For calculation and constructing the devices of nanoelectronics and nanophotonics, in which graphenes and graphenes-like 2D nanoallotropes of carbon, silicon and binary compounds of АВ type are used, the knowledge of elastic characteristics and depending on them piezoelectric, photo-elastic and other properties of 2D materials is significant. The method for determining isothermal values of the force constants, elastic rigidities, Young’s modulus and Poisson’s ratio for 2D nanoallotropes of the elements of IV group of the periodic table and binary compounds of АВ type, simple and convenient for engineering calculations, has been offered. The method is based on the modified by S.Yu. Davydov method, connecting the Harrison orbitals and R.Keating models the descriptions of elastic properties of such materials. It has been shown that the method allows to provide the estimated calculations for the elastic properties both, the well-known synthesized 2D crystal structures, as well as for the theoretically constructed structures. It has been shown that along with graphene, the monolayer hexagonal boron nitride and other binary compounds of АВ type in a form of 2D nanoallotropes of different symmetry, which, besides, are piezoelectric, can become very promising. It expands the range of possible practical applications of the studied materials (C, Si, BN, GaN, AlN, GaP) both with the graphene-like and more complex structure. The results of the work can be used when developing acoustoelectronic delay lines of terahertz frequency range, piezoelectric transduces for elastic waves excitation and receiving in the nanoscale 2D acoustic lines and piezoelectric sensors.

- Key words: force constants, elastic rigidities’ Young’modulus, Poisson’s ratio
- Published in: ectronics materials
- Bibliography link: Brazhe R.A., Dolgov D.A. Method of finding elastic characteristics of graphene and other 2D nanoallotropes. Proc. Univ. Electronics, 2020, vol. 25, no. 1, pp. 7–18. DOI: 10.24151/1561-5405-2020-25-1-7-18

Rudolf A. Brazhe

Ulyanovsk State Technical University, Ulyanovsk, Russia

Ulyanovsk State Technical University, Ulyanovsk, Russia

Dmitry A. Dolgov

Ulyanovsk State Technical University, Ulyanovsk, Russia

Ulyanovsk State Technical University, Ulyanovsk, Russia

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381 p. (in Russian).

25. Davydov S.Yu. On the elastic characteristics of graphene and silicone. Phys. Solid State, 2010, vol. 52, no.1, pp. 184–187.

26. Davydov S.Yu., On the force constants of grapheme. Phys. Solid State, 2010, vol. 52, no. 9,

pp. 1947–1951.

27. Davydov S.Yu. Contribution of π-bonds to effective charges, cohesive energy, and force constants of graphene-like compounds. Phys. Solid State, 2016, vol. 58, no. 2, pp. 402–412.

28. Keating P.N., Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys. Rev., 1986, vol. 145, pp. 637–645.

29. Brazhe R.A., Kochaev A.I., Nefedov V.S. Young’s modulus and the Poisson’s ratio of planar and nanotubular supracrystalline structures. Phys. Solid State, 2012, vol. 54, no. 7, pp. 1430–1432.

30. Le M.-Q., Prediction on Young’s modulus of hexagonal monolayer sheets based on molecular mechan-ics. Int. J. Mech. and Mat. in Design, 2015, no. 1, pp. 15–24.

31. Boldrin L., Scarpa F., Chowdhury R., Adhikari S. Effective mechanical properties of hexagonal boron nitride nanosheets. Nanotechnology, 2011, vol. 22, pp. 505702–505709.

2. Malyba P., Yamaguchi H., Eda G. et al. Graphene and mobile ions: The кey to all-plastic, solution-processed light-emitting devices. Am. Chem. Soc., 2010, vol. 4, no. 1-2, pp. 637–642.

3. Bunch J.S., Van Der Zande A.M., Verbridge S.S. et al. Electromechanical resonators from graphene sheets. Science, 2007, vol. 315, pp. 490–493.

4. Avaz S., Roy R.B., Mokkapati V.R.S.S. et al. Graphene based nanosensor for aqueous phase detection of nitroaromatics. RCS Adv., 2017, vol. 7, no. 7, pp. 25519–25527.

5. Neek-Amal M., Beheshtian J., Sadeghi A. et al. Boron nitride monolayer: A strain-turnable nanosensor. J.Phys. Chem. C, 2013, vol. 117(25), pp. 1361–1367.

6. Brazhe R.A., Kochaev A.I., Sovetkin A.A. Piezoelectric effect in graphene-like 2D supracrystalls with a periodic perforation breaking the central symmetry. Phys. Solid State, 2013, vol. 55, no. 9, pp. 1925–1928.

