On the structure and homogeneity of solid solutions: The limits of conventional X-ray diffraction

The characterization of solid solutions by conventional X-ray diffraction (XRD) is critically assessed using the example of Cu-Co alloys. In particular, the limits of this technique for investigating compositional inhomogeneities are discussed. Coherent Cu-Co multilayer films are taken as a model for a decomposed solid solution, with the layer thicknesses being taken as representative for the sizes of heterogeneous domains. It is shown that the XRD patterns of these multilayer films continuously change with decreasing layer thickness from that of two bulk phases to a single pattern identical to that of a homogeneous solid solution, the transition occurring at a layer thickness of about 10 nm. Below this layer thickness, the lattice spacing derived from the single diffraction pattern exhibits an average value determined by the overall composition. By definition, this average lattice spacing varies continuously between the pure elements with a Vegard law dependence when the overall composition is changed. However, since the multilayer is heterogeneous, the average lattice spacing is nowhere present in the specimen. The results indicate that coherent inhomogeneities in Cu-Co solid solutions must be larger than several nanometres before they can be detected using conventional XRD. With these conclusions XRD measurements of Cu-Co alloys after preparation as well as during subsequent annealing are considered. The results demonstrate the important role of structural coherence on diffraction measurements. It is concluded that it is not possible to determine the supersaturation of a solid solution using conventional XRD. Complementary measurements have to be performed in order to prove the homogeneity of a supersaturated alloy.