THE ELASTIC STRAIN-ENERGY ASSOCIATED WITH THE OLIVINE-SPINEL TRANSFORMATION AND ITS IMPLICATIONS

Eshelby's theory is used to calculate the elastic strain energy associated with coherent homogeneous nucleation for the olivine-spinel transformation. Incorporating the elastic strain energy, the activation energy, Delta G*, for homogeneous nucleation is estimated using a quasi-Newton's method, a finite-difference gradient, and assuming an orientation-independent interfacial energy. For the limiting case of coherent, homogeneous nucleation and interface-controlled growth, the overall transformation rate along a relatively cold subducting slab (approximately 500 degrees C at 400 km depth) is calculated for various nucleation rates (theoretical) and previously published growth rates (experimental). The result indicates that the transformation rate assuming coherent, homogeneous nucleation and interface-controlled growth may be comparable with that for grain boundary nucleation and interface-controlled growth in a relatively cold subducting slab. The large transformation strain energy and stresses can be greatly relaxed by plastic deformation of the olivine matrix. In a cold subducting slab, the deformation of olivine around a growing spinel grain or cluster of grains probably proceeds by the mechanism of low-temperature plasticity (dislocation glide). Under the influence of externally applied differential stresses, the interaction between the residual stresses around individual spinel inclusions may cause the formation of a through-going fault and initiate deep-focus earthquakes.