GRAIN-BOUNDARY GROOVING BY SURFACE-DIFFUSION - AN ANALYTIC NONLINEAR MODEL FOR A SYMMETRICAL GROOVE

The fourth-order nonlinear boundary-value problem for the evolution of a single symmetric grain-boundary groove by surface diffusion is mode lled analytically. A solution is achieved by partitioning the surface into subintervals delimited by lines of constant slope. Within each su binterval, the advance of the surface is described by an integrable no nlinear evolution equation. The model is capable of incorporating the actual nonlinearity arbitrarily closely. The surface profile is determ ined for various values of the central groove slope including the limi ting case of a groove which has a root that is vertical. Such a soluti on exists only because of the nonlinearity.