Estimation of CE�?�CVM energy parameters from miscibility gap data

[摘要] The powerful framework of cluster expansionâ€�?�cluster variation methods (CEâ€�?�CVM) expresses alloy free energy in terms of energy (model) parameters, macroscopic variables (composition and temperature) and microscopic variables (correlation functions). A simultaneous optimization of thermodynamic and phase equilibria data using CEâ€�?�CVM is critically dependent on giving good initial values of energy parameters, macroscopic and microscopic variables, respectively. No standard method for obtaining the initial values of the energy parameters is available in literature. As a starting point, a method has been devised to estimate the values of energy parameters from consolute point (miscibility gap maximum) data. Empirical relations among energy parameters, temperature (ð‘�??_c), composition (ð‘�?_c) and ð‘�??²}ð‘�??/ð‘�?�ð�?��?² at the consolute point, have been developed using CEâ€�?�CVM free energy functions for bcc and fcc structures in the tetrahedron and tetrahedronâ€�?�octahedron approximations, respectively. Thus from the observed data of ð‘�??_c, ð‘�?_c and ð‘�??²}ð‘�??/ð‘�?�ð�?��?² in the above relations, good initial values of energy parameters can be obtained. Further, a necessary modification to the classical NR method for solving simultaneous nonlinear/transcendental equations with a double root in one variable and a simple root in the other has been presented.

[学科分类] 材料工程

[关键词] Cluster expansion method;cluster variation method;bcc and fcc structures;consolute point;miscibility gap;Newtonâ€�?�Raphson method.