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The geometry of internal conical refraction occurring when the pure transverse mode is propagated along the threefold symmetry axis [001] of a trigonal crystal. The angle B is given by tan B = cujc2b. where tan B = (c^/c^). In this case, shown in Fig. 1-5, the semiangle of the cone of refraction is given by tan _1 [(c2 5 + Ci4)1/2/c44]. 38 11. 1. PROPAGATION OF STRESS WAVES IN SOLIDS STRESS WAVES IN PIEZOELECTRIC CRYSTALS The propagation of high-frequency stress waves in a piezoelectric crystal produces electromagnetic waves that accompany the stress waves, and vice versa.
1) Hence, one needs to compute only Dn, D12, D1Z, D22, Z>44, and Z>55 from Eqs. 4). Using Table 1-2, we may write down the elastic constants in the crystal coordinates { a j for any crystal system. This is done in Table B-l, Appendix 9. NUMERICAL RESULTS FOR MISORIENTATION EFFECTS 31 B, for four systems of interest, with the symmetry elements Si7 listed for each system. Velocities rather than elastic moduli are measured experimentally ; hence, it is appropriate to give results in terms of fractional changes in velocity, defined by Avi==AjM = , μί - a°i , The resulting velocities, fractional changes in velocity, and eigenvectors are given in Appendix B, correct to lowest-order terms in the polar misorientation angle Θ.
As a trial solution, let sx = g(x) cos 2(œt — kx) + h(x) [3 cos(co£ — kx) + cos 3(cot — kx)]. 25) Applications of this one-dimensional solution involving the second and third harmonic terms will be discussed in Chapter 3. 2 Measurement of Attenuation and Velocity by Pulse Methods 13. THE PULSE ECHO METHOD Pulsed ultrasonic radiation for attenuation measurements in solids has come into use relatively recently, although for some time wide use has been made of pulse methods for velocity measurements to obtain elastic moduli.