Extreme Poisson's ratios and related elastic crystal properties

With the aim of understanding anisotropic crystals that possess a negative Poisson's ratio and to lay a foundation for investigating molecular mechanisms, we discuss the definition of the ratio and establish conditions on the compliance that govern its sign. We derive results on orientation averaging that are useful in the context of anisotropy and helpful in the investigation of isotropic polycrystals. We discuss αα-cristobalite, a polymorph of silicon dioxide that possesses interesting negative ratio properties in single crystals and hypothetical polycrystals. In this connection, we draw attention to the transverse compliance as an alternative and simpler metric for gaging the ratio and for orientation averaging. For αα-cristobalite, we arrive at new results for the directions that yield the most negative Poisson's ratio. This result should be of value in divining the underlying molecular mechanism that explains the negative values of Poisson's ratio in αα-cristobalite, a crystal of tetragonal symmetry that possesses six independent elastic constants.