Physics and Chemistry of Minerals

, Volume 44, Issue 9, pp 627–637 | Cite as

Anisotropic viscoelastic properties of quartz and quartzite in the vicinity of the αβ phase transition

  • Steffen Klumbach
  • Frank R. Schilling
Original Paper


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 αβ 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 αβ 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 αβ phase transition that we observed as an in situ temperature probe for seismic studies of the Earth’s continental crust.


Quartz Transition Stiffness Viscoelasticity Anisotropy 



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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institute of Applied Geosciences, Technical PetrophysicsKIT Karlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Bavarian Research Institute of Experimental Geochemistry and Geophysics (BGI, since 1st June 2016)University of BayreuthBayreuthGermany

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