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

TL;DR

This study investigates how electronic entropy influences the temperature-dependent vibrational properties and stability of beta-zirconium, using a 2D effective potential and stochastic modeling to identify the transition temperature.

Contribution

It introduces a temperature-dependent effective potential for interacting phonons in beta-zirconium and analyzes the impact of electronic entropy on its structural stability.

Findings

The calculated transition temperature aligns with experimental data.

Electronic entropy significantly affects the vibrational stability of beta-zirconium.

Spectral density analysis reveals instability points related to phase transition.

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.