Elastic phase transitions in metals at high pressures

Crystalline lattices can become unstable to uniform shear strains, which may lead to a structural transformation to less symmetric structures. Transitions of this type are called elastic phase transitions. In this paper, elastic phase transitions in metals with cubic and hexagonal structures are considered. The relation between the elastic constants of second, third, and fourth order corresponding to the case of a first-order elastic phase transition are given. As an example, the structural transformation in vanadium, which is experimentally observed at $P\approx 69$ GPa, and the possibility of structural transformation in molybdenum at $P$ higher than $700$ GPa are analyzed.