Epitaxial free energy and stability under epitaxial strain

First-principles ground-state total-energy calculations show that tetragonal crystals generally have two structures at which the energy is a minimum, which are appropriately called tetragonal phases in equilibrium. The calculations also show that a small isotropic two-dimensional (epitaxial) strain in the basal plane of a tetragonal phase produces a first-order phase transition to another tetragonal phase. By defining and calculating a special free energy for the states produced by epitaxial strain, the stability limits of each phase and the occurrence of a first-order phase transition between them are clearly demonstrated. Epitaxially strained states and the epitaxial free energy are calculated for vanadium. The epitaxial free energy as a function of the epitaxial stress for these strained states is shown to be similar to free-energy curves calculated for other first-order phase transitions which have analytic descriptions.