Analytical methods for calculation of the short-range order in alloys: II. Numerical accuracy study

The numerical accuracy of the analytical approximations elaborated in part I and of a variety of other approximations advanced to date is examined, accepting the data on the short-range order parameters obtained by the Monte Carlo method as a standard. The approximations exhibiting the most promise for description of actual alloys and other lattice systems (for instance, interstitial alloys, semiconductors and magnetics) including those with a long-range character of atomic interactions are revealed. It is stated that, in the framework of the lattice gas model within a modified thermodynamic perturbation theory, the choice of the inverse effective number of atoms interacting with one fixed atom as a small parameter of the cumulant expansion along with taking account of the contributions from only linked irreducible diagrams ensures the fastest convergence of expansion. It is demonstrated that the use of the grand canonical ensemble yields the highest numerical accuracy in the statistical-thermodynamic description within the framework of all approximations elaborated in part I.