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Elasticity of single-crystal quartz to 10 GPa

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Abstract

The second-order elastic constants of quartz were determined by Brillouin spectroscopy to 10 GPa in a diamond anvil cell. All elastic constants exhibit smooth pressure trends. A decrease in the magnitudes of C 14 and C 66 with pressure is observed, while C 44 shows a weak pressure dependence. Our measured elastic constants are more consistent with previous density functional theory calculations than with earlier experimental results. Aggregate elastic moduli were calculated and fit to a finite-strain equation of state, yielding values for the pressure derivatives of the adiabatic bulk modulus, K 0Sʹ, and shear modulus, G 0ʹ, of α-quartz of 6.2(2) and 0.9(1), respectively. The equation of state obtained from our data is consistent with static X-ray diffraction data. A finite-strain extrapolation of our data predicts a violation of a Born stability criterion, indicating a mechanical instability in the structure, at ~26 GPa which is broadly consistent with the pressure range at which a phase transition and pressure-induced amorphization in quartz are observed.

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References

  • Ackerman RJ, Sorrell C (1974) Thermal-expansion and high-low transformation in quartz.1. High-temperature X-ray studies. J Appl Crystallogr 7:461–467. doi:10.1107/S0021889874010211

    Article  Google Scholar 

  • Angel RJ, Allan DR, Miletich R, Finger LW (1997) The use of quartz as an internal pressure standard in high-pressure crystallography. J Appl Crystallogr 30:461–466. doi:10.1107/S0021889897000861

    Article  Google Scholar 

  • Angel RJ, Bujak M, Zhao J et al (2007) Effective hydrostatic limits of pressure media for high-pressure crystallographic studies. J Appl Crystallogr 40:26–32. doi:10.1107/S0021889806045523

    Article  Google Scholar 

  • ANSI/IEEE standard 176-1988 (1988) IEEE Standard on Piezoelectricity. Institute of Electrical and Electronic Engineers, New York

  • Ballato A (2008) Basic material quartz and related innovations. Piezoelectricity. Springer, Berlin, pp 9–35

    Chapter  Google Scholar 

  • Binggeli N, Chelikowsky J (1992) Elastic instability in alpha-quartz under pressure. Phys Rev Lett 69:2220–2223. doi:10.1103/PhysRevLett.69.2220

    Article  Google Scholar 

  • Binggeli N, Keskar N, Chelikowsky J (1994) Pressure-induced amorphization, elastic instability, and soft modes in alpha-quartz. Phys Rev B 49:3075–3081. doi:10.1103/PhysRevB.49.3075

    Article  Google Scholar 

  • Birch F (1978) Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high-pressures and 300-degree-K. J Geophys Res 83:1257–1268. doi:10.1029/JB083iB03p01257

    Article  Google Scholar 

  • Born M, Huang K (1954) Dynamical theory of crystal lattices. Oxford University Press, London

    Google Scholar 

  • Calderon E, Gauthier M, Decremps F et al (2007) Complete determination of the elastic moduli of α-quartz under hydrostatic pressure up to 1 GPa: an ultrasonic study. J Phys: Condens Matter 19:436228. doi:10.1088/0953-8984/19/43/436228

    Google Scholar 

  • Carpenter MA, Salje EKH (1998) Elastic anomalies in minerals due to structural phase transitions. Eur J Miner 10:693–812

    Article  Google Scholar 

  • Choudhury N, Chaplot SL (2006) Ab initio studies of phonon softening and high-pressure phase transitions of α-quartz SiO2. Phys Rev B 73:094304. doi:10.1103/PhysRevB.73.094304

    Article  Google Scholar 

  • Christensen NI (1996) Poisson’s ratio and crustal seismology. J Geophys Res 101:3139. doi:10.1029/95JB03446

    Article  Google Scholar 

  • Duffy TS, Zha C, Downs RT et al (1995) Elasticity of forsterite to 16 GPa and the composition of the upper mantle. Nature 378:170–173. doi:10.1038/378170a0

    Article  Google Scholar 

  • Every AG (1980) General closed-form expressions for acoustic-waves in elastically anisotropic solids. Phys Rev B 22:1746–1760. doi:10.1103/PhysRevB.22.1746

    Article  Google Scholar 

  • Every AG, McCurdy AK (1992) The elastic constants of crystals. In: Nelson DF (ed) Landolt-Börnstein tables III29. Springer, Berlin/Heidelberg, pp 1–634

    Google Scholar 

  • Glinnemann J, King HE, Schulz H et al (1992) Crystal structures of the low-temperature quartz-type phases of SiO2 and GeO2 at elevated pressure. Z Für Krist 198:177–212. doi:10.1524/zkri.1992.198.3-4.177

