Abstract
A theory is presented on the free osculations of a rectangular parallelepiped of piezoelectric crystal, by extending the theory of the rectangular parallelepiped resonance (RPR) method to determine elastic constants of crystals, as exemplified by an alpha-quartz specimen. The piezoelectric contribution to resonance frequencies was examined numerically on the specimen, and it was revealed that piezoelectricity causes approximately 5 kHz increase around 1 MHz. The resonance frequencies of the specimen were measured and inverted to elastic constants by least squares inversion. The inversion was by both the previous non-piezoelectric or elastic theory and by the present piezoelectric theory. The use of the non-piezoelectric theory resulted in an overestimate of 2σ or 0.6% in c 11 and underestimate of σ or 6% in c 12. These are the constants expected to be most affected by piezoelectricity. Errors are less than σ in the other constants. During measurement, it was found that the force applied to hold the specimen caused deviations from free oscillation and experimental errors of 5 kHz. The correction for this force is of some importance in RPR studies of piezoelectric crystals.
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Alexandrov KS, Ryzhova TV (1961) The elastic properties of crystals. Sov Phys Crystallogr 6:228–252
Babuška V, Fiala J, Kumazawa M, Ohno I, Sumino Y (1978) Elastic properties of garnet solid-solution series. Phys Earth Planet Inter 16:157–176
Bechmann R (1958) Elastic and piezoelectric constants of alpha-quartz. Phys Rev 110:1060–1061
Berlincourt DA, Curran DR, Jaffe H (1964) Piezoelectric and piezomagnetic materials and their function in transducers. In: Mason WP (ed) Physical Acoustics, vol 1 A: 169–219, Academic Press, New York, London, p. 188
Demarest H (1971) Cube resonance method to determine the elastic constants of solids. J Acoust Soc Am 49:768–775
Eer Nisse EP (1967) Variational method for electroelastic vibration analysis. IEEE Trans Sonics Ultrasonics SU-14:153–160
Goto T, Ohno I, Sumino Y (1976) The determination of elastic constants of natural almandine-pyrope garnet by means of rectangular parallelepiped resonance method. J Phys Earth 24:149–156
Hearmon RSF (1946) The elastic constants of anisotropic materials. Rev Mod Phys 18:409–440
Holland R (1967) Resonant properties of piezoelectric ceramic rectangular parallelepipeds. J Acoust Soc Am 43:988–997
Holland R, Eer Nisse EP (1968) Variational evaluation of admittances of multielectroded three-dimensional piezoelectric structures. IEEE Trans Sonics Ultrasonics SU-15:119–132
Huntington HB (1958) The elastic constants of crystals. In: Seitz F and Turnbull D (ed) Solid State Physics, vol 7. Academic Press, New York, pp 213–285
Koga I, Aruga M, Yoshinaka Y (1958) Theory of plane elastic waves in a piezoelectric crystalline medium and determination of elastic and piezoelectric constants of quartz. Phys Rev 109:1467–1473
Mason WP (1964) Piezoelectric crystals and their application to ultrasonics. Van Nostrand, Princeton, pp 39 and 450
Mayer G, Gigon J (1957) Fast neutron irradiation effects on certain physical constants of crystalline quartz and vitreous silica. J Phys Rad 18:109–114
McSkimin HJ, Andreatch P, Thurston RN (1965) Elastic moduli of quartz versus hydrostatic pressure at 25° C and -195.8° C. J Appl Phys 36:1624–1632
Mochizuki B (1987) Application of group theory to free oscillations of an anisotropic rectangular parallelepiped. J Phys Earth 35:159–170
Ohno I (1976) Free vibration of a rectangular parallelepiped crystal and its application to determination of elastic constants of orthorhombic crystals. J Phys Earth 24:355–379
Ohno I, Yamamoto S, Anderson OL, Noda J (1986) Determination of elastic constants of trigonal crystals by the rectangular parallelepiped resonance method. J Phys Chem Solids 47:1103–1108
Sumino Y, Ohno I, Goto T, Kumazawa M (1976) Measurement of elastic constants and internal frictions of single-crystal MgO by rectangular parallelepiped resonance. J Phys Earth 24:263–273
Sumino Y, Kumazawa M, Nishizawa O, Pluschkell W (1980) The elastic constants of single crystal Fe1-x O, MnO and CoO and the elasticity of stoichiometric magnesiowustite. J Phys Earth 28:475–495
Sumino Y, Anderson OL, Suzuki I (1983) Temperature Coefficients of Elastic Constants of Single Crystal MgO between 80 and 1300 K. Phys Chem Minerals 9:38–47
Suzuki I, Anderson OL, Sumino Y (1983) Elastic Properties of a Single-Crystal Forsterite Mg2SiO4, up to 1,200 K, Phys Chem Minerals 10:38–46
Yamamoto S, Anderson OL (1987) Elasticity and Anharmonicity of Potassium Chloride at High Temperature. Phys Chem Minerals 14:332–340
Yamamoto S, Ohno I, Anderson OL (1987) High temperature elasticity of sodium chloride. J Phys Chem Solids 48:143–151
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Ohno, I. Rectangular parallellepiped resonance method for piezoelectric crystals and elastic constants of alpha-quartz. Phys Chem Minerals 17, 371–378 (1990). https://doi.org/10.1007/BF00212204
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DOI: https://doi.org/10.1007/BF00212204