Variability of Poisson's ratio forhexagonal crystals underpressure

Аuthors

Gol'dshtein R. V.^*, Gorodtsov V. A.^**, Lisovenko D. S.^***

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101-1, prospekt Vernadskogo, Moscow, 119526, Russia

*e-mail: goldst@ipmnet.ru
**e-mail: gorod@ipmnet.ru
***e-mail: lisovenk@ipmnet.ru

Abstract

In the paper variability of Poisson's ratio for the different hexagonal crystals under hydrostatic pressure is analyzed theoretically. As a result, all extreme values of Poisson's ratio are determined analytically. Special attention is paid materials with negative Poisson's ratio. Seven hexagonal auxetics at zero pressure (crystals with a negative Poisson's ratio) MoS₂, Zn, Be, BeCu alloy (2.4% at.Cu), TiB2, C₇H₁₂, MnAs are identified. Variability of Poisson's ratio is analyzed for these crystals at zero pressure and two nonauxetics at zero pressure (graphite and SiC). Numerical values for all еxtrema of Poisson's ratios were obtained. Auxetic surfaces (the surface of the zero Poisson's ratio) were plotted for all auxetic hexagonal crystals and two nonauxetics (graphite and SiC) depending on the crystal orientation and the hydrostatic pressure. It is shown that the seven hexagonal partial auxetics MoS₂, Zn, Be, BeCu alloy (2.4% at.Cu), TiB₂, C₇H₁₂, MnAs can become complete auxetics under certain pressures. Partial auxetics are crystals whose Poisson`s ratio can change the sign with the change of orientation, while complete auxetics are crystals, in which Poisson's ratio is always negative regardless of orientation. Analysis of the pressure influence on Poisson`s ratio shows that crystals MoS₂, TiB₂ and MnAs are auxetics in the whole range of pressure values at which the crystal is stable. Auxetics Be, BeCu alloy, C₇H₁₂ and Zn have one nonauxetic zone in a range of pressure variation. The crystals of graphite and SiC, which are nonauxetics at zero pressure, also become partial or complete auxetics at some negative pressure (at isotropic stretching). As a result, numerical and analytical analysis shows that all hexagonal crystals may be partial and complete auxetics depending on the values of hydrostatic pressure. It has been found that Poisson ratio corresponding stretching in the [010] direction and the transverse deformation in the  direction, approaches -1 if the negative pressure tends to the limit of stability of MoS₂, Zn, Be, BeCu alloy (2.4% at.Cu), TiB₂, C₇H₁₂, MnAs, graphite and SiC crystal.

Keywords:

hexagonal crystals, auxetics, pressure, elastic properties

References

1. Born M. On the stability of crystal lattices. Mathematical Proceedings of the Cambridge Philosophical Society, 1940, vol. 36, no. 2, pp.160-172.

2. Born M., Huang K. Dynamical theory of crystal lattices. Clarendon, London — New York: Oxford University Press. 1954. 420p.

3. Huang K. On the atomic theory of elasticity. Proceedings of the Royal Society A, 1950, vol. 203, no. 1073, pp.178-194.

4. Leibfried G., Ludwig W. Theory of anharmonic effects in crystals. Solid State Physics, 1961, vol. 12, pp.275-444.

5. Barron T.H.K., Klein M.L. Second-order elastic constants of a solid under stress. Proceedings of the Physical Society, 1965, vol. 85, no. 3, pp.523-532.

6. Wallace D.C. Thermodynamics of crystals. New York: Wiley. 1972. 485p.

7. Vekilov Yu.Kh., Krasil’nikov O.M. Uspekhi fizicheskikh nauk, 2009, vol.179, no. 8. pp. 883–886.

8. Krasil’nikov O.M., Vekilov Yu.Kh., Mosyagin I.Yu. Zhurnal eksperimental’noi i teoreticheskoi fiziki, 2012, vol. 142. pp. 266-270.

9. Vekilov Yu.Kh., Krasil’nikov O.M., Belov M.P., Lugovskoi A.V. Uspekhi fizicheskikh nauk, 2014, vol.184, no. 9. pp. 967–973.

10. Vekilov Yu.Kh., Krasil’nikov O.M., Lugovskoi A.V. Uspekhi fizicheskikh nauk, 2015, vol. 185, no. 11, pp. 1215–1224.

11. Wojciechowski K.W. Negative Poisson ratios at negative pressures. Molecular Physics Reports, 1995, vol. 10, pp.129-136.

12. Branka A.C., Heyes D.M., Wojciechowski K.W. Auxeticity of cubic materials under pressure. Physica Status Solodi B, 2011, vol. 248, no. 1, pp.96-104.

13. Grima J.N., Cassar R.N., Gatt R. On the effect of hydrostatic pressure on the auxetic character of NAT-type silicates. Journal of Non-Crystalline Solids, 2009, vol.355, no. 24-27, pp.1307-1312.

14. Grima J.N., Gatt R. On the behaviour of natrolite under hydrostatic pressure // Journal of Non-Crystalline Solids, 2010, vol. 356, no. 37-40, pp.1881-1887.

15. Landolt-Börstein — Group III Condensed Matter. Berlin: Springer. 1992. vol. 29a. pp.105-128.

16. Sirotin Yu.I., Shaskol’skaya M.P. Osnovy kristallofiziki (Fundamentals of Crystal Physics), Moscow, Mir, 1982, 654 p.

17. Nye J.F. Fizicheskie svoistva kristallov (Physical properties of crystals), Moscow, Izd-vo IL, 1967, 386 p.

Download