Auxetics among 6-constant tetragonal crystals

R. Goldstein1, V. Gorodtsov1, D. Lisovenko1, M. Volkov1
1A.Yu. Ishlinsky Institute for Problems in Mechanics RAS, prospect Vernadskogo 101, b1, Moscow, 119526
Abstract
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-Börnstein 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. The ten crystals may have Poisson's ratio greater than unity, and Poisson's ratio for the 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.
Received: 19 March 2015   Revised: 02 April 2015   Accepted: 03 April 2015
Views: 95   Downloads: 39
References
1.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko.Physica status solidi (b), 250 (10), 2038 (2013). DOI: 10.1002 / pssb.201384233.
2.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko, M. A. Volkov. Physical Mesomechanics, 17 (2), 97 (2014). DOI: 10.1134 / S1029959914020027.
3.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko. PhysicalMesomechanics, 18, (2015).
4.
R. H. Baughman, J. M. Shacklette, A. A. Zakhidov, S. Stafström. Nature, 392, 362 (1998). DOI: 10.1038 / 32842.
5.
A. C. Branka, D. M. Heyes, K. W. Wojciechowski. Physica status solidi (b), 246 (9), 2063 (2009). DOI: 10.1002 / pssb.200982037.
6.
K. W. Wojciechowski. Comput. methods sci. technology,11 (1), 73 (2005). DOI: 10.12921 / cmst.2005.11.01.73 – 79
7.
A. Norris. Proceedings of the Royal Society ofN. London A. 462, 3385 (2006).
8.
V. N. Belomestnykh, E. G. Soboleva. Letters on Materials, 1 (2), 84 (2011). (in Russian).
9.
Landolt-Börnstein. Group III: Crystal and Solid State Physics. Vol.29a. (Berlin. Springer, 1992).