A dynamical approach to the $\alpha$-$\beta$ displacive transition of quartz

TL;DR

This paper investigates the alpha-beta transition in quartz using molecular dynamics, revealing it as a Hamiltonian bifurcation involving a subsystem of four normal modes, and explains the soft mode phenomenon.

Contribution

It provides a dynamical, Hamiltonian-based model of quartz's alpha-beta transition, focusing on a specific subsystem and calculating the effective potential.

Findings

Transition involves four normal modes acting as a subsystem.

Transition described as a pitchfork bifurcation with a soft mode.

Estimated critical exponent for the transition.

Abstract

General features of the $\alpha-\beta$ transition of quartz are investigated. Molecular dynamics methods are mainly used, an analytic treatment being deferred to a work in preparation. A basic preliminary observation is that the transition involves only a subsystem of four normal modes on which the remaining ones just act as a reservoir. The dynamics of the relevant subsystem turns out to be Hamiltonian, being governed by an effective potential that depends on the specific energy of the total system. The effective potential is actually calculated through time averages. It describes the transition as a pitchfork bifurcation, and also explains the phenomenon of the soft mode, since it exhibits a frequency that vanishes at the transition. The critical exponent too is estimated.