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

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.

arXiv comment10 pages, 5 figures

References in corpus (11)

• Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory
• Stacking Entropy of Hard Sphere Crystals
• $C_6$ coefficients and dipole polarizabilities for all atoms and many ions in rows 1-6 of the periodic table
• Phase diagram of softly repulsive systems: The Gaussian and inverse-power-law potentials
• Lattice distortion and atomic displacements during the fcc/bcc martensitic transformation
• The Lennard Jones Potential Revisited -- Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices
• The instability of Alexander-McTague crystals and its implication for nucleation
• From Sticky-Hard-Sphere to Lennard-Jones-Type Clusters
• Mechanism of the fcc-hcp Phase Transformation in Solid Ar
• Collisional properties of trapped cold chromium atoms
• Theory of dynamical stability for two- and three-dimensional Lennard-Jones crystals