Elastic Stiffnesses and Internal Frictions of Monocrystal Quartz

Published

October 16, 2008

Author(s)

H M. Ledbetter, Sudook A. Kim, M Lei

Abstract

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 C_ij of a cultured quartz monocrystal. With trigonal symmetry (32 point group, P3₁2 space group), quartz possesses six independent C_ij. For the troublesome C₁₄ elastic-stiffness coefficient, we found C^D/₁₄ = -18.15 GPa 0.08 GPa or C^E/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 C^E/₁₄ = -17.88 GPa 0.55 GPa. We measured the C^D/_ij and converted them to C^E/_ij by using Bechmann's C^D/_ij - C^E/_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 C^D/_ij, we calculated a Debye characteristic temperature θ of 563 K. The C^E/_ij yield θ = 561K.

Citation

Journal of Applied Physics

Pub Type

Journals

Keywords

debye temperature, dislocations, elastic constants, internal friction, piezoelectricity, quartz

Citation

Ledbetter, H. , Kim, S. and Lei, M. (2008), Elastic Stiffnesses and Internal Frictions of Monocrystal Quartz, Journal of Applied Physics (Accessed September 13, 2024)