    Article  Google Scholar 

  • Gregoryanz E, Hemley RJ, Mao H-k, Gillet P (2000) High-pressure elasticity of α-quartz: instability and ferroelastic transition. Phys Rev Lett 84:3117–3120. doi:10.1103/PhysRevLett.84.3117

    Article  Google Scholar 

  • Haines J, Léger JM, Gorelli F, Hanfland M (2001) Crystalline post-quartz phase in silica at high pressure. Phys Rev Lett 87:155503. doi:10.1103/PhysRevLett.87.155503

    Article  Google Scholar 

  • Hazen RM, Finger LW, Hemley RJ, Mao HK (1989) High-pressure crystal chemistry and amorphization of α-quartz. Solid State Commun 72:507–511. doi:10.1016/0038-1098(89)90607-8

    Article  Google Scholar 

  • Heaney PJ, Prewitt CT, Gibbs GV (1994) Silica: physical behavior, geochemistry and materials applications. Rev Mineralogy, 29 Mineralogical Society of America, Washington, DC

  • Hemingway BS (1987) Quartz-heat-capacities from 340-K to 1000-K and revised values for the thermodynamic properties. Am Miner 72:273–279

    Google Scholar 

  • Hemley RJ (1987) Pressure dependence of Raman spectra of SiO2 polymorphs: α-quartz, coesite, and stishovite. In: Manghnani H, Syono M (eds) High-pressure research in mineral physics. American Geophysical Union, pp 347–359

  • Hemley RJ, Jephcoat AP, Mao H-k et al (1988) Pressure-induced amorphization of crystalline silica. Nature 334:52–54. doi:10.1038/334052a0

    Article  Google Scholar 

  • Hemley RJ, Prewitt CT, Kingma KJ (1994) High-pressure behavior of silica. In: PJ Heaney, CT Prewitt, GV Gibbs (eds) Silica: physical behavior, geochemistry and materials applications. Rev Mineralogy, 29 Rev. Mineral. Geochem. pp 41–81

  • Heyliger P, Ledbetter H, Kim S (2003) Elastic constants of natural quartz. J Acoust Soc Am 114:644. doi:10.1121/1.1593063

    Article  Google Scholar 

  • Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11:357–372. doi:10.1016/0022-5096(63)90036-X

    Article  Google Scholar 

  • Holm B, Ahuja R (1999) Ab initio calculation of elastic constants of SiO2 stishovite and α-quartz. J Chem Phys 111:2071–2074. doi:10.1063/1.479475

    Article  Google Scholar 

  • Kimizuka H, Ogata S, Li J, Shibutani Y (2007) Complete set of elastic constants of α-quartz at high pressure: a first-principles study. Phys Rev B 75:054109. doi:10.1103/PhysRevB.75.054109

    Article  Google Scholar 

  • Kingma K, Hemley R, Mao H-k, Veblen D (1993a) New high-pressure transformation in alpha-quartz. Phys Rev Lett 70:3927–3930. doi:10.1103/PhysRevLett.70.3927

    Article  Google Scholar 

  • Kingma K, Meade C, Hemley R et al (1993b) Microstructural observations of alpha-quartz amorphization. Science 259:666–669

    Google Scholar 

  • Lakshtanov DL, Sinogeikin SV, Bass JD (2006) High-temperature phase transitions and elasticity of silica polymorphs. Phys Chem Miner 34:11–22. doi:10.1007/s00269-006-0113-y

    Article  Google Scholar 

  • Levien L, Prewitt CT, Weidner DJ (1980) Structure and elastic properties of quartz at pressure. Am Mineral 65:920–930

    Google Scholar 

  • Machon D, Meersman F, Wilding MC et al (2014) Pressure-induced amorphization and polyamorphism: inorganic and biochemical systems. Prog Mater Sci 61:216–282. doi:10.1016/j.pmatsci.2013.12.002

    Article  Google Scholar 

  • Mao HK, Xu J, Bell PM (1986) Calibration of the ruby pressure gauge to 800-Kbar under quasi-hydrostatic conditions. J Geophys Res 91:4673–4676. doi:10.1029/JB091iB05p04673

    Article  Google Scholar 

  • McSkimin HJ, Andreatch P Jr, Thurston RN (1965) Elastic moduli of quartz versus hydrostatic pressure at 25 and −195.8 C. J Appl Phys 36:1624–1632. doi:10.1063/1.1703099

    Article  Google Scholar 

  • Mirwald PW, Massonne H-J (1980) The low-high quartz and quartz-coesite transition to 40 kbar between 600 and 1600 C and some reconnaissance data on the effect of NaAlO2 component on the low quartz-coesite transition. J Geophys Res Solid Earth 85:6983–6990. doi:10.1029/JB085iB12p06983

