Viscous constitutive relations of solid-liquid compositesin terms of grain boundary contiguity: 2. Compositional model for small melt fractions

摘要

We develop a compositional model for the grain boundary (GB) diffusion creep ofmelt-bearing polycrystalline aggregates. This model is an extension of the GB diffusioncontrol model by taking into account the effects of finite liquid diffusivity and finitereaction rates, which are important at small melt fractions (0). For shear viscosity 7/, thereexists a critical melt fraction 07,/ below which the rate-limiting process changes fromdiffusion through GB to diffusion through the liquid, and for bulk viscosity e, there existsa critical melt fraction c& below which the rate-limiting process changes from diffusionthrough GB to reaction at the pore surface. The implication of the model results is thatdifferent processes may limit the kinetics of bulk and shear viscosities at small 0. Themodel also predicts that stress can cause compositional and hence volumetric asymmetryin pores. As melt fraction increases from zero to the critical melt fractions, rapid decreasesoccur in n, from 77, to 0.277, and in e, from Do to 0.476, where n, represents I/ for Coblecreep. In the GB diffusion control model, these decreases occur discontinuously at zeromelt fraction, but this singularity is removed in the compositional model. For a typicalgrain size in the mantle (3 mm), the critical melt fractions are estimated semiquantitativelyas 0'2. = 10-4 and < 6 x 10-8, demonstrating the significant effect of very small amountof melt on the viscosities in the mantle.