7. Brazhe R.A., Kochaev A.I., Meftakhutdinov R.M. Photoelastic properties of graphenes. Phys. Solid State, 2017, vol. 59, no. 2, pp. 334–337

8. Hartree D.R. The wave mechanics of an atom with a non-Сoulomb central field. Part I: Theory and methods. Proc. Cambridge Philos. Soc., 1928, vol. 24, pp. 89–110.

9. Fock V. Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Z. Phys., 1930, vol. 61, iss. 1-2, pp. 126–48.

10. Jones R.O. The density functional formalism, its applications and prospects. Rev. Mod. Phys., 1989, vol. 61, no. 3, pp. 689–746.

11. Staroverov V.N., Scuseria G.E. Optimization of density matrix functionals by the Hartree–Fock–Bogoliubov method. J. Chem. Phys., 2002, vol. 117, no. 24, pp. 1107–1112.

12. Kohn W. Nobel lecture: Electronic structure of matter – wave function and density functional. Rev. Mod. Phys., 1999, vol. 71, pp. 1253–1266.

13. Glukhova O.E., Kirillova I.V., Saliy I.N. et. al. Theoretical methods of nanostructures investigation. Vestnik Samarskogo universiteta. Estestvennonauchnaya seriya = Vestnik of Samara University. Natural Science Series, 2012, iss. 9(100), pp. 106–117. (in Russian).

14. Fedorov A.S., Sorokin P.B., Avramov P.V., Ovchinnikov S.G. Modeling of the properties, electron structure of series of carbon and not carbon nanoclusters and their interaction with easy elements. Novosibirsk, Siberian Branch of the Russian Academy of Science publishing house, 2006. Available at: http:\\www.kirensky.ru/masterparticles/monogr/Book/About.htm (accessed: 20.06.2019). (in Russian).

15. Lennard-Jones J.E. Wavefunction of many-electron atoms. Proc. Roy. Soc., 1924, vol. A106,

pp. 463–477.

16. Morse P.M. Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys.Rev., 1929, vol. 34, pp. 57–64.

17. Enyashin A.N., Ivanovskii, A.L. Graphene allotropes. Phys. Status Solidi (b), 2011, iss. 8,

pp. 1879–1883.

18. Belenkov E.A., Grexhnyakov V.A. Classification of structural modifications of carbon. Phys. Solid State, 2013, vol. 55, no. 8, pp. 1754–1764.

19. Kara A., Enriquez H., Seitsonen A.P. et al. A review on silicone – New candidate for electronics. Surf. Sсi. Rep., 2012, vol. 67, pp. 1–18.

20. Park J.-H., Park J.-C., Yun S.J. et al. Large-area monolayer hexagonal boron nitride on Pt foil. ACS

Nano, 2014, vol. 8, pp. 8520–8528.

21. Davydov S.Yu., Posrednik O.V. On the theory of elastic properties of two-dimensional hexagonal struc-tures. Phys. Solid State, 2015, vol. 57, no. 4, pp. 837–843.

22. Brazhe R.A., Karenin, A.A. Computer simulation of the supracrystals physical properties. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences, 2011, no. 2(18), pp. 105–112. (in Russian).

23. Brazhe R.A., Karenin A.A., Kochaev A.I., Meftakhutdinov R.M. Elastic characteristics of 2D supracrystals as compared to grapheme. Phys. Solid State, 2011, vol. 53, iss. 7, pp. 1481–1483.

24. Harisson W. Electron structure and properties of solids. Part 1. Moscow, Mir Publ., 1983, vol. 1.

381 p. (in Russian).

25. Davydov S.Yu. On the elastic characteristics of graphene and silicone. Phys. Solid State, 2010, vol. 52, no.1, pp. 184–187.

26. Davydov S.Yu., On the force constants of grapheme. Phys. Solid State, 2010, vol. 52, no. 9,

pp. 1947–1951.

27. Davydov S.Yu. Contribution of π-bonds to effective charges, cohesive energy, and force constants of graphene-like compounds. Phys. Solid State, 2016, vol. 58, no. 2, pp. 402–412.

28. Keating P.N., Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys. Rev., 1986, vol. 145, pp. 637–645.

29. Brazhe R.A., Kochaev A.I., Nefedov V.S. Young’s modulus and the Poisson’s ratio of planar and nanotubular supracrystalline structures. Phys. Solid State, 2012, vol. 54, no. 7, pp. 1430–1432.

30. Le M.-Q., Prediction on Young’s modulus of hexagonal monolayer sheets based on molecular mechan-ics. Int. J. Mech. and Mat. in Design, 2015, no. 1, pp. 15–24.

31. Boldrin L., Scarpa F., Chowdhury R., Adhikari S. Effective mechanical properties of hexagonal boron nitride nanosheets. Nanotechnology, 2011, vol. 22, pp. 505702–505709.

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