Elastic Constants of and Wave Propagation in Antimony and Bismuth

Ultrasonic wave velocities for 14 different modes were obtained on two differently oriented single-crystal antimony cubes from the time between successive unrectified radio-frequency pulse echoes. This redundant set of data was fitted by a least-squares technique to Voigt theory to yield the six room-temperature adiabatic elastic-stiffness constants. In units of 10¹⁰ dyn/cm², c₁₁=99.4(1), c₃₃=44.5(9), c₄₄=39.5(5), c₆₆=34.2(3), c₁₃=26.4(4), and c₁₄=+21.6(4), the positive sign for c₁₄ following from our choice of positive Cartesian axes. When similarly treated, Eckstein, Lawson, and Reneker's bismuth data yield in these same units: c₁₁=63.22, c₃₃=38.11, c₄₄=11.30, c₆₆=19.40, c₁₃=24.40±0.09, c₁₄=+7.20. Also included are a visual method of fixing the laboratory coordinate system in antimony by means of an imperfect cleavage plane, a calculation of the pure-mode directions in the mirror plane, a simple formula for choosing the nonextraneous value of c₁₃ for trigonal crystals having six independent elastic constants without resorting to lattice-stability criteria, and a calculation of the deviation of elastic-wave particle displacement and energy-flux directions from the propagation direction. For waves propagating in the (0,1,1) and (0,1̄,1) directions, the particle-displacement deviations for antimony and bismuth do not exceed 15^∘{} and 13^∘{}, respectively, and corresponding energy-flux deviations up to 45^∘{} and 27^∘{} are obtained.