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Elasticity and Viscoelasticity of Solid SiO2 as a Function of Frequency and Temperature

Elasticity and Viscoelasticity of Solid SiO2 as a Function of Frequency and Temperature

Prof. F.R. Schilling

Prof. J.-D. Eckhardt

person in charge:

Dr. S. Klumbach

Online publication: KIT Bibliothek Dissertation S. Klumbach


Quartz is one of the most abundant rock‐forming minerals within the Earth´s crust and used in numerous modern technical applications. A profound knowledge of its physical properties, especially the complex elastic behaviour, decisively influences our understanding of the subsurface, which is mainly based on the interpretation of seismic waves. To quantify and to better understand the complex elastic properties of quartz and quartz‐bearing rocks dynamic mechanical laboratory experiments are performed in the frequency range of seismic waves. In consequence to this, quartz shows a unique complex elastic behaviour in the vicinity of its alpha-beta phase transition. This may help to estimate temperatures underground and to clearly distinguish between a fully crystallised and a partly molten crust.

The laboratory experiments of this study comprise the determination of the complex Young’s moduli of synthetic and natural quartz crystals, quartz‐bearing rocks as well as fused silica as a function of frequency and temperature in symmetrical three‐point bending set‐ups with support spacings of 20 and 40 mm. Plate‐like specimens are loaded sinusoidally between 0.1 and 20 Hz. Dynamic stresses and strains as well as their phase lags are recorded isothermally from ambient temperature across the alpha-beta transition in quartz to temperatures > 600 °C. For the interpretation of the observed mechanical behaviours, the samples are additionally investigated by differential thermal analysis, X‐ray diffraction, X‐ray fluorescence, ultrasonic velocity measurements as well as by uniaxial and triaxial compression tests.

Dynamic mechanical analyses between ambient temperature and ≈ 500 °C reveal that the complex Young’s modulus of single‐crystal alpha‐quartz is anisotropic and frequency‐independent, within the experimental uncertainties. An increasing frequency dependence of the complex Young’s modulus of quartz is observed at higher temperatures towards the alpha-beta transition. The storage modulus (real part) increases sigmoidally with frequency, while the dissipation modulus (imaginary part) reaches a maximum at ≈ 1 Hz. The dispersion of the storage modulus and the dissipation maximum are low (40 mm support spacing: ≈ 7.6 and ≈ 2.6 GPa, respectively) parallel to the c‐axis of the crystal and comparably high (40 mm support spacing: ≈ 15.1 and ≈ 7.1 GPa, respectively) perpendicular to it. The frequency dependence of the complex Young’s modulus for beta‐quartz vanishes just a few degrees centigrade above the phase transition.