First-principles study of phonon anomalies and the bcc-hcp martensitic phase transition

First-principles total energy calculations have been performed for transition metal Zr in the ω, bcc, hcp, fcc structures and for Ba in the bcc, fcc structures. From our calculations we obtained equilibrium lattice constants, cohesive energies, bulk moduli and energy difference between the bcc and the hcp phases which are in good agreement with experiment. The total energy of ω phase was found to be very close to that of hcp phase in Zr. Recent neutron scattering experiments on a single crystal of bcc Ba have revealed that the longitudinal branch along the [100] direction is lower than the transverse branch. This anomalous behavior has been studied with use of the frozen-phonon method and is shown to arise from d-electron interactions. For the pressure induced bcc-hcp transition in Ba, the volume dependence of the complete energy surface from the bcc to the hcp structure has been determined as a function of the atomic displacements corresponding to the T1 N-point phonon mode and a long wavelength shear. Results from frozen phonon calculations for Zr indicate an instability toward the hcp phase at t = 0 K in the bcc-hcp transition and determine the third and fourth order anharmonic coupling strengths which were used to evaluate the temperature dependence of selected frequencies. 135 refs., 29 figs., 13 tabs