Open AccessConcentration wave method for description of all possible energy states of A2BC ordered alloy
Author(s) -
Albert R. Khalikov,
В Т Нгуен,
В. А. Валитов,
Sergey V. Dmitriev
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1008/1/012072
Subject(s) - superposition principle , alloy , lattice (music) , enumeration , plane wave , energy (signal processing) , regular polygon , plane (geometry) , point (geometry) , order (exchange) , spheres , mathematics , mathematical analysis , physics , combinatorics , materials science , geometry , quantum mechanics , finance , astronomy , acoustics , economics , composite material
The procedure for describing all possible energy states of an alloy based on the concentration wave method proposed by Khachaturian is employed to describe all possible energy states of ordered A 2 BC alloy based on N-dimensional lattice. Within the framework of this method, a complete enumeration of the structures obtained by the superposition of N plane concentration waves with all possible wave vectors is carried out, provided that the given stoichiometry is preserved. For each such superposition, the order parameters on the first I coordination spheres are calculated, thereby determining the point in the I-dimensional order parameter space corresponding to the given structure. For the case of I = 2 it is shown that a complete enumeration of all structures generated by one plane concentration wave fills a non-convex figure in the space of two order parameters.