Ni-Al based alloys remain a material of technological importance for high strength and high temperature applications. A design that optimizes desirable properties, such as strength, or creep and oxidation resistance, requires a deep understanding of thermodynamics and kinetics. This thesis uses ab initio methods to model both phase stability and diffusion processes. Starting from Density Functional Theory (DFT), formation energies of different crystal orderings are used to parameterize cluster expansion models. Used in conjunction with Monte Carlo techniques, these models can be used to derive macro scale properties at finite temperature.

We use DFT calculations to explore orderings on FCC and BCC, first for the Ni-Al binary, and then the Ni-Al-Cr ternary. Our calculations not only predict the stability of known phases, but also reveal new families of previously unknown ordered phases. We introduce strain order parameters to systematically analyze orderings on both FCC and BCC lattices. Many of these orderings are predicted to be unstable around x N i = 0.625, where a martensitic phase transformation is known to occur.

DFT calculations serve as training data for cluster expansion effective Hamiltonians, which accurately predict formation energies of arbitrary orderings without costly computations. We use these effective Hamiltonians in Monte Carlo simulations to calculate free energies, with which we construct phase diagrams. The difficulty of parameterizing a cluster expansion grows exponentially with the number of possible components. We introduce a recursive approach to parameterize multi-component alloy Hamiltonians using interaction parameters from simpler subsystems as Bayesian informative priors. We applied this approach to expand the statistical mechanics study of Ni-Al to Ni-Al-Cr, and explore Cr behavior within the L12 ordering.

The same cluster expansion methods can be used to model hop barriers of kinetic processes as a function of the ordering on the crystal. Diffusion barriers for Al hops have a strong dependence on the immediate local composition, while Ni hops are largely independent of their local ordering. We have developed a rigorous Kinetic Monte Carlo model that incorporates these relationships of hop barriers with local ordering, and applied it to the Ni-Al binary. Ni and Al exhibit different diffusion properties in the γ and γ' phases, which we discuss using various metrics of diffusion.