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PHASE TRANSFORMATIONS IN HEXAGONAL-CLOSE-PACKED ALLOYS: ANALYSIS WITH THE CLUSTER VARIATION METHOD RYAN McCORMACK*, MARK ASTA*, GERBRAND CEDERt, and DIDIER de FONTAINE* * Department of Materials Science and Mineral Engineering, University of California, and Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 tDepartment of Materials Science, Massachusetts Institute of Technology, Cambridge, MA 02139 ABSTRACT We present a study of the hexagonal close-packed (hcp) Ising model for binary alloys within the cluster variation approximation. Groundstates of order stabilized by nearest-neighbor (NN) pair, triplet, and tetrahedron interactions were determined using the cluster configuration polyhedron method; no previous hcp ground-state study has considered all of these interactions. We predict physically realizable groundstates with stoichiometries A, AB (3 distinct structures), A2B, A3 B, and A4B 3 . The previously unpredicted A4B3 structure is stabilized by multiatom (i.e. triplet, tetrahedron) interactions, while the others are stabilized by the two NN pair interactions. The Cluster Variation Method (CVM) was used to calculate the finite-temperature phase-equilibria for prototypical binary alloys. We present the first ordering phase diagrams computed with the CVM which contain all relevant groundstates for both isotropic and anisotropic NN pair interactions. INTRODUCTION In many problems concerning phase-equilibria of binary alloys AxB l-x, the thermodynamic behavior of (solid) alloys can be approximated by an Ising model. The configurational energy associated with a given arrangement of atoms is then calculated using the Ising model Hamiltonian with a specified set of effective interaction parameters. These interactions can either be pairwise or multiatom, depending on the level of complexity required by the problem at hand. In general, the problems associated with the configurational statistical mechanics become more intractable as the range of the interactions increases. For either antiferromagnetic or ferromagnetic interactions on the chosen lattice, there are two distinct, yet related, domains of study: 1) Analysis of the structures with the lowest configurationalenergy (ground-states) as a function of composition at T=O K, and 2) Analysis of finite-temperature phase behavior. Several approximate methods of computing groundstates of the Ising model on a given lattice have been used, most of which revolve around constructing a set of constraints on some set of configurational variables. The methods of Allen and CahnI and Kanamori 2 are the most widely used for ground-states of binary alloys. Ground-state analyses have been performed for numerous Ising lattices (see Ref. [3] for a complete listing), but in the field of alloy theory, perhaps the most widely studied of these are the fcc and bcc lattices. Groundstates of the hexagonal-close-packed structure have not been analyzed as extensively as those of fcc and bcc. The study of finite-temperature equilibrium can be carried out usin