Elastic Stiffnesses and Internal Frictions of Monocrystal Quartz
H M. Ledbetter, Sudook A. Kim, M Lei
Using acoustic-resonance spectroscopy (with only two point contacts with the specimen), we measured both the real and imaginary parts of the elastic-stiffness tensor Cij of a cultured quartz monocrystal. With trigonal symmetry (32 point group, P312 space group), quartz possesses six independent Cij. For the troublesome C14 elastic-stiffness coefficient, we found CD/14 = -18.15 GPa 0.08 GPa or CE/14 = -17.97 GPa 0.08 GPa. The average of eleven previous measurements is C E/14 = -17.88 GPa 0.08 GPa. The average of eleven previous measurements is CE/14 = -17.88 GPa 0.55 GPa. We measured the CD/ij and converted them to CE/ij by using Bechmann's CD/ij - CE/ij values. Our measurement frequencies were around 250 kHz. Our internal friction tensor Q-1/ij satisfied all thermodynamic constraints but differed strongly from that reported by Lamb and Richter at 0.5 Ghz to 5 GHz. Thus, different mechanisms seem to dominate these two frequency regions (or the two different crystals). Strain-amplitude measurements for C33 near 250 kHz showed a strong dislocation contribution to Q-1/ij. We found that Q-1 varies as f-1, consistent with the high-frequency limit of the Koehler-Granato-Luke string theory of dislocation vibrations. To make the measurements, we had to solve equations for the natural macroscopic vibration frequencies of a right-circular cylinder with trigonal symmetry and including C14 = -C24 = C56. When the C14 mode is neglected, Q-1/ij is isotropic within measurement error. This implies a defect mechanism independent of deformation mode, a rare occurrence. From the CD/ij, we calculated a Debye characteristic temperature θ of 563 K. The CE/ij yield θ = 561K.