Anharmonic motion and aspherical nuclear probability density functions in cesium halides

Abstract

The cesium halides ($\mathrm{Cs}X$) are ionic high-symmetry compounds, which at first would seem like well-understood systems. However, recent studies have shown that using the simple Perdew-Burke-Ernzerhof (PBE) functional in density-functional theory (DFT) calculations, $\mathrm{Cs}X$ materials do not adopt their namesake structure. Furthermore, peculiar low thermal conductivities have been observed experimentally in both CsCl and CsI at room temperature, and the origin has been linked to low-temperature anharmonicity derived from different types of experiments. In the case of CsCl the anharmonicity was observed from x-ray diffraction as an octahedral nuclear probability density function (nPDF), which, in contrast to expectations, becomes spherical at elevated temperature. Here, we study the nPDF of CsBr and CsI from single-crystal x-ray diffraction to compare with the findings of CsCl. It is shown that the aspherical features become less pronounced when substituting for a heavier halide. From periodic DFT calculations on CsCl, CsBr, and CsI probing the potential-energy surfaces this can be explained by progressively more similar masses upon substitution linked with Pauli repulsion. The apparent disappearance of the anharmonic features in CsCl with increasing temperatures can be understood as relatively larger population of acoustic phonons compared to the optical phonons following the Bose-Einstein distribution function. Finally, it is shown that theory can reproduce the correct equilibrium structures as well as phonon dispersions comparable to experimental values when adding a functional form of van der Waals interactions to a PBE DFT calculation.