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

Abstract

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.