Applications of the Cluster Expansion to Substitutional Disorder in Ternary and Hexagonal-Close Binary Alloys.

Various issues related to substitutional disorder in ternary and hexagonal-close-packed binary alloys are discussed. The alloy problem is formulated using a multicomponent cluster expansion which is linear and complete in the space of atomic configurations. The expansion is used to consider both the configurational energy and probability density for binary and ternary alloys. Expansion coefficients for the configurational energy (ECI's) can be computed using first-principles quantum-mechanical (QM) techniques, thus allowing the cluster expansion to be applied to real alloy systems. Ground-state analyses are used to enumerate possible ordered structures at T = 0 K for different alloys, and finite-temperature studies using the cluster variation method (CVM) illustrate alloy phase equilibria. These methods are first applied to a study of substitutional disorder in binary hexagonal-close-packed alloys. The ground-state problem is solved exactly within the range of the nearest-neighbor octahedron in the hcp lattice and yields a set of 32 physically-realizable groundstates. Prototype hcp phase diagrams are also computed using the CVM for different values of the pair interactions. The remainder of the dissertation focuses on order-disorder phenomena in ternary alloys. Prototype analyses are performed for ternary phase diagrams on the fcc lattice and for ordering in bcc-based Heusler alloys. Each of these studies illustrate the increased complexity of ternary phase equilibria, and the latter demonstrates the competition between ordering tendencies which govern Heusler alloy phase stability. First -principles QM total energy calculations are used to study the bcc W-Mo-Cr phase diagram and the Heusler alloy Cd _2AgAu. ECI's are computed in W -Mo-Cr using an inversion method (SIM) and the method of direct configurational averaging (DCA). The W-Mo-Cr phase diagram is then calculated using DCA interactions with the tetrahedron approximation to the CVM. Phase transitions in the Heusler alloy Cd_2AgAu are computed with the CVM using ECI's calculated with the SIM. Qualitative agreement exists between ab initio results and experiment, thus demonstrating the viability of cluster expansion techniques to study ordering problems in real ternary alloys.