Skip to main content

Advertisement

SpringerLink
Log in

Anisotropic viscoelastic properties of quartz and quartzite in the vicinity of the α–β phase transition

  • Original Paper
  • Published:
Physics and Chemistry of Minerals Aims and scope Submit manuscript

Abstract

In this study we performed high-temperature, dynamic (i.e. sinusoidal), three-point bending experiments of quartz single crystals and quartzite samples within the frequency range of seismic surveys (i.e. 0.1–20 Hz). At constant temperature close to the α–β phase transition we observed a unique complex elastic behaviour of both quartz and quartzite. We find a frequency dependence of the complex Young’s modulus of α-quartz, including a dissipation maximum at ≈1 Hz supposedly related to the formation and variation of Dauphiné twin domains. Based on our experimental results for different crystallographic directions and additional modelling, we are able to describe the complex Young’s modulus of quartz at its α–β phase transition in a 3D diagram. We derive a frequency-dependent elasticity tensor, using a three-element equivalent circuit, composed of two springs E 1 and E 2 as well as a dashpot η. E 1 and η are connected parallel to each other, E 2 is added in series. Compliance coefficients yield (S 11) E 1 = 572 GPa, E 2 = 70.0 GPa, η = 64.6 GPa·s, (S 33) E 1 = 127 GPa, E 2 = 52.1 GPa, η = 22.9 GPa·s, (S 44) E 1 = 204 GPa, E 2 = 37.5 GPa, η = 26.4 GPa·s, (S 12) E 1 = 612 GPa, E 2 = 106.7 GPa, η = 78.5 GPa·s, (S 13) E 1 = 1546 GPa, E 2 = 284 GPa, η = 200 GPa·s; S 14 ≈−0.0024 GPa-1. We use the derived direction-dependent coefficients to predict the frequency-dependent complex elastic properties of isotropic polycrystalline quartz. These predictions agree well with the experimental results of the investigated quartzite. Finally, we explore the potential of using the anomalous frequency-dependent complex elastic properties of quartz at the α–β phase transition that we observed as an in situ temperature probe for seismic studies of the Earth’s continental crust.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Aslanyan TA, Levanyuk AP (1979) On the possibility of the incommensurate phase near the α–β transition point in quartz. Solid State Commun 31:547–550. doi:10.1016/0038-1098(79)90250-3

    Article  Google Scholar 

  • Bragg WFRS, Gibbs RE (1925) The structure of α and β and quartz. Proc R Soc Lond A 109:405–427. doi:10.1098/rspa.1925.0135

    Article  Google Scholar 

  • Brown CS, Kell RC, Thomas LA, Wooster N, Wooster WA (1952) The growth and properties of large crystals of synthetic quartz. Mineralog Mag 29:858–874. doi:10.1180/minmag.1952.029.217.03

    Article  Google Scholar 

  • Dolino G (1990) The – transitions of quartz: a century of research on displacive phase transitions. Phase Transit 21:59–72. doi:10.1080/01411599008206882

    Article  Google Scholar 

  • Fielitz K (1971) Elastic wave velocities in different rocks at high pressure and temperature up to 750 °C. Z Geophys 37:943–956

    Google Scholar 

  • Fielitz K (1976) Compressional and shear wave velocities as a function of temperature in rocks at high pressure. In: Giese P, Prodehl C, Stein A (Ed) Explosion seismology in Central Europe. Springer, Berlin, pp 40–44. doi:10.1007/978-3-642-66403-8_8

    Google Scholar 

  • Frondel C (1945) Secondary Dauphiné twinning in quartz. Am Miner 30:447–460

    Google Scholar 

  • Grau P, Berg G, Gießmann E-J (1983) Rheologische Untersuchungen fester Stoffe mit Dehnungsratenwechselversuchen. Tech Mech 4:54–58

    Google Scholar 

  • Haussühl S (1983) Physical properties of crystals—an introduction (2007 edition). Wiley, Weinheim

    Google Scholar 

  • Hill R (1952) The elastic behaviour of a crystalline aggregate. Proc Phys Soc 65:349–354. doi:10.1088/0370-1298/65/5/307

    Article  Google Scholar 

  • Iliescu B, Chirila R (1995) Electric twinning in quartz by temperature gradient. Cryst Res Technol 30:231–235. doi:10.1002/crat.2170300219

