Absence of diagonal force constants in cubic Coulomb crystals
Abstract
The quasiharmonic model proposes that a crystal can be modelled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss's law shows that the ionion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modelled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tightbinding and density nearlyfree electron models. For the bare ionic model, we demonstrate the zero elements in the force constants matrix and explain this phenomenon as a natural consequence of Poisson's law. In the density tightbinding model, we confirm that the inclusion of localized electrons stabilizes all major crystal structures at harmonic order and we construct a phase diagram of preferred structures with respect to core and valence electron radii. In the density nearlyfree electron model, we verify that the inclusion of delocalized electrons, in the form of a background jellium, is enough to counterbalance the diagonal force constants matrix from the ionion potential in all cases and we show that a firstorder perturbation to the jellium does not have a destabilizing effect. We discuss our results in connection to Wigner crystals in condensed matter, Yukawa crystals in plasma physics, as well as the elemental solids.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 December 2020
 DOI:
 10.1098/rspa.2020.0518
 arXiv:
 arXiv:2007.00476
 Bibcode:
 2020RSPSA.47600518A
 Keywords:

 Condensed Matter  Materials Science;
 Condensed Matter  Other Condensed Matter
 EPrint:
 10+12 pages, 6+7 figures