Effective coordination numbers in ultrathin metallic films

Nanostructures have 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 EXAFS data it is useful to be able to place limits on the coordination numbers or their ratios. We have calculated the effective coordination numbers N-i, i = 1 to 5 for thin films with different crystal structures. The thickness of the film is specified by the number of layers N-Z in the z-direction and the area in the xy plane by the number of 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 N-i approach hyperbolically the coordination number for a layer of infinite area Simple analytical expressions are fitted to the numerical results for bcc and fee crystals from which the N-i on be calculated for both N-XY and N-Z greater than or equal to 2. Comparison is made with the effective coordination numbers obtained from polarized EXAFS measurements on epitaxial metallic films less than 10 monolayers thick.