Mathematical Analysis of the Reflection Phenomenon of Longitudinal Waves at Nano Anisotropic Thermo-Piezoelectric Medium

Two-dimensional mathematical model is developed to investigate the reflection of waves at the boundary between a vacuum and a half-space that is occupied by an elastic, transversely isotropic, thermo-piezoelectric material. The suitable boundary conditions is investigated the non-classical (generalized) theories of linear thermo-piezoelectric materials is included. We discuss the characteristics of the reflection coefficients when incident waves, such as quasi-longitudinal, thermal-mode and electrical potential-mode (qP or T-mode and ϕ-mode) waves, encounter the interface between the vacuum and the half-space. It was found that there are three different groups of reflected waves: (i) two elastic waves, namely, qP and qSV; (ii) two thermal waves; and (iii) two electrical potential waves. In addition, the last two kinds of waves were found to be proportional to qP waves. We have shown analytically that the reflection coefficients of plane quasi-longitudinal waves (qP-waves) depend upon the angle of incidence, the parameters of the electrical potential, the material constants of the medium, the thermal parameters and the thermal relaxation times of the medium. The special cases of normal and grazing incidence are also derived and discussed. The reflection coefficients are computed for Cadmium selenide. The significant effects of the thermal and electrical potentials and the anisotropy of the materials on the various reflection coefficients can be observed from the results. The effect of the thermal relaxation time parameters on the various reflection coefficients is also observed to be significant. Molecular modeling is utilized at D-Gauss level to calculated vibrational frequencies and HOMO–LUMO band gap energy.