First-principles cluster variation calculations of tetragonal-cubic transition in ZrO₂

It is attempted to extend the basic idea of continuous displacement cluster variation method (CDCVM) to the study of a displacive phase transition. As a preliminary study, we focus on cubic to tetragonal transition in ZrO₂ in which oxygen atoms on the cubic lattice are displaced alternatively in the opposite direction (upward and downward) along the tetragonal axis. Within the CDCVM, displaced atoms are regarded as different atomic species, and two distinguished atoms, A-oxygen (upward shifting) and B-oxygen (downward shifting), are introduced in the description of the free energy. FLAPW electronic structure total energy calculations are performed to extract effective interaction energies among displaced oxygen atoms, and by combing them with CDCVM, the transition temperature is calculated from the first-principles.