We present an extensive study of the pressure-induced bcc to hcp martensitic transformation in iron, using a spin-polarized full-potential total energy technique. The calculated pressure where the phases have equal enthalpies, 10.3 GPa, agrees well with the experimental value. Total energy surfaces as a function of the atomic displacements, which in the bcc phase correspond to the T 1 N-point phonon mode and a long-wavelength shear, are calculated for six different volumes. We observe that the bcc phase is thermodynamically unstable with respect to the hcp phase, long before it becomes dynamically unstable. The transition pressure at room temperature is estimated to approximately 50 GPa. We find that magnetism is the primary stabilizing mechanism of the bcc structure. Furthermore, we observe a sudden drop in the magnetic moment at a certain point in the transition path, which results in a discontinuous derivative in the energy surface. This is a clear signature of a first order ferromagnetic to nonmagnetic transition, responsible for the main part of the latent heat developed in this martensitic transformation. We also observe low-spin states at certain structures and pressures. Finally we employ Stoner theory to explain the behavior of the magnetism along the transition path. ͓S0163-1829͑98͒06030-5͔
The lattice dynamics of the elements Sc, Ti, La, and Hf in the bcc structure is studied using the densityfunctional linear-response theory. The elements exhibit similar phonon instabilities which cover large parts of the Brillouin zone. In particular, the entire T [11 0] ͓0͔ branch, where the zone-boundary phonon is responsible for the bcc→hcp transition, and the L͓ 2 3 2 3 2 3 ͔ mode (bcc→omega) are unstable. However, the T͓͔ branch is unstable for all elements except Sc, and Ti and Sc exhibit distorted bcc energy minima not seen in the other elements.
The dynamical and thermodynamical stability of the bcc and fcc disordered Re x W 1Ϫx system is studied within the density-functional theory. The configurational part of the free energy is obtained from ab initio electron structure calculations together with the cluster expansion and the cluster variation formalism. Electronic excitations are accounted for through the temperature-dependent Fermi-Dirac distribution. The lattice dynamics of Re and W is studied using the density-functional linear-response theory. The calculated dispersion curves show that fcc Re is dynamically stable while bcc Re exhibits phonon instabilities in large parts of the Brillouin zone, similar to previous results for fcc W. Interestingly, the phonon dispersion curves for fcc Re show pronounced phonon anomalies characteristic of superconductors such as TaC and NbC. Due to the instabilities in bcc Re and fcc W the vibrational entropy, and therefore the free energy, is undefined. In order to predict the regions where the disordered Re x W 1Ϫx alloy is unstable we calculate the phonon dispersion curves in the virtual crystal approximation. Then we apply a concentration-dependent nonlinear interpolation to the force constants, which are calculated through a Born-von Kármán fit to the ab initio obtained dynamical matrices. The vibrational free energy is calculated in the stable regions for the phases as a function of concentration. The complete analysis gives a region where the bcc phase would become thermodynamically unstable towards a phase decomposition into disordered bcc and fcc phases.
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