Original paper

Elastic and anelastic properties of α- and b-quartz single crystals

Klumbach, Steffen; Schilling, Frank R.


The anisotropic complex Young's modulus of synthetic quartz single crystals is investigated, using a symmetric three-point bending experimental setup in a Dynamic Mechanical Analysis (DMA) testing system. The storage modulus and the dissipation modulus are examined at ambient pressure between room temperature and 620 °C, across the α-β phase transition (573 °C). The moduli are determined from measured stress, strain and phase lag data of oriented single crystals at five to ten distinct frequencies between 0.5 and 20 Hz. Quartz shows a strong frequency and temperature dependence of its complex mechanical properties, especially in the vicinity of the α-β phase transition. Around 573 °C, the storage modulus steadily increases with frequency, while the dissipation modulus reaches a maximum between 1 and 2 Hz. The observed elastic and anelastic behaviour can be well described by the Poynting-Thomson model, yielding low- and high-frequency limits of the Young's modulus. This accounts for differences among published data obtained with different experimental techniques, where inconsistent Young's moduli are reported for similar temperature conditions, especially close to the α-β phase transition. Softening of the Young's modulus of a -quartz with increasing temperature is accompanied by a decrease of the dynamic viscosity over several orders of magnitude and can be described by two Arrhenian processes. Using published shear moduli and the derived dynamic viscosity, mean relaxation times are derived, which decline from > 1700 s to < 2 s parallel to the c-axis and from < 700 s to 0.5 s perpendicular to the c-axis of the crystal, when increasing the temperature from 59 °C to 571 °C. The ratio of storage to dissipation modulus corresponds to the seismic quality factor Q, a measure of the attenuation of seismic waves. It exhibits a strong frequency and temperature dependence and reaches a minimum at the α-β phase transition. Longitudinal sound wave velocities show significant dispersion of < 6 % parallel and < 14 % perpendicular to the c-axis of the crystal at 571 °C, between 1 and 20 Hz. The characteristics of both attenuation and dispersion of seismic waves close to the α – β phase transition could be used as an in situ temperature probe for quartz-rich crustal rocks.


anelasticityanisotropyattenuationcomplex young's modulusdispersionelasticitypetrophysical propertiesphase transitionpoynting-thomsonquartzviscosity