Estimation of the geometrical rate constant in idealized three dimensional grain growth

An estimate is made of the geometrical rate constant G₃ in the parabolic grain growth law d〈r〉²/dt = kG₃ in three dimensions, where 〈r〉 is the average volume-equivalent grain radius and where k = -u_n/K is a positive constant in which u_n is the local boundary velocity along an outward pointing normal and K is the local mean curvature (positive for a sphere). The parabolic law follows from the above velocity rule and a hypothesis of statistical self-similarity of the structure. The estimate is based on (l) a theorem deduced from the preceeding assumptions, (2) an approximate formula for the rate of change of the volume of a given grain, (3) a model of polyhedral geometry and (4) the experimental data of Hull on separated β-brass grains. We estimate G₃ = 0.5 ± 0.l. Comparison with previous estimates is made.