On the first principles calculation of phase diagrams

First-principles methods which make possible the calculation of, among others, phase diagrams, thermodynamical parameters, lattice parameters and elastic constants of binary alloys, without reliance on any experimental data, are presented and applied.;A study of general tendencies toward ordering and phase separation at 0 K in binary transition-metal alloys shows that, even in a simple rectangular electronic density of states approximation, electronic contributions are governing the ground states of alloys. When, however, effects of temperature, off-stoichiometry, and short- and long-range order are to be considered, configurational aspects of alloying must be taken into account. The cluster variation method is well suited to describe these aspects, as is exemplified in a study of order-disorder transitions on the bcc lattice.;First-principles approaches combine electronic-bandstructure calculations, such as those obtained by the tight-binding method and the full-potential linearized augmented plane-wave method, with statistical mechanical techniques, such as the cluster variation method. These approaches are in principle capable of describing alloy behavior not only at 0 K, but at elevated temperatures as well.;Two approaches, (i) one based on the disordered state, and (ii) one based on a small set of stoichiometric ordered compounds, are described in detail and applied to the calculation of phase equilibria in the titanium - rhodium system and the aluminum - lithium system, respectively. Both first-principles calculations produce results which resemble the experimental findings to a remarkable degree. Furthermore, a critical examination and comparison of these two approaches is presented.