Phonon dispersions of cluster crystals

TL;DR

This paper investigates the low-temperature phonon spectra and phase transitions of cluster crystals, revealing an infinite cascade of isostructural transitions and the analytical calculation of phonon modes and free energy.

Contribution

It provides the first analytical calculation of phonon spectra for cluster crystals and uncovers a series of low-temperature phase transitions with critical points.

Findings

Existence of an infinite cascade of isostructural transitions.

Optical phonon modes are degenerate and flat, resembling Einstein crystals.

Phase transitions terminate at critical points due to anharmonic effects.

Abstract

We analyze the ground states and the elementary collective excitations (phonons) of a class of systems, which form cluster crystals in the absence of attractions. Whereas the regime of moderate-to-high-temperatures in the phase diagram has been analyzed in detail by means of density functional considerations (Likos C N, Mladek B M, Gottwald D and Kahl G 2007 {\it J.~Chem.~Phys.}\ {\bf 126} 224502), the present approach focuses on the complementary regime of low temperatures. We establish the existence of an infinite cascade of isostructural transitions between crystals with different lattice site occupancy at $T=0$ and we quantitatively demonstrate that the thermodynamic instabilities are bracketed by mechanical instabilities arising from long-wavelength acoustical phonons. We further show that all optical modes are degenerate and flat, giving rise to perfect realizations of Einstein crystals. We calculate analytically the complete phonon spectrum for the whole class of models as well as the Helmholtz free energy of the systems. On the basis of the latter, we demonstrate that the aforementioned isostructural phase transitions must terminate at an infinity of critical points at low temperatures, brought about by the anharmonic contributions in the Hamiltonian and the hopping events in the crystals.