Displacement fields of a Cuboid crystal in a Photoacoustic Cell: Mathematical aspects

Abstract

Photo acoustic effect is popular due to a minimal sample preparation during execution, the ability to examine scattering and opaque sample along with the capability to access depth profile. These features enable Photoacoustic spectroscopy to be used in depth-resolved characterization of solids. Thermal interaction is a basic perspective in solid state physics research regarding industrial devices and components. It is a key factor of fabrication and performance of such devices and components. Today, crystalline solids are widely studied due to their wide scientific and industrial applications. Displacement field resulting in thermal stresses
is one of the important aspects of premature failure of industrial components and devices. In this paper, displacement fields in photoacoustic effect with solid cuboid crystal are mathematically presented. According to our opinion, displacement fields in photoacoustic effect in three dimensional analysis are not reported earlier. Hence that will be a major contribution of this paper. For a simple cuboid homogeneous crystal kept in a photoacoustic cell, an airy stress function is determined based on laser interaction with surface of the crystal. By applying the finite Marchi-Fasulo integral transform method within the crystal size limitations, displacement field is exactly determined.