Mechanism of Interfacial Coarsening in Molecular Beam Epitaxy Growth on (001) Surfaces

We theoretically address epitaxial growth on (001) crystalline surfaces symmetry, in the regime when pyramids are formed across the growing interface due to Schwoebel step-edge barriers. We develop a kinetic scaling theory that analytically explains numerous experiments and simulations suggesting that pyramid size grows, via coarsening, as a fourth root of the deposition time. Pyramid dynamics is elucidated in terms of pyramid edges that form a growing self-organized square lattice across the growing interface. The edge lattice of pyramids is disordered by topological defects that are characterized here as dislocations. We show that pyramid coarsening is mediated by climb-motion of the dislocations of the edge lattice.

Role of a Free Energy Action Principle in Predicting Microstructure Formation

It is demonstrated that some twenty representative free boundary diffusion-reaction and hydrodynamic patterning systems fall within the compass of the isothermal variational principle where the Lagrangian density is the free energy density g, and η is an appropriate order parameter. To illustrate the universality of the formulation we survey in some detail its degree of equivalence to twenty-one currently adopted or promoted procedures for resolving pattern degeneracies, and critically reappraise theoretical descriptions of grain growth, ordinary diffusion, spinodal decomposition and Ostwald Ripening and their predictive success. The importance of a hierarchy of kinetic scaling laws is discussed. The physics of fluctuations is essential to understanding.