Reflection and refraction of waves in nano-smart materials: Anisotropic thermo-piezoelectric materials

Abstract

In this paper, the basic equations (equations of motion, Gauss and heat conduction equations) and constitutive relations for the thermo-piezoelectric media in the framework of generalized theories of thermoelasticity have been written. The reflection and refraction coefficients have been obtained by solving a set of linear algebraic equations when an incident waves (qP,-mode and T -mode) which are falling upon the interface between two different anisotropic thermo-piezoelectric media (each of them are having hexagonal symmetry). Numerical calculations are performed when the lower medium is (CdSe) while the upper medium is (BaTiO3). Numerical results of the reflection and refraction coefficients are obtained and presented graphically. It is found that different kinds of reflected and refracted waves are produced which may be organized as follows: (i) Two reflected elastic waves in the lower medium, one of them is qP wave and the other is qSV wave and similar of them when refracted in the upper medium. (ii) Two reflected thermal waves in the lower medium and similar of them but refracted in the upper medium. (iii) Two reflected potential electric waves in the lower medium and similar of them however refracted in the upper medium. It is noticed that the reflected and refracted coefficients of the last two kind waves are proportional to the reflected and refracted coefficients of the first kinds of waves. Furthermore, the parameters of the proportional are functions of the incident angles and the thermal relaxation times. Moreover, it is observed that the amplitudes ratios of reflection and refraction coefficients depend upon the angle of incidence, the electric potential, thermal field, elastic constants of the medium as well as the thermal relaxation times (which are very small and has the order of pico-second). This study is useful in signal processing, sound system and wireless communication in addition to improvement of SAW wave devices and military defense equipment. Furthermore, PM5 semiemeprical method proves that this class of materials interface has their optimal electronic properties in nano scale Copyright © 2014 American Scientific Publishers.