Study of the Martensitic Phase Transition in Sodium

The martensitic transformation in sodium is studied by means of a local pseudopotential theory. The total Helmholtz free energy is calculated as a function of temperature and crystal configuration for both the bcc and hcp phases of sodium. At $T=0$, the hcp phase is found to be stable, while the bcc phase is found to be stable at high temperatures. The inclusion of the zero-point energy at $T=0$ gives improved agreement with the experimentally determined energy differences between the bcc and hcp phases. It is found that the thermal expansion of the crystal does not play a significant role in the phase transition and the transition from hcp to bcc as the temperature increases can be explained by thermodynamic arguments.