We develop a new, combined experimental and theoretical approach to make reliable predictions for the limiting case of surface reaction kinetics controlled growth. We solve the inverse problem of determining the growth velocity from observations of the evolution of the morphology of GaN islands grown by metalorganic chemical vapor deposition and make use of crystal symmetry and established theorems. We are able to predict the growth for both convex and concave surfaces, with faceted and curved features. We also give a general guideline for deducing growth velocities from experimental observations.
It is known from the theory of group representations that, in principle, a tensor of any finite order can be decomposed into a sum of irreducible tensors. This paper develops a simple and effective recursive method to realize such decompositions in both two-and three-dimensional spaces. Particularly, such derived decompositions have mutually orthogonal base elements. Quite a few application examples are given for generic and various physical tensors of orders up to six.
A series of molecular dynamics simulations was performed on a bicrystal to which a fixed shear rate was applied parallel to the boundary plane. Under some conditions, grain boundary motion is coupled to the relative tangential motion of the two grains. In order to investigate the generality of this type of coupled shear/boundary motion, simulations were performed for both special (low AE) and general (non-AE) [010] tilt boundaries over a wide range of grain boundary inclinations. The data point to the existence of two critical stresses: one for coupled shear/boundary motion and the other for grain boundary sliding. For the non-AE boundaries, the critical stress for coupled shear/boundary motion is typically smaller than that for sliding; coupled shear/boundary motion occurs for all inclinations. For AE5 boundaries, for which the critical stress is smaller and depends on boundary inclination, coupled shear/boundary motion occurs for some, but not all inclinations.
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