The projector augmented wave method is used within the Perdew-Burke- Ernzerhof form of generalized gradient approximation to investigate the effect of hydrostatic pressure on the structures of hafnium metal. The obtained phase transformation pressures and the elastic constants at zero pressure are in excellent agreement with the experimental values. The elastic constants of -Hf under high pressures are predicted for the first time. We find that the modulus and the averaged aggregate wave velocities increase monotonically with increasing pressure. The Debye temperature of -Hf is also calculated at different pressures. The obtained result is well-consistent with the available experimental data.
Bibliographical noteFunding Information:
We acknowledge the support for this study by the Fundamental Research Funds for the Central Universities (2009SCU11124) and the National Key Laboratory Fund for Shock Wave and Detonation Physics Research (9140C6701010901).
- density functional theory
- elastic properties
- phase transition