Effect of temperature on elastic properties of biotite and biotite-rich rocks: estimation from experiment and molecular dynamics simulation

We measured the P-wave velocities (VP) of mafic high-grade metamorphic rocks at 1.0 GPa pressure and a range of temperatures from 25 to 400 °C, along orthogonal directions corresponding to macroscopic fabric elements in the specimen. Our results showed that biotite-rich rocks (over 15 vol per cent biotite) displayed a strong decrease in VP with increasing temperature whereas biotite-free rocks did not. The anisotropy of VP (AVP) in biotite-rich rocks also increased with increasing temperature because of differential VP reduction, indicating a thermal dependence of the elastic properties of biotite. We conducted molecular dynamics simulations to investigate the effect of temperature on the elastic stiffness constants (Cij) of phlogopite, an end member of the biotite solid-solution series. The simulations indicated that Cij of phlogopite have a strong anisotropy and temperature dependence. We then estimated Cij of the bulk rock by using the Voigt-Reuss-Hill average procedure based on the estimated Cij of phlogopite, reference values for Cij of hornblende and plagioclase and measured crystal preferred orientations. From the resulting values of bulk-rock Cij, we calculated the quasi-VP and anisotropy parameter ϵ, under the assumption of transverse isotropy, and confirmed that temperature had a clear effect on velocity whereas AVP remained stable. This result suggests that the thermal effect on VP of biotite-rich rocks can be explained by the thermal dependence of Cij of phlogopite, which we attribute to a lattice rearrangement in phlogopite. This finding implies that the elastic properties of micas may change and affect the elastic properties of bulk rocks in the absence of mechanical breakage, dehydration reactions or phase changes. The thermal effect on AVP of biotite-rich rocks cannot be explained by a thermal dependency of the elastic constants of phlogopite. We speculate that the local concentration of thermal stress on biotite may account for the thermal dependency of AVP of biotite-rich rocks.