Coordination number determination in binary alloys using electron diffraction

Abstract

The theory for the extraction of accurate coordination numbers from diffraction data is extended to the case of systems containing more than one type of atom. The cases where the atoms have atomic scattering factors which are not related by a simple scale factor is treated in detail. However, it is found that by the use of known test structures the general method is only required in extreme cases if 2% error is regarded as satisfactory.Electron diffraction is a convenient method for studying structure in amorphous and polycrystalline materials, especially when they are in the form of a thin film. Techniques have been developed, for example by Graczyk and Moss (1969), Cockayne and McKenzie (19SS), and Cockayne et al. (1991), for rapidly collecting the electron diffraction intensity from amorphous and polycrystalline thin films, and for transforming it to a reduced density function G ( r ) . While the electron diffraction technique gives accurate (to 0.0 1 A) nearest-neighbour distances for both elemental and alloy films, it has been found in practical situations that there are considerable difficulties in obtaining accurate coordination numbers from G ( r ) in the case of binary materials. In this paper, the existing methods for determining the coordination numbers of binary materials are refined in order to improve their accuracy. As an example, carbon-nitrogen alloys will be used. 2. THEORY FOR BINARY ALLOYSThe calculation of the diffracted intensity from an amorphous material with more than one type of atom was discussed by Warren (1990). Here we present a new formulation and derive results which are in a form ready to use. We illustrate the application of the formulation using artificially generated data. We begin with the Debye (1915) equation for the diffracted intensity from an array of atoms which takes all orientations in space relative to a fixed incident beam direction. The Debye (1915) equation is exact in the first Born approximation and may be written as t