Auxetics among 6-constant tetragonal crystals

Analytical and numerical features of the elastic properties of the stretched rectilinearly anisotropic 6-constant tetragonal crystals are considered. Analytical formulas for Young's modulus and Poisson's ratio are obtained. They are expressed in terms of the elastic compliance coefficients in Voight notation and the parameters of crystal orientation. Numerical calculations are performed using these formulas and data on the elastic constants from the Landolt-Bornstein Handbook. Possible types of Young's modulus and Poisson's ratio are analyzed. More than eighty tetragonal crystals were studied. About 60% of them are characterized by negative Poisson's ratio for certain particular orientations of the crystals. Such auxetics are listed in the Tables. Ten crystals can have Poisson's ratio greater than unity, and Poisson's ratio for six crystals is less than -0.5. The same six crystals are characterized by high variability of Young's modulus. Young's modulus for more than ten crystals exceeds 300 GPa.