Kinematics and thermodynamics of a growing rim of high-pressure phase

• Strain is calculated incorrectly in existing analyses of wadsleyite rim growth.
• Using the correct strain, wadsleyite strength is estimated as ∼ 1 GPa at 1303 K.
• Previous erroneous analyses infer a strength over 3 times that value.
• The new estimate is compatible with published values from independent experiments.
• Behaviour predicted by the new analysis may bear on the origins of deep earthquakes.

We have reanalysed the problem of growth of a dense product rim on a sphere of parent phase. To decouple the problem of calculating deformation from rheology, we assume spherical symmetry, and incompressible phases. Within the product, the radial deviatoric strain and its time-derivative prove to be of opposite sign: strain is compressive, but the strain rate is tensile. Further, the radial deviatoric strain in the new product adjacent to the interface is invariant in time. Propagation of the phase interface is determined by a competition between two mechanisms: as an element of material is transformed, its shear strain energy is increased; and the core pressure performs work compressing it. For elastic phases, this competition results in metastability. Within a certain pressure range, either phase can occur alone, but the two phases can not coexist. Because this result is inconsistent with experiments by Kawazoe et al. (2010) in which a rim of high-pressure phase (wadsleyite) coexists with a central core of low-pressure phase (olivine), we then incorporate plastic flow. Assuming perfect plasticity, we show that for a given applied pressure exceeding the coexistence pressure, a rim of product can now nucleate if the excess pressure ΔpΔp exceeds a critical value depending on yield stress. Increasing ΔpΔp above this value allows product to grow into the parent phase. There are now two possibilities, depending on the value of ΔpΔp. Growth may eventually cease to produce a state in which the product rim is in equilibrium with a parent core; or growth may follow a more complicated path: within a range of excess pressures, the growth rate can decrease strongly from its initial value to produce a quasi-equilibrium state, before increasing again to a rate similar to that at which transformation began. We interpret these results to mean that if ΔpΔp is increased slowly in a series of experiments with constant yield stress, the sample passes through a series of equilibria until ΔpΔp is large enough for the second type of growth to be possible; transformation is then completed rapidly on the timescale set by interface kinetics. This result may be relevant to the problem of deep earthquakes. Lastly, using existing experiments in which a wadsleyite rim grows on an olivine sphere, we apply the theory to estimate the yield strength of wadsleyite: our estimates are consistent with measurements by independent methods.