β --Phase Rheology of Olivine Using the α --β Transformation: Implications for Modelling Metastable Wedges

Transformation kinetics determine the structure of the metastable wedge of low--pressure α --phase in cold subducting lithosphere; through it, they may influence deep focus earthquakes, and slab penetration into the lower mantle. Experiments in which single crystals are transformed show that rapid nucleation on the sample surface creates a thin rim of dense β --phase, which then grows into the α --phase core at a speed decreasing in time (Kubo et al 1998; Mosenfelder et al 2000). That time--dependence is inconsistent with analyses assuming isobaric, mechanically passive phases. We apply a growth model coupling interface kinetics to transformation--induced viscoelastic deformation within the rim (Morris 2002 J. Mech. Phys. Solids, 50). The creep component of that deformation is taken to follow the Guyot--Dorn equation for creep by dislocation glide; the zero temperature flow stress σ _o and ratio q=Q/RT_s of activation energy to the product of the gas constant and solidus temperature T_s are found empirically. Though existing data are fitted by the model with an error of less than 15%, they do not determine σ _o precisely, being consistent with a range of values from 15 to 30 GPa; allowable values of q range from 30--35. We use our model to suggest how experiments might be performed to narrow this range. Lastly, we use the model to argue that coupling of kinetics and transformation--induced strain must be included when modelling metastable wedges.