Surface acoustic waves in layer – substrate structures of arbitrary anisotropy

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The existence of surface acoustic waves in a semi-infinite substrate with a solid layer is theoretically investigated. The substrate and the layer are not piezoelectrics, but can belong to any class of crystallographic symmetry. By presenting the dispersion equation as a condition on the substrate and layer impedance matrices, it is possible to determine, using the properties of impedances, the maximum allowable number of surface waves depending on the type of contact and the ratio between the velocities of the bulk waves in the substrate and the layer materials. In addition, a dispersion equation is derived for the symmetrical orientation of an orthorhombic substrate with a deposited monoatomic layer and the possibility of a purely flexure surface acoustic wave in the case of a very hard surface layer, for example, a monolayer of graphene on a soft polymer substrate, is shown.

Full Text

Restricted Access

About the authors

A. N. Darinskii

National Research Center “Kurchatov Institute”

Author for correspondence.
Email: Alexandre_Dar@mail.ru

Shubnikov Institute of Crystallography of the Kurchatov Complex Crystallography and Photonics

Russian Federation, Moscow

Yu. A. Kosevich

Semenov Federal Research Center for Chemical Physics of the Russian Academy of Sciences; Plekhanov Russian University of Economics

Email: yukosevich@gmail.com
Russian Federation, Moscow; Moscow

References

  1. Бреховских Л.М., Годин О.А. Акустика слоистых сред. М.: Наука, 1989. 411 с.
  2. Novoselov K.S., Jiang D., Schedin F., Geim A.K. // Proc. Natl. Acad. Sci. USA. 2005. V. 102. P. 10451. https://doi.org/10.1073/pnas.0502848102
  3. Geim A.K., Novoselov K.S. // Nat. Mater. 2007. V. 6. P. 183. https://doi.org/10.1038/nmat1849
  4. Buravets V., Hosek F., Burtsev V. et al. // Inorg. Chem. 2024. V. 63. P. 8215. https://doi.org/10.1021/acs.inorgchem.4c00475
  5. Booth T.J., Blake P., Nair R. et al. // Nano Lett. 2008. V. 8. P. 2442. https://doi.org/10.1021/nl801412y
  6. Ye Ch., Peng Q. // Crystals. 2023. V. 13. P. 12. https://doi.org/10.3390/cryst13010012
  7. https://en.wikipedia.org/wiki/Transition_metal_dichalcogenide_monolayers
  8. Lee C., Wei X., Kysar J.W., Hone J. // Science. 2008. V. 321. P. 385. https://doi.org/10.1126/science.1157996
  9. Akinwande D., Brennan Ch., Bunch J. et al. // Extreme Mech. Lett. 2017. V. 13. P. 42. https://doi.org/10.1016/j.eml.2017.01.008
  10. Roldán R., Chirolli L., Prada E. et al. // Chem. Soc. Rev. 2017. V. 46. P. 4387. https://doi.org/10.1039/C7CS00210F
  11. Андреев А.Ф., Косевич Ю.А. // ЖЭТФ. 1981. Т. 81. С. 1435. http://jetp.ras.ru/cgi-bin/dn/e_054_04_0761.pdf
  12. Косевич Ю.А., Сыркин Е.С. // ЖЭТФ. 1985. Т. 89. С. 2221. http://www.jetp.ras.ru/cgi-bin/dn/e_062_06_1282.pdf
  13. Kosevich Yu.A., Syrkin E.S. // Phys. Lett. A. 1987. V. 122. P. 178. https://doi.org/10.1016/0375-9601(87)90801-2
  14. Косевич Ю.А., Сыркин Е.С. // Кристаллография. 1988. Т. 33. С. 1339.
  15. Kosevich Yu.A., Syrkin E.S. // Phys. Lett. A. 1989. V. 135. P. 298. https://doi.org/10.1016/0375-9601(89)90118-7
  16. Kosevich Yu.A., Syrkin E.S. // Low Temp. Phys. 1994. V. 20. P. 517. https://doi.org/10.1063/10.0033673
  17. Kosevich Yu.A. // Prog. Surf. Sci. 1997. V. 55. P. 1. https://doi.org/10.1016/S0079-6816(97)00018-X
  18. Kosevich Yu.A., Kistanov A.A., Strelnikov I.A. // Lett. Mater. 2018. V. 8. P. 278. https://doi.org/10.22226/2410-3535-2018-3-278-281
  19. Kosevich Yu.A. // Phys. Rev. B. 2022. V. 105. P. L121408. https://doi.org/10.1103/PhysRevB.105.L121408
  20. Лехницкий С.Г. Анизотропные пластинки. М.: Наука, 1957. 463 с.
  21. Ландау Л.Д., Лифшиц Е.М., Косевич А.М., Питаевский Л.П. Теоретическая физика. Теория упругости. 4-е изд., испр. М.: Наука, 1987. 248 с.
  22. Androulidakis Ch., Koukaras E., Frank O. et al. // Sci. Rep. 2014. V. 4. P. 5271. https://doi.org/10.1038/srep05271
  23. Ingebrigtsen K.A., Tonning A. // Phys. Rev. 1969. V. 184. P. 942. https://doi.org/10.1103/PhysRev.184.942
