Topological rearrangements during 2D normal grain growth

Abstract

Topological rearrangements during grain growth in polycrystals provide an example of the strongest possible non-linearity in the grain population evolution dynamics. For a 2D grain the equation of growth is linear (von Neumann-Mullins law) until there is a topological change. The inevitable occurence of a topological rearrangement makes the system intrinsically non-linear, and the non-linearity effects are critical to understanding grain growth dynamics. In situ experimental investigation of topological rearrangements in thin polycrystalline films of succinonitrile (SCN) show that according to theoretical considerations (and contrary to conventional wisdom) small 4- and 5-sided quasi-2D grains usually shrink almost to the vanishing limit, without losing sides through the expected topological cascade of neighbor switchings. Vanishing grains generally do not create multiple vertices in the system. They do not shrink to a point as 2D soap froth bubbles do, but rather shrink to a line, with 2 vertices (in the case of 4-sided grains) or to two lines with 3 vertices (in the case of 5-sided grains). The experimental results are compared with those of direct computer simulation of 2D grain shrinking. The simulation shows also that the main topological results remain valid both in systems with uniform and anisotropic boundaries.