Phonons and the lattice dynamics in crystals with atomic diffusion: Concept and application to superionic ices
Phys. Rev. B 114, 024101 – Published 1 July, 2026
DOI: https://doi.org/10.1103/m1s6-6hdf
Abstract
Phonons, the quantized collective excitations of crystal lattice vibrations, require long-range periodic order for momentum to be a well-defined quantum number—a condition that breaks down in disordered systems. However, many systems exhibit a complex interplay between ordered and disordered components. A prime example is superionic ice, a novel phase of ice at high temperatures and pressures, where hydrogen ions (protons) diffuse like a liquid while oxygen ions maintain a solidlike vibrational framework. Previous research has mainly focused on the diffusive aspect of the superionic phase, leaving the rich physics of its vibrational lattice dynamics relatively unexplored. Here, we investigate the phonon properties of superionic ices with both body-centered-cubic (bcc) and face-centered-cubic (fcc) oxygen sublattice. Despite the fully disordered protons, the oxygen sublattice exhibits similar phonon dispersion with typical bcc/fcc solids. This similarity is not a trivial regression, but direct evidence of the emergence of higher symmetry and effective interaction degeneracy resulting from hydrogen-bond dissociation, accompanied by strong damping and anharmonicity. Notably, we identify that specific softened phonon modes drive the mechanical instability of the bcc oxygen sublattice, providing a key kinetic mechanism for phase transitions between superionic ices. By extending the phonon concept to a hybrid ordered-disordered system, our work provides a powerful framework for characterizing lattice dynamics in superionic and related complex materials.