Mechanical instabilities and structural phase transitions: The cubic to tetragonal transformation

A variety of technologically important crystalline phases are predicted by first-principles electronic structure methods to be mechanically unstable at 0 K, raising fundamental questions about the finite temperature excitations that stabilize these phases at high-temperature. Here, we show that anharmonic vibrational degrees of freedom can stabilize a cubic phase that is mechanically unstable at 0 K with respect to a tetragonal distortion. We develop an effective anharmonic strain Hamiltonian for a cubic lattice and parameterize its coefficients to first-principles calculations of the energy surface of TiH2, a compound that undergoes a cubic to tetragonal transformation around 300 K and for which the cubic phase is predicted to be mechanically unstable. Monte Carlo simulations applied to the effective Hamiltonian predict a cubic to tetragonal phase transition and provide insight about the true nature of the high-temperature cubic phase.