Phase stability limits via non-equilibrium normal mode analysis

Abstract

Alkali chlorides in both their rock-salt and CsCl modifications were isotropically expanded or compressed to produce non-equilibrium structures while preserving the crystal symmetries and perfect force balance. These structures were analysed by determining the eigenvalues of the linearized Hamiltonian equations of motion. This procedure, which is similar to normal mode analysis, yields all elastic coefficients and the spectrum of rates of motion, which can include oscillatory as well as aperiodic modes. In balanced structures, the onset of aperiodic modes of motion coincides with singularities or roots in the density dependence of elastic coefficients. This onset is interpreted as the limit of stability for a given crystallographic phase and, by comparing the values of the various elastic constants, some information about the type of transition that is impending at those densities can be obtained. Results for chlorides with varying alkali cation are consistent with the experimentally observed phase stability trends.

Violation of the symmetry due to thermal disorder or lattice defects, however, affects the onset of unstable modes and the roots of elastic constants in opposite ways, suggesting that the phase stability is sensitive to localized extreme states, while the mechanical properties are derived from ensemble averages.