The effect of electronic entropy on temperature peculiarities of the frequency characteristics of two interacting anharmonic vibrational modes in β−\beta-Zr

A 2D temperature-dependent effective potential is calculated for the interacting longitudinal and transverse $L-$phonons of $\beta$ zirconium in the frozen-phonon model. The effective potentials obtained for different temperatures are used for the numerical solution of a set of stochastic differential equations with a thermostat of the white-noise type. Analysis of the spectral density of transverse vibrations allows one to determine the temperature at which $\beta$-Zr becomes unstable with respect to the longitudinal $L-$vibrations. The obtained temperature value practically coincides with the experimental temperature of the $\beta \to \alpha$ structural transition in zirconium. The role of electronic entropy in the $\beta-$Zr stability is discussed.Comment: 9 pages, 10 figures (submitted in Phys.Rev.

Calculation of the P-T phase diagram and tendency toward decomposition in equiatomic TiZr alloy

Electronic, structural and thermodynamic properties of the equiatomic alloy TiZr are calculated within the electron density functional theory and the Debye-Gruneisen model. The calculated values of the lattice parameters a and c/a agree well with the experimental data for the alpha, omega and beta phases. The omega phase is shown to be stable at atmospheric pressure and low temperatures; it remains energetically preferable up to T=600K. The alpha phase of the TiZr alloy becomes stable in the range 600K<T<900K, and the beta phase at temperatures above 900K. The constructed phase diagram qualitatively agrees with the experimental data available. The tendency toward decomposition in the equiatomic alloy omega-TiZr is studied. It is shown that in the ground state the omega phase of the ordered equiatomic alloy TiZr has a tendency toward ordering, rather than decomposition.Comment: 6 pages, 8 figure