The role of particle softness in determining the value of Poisson's ratio for soft sphere solids

Abstract

The influence of particle softness on the Poisson's ratio of model solids has been investigated. We have used the repulsive inverse power potential (∼r − n for particle separations, r) between the particles, which is conveniently characterised by one adjustable parameter, ϵ = 1/n. For large ϵ, the interaction is soft whereas in the ϵ → 0 limit the particles approach hard spheres. The pressure and elastic constants of the solid phase have been calculated at various densities with constant temperature molecular dynamics (MD) simulation for a range of the softness parameter in the range, n>12. Density-softness surfaces of these quantities were determined which revealed hitherto unrecorded trends in the behaviour of the elastic moduli and Poisson's ratio. It was found that the pressure and some elastic properties, e.g. the C12 elastic constant and the bulk modulus, manifest a maximum value or ‘ridge’ on this surface. The height of the maximum increases with density and interaction steepness (small ϵ). The Poisson's ratio varies essentially linearly with softness and is relatively insensitive to density. However, at higher densities and for larger steepness a considerable lowering of the Poisson's ratio is observed. In order to identify possible mechanisms for reducing the value of Poisson's ratio, ν, the fluctuation and Born-Green contributions were analysed. Changes in the Poisson's ratio are mainly determined by the fluctuation contribution which can cause a considerable decrease as well as increase of its value.