  24. Lothe J., Barnett D.M. // J. Appl. Phys. 1976. V. 47. P. 428. https://doi.org/10.1063/1.322665
  25. Lothe J., Barnett D.M. // J. Appl. Phys. 1976. V. 47. P. 1799. https://doi.org/10.1063/1.322895
  26. Lothe J., Barnett D.M. // Phys. Norvegica. 1977. V. 8. P. 239.
  27. Lothe J., Barnett D.M. // Proc. R. Soc. Lond. A. 1985. V. 402. P. 135. https://doi.org/10.1098/rspa.1985.0111
  28. Barnett D.M., Lothe J., Gavazza S.D., Musgrave M.J.P. // Proc. R. Soc. Lond. A. 1985. V. 402. № 1822. https://doi.org/10.1098/rspa.1985.0112
  29. Peach R.C. // IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2001. V. 48. P. 1308. https://doi.org/10.1109/58.949740
  30. Barnett D.M., Gavazza S.D., Lothe J. // Proc. R. Soc. London. A. 1988. V. 415. P. 389. https://doi.org/10.1098/rspa.1988.0020
  31. Abbudi M., Barnett D.M. // Proc. R. Soc. London. A. 1990. V. 429. P. 587. https://doi.org/10.1098/rspa.1990.0075
  32. Alshits V.I., Darinskii A.N., Lothe J. // Wave Motion. 1992. V. 16. P. 265. https://doi.org/10.1016/0165-2125(92)90033-X
  33. Alshits V.I., Barnett D.M., Darinskii A.N., Lothe J. // Wave Motion. 1994. V. 20. P. 233. https://doi.org/10.1016/0165-2125(94)90049-3
  34. Darinskii A.N., Shuvalov A.L. // Phys. Rev. B. 2018. V. 98. P. 024309. https://doi.org/10.1103/PhysRevB.98.024309
  35. Darinskii A.N., Shuvalov A.L. // Phys. Rev. B. 2019. V. 99. P. 174305. https://doi.org/10.1103/PhysRevB.99.174305
  36. Darinskii A.N., Shuvalov A.L. // Phys. Rev. B. 2019. V. 100. P. 184303. https://doi.org/10.1103/PhysRevB.100.184303
  37. Darinskii A.N., Shuvalov A.L. // Proc. R. Soc. A. 2019. V. 475. P. 20190371. https://doi.org/10.1098/rspa.2019.0371
  38. Darinskii A.N., Shuvalov A.L. // Ultrasonics. 2021. V. 109. P. 106237. https://doi.org/10.1016/j.ultras.2020.106237
  39. Бирюков С.В., Гуляев Ю.В., Крылов В.В., Плесский В.П. Поверхностные акустические волны в неоднородных средах. М.: Наука, 1991. 414 с.
  40. Stroh A.N. // Philos. Mag. 1958. V. 41. P. 625. https://doi.org/10.1080/14786435808565804
  41. Anderson P.M., Hirth J.P., Lothe J. Theory of Dislocations. 3rd ed. Cambridge: Cambridge University Press, 2017. 699 p.
  42. Elastic strain fields and dislocation mobility / Eds. Indenbom V.L., Lothe J. Amsterdam: North-Holland, 1992. 778 p.
  43. Ting T.C.T. Anisotropic Elasticity: Theory and Applications. New York: Oxford University Press, 1996. 592 р.
  44. Chadwick P., Smith G.D. // Adv. Appl. Mech. 1977. V. 17. P. 303. https://doi.org/10.1016/S0065-2156(08)70223-0
  45. Tanuma K. // J. Elasticity. 2007. V. 89. P. 5. https://doi.org/10.1007/s10659-007-9117-1
  46. Shuvalov A.L. // Proc. R. Soc. London. A. 2000. V. 456. P. 2197. https://doi.org/10.1098/rspa.2000.0609
  47. Hwu Ch. Anisotropic Elastic Plates. New York: Springer, 2010. 673 p.
  48. Rokhlin S.I., Chimenti D.E., Nagy P.B. Physical Ultrasonics of Composites. Oxford: Oxford University Press, Inc. 2011. 378 p.
  49. Альшиц В.И., Любимов В.Н., Шувалов А.Л. // ЖЭТФ. 1994. Т. 106. С. 828.
  50. Shuvalov A.L., Every A.G. // Wave Motion. 2002. V. 36. P. 257. https://doi.org/10.1016/S0165-2125(02)00013-6
  51. Shuvalov A.L., Every A.G. // Ultrasonics. 2002. V. 40. P. 939. https://doi.org/10.1016/S0041-624X(02)00235-4
  52. Politano A., Chiarello G. // Nano Res. 2015. V. 8. P. 1847. https://doi.org/10.1007/s12274-014-0691-9

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Appendix
Download (162KB)
Indexing metadata
3. Fig. 1. Slowness curve sx,z = kx,z/ω of the slowest body wave in the sagittal plane XZ. The dotted line is the tangent to the slowness curve. The body wave at vlim = min(sx–1) is the limiting body wave for the direction m (|m| = 1). The vector sph indicates the direction of its phase velocity, and the vector gxz is the projection of the group velocity of the limiting body wave onto the plane XZ. There are no body waves in the interval sx > vlim–1. The unit vector n is the normal to the surface of the medium.

Download (45KB)
Indexing metadata
4. Fig. 2. Three variants (a), (b) and (c) of the dependence of the eigenvalues λ1,2,3 on the velocity v. SAWs exist at v = vsaw.

Download (95KB)
Indexing metadata

Copyright (c) 2025 Russian Academy of Sciences