First-principles calculations of thermodynamic properties and phase diagrams of binary substitutional alloys

In this dissertation it is shown how quantum and statistical mechanical computational techniques can be combined in order to make possible the calculation of thermodynamic properties for solid-state binary substitutional alloy phases from first principles, i.e., from a knowledge of only basic crystallographic information and the atomic numbers of the alloy constituents. The framework which is discussed here for performing such calculations is based on the formalism of cluster expansions. Using this formalism the statistical mechanical problem of computing substitutional alloy thermodynamic properties can be reduced to that of solving a generalized Ising model. It is shown how the parameters describing atomic interactions in such an Ising model can be derived with the structure inversion method from the results of quantum mechanical calculations of zero-temperature total energies for a number of ordered stoichiometric alloy compounds sharing a common underlying parent structure. Once the parameters in the generalized Ising model have been derived, alloy thermodynamic properties can be calculated by a variety of statistical mechanical techniques. In the work presented here the quantum and statistical mechanical calculations have been performed using the linear muffin-tin orbital and cluster variation methods, respectively. These computational methods are both described in some detail.;The formalism and computational techniques mentioned in the previous paragraph are applied to the study of alloy phase stability in the Ti-Al and Cd-Mg systems. For Cd-Mg an effort is made to determine the relative magnitudes of the contributions to the alloy free energy arising from configurational disorder, structural relaxations, as well as vibrational and electronic excitations. It is shown that when all of these different contributions to the free energy are included, the calculated solid-state portion of the composition-temperature phase diagram for the Cd-Mg system is in excellent agreement with experimental measurements. For the Ti-Al system, the thermodynamic stability of phases with fcc- and hcp-based crystal structures is studied. It is shown that the complexity of the Ti-Al phase diagram can be understood as being the result of a very close competition between stable and metastable ordered phases in this system.