Anomalous elastic behavior in crystalline silica

Abstract

A low-density polymorph of silica, \ensuremath{\alpha}-cristobalite, has been observed to have a negative Poisson ratio, i.e., when subjected to a uniaxial compression, this crystal contracts in the transverse direction. This behavior is uncommon. Other low-density polymorphs of silica, which have a similar chemical environment, have been reported to have positive Poisson ratios. We have investigated the elastic behavior of several silica phases: \ensuremath{\alpha}-quartz, \ensuremath{\beta}-quartz, and \ensuremath{\alpha}-cristobalite, with first-principles quantum-mechanical calculations, and with interatomic potentials. Our calculations confirm a negative Poisson ratio in \ensuremath{\alpha}-cristobalite. We predict that \ensuremath{\alpha}-quartz will have a negative Poisson ratio at high tensile strains, and that \ensuremath{\beta}-quartz will never assume a negative ratio. We compute the second-order elastic constants of \ensuremath{\alpha}-quartz and \ensuremath{\alpha}-cristobalite using interatomic potentials and apply them in discussing the anisotropy of Poisson ratios in these materials. We demonstrate that the rigidity of the ${\mathrm{SiO}}_{4}$ tetrahedral units is intimately related to the occurrence of negative Poisson ratios in crystalline forms of silica.