High-temperature viscoelasticity and seismic wave attenuation: materials, methods and micromechanical modelling
Myall Hingee1, Harri Kokkonen1, John Fitz Gerald1, Ian Jackson1, Craig Saint1,2 , Auke Barnhoorn1,3,Yoshitaka Aizawa1,4, Ulrich Faul5, Stephen Morris6
1 Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
2 Now at Department of Electronic Materials Engineering, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia
3 Now at Department of Earth Sciences, Utrecht University, 3508 TA Utrecht, The Netherlands
4 Now at Japan Manned Space Systems Corp., Kawaguchi, Tsuchiura, Ibaraki 300-0033, Japan
5 Department of Earth Sciences, Boston University, Boston, MA 02215 USA
6 Department of Mechanical Engineering, University of California, Berkeley, CA 94720 USA
At sufficiently high temperatures in the Earth's interior, the mechanical behavior changes from elastic to viscoelastic with profound implications for mantle rheology and also seismic wave speeds and attenuation. Such viscoelastic behaviour results from the stress-induced migration of vacancies and dislocations (extended defects reflecting prior or current deformation). As part of an ongoing study of high-temperature viscoelasticity, focused on olivine-rich upper-mantle materials, we have made substantial progress this year on several fronts:
Testing of novel materials: It has recently been demonstrated that high-purity synthetic Fo90 olivine (Mg0.9Fe0.1)2SiO4 prepared from a sol-gel-derived precursor is much stronger than its natural counterpart [1]. A possible role for grain-boundary chemistry in explaining these differences has been explored this year by modifying the sol-gel procedure to incorporate ~1% Ca which is preferentially accommodated in the grain boundaries of the polycrystalline material. Deformation experiments suggest that the Fo90:Ca specimens are not significantly weaker than the pure Fo90 material. Small concentrations of water, accommodated within nominally anhydrous minerals like olivine, may enhance the concentration and/or mobility of the defects responsible for high-temperature viscoelastic relaxation. In order to study such effects in fine-grained polycrystalline olivine, it is necessary to suppress grain growth that is typically dramatically enhanced by the presence of water. We have explored the feasibility of restricting grain growth by changing the stoichiometry of the sol-gel precursor to yield ~50% of the additional silicate phase orthopyroxene. Comparison of the microstructures (Fig. 1 '6465' and '6626' respectively) for pure olivine and olivine-orthopyroxene mixtures, hot-pressed with added water, clearly demonstrates the effectiveness of the added orthopyroxene in inhibiting grain growth.
Improved experimental methods: The experimental procedure used in our laboratory for the study of high-temperature viscoelastic relaxation in geological materials involves low-amplitude forced torsional oscillation of a specimen assembly in which a cylindrical specimen is sandwiched between ceramic torsion rods (Fig. 2). Direct contact and chemical reaction between the specimen and the torsion rods is prevented by metal foils that also serve to relax thermal stress concentrations at the interface and to impose appropriate redox conditions. This year, we have newly quantified a contribution to the overall torsional compliance of the specimen assembly from the interfaces between the metal foil and alumina torsion rod at each end of the specimen. We have demonstrated that this (previously neglected) extraneous contribution to the apparent compliance of the specimen can be removed by subtraction of the torsional compliance of a foil-bearing reference assembly similarly containing two alumina-foil interfaces. This new strategy provides more accurate determination of the shear modulus and associated strain-energy dissipation 1/Q. Correction of previously published data for fine-to-medium grained polycrystalline olivine for the interfacial compliance suggests somewhat milder frequency and temperature dependence of 1/Q than previously reported and substantially stronger grain-size sensitivity.
Micromechanical modelling: Experimental data for high-temperature viscoelastic relaxation in fine-grained ceramic and geological materials have proved difficult to reconcile with the classic models of grain-boundary sliding [2]. Collaboration with Stephen Morris at the University of California, Berkeley, has resulted in a more comprehensive analysis of grain-boundary sliding in which both viscous sliding and diffusional transport of matter along the boundary have been incorporated for the first time. An analytical (perturbation) solution, valid in the limit of vanishing boundary slope, indicates that 1/Q ~ 1/ω at sufficiently low frequency ω as expected for viscous rheology (diffusional creep). At much higher frequency, the 1/Q peak of (anelastic) elastically accommodated sliding is predicted with a peak height varying inversely with the boundary slope - suggesting that elastically accommodated sliding might be suppressed in this model for boundaries of finite slope. At intermediate frequencies, 1/Q ~ 1/|ln ω| - a milder frequency dependence than previously predicted. The new model, now being extended through numerical simulations of the behaviour of arrays of elastic crystals undergoing diffusionally assisted grain-boundary sliding, should ultimately provide a more robust framework for the interpretation of experimental data for fine-grained materials.
Faul UH, Jackson I (2007) Diffusion creep of dry, melt-free olivine. J. geophys. Res. 112, B04204, doi 10.1029/2006JB004586.
Jackson I, Faul UH, Fitz Gerald JD, Morris SJS (2006) Contrasting viscoelastic behaviour of melt-free and melt-bearing olivine: implications for the nature of grain-boundary sliding. Mat. Sci. Eng. A 442:170-174.