Recent work has suggested that vibrational effects can play a significant role in determining alloy phase equilibria. In order to better understand these effects and the methods used in their calculation, we investigate the vibrational properties of disordered Ni3A1 using the Embedded-Atom Method. We examine the effectiveness of the Special Quasirandom Structure (SQS) approximation, and find that an SQS-8 can accurately represent the vibrational thermodynamics of the disordered state. By the use of Monte Carlo (MC) techniques, we also find that the quasiharmonic approximation becomes less accurate as we approach the melting temperature, but that the accuracy may be extended to higher temperatures by resorting to the MC equation of state giving the specific volume as a function of temperature.

The following is an edited version of the David Turnbull Lectureship address, given by recipient Didier R. de Fontaine at the 1995 MRS Fall Meeting, De Fontaine received the lectureship “in recognition of fundamental contributions and insights in the fields of order/disorder phenomena in materials and computational techniques for phase diagrams.” De Fontaine is a professor in the Department of Materials Science and Mineral Engineering at the University of California—Berkeley and holds a joint appointment with the Lawrence Berkeley National Laboratory.

Thermodynamic and structural properties of fcc- and hcp-based Ti–Al alloys are calculated from first-principles and are used to perform an ab initio study of phase stability for the intermetallic compounds in this system. The full potential linear muffin tin orbital method is used to determine heats of formation and other zero-temperature properties of 9 fcc- and 7 hcp-based intermetallic compounds, as well as of elemental fcc and hcp Ti and Al. From the results of these calculations, sets of effective cluster interactions are derived and are used in a cluster variation method calculation of the solid-state portion of the composition-temperature phase diagram for fcc- and hcp-based alloy phases. The results of our calculations are compared with those of experimental studies of stable and metastable phases in the Ti–Al system.

An explanation of the occurrence of unphysical solutions in the cluster variational method is given. A simple algorithm for the construction of an optimal maximal cluster, i.e., a cluster that guarantees correct results for any set of interatomic interactions, is suggested. Examples of optimal maximal clusters for various two- and three-dimensional lattices are presented.

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, A3B, and A4B3. 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.

In this paper we present results of a first-principles phase stability study of fcc-based Ti-Al alloys. In particular, the full-potential linear muffin tin orbital method has been used to determine heats of formation and other zero-temperature properties of 9 fcc ordered superstructures as well as fcc and hcp Ti, and fcc Al. From these results a set of effective cluster interactions are determined which are used in a cluster variation method calculation of the thermodynamic properties and the composition-temperature phase diagram of fcc-based alloys.

The relationship between oxygen structure, charge transfer (hole count), and oxygen content in the YBa2Cu3Oz superconductor is studied by combining Monte-Carlo simulation with existing electronic structure calculations. The present model proposes an expansion of the hole count in terms of oxygen configuration variables for states of an arbitrary degree of order. Calculations of hole count as a function of oxygen content suggest that oxygen ordering is, at least in part, responsible for the observed plateau structure of Tc vs. oxygen content z.

In this paper we present results of a first-principles study of phase stability and structural and thermodynamic properties of fcc- and hcp-based Ti-Al alloys. In particular, the full-potential linear muffin tin orbital method has been used to determine heats of formation and other zero-temperature properties of 9 fcc and 7 hcp ordered superstructures as well as fcc and hep Ti and Al. From these results a set of effective cluster interactions are determined which are used in a cluster variation method calculation of the solid-state portion of the composition-temperature phase diagram for fcc- and hcp-based alloys.

We present a formulation of the Korringa-Kohn-Rostoker coherent potential approximation (KKPt-CPA) for the treatment of substitutionally disordered alloys within the KKR atomic-sphere approximation (ASA). This KKR-ASA-CPA represents the first step toward the implementation of a full cell potential CPA, and combines the accuracy of the KKR-CPA method with the flexibility of treating complex crystal structures. The accuracy of this approach has been tested by comparing the self-consistent-field (SCF) KKR-ASA-CPA calculations of Cu-Pd alloys with experimental results and previous SCF-KKR-CPA calculations.

Coherent phase diagrams are defined as pertaining to equilibria between phases which differ from one another merely by the distribution of different types of atoms on fixed crystallographic sites. Resulting ordered structures must then all be superstructures of one parent lattice, and corresponding phase diagrams are isomorphous to those of the Ising model with non–vanishing magnetic field. Rather complex phase diagrams can then be obtained from a single free energy functional by means of the cluster variation method. Calculated phase diagrams will be shown for the case of the fcc parent lattice with various positive and negative ratios of the values of second-to-first-neighbor pair interactions, this ratio being the only parameter which enters the calculation. Results will be compared to those of Monte Carlo calculations. The possibility of performing these first-principle calculations of coherent phase diagrams will be briefly touched upon.