hcp Ising model in the cluster-variation approximation

We present a study of the hexagonal-close-packed Ising model for binary alloys within the cluster-variation approximation. Ground states of order stabilized by interactions that span the next-nearest-neighbor (NNN) distance (octahedron and all of its subclusters) were determined with the cluster-configuration polyhedron method. We predict 32 physically realizable ground states with stoichiometries A, AB, ${\mathit{A}}_{2}$B, ${\mathit{A}}_{3}$B, ${\mathit{A}}_{5}$B, and ${\mathit{A}}_{4}$${\mathit{B}}_{3}$. Of these structures, six are stabilized by NN pairs and eight by NNN pairs; the remaining 18 structures require multiplet interactions for their stability. The results in this study are consistent with previous pair-interaction studies. Information concerning ground states and their domains of stability was then used in conjunction with the cluster-variation method (CVM) to calculate the finite-temperature phase equilibria for prototypical binary alloys. We present ordering phase diagrams computed with the CVM that contain all relevant ground states for both isotropic and anisotropic NN pair interactions. The results of the ground-state and CVM calculations are compared with those for ordering on the face-centered-cubic lattice.