Discovering the mechanisms that form the auxetic properties of single crystals in a monoclinic crystal system
DOI:
https://doi.org/10.15587/1729-4061.2020.215167Keywords:
axial, non-axial auxeticity, Poisson coefficient, elasticity modules, pointing auxeticity surfacesAbstract
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 constructedReferences
- Konek, D. A., Voytsehovski, K. V., Pleskachevskiy, Yu. M., Shil'ko, S. V. (2004). Materialy s otritsatel'nym koeffitsientom Puassona (obzor). Mehanika kompozitnyh materialov i konstruktsiy, 10 (1), 35–69.
- Turley, J., Sines, G. (1971). The anisotropy of Young’s modulus, shear modulus and Poisson’s ratio in cubic materials. Journal of Physics D: Applied Physics, 4 (2), 264–271. doi: https://doi.org/10.1088/0022-3727/4/2/312
- Goldstein, R. V., Gorodtsov, V. A., Lisovenko, D. S. (2010). Auxetic mechanics of crystalline materials. Mechanics of Solids, 45 (4), 529–545. doi: https://doi.org/10.3103/s0025654410040047
- Goldstein, R. V., Gorodtsov, V. A., Lisovenko, D. S. (2011). Young’s modulus of cubic auxetics. Letters on Materials, 1 (3), 127–132. doi: https://doi.org/10.22226/2410-3535-2011-3-127-132
- Belomestnykh, V. N., Soboleva, E. G. (2011). Lateral strain ratios for cubic ionic crystals. Letters on Materials, 1 (2), 84–87. doi: https://doi.org/10.22226/2410-3535-2011-2-84-87
- Raranskyi, M. D., Balaziuk, V. N., Kovaliuk, Z. D. (2012). Pruzhni vlastyvosti ta dynamika krystalichnoi gratky deiakykh napivprovidnykovykh monokrystaliv. Chernivtsi: Zoloti lytavry, 200.
- Raransky, M. D., Balazyuk, V. N., Melnyk, M. I., Gunko, M. M., Verebchan, Ya. S. (2014). The Peculiarities of Young's Modulus Surfaces of Cubic Single Crystals Formation. Physics and chemistry of solid state, 15 (4), 721–727.
- Harrison, U. (1983). Elektronnaya struktura i svoystva tverdyh tel. Moscow: Mir, 381.
- Raranskyi, M., Balaziuk, V., Hunko, M. (2016). Yavyshche auksetychnosti v tverdykh tilakh. Chernivtsi: «Druk Art», 178.
- Lisovenko, D. S., Gorodtsov, V. A. (2011). Cubic crystals with negative Poisson's ratio (cubic auxetics). Vestnik Nizhegorodskogo universiteta im. N. I. Lobachevskogo, 4 (2), 488–489.
- Goldstein, R. V., Gorodtsov, V. A., Lisovenko, D. S. (2014). Young's modulus and Poisson's ratio for seven-constant tetragonal crystals and their nano/microtubes. Fizicheskaya mezomehanika, 17 (5), 5–14. doi: http://doi.org/10.24411/1683-805X-2014-00015
- Raransky, M. D., Balazyuk, V. N., Gunko, M. M. (2016). Criteria and Mechanisms of Appearance of Auxeticity in Cubic Syngony Crystals. Metallofizika i noveishie tekhnologii, 37 (3), 379–396. doi: https://doi.org/10.15407/mfint.37.03.0379
- Raransky, M. D., Balazyuk, V. N., Gunko, M. M. (2015). Auxeticity Properties of Hexagonal Syngony Crystals. Physics and chemistry of solidstate, 16 (1), 34–43. doi: https://doi.org/10.15330/pcss.16.1.34-43
- Raransky, M. D., Tretiak, C. R., Gunko, M. M., Balazyuk, V. N. (2016). The Impact of d– and f–compression on Anisotropy of Elastic Properties of Single Crystals with Hexagonal Close Packing of Lattice. Physics and chemistry of solidstate, 17 (2), 170–179. doi: https://doi.org/10.15330/pcss.17.2.170-179
- Raransky, M. D., Balazuyk, V. N., Gunko, M. M. (2015). Abnormal deformation properties of some single crystals of tetragonal syngony. Uzhhorod University Scientific Herald. Series Physics, 37, 8–19. doi: https://doi.org/10.24144/2415-8038.2015.37.8-19
- Landolt-Börnstein. Numerical Data and Functional Relationships in Science and Technology. Group III: Crystal and Solid state Physics. Second and Higher Order Constants (1992). Berlin: Springer, 682.
- Sirotin, Yu. I., Shaskol'skaya, M. P. (1975). Osnovy kristallofiziki. Moscow: Nauka, 680.
- Ledd, M., Palmer, R. (Eds.) (1983). Pryamye metody v rentgenovskoy kristallografii. Moscow: Mir, 416.
- Landau, L. D., Lifshits, E. M. (1968). Teoriya uprugosti. Moscow: Nauka, 209.
- Hearmon, R. F. S. (1956). The elastic constants of anisotropic materials – II. Advances in Physics, 5 (19), 323–382. doi: https://doi.org/10.1080/00018732.1956.tadp0323
- Kitaygorodskiy, A. I. (1971). Molekulyarnye kristally. Moscow: Nauka, 424.
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