Instability of the Body-Centered Cubic Lattice within the Sticky Hard Sphere and Lennard-Jones Model obtained from Exact Lattice Summations

TL;DR

This study analytically examines the stability of the body-centered cubic lattice under Lennard-Jones and sticky hard sphere models, revealing its inherent instability and suggesting higher-order forces influence low-temperature bcc phases.

Contribution

It provides exact lattice sum expressions for cohesive energy and demonstrates bcc phase instability across various potentials, highlighting the role of many-body forces.

Findings

bcc phase is unstable or metastable under LJ and SHS models

Exact lattice sums are derived for cohesive energy calculations

Higher than two-body interactions likely cause low-temperature bcc phases

Abstract

A smooth path of rearrangement from the body-centered cubic (bcc) to the face-centered cubic (fcc) lattice is obtained by introducing a single parameter to cuboidal lattice vectors. As a result, we obtain analytical expressions in terms of lattice sums for the cohesive energy. This is described by a Lennard-Jones (LJ) interaction potential and the sticky hard sphere (SHS) model with an $r^{-n}$ long-range attractive term. These lattice sums are evaluated to computer precision by expansions in terms of a fast converging series of Bessel functions. Applying the whole range of lattice parameters for the SHS and LJ potentials demonstrates that the bcc phase is unstable (or at best metastable) toward distortion into the fcc phase. Even if more accurate potentials are used, such as the extended LJ potential for argon or chromium, the bcc phase remains unstable. This strongly indicates that the appearance of a low temperature bcc phase for several elements in the periodic table is due to higher than two-body forces in atomic interactions.