Reflection Coefficients for Defective Diffusion Bonds

The quality of diffusion bonds can, to some degree, be characterized using ultrasonic probes. Consequently, considerable effort has gone into the development of theories that predict the ultrasonic scattering from defective bonds. There are three major lines of development. First Baik and Thompson [1] and Angel and Achenbach [2] have examined the low frequency limit; they have described the elastic scattering by an “effective” spring-model in this regime. Second Sotiropolous and Achenbach [3,4] have developed a rigorous approach that is valid at all frequencies for the case of microcracks at the bondplane; the crucial theoretical tool in this case is the crack opening displacement. Their work is, however, restricted to the case of normally incident plane waves. Rose [5] presented an approximate method, the single scattering approximation, for computing the reflection coefficients at normal incidence; it is based on using the scattering amplitudes for the various defects at the bondplane