Reflection and transmission of ultrasound from a planar interface

Abstract

Information about the local forces at an interface between two solids is of considerable technological interest. We have used a simple model of a homogeneous solid. We consider a cubic crystal with springs connecting the nearest and the next nearest neighbors. Two such crystals can be joined by a different set of springs at the interface. The force constants of the springs at the interface describe the local forces at the interface. If a longitudinal wave is incident on such an interface at an angle less than the critical angle, it will be partly reflected and transmitted as a longitudinal and transverse wave. We have derived the equations for the transmitted and reflected amplitudes. These can be expressed in terms of the macroscopic properties of solids on either side of the interface, and in terms of the force constants at the interface. It is shown that at low frequencies our equations reduce to those derived from macroscopic theory in which it is assumed that the bond at the interface is perfect and that the boundary atoms on both sides of the interface have equal displacements. If the force constants at the interface are weak compared with the force constants in the bulk media on either side of the interface, deviations from the macroscopic results occur. Thus, measurements of scattered wave amplitudes at frequencies where the deviation from macroscopic results occurs can provide valuable information about the nature of forces at the interface.