A model of transformational superplasticity in the upper mantle

Abstract

We develop a model of transformational superplasticity of the mantle as it undergoes a solid–solid phase change. By considering various scenarios of the evolution of grain geometry in a polycrystalline material composed of two phases of different densities, we estimate the strain rate associated with the reshaping of the grains required to accommodate the volume change. We relate the deviatoric strain rate of the reshaping grains to the macroscopic dilatation rate of the entire composite, where the latter is evaluated both by applying a kinetic theory of the transformation and by implementing the seismically observed sharpness of the phase transformation. We estimate that, depending on the grain geometry and the kinetics, the deviatoric strain rates can exceed the dilatational strain rates by an order of magnitude. We calculate the degree of softening of the mantle that would occur at the beginning of the phase transformations at 400 and 670 km depths. For a power-law rheology with stress exponent n = 3, mantle viscosity decreases by up to one to two orders of magnitude within the first 1.5 km of the upper transition, and by two to three orders of magnitude within the first 1 km for the transition at 670 km depth. To account for uncertainties in strain rate (or stress) and grain size, we construct a deformation mechanism map for a three-component mantle and a variety of grain sizes, tectonic stresses and strain rates. In the dislocation creep regime, the high transformational stresses place an upper bound on the effective viscosity of the composite. We calculate the transformational-superplasticity (TS) field for a particular mantle flow model and show that variations of effective viscosity of the order of one order of magnitude occur at half of the dominant flow wavelength. We describe the effects of a phase transformation on mantle dynamics as jump conditions on the vertical and lateral velocities across the thin two-phase layer. An abrupt change in the azimuthal velocity would facilitate mixing across the phase-change region and cause refraction of currents passing through this depth. The largest deviation of the flow velocities occurs within the major up- and downwellings. We also show that, when TS is included, the change in the long-wavelength geoid is comparable to that caused by a 50 per cent increase in the viscosity of the lower mantle, and the change in the short-wavelength geoid is similar to an extension of an upper-mantle low-viscosity zone down to 450 km depth.