ON IDEALIZED 2 DIMENSIONAL GRAIN-GROWTH

The parabolic law of grain (or cell) growth holds in two and three dimensions under the following two conditions: 1) Consecutive configurations of the structure are self-similar in a statistical sense; 2) The velocity of boundary elements obeys a scaling relation that is satisfied both by the soap bubble model and the model based on the local curvature rule (boundary velocity proportional to the local curvature). The velocities of boundary elements in the soap bubble model do not, in general, obey the local curvature rule; they are determined, in part, by the requirement of a uniform pressure in each bubble which has no counterpart for a physical grain. Therefore, the local curvature model, resulting from the assumed proportionality of local boundary velocity to local thermodynamic driving force, is a better representation of physical grain growth. In the two dimensional case, an expression is derived for the coefficient of the time in the parabolic law in terms of the time invariant statistical parameters of the configuration of grains or cells. 13 Refs.