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 be applied to binary ordered intermetallic compounds. Calculation of the partition function by this method is possible not only for one-dimensional and two-dimensional lattices, but also for three-dimensional cases. Ordering of a three-dimensional lattice with NaCl structure is analyzed in detail. The 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 applicable up to a temperature of T/T(c)approximate to0.4. (C) 2001 Elsevier Science B.V. All rights reserved.