The absolute free energies of the hcp and bcc phases of zirconium have been calculated as a function of temperature by the Einstein-crystal method, using Monte Carlo simulations of a tight-binding model. The thermodynamic transition temperature of the hcp-bcc transition is found to be close to the transition temperature observed in constant-pressure molecular-dynamics simulations. The calculated value of the entropy difference of the hcp and bcc phases is in good agreement with the experimental value, taking into account the contribution of the electronic excitations. The temperature dependence of the enthalpy difference of the hcp and bcc phases is found to contribute considerably to the temperature dependence of the free-energy difference of the hcp and bcc phases.

• Received 22 October 1990

DOI:https://doi.org/10.1103/PhysRevB.43.6167