A GEOMETRICALLY GENERAL-THEORY OF DIFFUSION CONTROLLED COARSENING

The new theory of diffusion controlled coarsening presented in this paper differs from traditional developments in three decisive aspects: (1) The theory is geometrically general, applying to microstructures of arbitrary complexity; (2) It discards the mean field visualization of the coarsening process and treats interactions with neighboring elements explicitly by introducing the concept of communicating neighbors; (3) In its application to scale factor coarsening of sparse sphere size distributions, the theory yields results that are in sharp contrast with the classical theory of diffusion controlled coarsening. This latter result leads to an assertion that the classical LSW theory is flawed; and hence that all mean field theories that reduce to the classical result in the sparse sphere distribution limit propagate that flaw.