Deformation mechanisms leading to auxetic behaviour in the α-cristobalite and α-quartz structures of both silica and germania

Analytical expressions have been developed in which the elastic behaviour of the α-quartz and α-cristobalite molecular tetrahedral frameworks of both silica and germania are modelled by rotation, or dilation or concurrent rotation and dilation of the tetrahedra. Rotation and dilation of the tetrahedra both produce negative Poisson’s ratios (auxetic behaviour), whereas both positive and negative values are possible when these mechanisms act concurrently. Concurrent rotation and dilation of the tetrahedra reproduces with remarkable accuracy both the positive and negative nu31 Poisson’s ratios observed in silica α-quartz and α-cristobalite, respectively, when loaded in the x3 direction. A parametric fit of the concurrent model to the germania α-quartz experimental nu31 Poisson’s ratio is used to predict nu31 for germania α-cristobalite, for which no experimental value exists. This is predicted to be +0.007. Strain-dependent nu31 trends, due to concurrent rotation and dilation in the silica structures, are in broad agreement with those predicted from pair-potential calculations, although significant differences do occur in the absolute values. Concurrent dilation and rotation of the tetrahedra predicts that an alternative uniaxial stress (sigma3)-induced phase exists for both silica α-quartz and α-cristobalite and germania α-cristobalite, having geometries in reasonable agreement with beta-quartz and idealised beta-cristobalite, respectively.