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Analytical solutions for the correlation functions of perfectly ordered binary phases based on bcc, fcc and cph structures using cluster variation method
Calphad ( IF 2.4 ) Pub Date : 2020-09-10 , DOI: 10.1016/j.calphad.2020.101773
Rajendra Prasad Gorrey , Vikas Jindal , Bandikatla Nageswara Sarma , Shrikant Lele

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.



中文翻译:

基于聚类变化法的基于bcc,fcc和cph结构的完美有序二元相相关函数的解析解

对于二元有序固溶体,根据相关函数(CF)描述系统的组态微观状态。在CE – CVM中,这些是CF点(与成分有关的u 0),Bragg-Williams远程有序参数(ξ),温度(T)和簇膨胀系数(CEC)的函数。在此通讯中,详细过程用于获取CF(在正交基础上定义)的极限值及其相对于u 0ξ的导数在化学计量组成上,基于bcc,fcc和cph结构的几种频繁出现的二元有序相给出了理想配比的极限。这是通过定义新的称为亚晶格溶剂碱的碱来实现的。对于使用CE – CVM的(不规则)四面体(T)近似的bcc结构,给出了B 2,B 32和D 0 3有序相的情况的结果,基于L 1 0L 1 2有序相使用(规则)四面体(T)和四面体八面体(TO)近似以及L 1 1使用TO逼近和B 19和D 0 19有序相基于cph结构使用三角四面体(TT)和TO逼近。在所有这些情况下,CF的极限值及其相对于u 0ξ的一阶导数与CEC和T无关,而高阶导数则取决于CEC和T的比率。结果表明,亚晶格溶剂基质中CFs的平衡值可以计算得比正交条件下CFs可能的温度低得多。

更新日期:2020-09-10
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