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

Eshelby's theory is used to calculate the elastic strain energy associ ated with coherent homogeneous nucleation for the olivine-spinel trans formation. Incorporating the elastic strain energy, the activation ene rgy, Delta G, for homogeneous nucleation is estimated using a quasi-N ewton's method, a finite-difference gradient, and assuming an orientat ion-independent interfacial energy. For the limiting case of coherent, homogeneous nucleation and interface-controlled growth, the overall t ransformation rate along a relatively cold subducting slab (approximat ely 500 degrees C at 400 km depth) is calculated for various nucleatio n rates (theoretical) and previously published growth rates (experimen tal). The result indicates that the transformation rate assuming coher ent, homogeneous nucleation and interface-controlled growth may be com parable with that for grain boundary nucleation and interface-controll ed growth in a relatively cold subducting slab. The large transformati on strain energy and stresses can be greatly relaxed by plastic deform ation of the olivine matrix. In a cold subducting slab, the deformatio n of olivine around a growing spinel grain or cluster of grains probab ly proceeds by the mechanism of low-temperature plasticity (dislocatio n glide). Under the influence of externally applied differential stres ses, the interaction between the residual stresses around individual s pinel inclusions may cause the formation of a through-going fault and initiate deep-focus earthquakes.