Abstract
The elastic moduli of single crystals of pyrope-rich garnet and San Carlos olivine have been measured over a 3 GPa pressure range at room temperature. The combination of improved ultrasonic techniques and this large pressure range provide for more reliable characterization of the pressure dependence of acoustic wave velocities than has previously been possible. First and second pressure derivatives of the velocities have been determined within ∼ 1 percent and ∼ 10 percent respectively. The Hashin-Shtrikman bounds for the pressure dependences of the bulk and shear moduli of the garnet used in this study are; K = 173.6 GPa, K′ = 4.93, K″ = −0.28 GPa−1, G= 94.9 GPa, G′ = 1.56, G″ = −0.08 GPa−1 and the Hashin-Shtrikman least-upper bounds and greatestlower bounds for the pressure dependences of the bulk and shear moduli of the San Carlos olivine are K=129.8 GPa, K′ = 4.66, K″= −0.15 GPa−1, G = 77.8 GPa, G′ = 1.93, G″ = −0.11 GPa−1 and K = 129.2 GPa, K′ = 4.63, K″= −0.15 GPa−1 G = 77.3 GPa, G′=1.96, G″ = −0.11 GPa−1 respectively. The determination of the room-pressure elastic moduli of this pyrope-almandine garnet removes the previously observed anomaly in the predictions of systematic treatments of variations of the elastic moduli of garnets with composition. The determination of the second pressure derivatives of the moduli of garnet and olivine illustrates the importance of these terms in extrapolations to higher pressures — with ϱK/ϱP for these crystals being reduced by ∼ 17 percent and ∼ 9 percent respectively over the 3 GPa pressure range.
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References
Babuska V, Fiala J, Kumazawa M, Ohno I, Sumino Y (1978) Elastic properties of garnet solid solution series. Phys Earth Planet Int 16:157–176
Bassett WA, Shimizu H, Brody EM (1982) Pressure dependence of elastic moduli of forsterite by Brillouin scattering in a diamond anvil cell. In: Akimoto S, Manghnani MH (eds) High-pressure research in geophysics. Center for Academic Publications Japan, Tokyo, pp 115–124
Bonczar LJ, Graham EK, Wang H (1977) The pressure and temperature dependence of the elastic constants of pyrope garnet. J Geophys Res 82:2529–2534
Christensen NI (1979) Compressional wave velocities in rocks at high temperatures and pressures, critical thermal gradients, and crustal low-velocity zones. J Geophys Res 84:6849–6857
Cook RK (1957) Variation of elastic constants and static strains with hydrostatic pressure: A method for calculation from ultrasonic measurements. J Acoust Soc Am 29:445–449
Graham EK, Barsch GR (1969) Elastic constants of single-crystal forsterite as a function of temperature and pressure. J Geophys Res 74:5949–5960
Hashin Z, Shtrikman S (1962a) On some variational principles in anisotropic and nonhomogeneous elasticity. J Mech Phys Solids 10:335–342
Hashin Z, Shtrikman S (1962b) A variational approach to the theory of the elastic behavior of polycrystals. J Mech Phys Solids 10:343–352
Isaak DG, Graham EK (1976) The elastic properties of an almandine-spessartine garnet and elasticity in the garnet solid solution series. J Geophys Res 81:2483–2489
Jackson I, Niesler H (1982) The elasticity of periclase to 3 GPa and some geophysical implications. In: Akimoto S, Manghnani MH (eds) High-pressure research in geophysics. Center for Academic Publications Japan, Tokyo, pp 93–113
Jackson I, Niesler H, Weidner DJ (1981) Explicit correction of ultrasonically determined elastic wave velocities for transducerbond phase shifts. J Geophys Res 86:3736–3748
Kieffer SW (1980) Thermodynamics and lattice vibrations of minerals: 4 Application to chain and sheet silicates and orthosilicates. Rev Geophys Space Phys, 18:862–886
Kumazawa M, Anderson OL (1969) Elastic moduli, pressure derivatives and temperature derivatives of single-crystal olivine and single-crystal forsterite. J Geophys Res 74:5961–5972
Leitner BJ, Weidner DJ, Liebermann RC (1980) Elasticity of single crystal pyrope and implications for garnet solid solution series. Phys Earth Planet Int 22:111–121
Niesler H, Jackson I, Morris EC (1988) Calibration and intercomparison of minalpha and manganin resistance pressure gauges to 3 GPa. High Temp High Press 20:495–508
Nye JF (1957) Physical properties of crystals. Oxford University Press, London
Reuss A (1929) Berechnung der Fließgrenze von Mischkristallen aufgrund der Plastizitätsbedingung für Einkristalle. Z Angew Math Mech 9:49–58
Ricoult DL, Kohlstedt DL (1983) Structural width of low-angle grain boundaries in olivine. Phys Chem Minerals 9:133–138
Robie RA, Finch CB, Hemingway BS (1982a) Heat capacity and entropy of fayalite (Fe2SiO4) between 51 and 383 K: comparison of calorimetric and equilibrium values for the QFM buffer reaction. Am Mineral 67:463–469
Robie RA, Hemingway BS, Takei H (1982b) Heat capacities and entropies of Mg2SiO4, Mn2iO4, and Co2SiO4 between 5 and 380 K. Am Mineral 67:470–480
Skinner BJ (1956) Physical properties of end-members of the garnet group. Am Mineral 48:428–436
Suzuki I (1975) Thermal expansion of periclase and olivine, fnand their anharmonic properties. J Phys Earth 23:145–159
Voigt W (1928) Lehrbuch der Kristallphysik. Teubner, Leipzig
Wang H, Huang K (1975) Elastic constants of natural pyrope. EOS 56:601
Waterman PC (1959) Orientation dependence of elastic waves in single crystals. Phys Rev 113:1240–1253
Watt JP, Davies G, O'Connell RJ (1976) The elastic propertiesof composite materials. Rev Geophys Space Phys 14:541–563
Weidner DJ (1985) A mineral physics test of a pyrolite mantle. Geophys Res Lett 12:417–420
Winchell AN (1933) Optical mineralogy II. Wiley and Sons, New York
Yeganeh-Haere A, Vaughan MT (1984) Single-crystal elastic constants of olivine. EOS 65:282
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Webb, S.L. The elasticity of the upper mantle orthosilicates olivine and garnet to 3 GPa. Phys Chem Minerals 16, 684–692 (1989). https://doi.org/10.1007/BF00223318
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DOI: https://doi.org/10.1007/BF00223318