Analytical solutions for the correlation functions of perfectly ordered binary phases based on bcc, fcc and cph structures using cluster variation method

Abstract

For a binary ordered solid solution, the configurational microscopic state of the system is described in terms of the correlation functions (CFs). In CE – CVM, these are functions of point CF (u0, which is related to the composition), the Bragg-Williams long range order parameter (ξ), temperature (T) and cluster expansion coefficients (CECs). In this communication, a detailed procedure for obtaining the limiting values of the CFs (defined in the orthogonal basis) and their derivatives with respect to u0 and ξ at the stoichiometric composition in the limit of perfect ordering is presented for several frequently occurring binary ordered phases based on bcc, fcc and cph structures. This is achieved by defining new bases called sublattice solvent bases. The results are given for the cases of the B2, B32 and D03 ordered phases based on the bcc structure using (irregular) tetrahedron (T) approximation of CE – CVM, the L10 and L12 ordered phases based on the fcc structure using (regular) tetrahedron (T) and tetrahedron-octahedron (TO) approximations as well as the L11 phase using TO approximation and the B19 and D019 ordered phases based on the cph structure using triangle-tetrahedron (TT) and TO approximations. In all these cases, limiting values of the CFs and their first derivatives with respect to u0 and ξ are independent of CECs and T, while the higher order derivatives are dependent on the ratios of CECs and T. It is shown that the equilibrium values of CFs in the sublattice solvent bases can be calculated to much lower temperatures than those possible with CFs in orthogonal basis.