Models for the prediction of Poisson's ratio in the 'alpha-cristobalite' tetrahedral framework

Analytical model derivations for predictions of the on-axis Poisson’s ratios of the ‘alpha-cristobalite’ framework of corner-sharing tetrahedra are presented in full, for the first time, for a previously reported second tetrahedral rotation mechanism. Parametric analyses are performed for each of three concurrent models (two 2-mode models where dilation acts with each rotation mechanism (the CTM1 and CTM2 models), and the model where all three mechanisms operate (CTM3)) to explore the Poisson’s ratio dependency on the key model geometrical and deformation strength parameters. Predictions in good agreement with all experimental on-axis Poisson’s ratios specifically for silica alpha-cristobalite are possible for the new CTM3 model comprising two tetrahedral rotation mechanisms acting concurrently with tetrahedral dilation when direction-dependent strength parameters are employed. This is a significant improvement over the previous analytical model incorporating the tetrahedral dilation and first tetrahedral rotation mechanisms and which only achieved good agreement for loading along the longitudinal x3 axis.

Keywords : auxetic, negative Poisson’s ratio, alpha-cristobalite, silica, tetrahedral framework