Grain size‐sensitive viscoelastic relaxation and seismic properties of polycrystalline MgO

Abstract

Torsional forced‐oscillation experiments on a suite of synthetic MgO polycrystals, of high‐purity and average grain sizes of 1–100 µm, reveal strongly viscoelastic behavior at temperatures of 800–1300°C and periods between 1 and 1000 s. The measured shear modulus and associated strain energy dissipation both display monotonic variations with oscillation period, temperature, and grain size. The data for the specimens of intermediate grain size have been fitted to a generalized Burgers creep function model that is also broadly consistent with the results for the most coarse‐grained specimen. The mild grain size sensitivity for the relaxation time τL, defining the lower end of the anelastic absorption band, is consistent with the onset of elastically accommodated grain boundary sliding. The upper end of the anelastic absorption band, evident in the highest‐temperature data for one specimen only, is associated with the Maxwell relaxation time τM marking the transition toward viscous behavior, conventionally ascribed a stronger grain size sensitivity. Similarly pronounced viscoelastic behavior was observed in complementary torsional microcreep tests, which confirm that the nonelastic strains are mainly recoverable, i.e., anelastic. With an estimated activation volume for the viscoelastic relaxation, the experimentally constrained Burgers model has been extrapolated to the conditions of pressure and temperature prevailing in the Earth's uppermost lower mantle. For a plausible grain size of 10 mm, the predicted dissipation Q−1 ranges from ~10−3 to ~10−2 for periods of 3–3000 s. Broad consistency with seismological observations suggests that the lower mantle ferropericlase phase might account for much of its observed attenuation.

The importance of grain size to mantle dynamics and seismological observations

“…We assume that the functional form of these relationships persists into the lower mantle [e.g., Abers et al ., ; Olugboji et al ., ]. This is supported by experiments showing that a broad range of materials, including ceramics [e.g., Barnhoorn et al ., ], silicates [ Jackson et al ., ; Gribb and Cooper , ; Jackson and Faul , ], inorganic compounds [ McCarthy et al ., ; Takei et al ., ; Yamauchi and Takei , ], and perovskite analogues [ Webb et al ., ] display an absorption band or “High Temperature Background” (HTB) behavior [see also Faul and Jackson , ]. These experiments indicate that the exponent, α , of the frequency dependence of attenuation, described using the power law , usually falls between 0.2 and 0.4 within the absorption band across the broad range of materials.…”

Viscoelastic Behaviour from Complementary Forced-Oscillation and Microcreep Tests

“…The duration of transient creep involving grain-boundary sliding has been identified with the Maxwell time τ M = ηJ U [19]. Accordingly, consistent with insights from more recent micromechanical modelling of grain-boundary sliding [20] and our recent practice [16], we here set τ H = τ M .…”

“…For the same reason, it may be desirable, as explored in the Results section, to fix certain parameters in the creep function model at values constrained by the forced oscillation data. For reasons of parametric economy, the Andrade creep function (Equation (3)) has thus far been preferred over the extended Burgers alternative (Equation (4)) for use in Equation 14 [16].…”

“…Accordingly, the fraction f R of the total inelastic strain βt n + t/η at time t that is ultimately recoverable following removal of the applied torque is [16].…”

“…In practice, time-domain microcreep studies have been used to constrain the value of steady-state viscosity for use in modelling the results of sub-resonant forced oscillation studies [10,11]. In our laboratory, consistency between forced-oscillation and microcreep data has been used as evidence of linearity of mechanical behaviour [14], and microcreep studies have been used to provide a qualitative or quantitative indication of the extent to which the inelastic strain is recoverable on removal of the applied stress [15,16]. However, we have not yet fully exploited the valuable complementarity between the forced-oscillation and microcreep methods.…”