Computer generation of binary and ternary phase diagrams via a convex hull method

A rapid computational technique for determining equilibrium phase diagrams of multicomponent systems by constructing the convex hull of the free energy surface is introduced. Rather than calculating tangent lines or planes, this method guarantees a convex representation of the equilibrium free energy surface on a discrete set of points in composition space. Although the accuracy of these phase diagrams is limited by the spacing of points, there are no restrictions on the number or types of free energy functions that may be considered; functions with singular or unknown derivatives may even be used. This method is then applied to generate several model binary and ternary phase diagrams. This paper was presented at the International Phase Diagram Prediction Symposium sponsored by the ASM/MSD Thermodynamics and Phase Equilibria Committee at Materials Week, October21–23,1991, in Cincinnati, Ohio. The symposium was organized by John Morral, University of Connecticut, and Philip Nash, Illinois Institute of Technology.     

Thermodynamics of binary phase diagrams with a miscibility gap and a congruently melting compound and binary phase diagrams with two miscibility gaps

The thermodynamics of phase diagrams with a miscibility gap and a congruently melting compound and phase diagrams with two miscibility gaps are treated using the Hoch-Arpshofen solution model and the Schottky- Wagner disorder model. We extended the Schottky-Wagner disorder model to the liquid phase. In phase diagrams with two miscibility gaps, a liquid compound between the two miscibility gaps must be present to obtain consistent thermodynamic data. We treated the Rb-I₂, Au-Se, and Sn-S binary systems.     

Thermodynamics of binary phase diagrams with a miscibility gap and a congruently melting compound and binary phase diagrams with two miscibility gaps

The thermodynamics of phase diagrams with a miscibility gap and a congruently melting compound and phase diagrams with two miscibility gaps are treated using the Hoch-Arpshofen solution model and the Schottky- Wagner disorder model. We extended the Schottky-Wagner disorder model to the liquid phase. In phase diagrams with two miscibility gaps, a liquid compound between the two miscibility gaps must be present to obtain consistent thermodynamic data. We treated the Rb-I₂, Au-Se, and Sn-S binary systems.     

Calculation of the binary chromiun-lanthanide phase diagrams

The Miedema model is used to calculate the interaction parameter Ω for binary chromium-lanthanide metal systems in the liquid state. The values of Ω found for the 15 systems range from +21.6 kJ/mol for Cr-Lu to +174.6 kJ/mol for Cr-Eu. The phase diagrams of the 15 systems are calculated using these values and assuming complete immiscibility for the solid state and regular solution behavior for the liquid state. Because of the positive values of Ω, most phase diagrams exhibit a liquid miscibility gap; only the Cr-Er, Cr-Tm, and Cr-Lu systems do not contain a miscibility gap. A comparison is made between the calculated and the experimentally determined Cr-Ce phase diagram.     

Computer representation of phase diagrams

The computer representation of phase diagrams is discussed from the point of view of user needs together with the form an ideal system might take for maximum utility. Current work in the field of computer representation of phase diagrams is reviewed and placed in the context of developing a more useful computerized alloy design system. Some new work on computerized interpolation of phase diagram data is also presented.     

Comment on thermodynamics of binary phase diagrams with a miscibility gap and a

The Gibbs energy of mixing and the excess Gibbs energy of mixing in the binary systems treated in an earlier study are calculated. In these types of systems, these functions cannot be described by an equation extending between the two end components and also represent the partial quantities correctly.     

Comment on thermodynamics of binary phase diagrams with a miscibility gap and a

The Gibbs energy of mixing and the excess Gibbs energy of mixing in the binary systems treated in an earlier study are calculated. In these types of systems, these functions cannot be described by an equation extending between the two end components and also represent the partial quantities correctly.     

Modeling of binary molten-salt phase diagrams via neural networks

Computational neural networks are used as implicit thermodynamic models for calculating phase diagrams of binary molten salts. The neural network model accurately describes conformai ionic solution theory in binary systems thereby providing an efficient scheme for determining phase diagrams. Preliminary results are presented formodel AC ₂-BC₂ systems.     

Modeling of binary molten-salt phase diagrams via neural networks

Computational neural networks are used as implicit thermodynamic models for calculating phase diagrams of binary molten salts. The neural network model accurately describes conformai ionic solution theory in binary systems thereby providing an efficient scheme for determining phase diagrams. Preliminary results are presented formodel AC ₂-BC₂ systems.     

