Theory of Curvature and Grooving Effects in DIGM I: The Physics
John W. Cahn, O Penrose
We take the formulation of steady-state diffusion-induced grain boundary motion from our earlier work , and combine it with the results of Mullins' theory for surface grooves from steadily moving grain boundaries, to formulate a theory of DIGM in thin plates. We solve this formulation approximately, and test the approximation again more accurate solutions in a companion paper.  Corresponding to experimental observations we find two types of solutions, termed connecting, when the boundary continues to traverse the specimen, and trailing, when the boundary near the surface moves too rapidly for the interior of the grain boundary to keep up, creating an elongated grain along the surface with a nonuniform composition profile. Both solutions span many orders of magnitude, but with limits for both. There is a large overlapping set of conditions where both types of solution can coexist. For the connecting solutions we find at least four regimes with different scaling behaviours, thin or thick specimens, or high or low driving forces, resulting in nearly uniform penetration or surface layering, relatively flat grain boundaries or highly curved ones. We find that grooving creates a threshold for DIGM, contrary to our earlier paper in which grooving was not considered.
grain boundary, scaling
and Penrose, O.
Theory of Curvature and Grooving Effects in DIGM I: The Physics, Acta Materialia
(Accessed June 1, 2023)