Related Experiment Video
Updated: Jun 22, 2026

On-Chip Crystallization and Large-Scale Serial Diffraction at Room Temperature
Published on: March 11, 2022
Homogenization of reconstructed crystal surfaces: Fick's law of diffusion
1Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
Abstract:
Fick's law for the diffusion of adsorbed atoms (adatoms) on crystal surfaces below roughening is generalized to account for surface reconstruction. In this case, material parameters vary spatially at the microscale, and the coarse graining for crystal steps via Taylor expansions is not strictly applicable. By invoking elements of the theory of composites in one independent space dimension, we homogenize the microscale description to derive the macroscopic adatom flux from step kinetics. This approach relies on a multiscale expansion for the adatom density. The effective surface diffusivity is determined through appropriate discrete averages of microscale kinetic parameters.
Related Concept Videos
Determination of Crystal Structures
X-ray Crystallography
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
Law of Rational Indices
Imperfections in Crystal Structure: Stoichiometric Point Defects
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Imperfections in Crystal Structure: Point, Line and Plane Defects
