Stress relief during solid-state transformations in minerals

Abstract

This work estimates the power dissipated by solid-state phase changes in the transition layer of the mantle. Earlier studies have shown these transitions occur by nucleation and growth, and that dislocations are induced in the matrix around the grain during growth. The small-scale flow allowed by the dislocations dissipates power as a sample transforms. This dissipation is easily found in high-pressure experiments by studying the growth of an isolated grain in a rigid, perfectly plastic solid, and using the observed dislocation densities to infer the yield stress. Extrapolation of this result to the mantle raises a difficulty. If the deviatoric stress depends on the strain rate, the high shear stresses inferred around the grains in the experiments may not occur at the low dilatation rates typical of the transition layer. This difficulty is treated here by studying growth in two limits. Either the growth rate is determined by: (i) the kinetics of interface propagation, or (ii) the kinetics of matrix deformation. In case (i) it is argued that the deviatoric stress in the matrix can be taken as independent of strain rate, and the problem of extrapolation is trivial. It is shown that some form of layered convection is likely in case (i), because the yield stress inferred from experiments is such that if all the volume flow in the mantle were to cross the transition layer, the extra power loss would exceed the total viscous dissipation outside the transition layer. In case (ii), the difficulty of extrapolation is significant, and a test is given to identify this case in practice. Such ‘ slip-controlled ’ growth is shown to have a characteristic signature: if the pressure is fixed, the volume of an isolated spherical grain grows exponentially with time if the matrix is isotropic, and the deviatoric stress is a functional of the strain history. The small-scale flow can then be used as a rheometer.