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Thermodynamics of Cu-Sn-X (X=Bi, Nb, Sb, Zn) liquid alloys

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A fundamental goal in materials science is to be able to control the final physical or chemical properties of a material. In order to do that one must understand the relations between raw materials, their chemical composition, processing conditions, microstructure and properties of the final material. During processing, and often in use, most materials undergo reactions and phase transformations. This is particularly obvious in melt processing where materials are completely or partially melted and then solidified. Phase diagrams are the fundamental aid for understanding interrelations between chemical composition, processing conditions and microstructure. Since a phase diagram is a representation of the thermodynamic properties of a system it is possible to calculate it, unless the thermodynamic properties are known. By combining the knowledge on the phase diagram and the thermodynamic properties a model description of the system suitable for phase diagram calculations can be created. Descriptions of low order systems can be combined to make extrapolations to higher order systems. For this purpose the Gibbs energy of each phase is described by a suitable model containing a relatively small number of variable coefficients. The thermodynamic properties of a binary system can be calculated using the Gibbs free energy expression comprising contributions of both elements in each phase existing in the system. Further parameters are introduced to describe the mutual interaction between elements in each phase. Difficulty in extension of the calculated results to higher order systems is much less than in the case of experimental work, since the essence of the calculation does not change so much between a binary system and a higher order one [1]. Sometimes, due to the lack of experimental data for ternary systems, parameters for ternary systems are calculated on the basis of values for binary ones and different simplifications and models[...]

Numerical approach to predicting thermodynamic properties of ternary alloys

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Phase diagrams are determined from experimental methods such as: thermal analysis, microstructure examination, pressure measurements and others. However, the experimental determination of phase diagrams is a time-consuming and costly task since the number of possible subsystems increase drastically as the number of elements increases. Experimental information for the entire phase diagram is available for most of the binary systems, but experimental information becomes increasingly sparse as the number of constituent elements increases (for ternary, quaternary and higher-component systems) [1]. There are many methods of modelling thermodynamic properties and calculations of phase diagrams in complex systems on the basis of thermodynamic properties and phase diagrams of binary alloys constituting the complex alloy. One of them is a semi- -empirical approach, referred as the CALPHAD method [2, 3]. It is a combination of experimental observation and theoretical modelling and depends on the quality of available experimental data. This approach is based on the modelling of multicomponent systems starting from pure components followed by more complex (binary and ternary). The basic mathematical method is a minimization of the Gibbs energy of the system for a given temperature, pressure and overall composition. This approach is common to all currently available software packages for the modelling of thermodynamic properties and phase diagrams of multicomponent systems [4]. This paper presents a new numerical approach to modelling of ternary systems on the basis of thermodynamic properties of binary systems included in the investigated ternary system. The idea of predicting exGϕ ijk values is regarded as calculation of values of exGϕ function inside a certain area (a Gibbs triangle) unless all boundary conditions, that is values of exGϕ on all legs of the triangle are known (exGϕ ij, exGϕ ik, exGϕ jk). [...]

Numerical prediction of the thermodynamic properties of ternary Al-Ni-Zr alloys


  Phase diagrams are the most concise representation of a given system, and are crucial for understanding phase transformations, interfacial reactions, solidification and related changes in microstructure. Therefore, they are essential for the development of new multicomponent materials. Phase diagrams are determined by experimental methods such as: thermal analysis, microstructure examination, pressure measurements and others. However, the experimental determination of phase diagrams is a timeconsuming and costly task because the number of possible systems increases drastically with the number of elements. Experimental information for entire phase diagrams is available for most of the binary systems, but experimental information becomes increasingly sparse as the number of constituent elements increases (for ternary, quaternary and higher order systems) [1]. In this context, it is useful to estimate thermodynamic data of multicomponent systems from the constituent binary systems. There are many methods of modelling thermodynamic properties and calculations of phase diagrams in complex systems on the basis of thermodynamic properties of binary alloys constituting the complex alloy. Geometrical models and thermochemical model may be used for prediction of excess Gibbs energies of a ternary homogenous solution from the corresponding binary data. Methods of extrapolating thermodynamic properties of alloys into multicomponent systems are based on the summation of the binary and ternary excess parameters. The formulas for doing this are based on various geometrical weightings of the mole fractions. Binary compositions are chosen by using geometric correlations in the isothermal Gibbs triangle. Typically, the binary compositions are obtained from the intersection of an isogram, passing through the ternary composition of interest and the sides of the triangle. An isogram is a line of constant value of a given quantity, such as mole fr[...]

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