Discovering the Mechanisms That Form the Auxetic Properties of Single Crystals in a Monoclinic Crystal System

Abstract

This paper reports the analysis of patterns and mechanisms that form the characteristic surfaces of the Young modulus, the angular distributions of Poisson coefficients, and the pointing surfaces of auxeticity of single crystals in cubic, hexagonal, tetragonal, and rhombic crystal system. The crystals have been detected that can reach the limit negative values predicted by the classical elasticity theory for isotropic environments. It was found that near the points of phase transition or melting temperatures, the pointing surfaces of auxeticity rapidly increase, thereby turning the crystals into absolute auxetics. It is shown that an array of negative Poisson coefficient values forms an image of the pointing surfaces of auxeticity. It is established that a reduction in the symmetry of crystals increases the number of crystallographic directions along which crystals gradually turn from "partial" to "mixed" or even "absolute" auxetics. An analysis of the anisotropy of elastic properties, characteristic surfaces of the Young modulus, and the pointing surfaces of auxeticity has revealed that most single crystals of the highest and middle category barely reach the minimum limit values of Poisson coefficients. Therefore, in order to obtain more reliable auxetic materials with high impact-energy and seismic-resistant characteristics, it is necessary to investigate the anisotropy of elastic properties of low-category single crystals. The characteristic surfaces of the Young modulus have been constructed. The volumetric images of the angular distributions of Poisson coefficients of the examined single crystals have been built, which make it possible to determine the absolute values and crystallographic orientation of the maximum and minimum values of Poisson coefficients. The pointing surfaces of the auxeticity of the studied single crystals have been constructed