Analytical methods for calculation of the short-range order in alloys: I. General theory

In the context of a modified thermodynamic perturbation theory within the grand canonical ensemble, by the use of the thermodynamic fluctuation method, a number of new analytical approximations for calculations of the grand thermodynamic potential as well as of the short-range order parameters and their Fourier transform in disordered binary alloys with a Bravais crystal lattice are elaborated. An alloy of an arbitrary composition is considered in the framework of the lattice gas model with pair atomic interactions of arbitrary effective radius of action. The inverse effective number of atoms interacting with one fixed atom and inverse temperature as well as the concentration of the impurity component are used as small parameters of expansion. The developed approach may be also followed in studies of magnetics within the framework of the Ising model, and of fluids and amorphous materials within the lattice gas model as well as in investigations of low-dimensional lattice systems.