Ultrasonic imaging of the group velocity surface about the cubic axis in silicon

Abstract

This article reports measurements of the group velocity surface of silicon in the region of the 〈100〉 axis. Pulsed ultrasonic beams generated by a piezoelectric longitudinal mode transducer are transmitted through water and focused onto a small spot on the surface of a (001) oriented silicon single crystal disk. This gives rise to transient elastic waves which propagate in a wide range of directions through the specimen and they are detected by a small piezoelectric longitudinal mode transducer fixed at the center of the opposite face. The imaging of the group velocity surface about the 〈100〉 axis is accomplished by scanning the focused beam in various directions along lines that intersect at epicenter. The scanned images reveal complex foldings of the slow transverse sheet of the ray surface about the 〈100〉 axis, in general agreement with the predictions of ray acoustics. However, the observed image manifests pronounced wave motions well beyond the cuspidal edges predicted by ray acoustics. This phantomlike feature or eidolon can be explained on the basis of diffraction resulting from the finite wavelength of the ultrasonic waves.