Debye model for the surface phonons

A quantum description of the surface waves in an isotropic elastic body without the use of the semiclassical quantization is proposed. The problem about the surface waves is formulated in the Lagrangian and Hamiltonian representations. Within the framework of the generalized Debye model, the contribution of the surface phonons (“rayleighons”) to thermodynamic functions is calculated. It is emphasized that the role of the surface phonons can be significant and even decisive in low-dimensional systems, granular and porous media, and that their contribution to the total heat capacity increases with decreasing temperature.

Key words: Rayleigh surface waves, phonon, Debye model, entropy, heat capacity.

References

1. P. Debye, Ann. Phys. 39, 789 (1912). CrossRef Google Scholar

2. Y. M. Poluektov, East Eur. J. Phys. 5, 4 (2018) arXiv:2004.06658v1. CrossRef Google Scholar

3. J. Rayleigh, Proc. London Math. Soc. s1-17, 4 (1885). CrossRef Google Scholar

4. A. Maradudin, Defects and Vibrational Spectrum of Crystals (Mir, Moscow, 1968). Google Scholar

5. I. M. Khalatnikov, Theory of Superfluidity (Nauka, Moscow, 1971). Google Scholar

6. A. Maradudin, E. Montroll, and G. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation (Mir, Moscow, 1965). Google Scholar

7. A. M. Kosevich, Foundation of Crystal Lattice Mechanics (Nauka, Moscow, 1972). Google Scholar

8. Y. M. Poluektov, Fiz. Nizk. Temp. 41, 1081 (2015) [Low Temp. Phys. 41, 922 (2015)]. Google Scholar

9. Y. M. Poluektov, East Eur. J. Phys. 3, 35 (2016). Google Scholar

10. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Nauka, Moscow, 1987). Google Scholar

11. V. B. Shikin and Y. P. Monarkha, Two-dimensional Charged Systems in Helium (Nauka, Moscow, 1989). Google Scholar

12. Y. Monarkha and K. Kono, Two-Dimensional Coulomb Liquids and Solids (Springer-Verlag, New York, 2004). Google Scholar

13. L. D. Landau and E. M. Lifshitz, Statistical Physics (Nauka, Moscow, 1976), Pt. 1. Google Scholar

14. N. Ashcroft and N. Mermin, Solid State Phys., edited by M. I. Kaganov (Mir, Moscow, 1979), Vol. 2, p. 422. Google Scholar

15. A. K. Breger and A. A. Zhukhovitskii, J. Chem. Phys. 14, 569 (1946). CrossRef Google Scholar

16. M. Dupuis, R. Mazo, and L. Onzager, J. Chem. Phys. 33, 1452 (1960). CrossRef Google Scholar

17. R. Stratton, J. Chem. Phys. 37, 2972 (1962). CrossRef Google Scholar

18. A. A. Maradudin and R. F. Wallis, Phys. Rev. 148, 945 (1966). CrossRef Google Scholar

19. I. A. Viktorov, Sound Surface Waves in Solids (Nauka, Moscow, 1981). Google Scholar

20. F. I. Fedorov, Theory of Elastic Waves in Crystals (Nauka, Moscow, 1965). Google Scholar