FRACTAL ANALYSIS OF CRYSTALLINE SURFACES AT ATOMIC RESOLUTION

High-resolution images of ceramic oxide surfaces (e.g. MgO, NiO and BaTiO3) have been obtained in digitized form. Analytical techniques were designed to search for self-similar scaling (fractal) geometries. Three measures of surface roughness were investigated, namely coastline analysis, height-difference correlation function and variance scaling analysis. In some cases, changes in surface topology occur with time. In principle this should be analysed using self-affine fractal geometry and scaling concepts. The scaling behaviour was in all cases complicated by atomic surface faceting. Analytical results are reported for all crystalline surfaces imaged. The results are interpreted in terms of Brownian motion or self-diffusion and Brownian motion with geometrical restriction (lattice string animal models).