Activities and ternary phase diagrams

A set of theoretical formulae for calculating activities along the liquid surface in ternary phase diagrams has been presented. These formulae are rigorous since no assumption is made in the derivation. The expressions are generalized and can be simplified to the forms presented by Pelton, Chou, Elliott and Gokcen under certain conditions. In practice, the activity of the components are desired at a fixed temperature instead of a variable temperature like that along a liquid surface. Under this situation, with reasonable assumptions the equations can be further simplified such that they do not contain any partial thermodynamic properties. Activities can then be readily calculated from phase diagrams. The method presented in this paper is for a ternary system and can be extended to multicomponent systems.     

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.     

Computerized prediction of phase diagrams of the eutectic binary systems of nontransition-nontransition metals

The relationship between the interaction parameters of liquid alloys and the atomic parameters of constituent elements has been investigated by artificial neural network method. The relationship found can be used for the computerized prediction of phase diagrams of the eutectic binary systems between non-transition elements.     

Computerized prediction of interaction parameters and phase diagrams of the immiscible binary systems of nontransition-nontransition metals

The relationship between the interaction parameters of liquid alloys and the atomic parameters of constituent elements has been investigated by artificial neural network method. The relationship found can be used for the computerized prediction of phase diagrams of liquid-liquid immiscible binary systems between non-transition elements.     

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 using partial phase diagram data

The interaction parameters for various phases were calculated using binary phase diagram data. Since two equilibrium compositions of a binary tie line have some errors in their measurements, a particular attention was paid to the effect of a small variation of the equilibrium compositions on the fluctuation in the calculated free energy curves. From this investigation, it was recommended that the widest possible tie line or tie lines located in the central region of a phase diagram be used to calculate the interaction parameters. Based on these facts, the interaction parameters for various phases in the Ti-W, Pd-W, Zr-W and Hf-W systems were estimated, which were subsequently used to calculate the phase diagrams of the above systems.     

Estimation of stability lobe diagrams in milling with continuous learning algorithms

The productivity of milling processes is limited by the occurrence of chatter vibrations. The correlation of the maximum stable cutting depth and the spindle speed can be shown in a stability lobe diagram (SLD). The stability is different for different width of cut and can change with the axis positions. Today it is already a great effort to estimate the SLD only for one position. Many experiments are necessary to measure the SLD or derive a detailed mathematical model to calculate the SLD. Moreover not only the cutting depth, but also the cutting width should be represented in the SLD. This paper presents a new approach to assess the process stability based on measured acceleration signals. The multidimensional stability lobe diagram (MSLD) are derived during the production using two new continuously learning algorithms. In this paper the application of a continuous learning support vector machine and a continuous neural network is shown. The support vector machine and the neural network are extended to make them capable for continuous learning and time-variant systems. A new trust criterion is introduced, which gives information about the prediction quality of the output for the selected input region. The learned MSLDs are evaluated against analytically calculated MSLDs and the learning algorithms can reproduce the analytical results very well.     

Algorithms useful for calculating multi-component equilibria,phase diagrams and other kinds of diagrams

Phase diagrams are important in materials science. They consist of lines separating regions with different sets of stable phases and different kind of axes can be used. Many available phase diagrams are drawn directly from experimental information. However, they are closely related to the thermodynamic properties of the phases and can be calculated from thermodynamic models of the phases using the Calphad technique. This paper presents a set of algorithms to calculate equilibria and several kinds of diagrams using a very flexible set of conditions and axes. The algorithms can be applied to multi-component systems using model parameters in thermodynamic databases.     

Models for the determination of kinetic phase diagrams and kinetic phase separation domains

Several theoretical models for the determination of kinetic phase diagrams for solid solution growth from the liquid phase are presented and compared to each other. These models include a Monte Carlo simulation model, used as a reference model, a previously defined analytical model, based on linear non-equilibrium thermodynamics, and a new model, rooted in the kinetics at kink sites.All models have in common that the composition of the growing solid phase tends to the liquid phase composition for increasing undercooling, enhancing mixing even for systems with a strong tendency to phase separation. However, depending on the system parameters considerable quantitative differences can occur between the results from the model based on non-equilibrium thermodynamics and the MC model. Instead, the new model follows very well the trends of the MC simulations, both for well-mixing systems and for phase separating systems.For phase separating systems the analytical models predict kinetic phase separation domains, zones in the kinetic phase diagram yielding steady state growth of more than one solid phase with different compositions. According to MC simulations such domains in phase space correspond to domain formation in real space. Also in this case the new model is consistent with the MC results.     

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).     

Calculation of the Fe-C-Ti ternary phase diagram

A thermodynamic analysis of phase equilibria in the Fe-Ti, Ti-C, and Fe-C-Ti systems has been carried out. The Gibbs energy has been expressed by the two-sublattice model being separated into the paramagnetic and ferromagnetic terms. In particular, the equilibrium between austenite and NaCl type Ti-carbide has been treated as a portion of the miscibility gap in the fcc phase. The thermodynamic parameters for each phase were evaluated on the basis of experimental phase equilibrium and activity data. The calculated phase boundary of austenite in equilibrium with Ti-carbide exhibited a characteristic shape, not only in the isothermal but also in the vertical section.     

Relationship between activity and three phase boundary in the ternary phase diagram

Theoretical formulae have been derived for determining the activity along a three-phase boundary in a three component system. The activities can be calculated from ternary phase diagrams from the partial thermodynamic properties and the use of a single integration constant. The latter is calculated from the binary phase diagrams. The formulae are rigorous and no assumption is made.     

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.     

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.