Ordered ground-state structures in binary h.c.p. alloys using the configuration polyhedron method

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Abstract
Ground-state structures in binary h.c.p. (non-ideal axial ratio) alloys have been studied taking interactions up to third-neighbour distances. The configuration polyhedron method was adopted for this purpose. The procedure for deriving the structural inequalities used in this method has been generalized. Tetrahedral, octahedral and another larger motif have been used. 15 ground-state structures (corresponding to vertices and points on edges of the configuration polyhedron) with the stoichiometries A5B, A3B, A2B, A9B5 and AB have been identified. In addition, the A7B5 structure and a series of structures with stoichiometries An+3Bn+1(n>1) (with points on the two-dimensional planar surfaces of the configuration polyhedron) are also ground states. The structural details of the former group of ground-state structures, such as the lattice, the number of atoms per unit cell, the equivalent positions of atoms and their site symmetries have been worked out. The stability of all experimentally observed superstructures has been explained. Four types of degenerate situation have been identified in the present study. Three are associated with alternate structures or solid solutions or phase mixtures representing the same point on the surface of the configuration polyhedron and thus having the same energy. The fourth is related to ideal h.c.p. structures. A three-dimensional configuration polyhedron, relevant to the ideal case, is obtained by projecting the vertices of the four-dimensional configuration polyhedron on a particular hyperplane to illustrate the nature of this degeneracy.