Ground state structures in binary h.c.p. alloys using multiatom interactions

Abstract

The cluster method is applied to binary (A-B) h.c.p. alloys having a non-ideal axial ratio in the tetrahedral approximation. Eight distinct cluster configurations are identified by populating A and B atoms on the distorted tetrahedral motif sites. The fractions of these clusters are the corresponding cluster variables. The configurational energy of the alloy is expressed as a function of four tetrahedral multiatom (four-body) interaction energy parameters, an effective pair interchange energy parameter and the cluster variables. The energy of the alloy is minimized for all possible triplets of clusters using the linear programming method. From the inequalities that minimize the energy and thus define the ground state, the permissible values of the multiatom interaction parameters in each case are clearly specified by a suitable geometric representation in a four-dimensional hyperspace spanned by the multiatom interaction parameters. Several ground state structures are obtained and the observed superstructures are shown to be ground state structures. Limitations of the linear programming method are examined and the effect of considering multiatom interactions is compared with that of increasing interaction distances in the pair approximation.