Directions with negative Poisson’s ratio in crystals

Abstract

Materials with negative Poisson’s ratio are peculiar in that they expand laterally when stretched. The Poisson’s ratio is the ratio of lateral strain in the direction n to the longitudinal strain during the stretching of a cylindrical rod along rod axis m. In the paper the stereographic projections of Poisson’s ratio for a set of acoustic crystals, metals, alloys, binary compounds, and for the elements of periodic system were computed. From these stereographic projections the cuts with extreme values of Poisson’s ratio were determined. Elastic modules of crystals from the manual [Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Group III, Vol.18, Berlin (1984)] were applied in calculations. Our evaluations have shown that for most fcc crystals the Poisson’s ratio receives negative values for directions of a stretch vector m located inside a cone with an axis [110], relevant to the Euler angles (45,0,90). The parameters of cone were spotted for a set of crystals. For beta cristobalite SiO2 a decrease of rod cross-section under the uniaxial compression was revealed for the directions of vector m oblique to [111]. Elastic modules of SiO2 have been taken from Kimizuka et al., Phys. Rev. Lett. 84, 5548–5551 (2000)]. Some possible applications of materials with a negative Poisson’s ratio basing on their unusual acoustic properties are discussed. For the elements of periodic system the results of calculations will also be submitted on the Web-site: www.akin.ru as the color table.