Dispersive Rayleigh type waves in layered systems consisting of piezoelectric crystals bismuth silicate and bismuth germanate

摘要

The lowest-order modes of the dispersive six-partial waves of Rayleigh type (RTW6) have been numerically obtained for two layered systems consisting of a layer on a substrate in [100] propagation direction of (001)cut for both cubic crystals of class 23. Dispersion relations are shown for both a layer of Bi12SiO20 on a substrate of Bi12GeO20 and vice versa. Dispersion relations show one mode in each case with clear maximum and minimum, at which it is analytically shown that the group velocity is equal to the phase velocity. It was concluded that in corresponding highly-symmetric cases, the obtained "non-dispersive" six-partial surface waves in the treated layered systems are a new non-dispersive type, termed Rayleigh-Zakharenko type (RZTW6) "non-dispersive" six-partial surface waves. These can exist in layered systems consisting of a layer on a substrate. The possibility of the existence in layered systems of "non-dispersive" waves of both the nine-partial Zakharenko, type (ZTW9) for centrosymmetrical crystals, and the thirteen-partial Zakharenko type waves (ZTW13) for non-centrosymmetrical crystals is suggested. In addition, it is shown that dependence of the phase velocity V-ph = V-ph (kh(1), kh(2),..., kh(m)) in a multi-layered system can be reduced to dependence V-ph = V-ph (kh) for a layered system consisting of a layer on a substrate. Thus, both systems can be studied in the same way.