    Article  Google Scholar 

  • Nye JF (1984) Physical properties of crystals: their representation by tensors and matrices. Clarendon Press, Oxford University Press, Oxford

    Google Scholar 

  • Oganov AR, Hemley RJ, Hazen RM, Jones AP (2013) Structure, bonding, and mineralogy of carbon at extreme conditions. In: Hazen RM, Jones AP, Baross JA (eds) Rev. Mineral, Geochem, pp 47–77

    Google Scholar 

  • Ogi H, Ohmori T, Nakamura N, Hirao M (2006) Elastic, anelastic, and piezoelectric coefficients of α-quartz determined by resonance ultrasound spectroscopy. J Appl Phys 100:053511. doi:10.1063/1.2335684

    Article  Google Scholar 

  • Ohno I (1990) Rectangular parallelepiped resonance method for piezoelectric-crystals and elastic-constants of alpha-quartz. Phys Chem Miner 17:371–378

    Article  Google Scholar 

  • Ohno I (1995) Temperature-variation of elastic properties of alpha-quartz up to the alpha–beta transition. J Phys Earth 43:157–169

    Article  Google Scholar 

  • Ohno I, Harada K, Yoshitomi C (2006) Temperature variation of elastic constants of quartz across the α–β transition. Phys Chem Miner 33:1–9. doi:10.1007/s00269-005-0008-3

    Article  Google Scholar 

  • Palmeri R, Frezzotti ML, Godard G, Davies RJ (2009) Pressure-induced incipient amorphization of α-quartz and transition to coesite in an eclogite from Antarctica: a first record and some consequences. J Metamorph Geol 27:685–705. doi:10.1111/j.1525-1314.2009.00843.x

    Article  Google Scholar 

  • Speziale S, Duffy TS (2002) Single-crystal elastic constants of fluorite (CaF2) to 9.3 GPa. Phys Chem Miner 29:465–472. doi:10.1007/s00269-002-0250-x

    Article  Google Scholar 

  • Tarumi R, Nakamura K, Ogi H, Hirao M (2007) Complete set of elastic and piezoelectric coefficients of α-quartz at low temperatures. J Appl Phys 102:113508. doi:10.1063/1.2816252

    Article  Google Scholar 

  • Tse J, Klug D (1991) Mechanical instability of alpha-quartz—a molecular-dynamics study. Phys Rev Lett 67:3559–3562. doi:10.1103/PhysRevLett.67.3559

  • Wang Q, Saunders GA, Lambson EF et al (1992) Temperature dependence of the acoustic-mode vibrational anharmonicity of quartz from 243 to 393 K. Phys Rev B 45:10242–10254. doi:10.1103/PhysRevB.45.10242

    Article  Google Scholar 

  • Wang Z, Liu Y, Song W et al (2011) A broadband spectroscopy method for ultrasonic wave velocity measurement under high pressure. Rev Sci Instrum 82:014501. doi:10.1063/1.3518953

    Article  Google Scholar 

  • Whitfield CH, Brody EM, Bassett WA (1976) Elastic moduli of NaCl by Brillouin scattering at high pressure in a diamond anvil cell. Rev Sci Instrum 47:942–947. doi:10.1063/1.1134778

    Article  Google Scholar 

  • Williams Q, Hemley R, Kruger M, Jeanloz R (1993) High-pressure infrared-spectra of alpha-quartz, coesite, stishovite and silica Glass. J Geophys Res-Solid Earth 98:22157–22170. doi:10.1029/93JB02171

    Article  Google Scholar 

  • Zha CS, Duffy TS, Downs RT et al (1998) Brillouin scattering and X-ray diffraction of San Carlos olivine: direct pressure determination to 32 GPa. Earth Planet Sci Lett 159:25–33. doi:10.1016/S0012-821X(98)00063-6

    Article  Google Scholar 

  • Zouboulis IS, Jiang F, Wang J, Duffy TS (2014) Single-crystal elastic constants of magnesium difluoride (MgF2) to 7.4 GPa. J Phys Chem Solids 75:136–141. doi:10.1016/j.jpcs.2013.09.014

    Article  Google Scholar 

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Acknowledgments

This research was supported by the NSF and the Carnegie-DOE Alliance Center.

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  1. Zhu Mao

    Present address: University of Science and Technology of China, Hefei, 230026, Anhui, China

Authors and Affiliations

  1. Department of Geosciences, Princeton University, Princeton, NJ, 08544, USA

    Jue Wang, Zhu Mao, Fuming Jiang & Thomas S. Duffy

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Correspondence to Jue Wang.

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Wang, J., Mao, Z., Jiang, F. et al. Elasticity of single-crystal quartz to 10 GPa. Phys Chem Minerals 42, 203–212 (2015). https://doi.org/10.1007/s00269-014-0711-z

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