Thermodynamic analysis of some binary phase diagrams involving liquid crystals

A computer-coupled thennodynamic/phase diagram analysis was performed on the phase diagram data of seven binary systems involving liquid crystals. These include five systems based on a homologous series of compounds and two others having 1:1 intermediate compounds. The excess Gibbs energies of the solution phases were thereby calculated, and evaluated phase diagrams were generated that are thermodynamically self-consistent. The results are discussed in the light of what is known about excess solution properties in such systems. The usefulness of the thermodynamic analysis is examined with respect to the prediction of the eutectics of ternary and higher order liquid crystal mixtures. The “Equal G Analysis” is also briefly discussed with reference to the estimation of the nonidealities of mesophase solutions.     

Thermodynamic analysis of some binary phase diagrams involving liquid crystals

A computer-coupled thennodynamic/phase diagram analysis was performed on the phase diagram data of seven binary systems involving liquid crystals. These include five systems based on a homologous series of compounds and two others having 1:1 intermediate compounds. The excess Gibbs energies of the solution phases were thereby calculated, and evaluated phase diagrams were generated that are thermodynamically self-consistent. The results are discussed in the light of what is known about excess solution properties in such systems. The usefulness of the thermodynamic analysis is examined with respect to the prediction of the eutectics of ternary and higher order liquid crystal mixtures. The “Equal G Analysis” is also briefly discussed with reference to the estimation of the nonidealities of mesophase solutions.     

Calculations of phase diagrams in associated solution model

The development of an ideal associated solution model concerned with complexes of various compositions, sizes, and shapes is described. Such models were used earlier to calculate thermodynamic characteristics and the position of the liquidus line for binary eutectic systems as well as those having a stable compound in the solid phase. In all the cases, the model parameters were not adjusted but were estimated from melting temperatures of the components. The latest studies deal with the influence of arbitrary stoichiometry associates on the equilibrium thermodynamic properties of liquid alloys. The application of the model to eutectic systems and systems having an unlimited miscibility in solid and liquid states close to the liquidus has been considered. It was shown that if the difference in melting temperatures of the components was small, different types of fusibility diagrams were possible: eutectic diagrams, cigar-shaped diagrams, or diagrams with upper or lower azeotropic points. Peritectic transformations could take place if the difference in melting temperatures of the components were large.     

Au-Ag-Al系相图的热力学优化和计算

使用计算相图方法(CALPHAD)计算Au-Ag-Al的三元相图时,三个边际二元相图(Au-Al,Au-Ag,Ag-Al)的准确性对三元相图的计算有很大的影响,目前Au-Al边际二元相图存在着一定的矛盾。在综合评估Au-Al体系实验数据的基础上,优化和计算了Au-Al合金体系的平衡相图,使用置换式溶体溶液模型描述Au-Al体系中液相、Bcc和Fcc相的吉布斯自由能,分别用亚点阵模型(Al)(Au)4、(Al)3(Au)8、(Al)(Au)2、(Al)(Au)和(Al,Au)2(Al,Au)描述AlAu4、Al3Au8、AlAu2、AlAu和Al2Au相,通过Pandat软件优化得到一组各相的热力学参数,计算得到的Au-Al相图与实验数据和热力学数据相吻合。结合Au-Ag和Ag-Al的热力学参数,计算了Au-Ag-Al液相面投影图和等温截面图,液相面投影图显示该三元系存在8个四相平衡反应,对Au-Ag-Al合金的研究具有指导意义。     

Thermodynamic database of the phase diagrams in the Mg-Al-Zn-Y-Ce system

The Mg-Al-Zn-Y-Ce system is one of the key systems for designing high-strength Mg alloys. The purpose of the present article is to develop a thermodynamic database for the Mg-Al-Zn-Y-Ce multicomponent system to design Mg alloys using the calculation of phase diagrams （CALPHAD） method, where the Gibbs energies of solution phases such as liquid, fcc, bcc, and hcp phases were described by the subregular solution model, whereas those of all the compounds were described by the sublattice model. The thermodynamic parameters describing Gibbs energies of the different phases in this database were evaluated by fitting the experimental data for phase equilibria and thermodynamic properties. On the basis of this database, a lot of information concerning stable and metastable phase equilibria of isothermal and vertical sections, molar fractions of constituent phases, the liquidus projection, etc., can be predicted. This database is expected to play an important role in the design of Mg alloys.     

Partial phase diagram of the Ti-Al binary system

The equilibrium temperature-composition coordinates of the β/(β + α), (β + α)/α,α/(α + γ), and (α γ @#@)/γ phase boundaries were determined for the binary Ti-Al phase diagram through the temperature range 1150 to 1400 °C by means of diffusion couples with subsequent EPMA examination. This was supplemented with microstructural examination of a two-phase alloy. No peritectoidal decomposition reaction of the type α→ β + γ reported by Murray [88Mur] at 1280 °C was found. Results indicate that the a phase persists to temperatures well above 1400 °C. The phase boundaries from the present work are in agreement with the Mc Cullough [88Mcc] binary phase diagram.