Epitaxial Bain Paths and Metastable Phases

A systematic two-stage procedure for finding metastable phases from first-principles total-energy calculations is derived and applied to tetragonal structures. In the first stage we calculate the system’s epitaxial Bain path (EBP) in the tetragonal plane, whose coordinates are the tetragonal lattice constants; the EBP is defined so that it goes through all tetragonal energy minima. In the second stage we prove or disprove metastability by evaluating the elastic constants at the minima and checking the stability conditions. Application of the procedure to some metallic elements and compounds has
led to a substantial number of metastable phases, many of them new, which exist in addition to the ground state. A generalization to finite hydrostatic pressure permits finding metastable phases under pressure, but a third stage must be added which converts the energy to a free energy whose minima now give the phases. Various properties of EBP’s are described, including the existence of inherently unstable states along the EBP which cannot be stabilized by application of external stresses, and de-termination of the point on the EBP at which a thermodynamic phase transition between tetragonal phases occurs that is produced by epitaxial strain.