Effective Coordination Numbers in Ultrathin Metallic Films

Abstract
Nanostructures bave become a major field in material science. With molecular beam epitaxy it is possible to engineer multilayers with unusual anisotropic properties and metastable structures. For ultrathin films, or particles of small size, the coordination numbers are less than their bulk values. In fitting E X A F S data it is useful to be able to place limits on the coordination numbers or their ratios. W e have calculated the effective coordination numbers N_i , i= 1 to 5 for thin films with different crystal structures. The thickness o f the film is specified by the number o f layers N_z in the z-direction and the area in the x y plane by the number o f rows of atoms N_XY along the side of a square domain. For fixed N_z, with the x-ray beam unpolarized or its electric vector parallel or perpendicular to the substrate (xy plane), the effective H approach hyperbolically the coordination number for a layer o f infinite area. Simple analytical expressions are fitted to the numerical results fix- bcc and fee crystals from which the H can be calculated for both N_XY and Nz ≥ 2. Comparison is made with the effective coordination numbers obtained from polarized E X A F S measurements on epitaxial metallic films less than 10 monolayers thick.