Electron Theory and Statistical Thermodynamics for Tegragonal Distortion

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The first-principles calculations of a phase diagram and thermodynamic quantities have been so far limited to the system with a high symmetric crystal structure. In reality, however, one finds various alloysystems with the tetragonal distortion. The deviation from the full cubic to tetragonal symmetries is not only closely related to the phase stability of ta given system but also affects various mechannical properties. The main objective o fht eproposed project is to establish the computational and theoretical basis to study tetragonal distortion effects based on electronic theory and statistical theomadynamics. Followings are the main outcomes of the projects.1. In order to derive the distant pair interaction energies which play crucial role in stabilizing the tetragonal structure, we employed the Cluster Expansion Method and extracted pair interactions up to fourth nearest neighbor.2. By employing the first-principles pseudopotential theory, we calcualted the lattice constant, Poisson's ratio and other elastic properties as a function of tetragonal distortion and optimized the structure.3. The tetrahedron approximatin of the Cluster Variation method of statistical mechanics is modified so that the tetragonal to calcualte the free energy as a fnctin of tetragonal distortion. The program is applied to culculate a disorder-L1o phase diagram with the tetragonal distortino explicitely incorporated in the L1o ordered phase.