Temporal development of fabric in uniaxially stressed polycrystalline media—A theory

We present a kinetic theory for the development of lattice-preferred orientation in a uniaxiallystressed aggregate consisting of elastically uniaxial crystals. The fabric is brought about by grain-boundary migration alone; other fabric-producing mechanisms, such as plastic deformation, syntectonic recrystallization, and dissolution/reprecipitation, are specifically excluded from the theory. The formulation statistically averages the mass transfer between a typical crystal and its adjacent neighbors over all the possible crystallographic orientations of these neighbors and over all the possible orientations of the interfaces between the neighbors and the crystal of interest. The rate of mass exchange between two adjacent crystals is proportional (1) to the difference between chemical potentials and (2) to the surface area common to them. With these assumptions we find an equation for the massfraction density of crystals that have a given orientation (with respect to the stress) at any given time. The theory predicts that beyond a certain time a gap develops in the distribution of crystal orientations allowed: the only crystals that continue to exist are those for which the c-axis is within a certain, timedependent range about the stress.