A GLOBAL ANALYSIS OF STRUCTURAL EVOLUTION IN A ROW OF GRAINS

When a polycrystalline fiber is heated for some time, grains change sh ape and may evolve to one of two equilibrium configurations: isolated spheres, or truncated spheres that remain connected. To which configur ation do the grains evolve? How long does this evolution take? These a re global questions, and call for a global way to look at the phenomen on. The fiber is a nonequilibrium structure. The free energy consists of the surface and grain-boundary energies; it is the reduction of thi s energy that drives the diffusive flux of atoms on the surfaces and t he grain boundaries. We describe the grain shape using two generalized coordinates, the grain length and the dihedral angle. The fret: energ y is expressed as a function of these coordinates. In the space of the free energy and the coordinates, the energy function is represented b y a surface, or a landscape. A point on the landscape represents a non equilibrium state in general, and the bottom of a valley represents an equilibrium state. We use a variational principle to assign a viscosi ty matrix to every point on the landscape. The approach leads to a set of ordinary differential equations that govern the evolution of the g eneralized coordinates.