    Article  Google Scholar 

  • Johannes W, Holtz F (1996) Petrogenesis and experimental petrology of granitic rocks. Springer, Berlin

    Book  Google Scholar 

  • Kern H (1978) The effect of high temperature and high confining pressure on compressional wave velocities in quartz-bearing and quartz-free igneous and metamorphic rocks. Tectonophysics 44:185–203. doi:10.1016/0040-1951(78)90070-7

    Article  Google Scholar 

  • Kern H (1979) Effect of high-low quartz transition on compressional and shear wave velocities in rocks under high pressure. Phys Chem Miner 4:161–171. doi:10.1007/BF00307560

    Article  Google Scholar 

  • Kimizuka H, Kaburaki H, Kogure Y (2003) Molecular-dynamics study of the high-temperature elasticity of quartz above the α–β phase transition. Phys Rev B 67:024105 (7pp). doi:10.1103/PhysRevB.67.024105

    Article  Google Scholar 

  • Klumbach S (2015) Elasticity and viscoelasticity of solid SiO2 as a function of frequency and temperature. Dissertation, Karlsruhe Institute of Technology

  • Klumbach S, Schilling FR (2014) Elastic and anelastic properties of α- and α–β quartz single crystals. Eur J Mineral 26:211–220. doi:10.1127/0935-1221/2014/0026-2362

    Article  Google Scholar 

  • Kuchling H (2004) Taschenbuch der Physik. Fachbuchverlag Leipzig

    Google Scholar 

  • Lakshtanov DL, Sinogeikin SV, Bass JD (2007) 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 

  • Le Chatelier HL (1889) Sur la dilatation du quartz. C R Ac Sci 108:1046–1049

    Google Scholar 

  • Li S, Patwardhan AG, Amirouche FM, Havey R, Meade KP (1995) Limitations of the standard linear solid model of invertebral discs subject to prolonged loading and low-frequency vibration in axial compression. J Biomech 28:779–790. doi:10.1016/0021-9290(94)00140-Y

    Article  Google Scholar 

  • Lu C, Jackson I (1998) Seismic-frequency laboratory measurements of shear mode viscoelasticity in crustal rocks II: thermally stressed quartzite and granite. Pure Appl Geophys 153:441–473. doi:10.1007/978-3-0348-8711-3_10

    Article  Google Scholar 

  • Mason WP (1943) Quartz crystal applications. Bell Syst Tech J 22:178–223. doi:10.1002/j.1538-7305.1943.tb00860.x

    Article  Google Scholar 

  • Mechie J, Sobolev SV, Ratschbacher L, Babeyko AY, Bock F, Jones AG, Nelson KD, Solon KD, Brown LD, Zhao W (2004) Precise temperature estimation in the Tibetan crust from seismic detection of the α–β quartz transition. Geology 32:601–604. doi:10.1130/G20367.1

    Article  Google Scholar 

  • Menard KP (2008) Dynamic mechanical analysis—a practical introduction. (2nd edition). CRC Press, Boca Raton

    Book  Google Scholar 

  • Neumann FE (1885) Vorlesungen über die Theorie der Elastizität der festen Körper und des Lichtäthers. Teubner, Leipzig

    Google Scholar 

  • Nikitin AN, Markova GV, Balagurov AM, Vasin RN, Alekseeva OV (2007) Investigation of the structure and properties of quartz in the α–β transition range by neutron diffraction and mechanical spectroscopy. Crystallogr Rep 52:428–435. doi:10.1134/S1063774507030145

    Article  Google Scholar 

  • Nye JF (1957) Physical properties of crystals- their representation by tensors and matrices (1992 edition). Clarendon, Oxford

    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 

  • Pabst W, Gregorová E (2013) Elastic properties of silica polymorphs—a review. Ceramics 57:167–184

    Google Scholar 

  • Peng Z, Redfern SAT (2013) Mechanical properties of quartz at the α–β phase transition: implications for tectonic and seismic anomalies. Geochem Geophys Geosyst 14:18–28. doi:10.1029/2012GC004482

    Article  Google Scholar 

  • Peng Z, Chien SY, Redfern SAT (2012) Dynamic mechanical relaxation and loss in the incommensurate phase of quartz. J Phys 24:255403. doi:10.1088/0953-8984/24/25/255403

