Thermodynamic and mechanical stability of many‐body systems interacting with coarse‐grained bounded potentials

Abstract

AbstractWe discuss the stability criteria of Fisher and Ruelle [J. Math. Phys. 7, 260 (1966)] which can be used to establish if a given pair potential satisfies the requirements for thermodynamic stability. The mechanical and thermodynamic stability are considered for systems composed of particles interacting with a bounded potential, which could be used to model a mesostructured material at a coarse‐grained level. The elastic moduli of fcc and bcc solids at zero temperature are calculated as a function of density for an assembly of particles interacting via the following (at r = 0 bounded potentials: (a) a Gaussian Core Model, GCM, potential, φ (r) = exp (–r2), and (b) the separation‐shifted Lennard–Jones, SSLJ, bounded potential, φ (r) = 4[1/α2 + r2)6 – 1/(α2 + r2)3], with α > 0, where in both cases the characteristic energy and lengthscale are set to unity, and r is the separation between the particles. For both potential forms, at low densities, the static fcc structure is the thermodynamically stable structural form but from above a certain density the bcc lattice becomes the stable structure. It is shown that for the SSLJ potential this transition density varies roughly as ∼α–3. In the T → 0 limit, auxetic behaviour is demonstrated to occur for both fcc and bcc structures, but at high pressure and for the bcc structural form its response to external strain can be entirely nonauxetic. A significant role of the attractive part of the interparticle interaction in enhancing auxetic behaviour is observed. The ranges of the mechanical stability are determined for both systems. At zero temperature, the lattice becomes mechanically unstable for α > αc, which appears to coincide with the value αc = (7/32)1/6 = 0.7762 proved previously to lead to thermodynamically unstable fluid states for this potential. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)