We show that the hcp $\left(\alpha \right)\to \mathrm{bcc}\left(\beta \right)$ structural phase transformation of titanium occurs via anharmonicity effect of thermal lattice vibrations. The full-potential linear muffin-tin orbital method in the local density approximation with the generalized gradient correction is used to derive the embedded atom potential for Ti, which allows us the analytic and realistic calculations of the thermodynamic quantities. We also discuss the similar phase transformation but slightly different mechanism occurring in zirconium in terms of the anharmonicity of thermal lattice vibrations.

• Received 29 July 2003

DOI:https://doi.org/10.1103/PhysRevB.70.184122