    Google Scholar 

  • Perrier A, de Mandrot R (1923) Elasticité et symétrie du quartz aux temperatures élevées. Mém Soc Vaud Sci Nat 7:333–363. doi:10.5169/seals-287448

    Google Scholar 

  • Raz U, Girsperger S, Thompson AB (2002) Thermal expansion, compressibility and volumetric changes of quartz obtained by single crystal dilatometry to 700 °C and 3.5 kilobars (0.35 GPa). Schweiz Mineral Petrogr Mitt 82:561–574. doi:10.5169/seals-62381

    Google Scholar 

  • Reuss A (1929) Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Z Angew Math Mech 9:49–58. doi:10.1002/zamm.19290090104

    Article  Google Scholar 

  • Ronov AB, Yaroshevsky AA (1969) Chemical composition of the Earth’s crust. Geophys Monogr Ser 13:37–57

    Google Scholar 

  • Savart MF (1829) Sur l’élasticité des corps qui cristallisent régulièrement. Ann Chim Phys 40:5–30

    Google Scholar 

  • Sheehan AF, de la Torre T, Monslave G, Abers GA, Hacker BR (2014) Physical state of the Himalayan crust and uppermost mantle: constraints from seismic attenuation and velocity tomography. J Geophys Res Solid Earth 119:567–580. doi:10.1002/2013JB010601

    Article  Google Scholar 

  • Thompson RM, Downs RT, Dera P (2011) The compression pathway of quartz. Am Mineral 96:1495–1502. doi:10.2138/am.2011.3843

    Article  Google Scholar 

  • Van Tendeloo G, van Landuyt J, Amelinckx S (1976) The α–β phase transition in quartz and AlPO4 as studied by electron microscopy and diffraction. Phys Status Solidi A 33:723–735. doi:10.1002/pssa.2210330233

    Article  Google Scholar 

  • Voigt W (1889) Über die Beziehung zwischen den beiden Elastizitätsconstanten isotroper Körper. Ann Phys 274:573–587. doi:10.1002/andp.18892741206

    Article  Google Scholar 

  • Voigt W (1910) Lehrbuch der Kristallphysik - mit Ausschluss der Kristalloptik. Johnson Reprint Corporation, New York 1966

  • Wooster WA, Wooster N, Rycroft JL, Thomas LA (1947) The control and elimination of electrical (Dauphiné) twinning in quartz. J Inst. Electr Eng 94:927–938. doi:10.1049/ji-3a-2.1947.0116

    Google Scholar 

  • Zubov VG, Firsova MM (1962) Elastic properties of quartz near the α–β transition. Sov Phys Crystallogr 7:374–376

    Google Scholar 

Download references

Acknowledgements

We thank Dr. Martin Herrenknecht for financial support throughout years that helped us to carry out the research leading to this paper. During his employment at KIT, Steffen Klumbach received funding from a Geotechnologies grant of the German Federal Ministry of Education and Research (support code: 03G0763A), which is greatly acknowledged. Currently, Steffen Klumbach is supported by a grant of the German Research Foundation (support code: DFG Ke 501/11-1) and Prof. Dr. Hans Keppler at BGI. We welcome the discussions with Dr. Birgit I. Müller and Dr. Christian Scheffzük during this study. Further, we thank Larissa F. Dobrzhinetskaya, two anonymous reviewers, and Eleonore Jennings for their constructive comments to improve the manuscript.

Author information

Authors and Affiliations

  1. Institute of Applied Geosciences, Technical Petrophysics, KIT Karlsruhe Institute of Technology, Adenauerring 20b, 76131, Karlsruhe, Germany

    Steffen Klumbach & Frank R. Schilling

  2. Bavarian Research Institute of Experimental Geochemistry and Geophysics (BGI, since 1st June 2016), University of Bayreuth, Universitätsstraße 30, 95447, Bayreuth, Germany

    Steffen Klumbach

Authors
  1. Steffen Klumbach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frank R. Schilling
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steffen Klumbach.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klumbach, S., Schilling, F.R. Anisotropic viscoelastic properties of quartz and quartzite in the vicinity of the α–β phase transition. Phys Chem Minerals 44, 627–637 (2017). https://doi.org/10.1007/s00269-017-0888-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00269-017-0888-z

Keywords

Search

Navigation