α⇆β phase transition in tin:: A theoretical study based on density-functional perturbation theory

The free energies of the alpha and beta phases of tin are calculated in the harmonic approximation using density-functional theory and density-functional perturbation theory, within the local-density approximation. At T=0 K the free energy of the beta phase lies approximate to 359 cal/mole above that of the alpha structure. The narrower frequency range spanned by the vibrational band in the beta phase makes its entropy larger at high temperature. As a consequence, the free energies of the two phases equal each other at a temperature of 38 degrees C, in close agreement with the observed transition temperature T-c approximate to 13 degrees C. [S0163-1829(98)03714-X].