Poisson´s ratios of technological materials

Poisson´s ratio (PR), the relation between lateral contraction of an elastic rod when subjected to a longitudinal extension, has a long and interesting history. For isotropic bodies, it can theoretically range from +frac12 to -1; the experimental gamut for anisotropic materials is even larger. For the vast majority of materials the PR is positive for all combinations of directions. But as far back as the 1800s, Voigt and others found that for some materials negative values were encountered. Negative PR (nPR) values remained for many years merely a curiosity, but more recently some of the interesting technological consequences have come to be recognized. Some of the counterintuitive acoustic possibilities of nPRs are analogous, in a certain fashion, to those arising with negative refraction electromagnetic materials. Even when a material does not have nPR properties, if it is piezoelectric, then the PR can be altered, sometimes by appreciable amounts, by changing the electrical boundary conditions. We review Poisson´s ratio in crystals, describing technologically important materials that have small, or negative PRs. Potential applications of the nPR property are also mentioned.