Ultrasonic Diffraction Loss and Phase Change in Anisotropic Materials

Abstract

The loss and phase change in progressive longitudinal waves from a finite circular piston source radiating into certain anisotropic media are calculated in this paper. Three-dimensional calculations are presented for propagation along 3-, 4-, and 6-fold symmetry axes. Relationships sufficient to permit the performance of the calculation for 2-fold axes are derived. The anisotropy is introduced as a term in the spatial part of the phase in the integral for the pressure in the field of the piston. Geometry proper for pulse-echo measurements was assumed in the calculation. The diffraction loss fluctuates with S = zλ/a2 (z is the distance into crystal, λ, is the wavelength, a is the transducer radius) before becoming monotonic increasing as the logarithm of S. The positions of the peaks in the loss are functions of the anisotropy of the medium. The phase change, on the other hand, increases monotonically to a limit of π/2 from S-0 to infinity. However, the phase has plateaus where the loss has peaks. Both new and previously published experimental data on diffraction loss along 3-, 4-, and 6-fold axes in crystals agree quantitatively with theory. Some data on 2-fold axes are also presented. The methods for correcting attenuation and velocity measurements for diffraction are given.