In models of nucleation and growth of crystals on surfaces, it is often assumed that the energy surface of the substrate is flat, that diffusion is isotropic, and that capture numbers can be calculated in the diffusion-controlled limit. We lift these restrictions and formulate the general time-dependent problem in a 2D potential field. We utilize the Master Equation Discretization(MED) method to solve the 2D time-dependent diffusion field of adparticles on general nonuniform (rectangular grid) substrates, and compare it against competing algorithms, including the FFT and hybrid-FFT methods previously introduced, for periodic boundary conditions. The physical context is set by the importance of repulsive interactions in the nucleation and growth of many nanostructures, e.g. metal nanoclusters, hut clusters and nanowires. The programs, realized in Matlab ® 6.5, are used to obtain quantitative capture numbers, aspect and direct impingement ratios, and other island growth quantities in the presence of potential fields, when particular surface processes are included. The case of no corner rounding is studied in detail. Strongly anisotropic potentials favor wire growth, which can be considerably influenced by alternate deposition and annealing, and the location of neighboring islands. Physical examples are given based on Ge/Si(001) material parameters.Essentially similar programs, differing only in outputs, are used to visualize the diffusion field and to produce realistic movies of crystal growth. Examples given here are linear deterministic calculations, but the framework allows for inclusion of non-linear and statistical effects for particular applications.

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The microstructure of rapidly quenched A1-Mn alloys were studied by TEM and SEM. The icosahedral phase in AI-Mn alloys was observed to show various types of fractal morphologies, which may be classified into four kinds: 1) dendritic shape, 2) flower-like shape, 3) granular shape and 4) grain-oscillation shape. After being digitized by a computer, the fractal dimensions (D) of these morphologies were calculated. Based on the traditional diffusion limited aggregation (DLA) model computer simulations were made with two-seeded and many-seeded clusters, which reflect the growing mechanism of some fractal structures in A1-Mn alloys. It is suggested that these fractal structures are formed by many icosahedral particles about 20 nm in size aggregating during the rapid quenching process.

In rate equation models of nucleation and growth on surfaces, and it has often been assumed that the energy surface of the substrate is flat, that diffusion is isotropic, and that capture numbers can be calculated in the diffusion-controlled limit. We lift these restrictions analytically, and illustrate the results using a hybrid discrete FFT method of solving for the 2D timedependent diffusion field of ad-particles, which has been implemented in Matlab ® 6.5. A general substrate energy surface is included by transformation of the field. The method can work with any boundary conditions, but is particularly clear for periodic boundary conditions, such as might be appropriate following nucleation on a regular (rectangular) array of defects. The method is instructive for visualizing potential and diffusion fields, and for demonstrating the time-dependence of capture numbers in the initial stages of deposition and annealing.