For the hcp metal titanium, the elastic constants show pronounced change with temperature. In particular, the elastic constant C12 exhibits an increase with temperature and C13 is approximately independent of temperature. In this study we calculate the elastic constants for hcp titanium in a first principles anisotropic quasi-harmonic approach which includes calculations of the phonon spectra as a function of strain. The temperature dependence of the elastic constants is obtained in agreement with the experiment with the exception of C13.
- Elastic constants
- Quasi Harmonic approximation