Order-disorder in binary alloys: a theoretical description by use of the Ising model

A new method for solving the Ising problem is presented, which can easily b e applied to binary ordered intermetallic compounds. Calculation of the par tition function by this method is possible not only for one-dimensional and two-dimensional lattices, but also for three-dimensional cases. Ordering o f a three-dimensional lattice with NaCl structure is analyzed in detail. Th e reduced critical temperature is found to be RTc/\ nu \ = 1.88. Since the method yields the different defect cluster concentrations, verification of the validity of the mean-field theory is possible. It could be shown that, in the case of alloys with the NaCl structure, mean-field theories are appl icable up to a temperature of T/T(c)approximate to0.4. (C) 2001 Elsevier Sc ience B.V. All rights reserved.