base covering the transition metals has been developed which permits coupling of thermochemical and phase diagram data and can readily be employed to compute ternary and higher order systems. The current paper, which is part of a series, details the following ten binary systems: aluminum-carbon, titanium-carbon, manganese-carbon, chromium-carbon, iron-carbon, cobalt-carbon, nickel-carbon, niobiumcarbon, molybdenum-carbon and tungsten-carbon. This brings the total of such systems covered to forty seven. This paper together with past and projected contributions will cover other binary members in order to permit calculation of a sufficiently wide range of ternary systems.     

图形语义理解的三维重建技术在相图中的应用

分析了目前进行金属相图的三维重建时面临的困难和存在的问题,介绍了基于图形语义理解的三维重建技术在相图领域中的应用方法,指出方法的可行性和必要性。最后,指明了目前研究的不足之处,以及下一步研究的方向和重点。     

PT-system, TX-system, PX-system: Three programs which calculate pressure-temperature-composition phase diagrams

PT-SYSTEM, TX-SYSTEM, and PX-SYSTEM are three FORTRAN 77 programs that calculate complete pressure-temperature (P-T), temperature-composition (T-X_H2O-CO2), and pressure-composition (P-X_H2O-CO2) diagrams. The output of these programs can be plotted for visual representation of phase relations, or inspected from tables. The programs initially generate all possible reactions in the user-specified compositional and PTX space. At the user's option, each point of every reaction is tested for stability with respect to all other phases in the system, and metastable extensions are erased. If a curve is metastable completely, the list of remaining reactions is pruned of those which are metastable entirely within the specified PTX limits of the diagram. Finally, all curves are labeled with stable assemblages.The software is distributed with a recommended thermodynamic database, but a variety of equations of state are provided so that the programs can be used with different data sets. Functions are provided for temperature-dependent disordering, polymorphic transitions, and solid solutions. Run-time options include setting the P, T, X limits of the diagram, the selection of different routines for calculating gas properties, and the specification of fixed phase activities. The user also can specify that only curves stable in the presence of a given phase or assemblage be computed, so that the stability fields of particular phases or assemblages can be identified readily.Copies of the programs (written in ANSI standard FORTRAN 77), the database, and accompanying documentation are available from the senior author.     

三元相图绘制编程与应用

为了能快速、精确地绘制出满意的三元体系的平衡相图,作者应用Inprise公司的快速开发工具Delphi 5设计实现了解决该问题的计算机绘图程序。程序具有较高的自动化程度,在相图区具有动态组成提示功能,对两相曲线可选用多项式拟合或样条函数平滑拟合,并可进行分段处理,能自动确定结线之间的最佳交点,从而确定有无新的化合物生成。应用本程序绘制了几种不同类型三元体系的平衡相图。实例运行结果表明,该程序使用方便、灵活、作图快速,图形效果满意。     

Effects of interaction parameters and melting points of pure metals on the phase diagrams of the binary alloy nanoparticle systems: A classical approach based on the regular solution model

The effects of thermodynamic properties on the phase stability of an imaginary A–B binary alloy nanoparticle system were examined using a regular solution model based on the CALPHAD method. When the two components of an alloy had the same melting points, both the liquidus and solidus temperatures decreased across the whole composition range, regardless of the sign of the interaction parameter. When the two substances had different melting points and , similar behavior was observed. However, when , the solidus and solvus lines, and the eutectic composition move to the pure substance side that has the lower melting point.     

Use of chemical potential of a compound in potential phase diagrams

Potential phase diagrams, where the chemical potential of a compound is used as an axis, do not obey the usual rules for potential phase diagrams. Examples are presented in order to help the interpretation of such diagrams. The thermodynamic background of the special properties is examined.