Here a new approach based on EXAFS simulations followed by linear combination of EXAFS spectra is presented. The simulations were performed on pure Cu and binary Cu-Fe clusters.The main result of this study concerns the proof that polydispersity does not affect XAFS studies on nano-clusters within a size of up to 140 atoms.
IntroductionMany elements, such as Cu and Ni, are not soluble in Fe even at low concentrations below approx. 1%, so that they segregate under special heat and/or mechanical treatments. The segregation leads to clustering, which may strongly modify the mechanical and physical-chemical properties of the material. Depending on the involved elements, their concentrations and the applied treatments, the clusters can be coherent, i.e. they have the same phase of the matrix, or incoherent, i.e. they crystallize in different phases. Furthermore, the size of the clusters can play an important role for materials properties, e.g. for the embrittlement of reactor pressure vessel (RPV) steels in nuclear power plants [1,2] or in completely different fields like catalysis or surface science. Due to its inherent sensitivity towards the local structure around an X-ray absorbing element, EXAFS spectroscopy is a powerful tool to investigate nanostructures like small clusters. As long as EXAFS is an element selective technique, it provides information from all the atoms of a chosen element, regardless whether these atoms belong to clusters or to the matrix. In real cases samples do not contain homogeneous clusters of just one size, and the determination of an average cluster size is strongly influenced by the specific size distribution of the clusters. Combinations of different cluster sizes can provide very similar results; this issue is called polydispersity. Moreover, it is known that polydispersity is a limit for EXAFS experimental analysis [3][4][5]. Here, only nano-clusters (with less than 225 atoms and with a radius less than 8.5 Å) are investigated, and their shape is always considered spherical. Cu is the main element investigated and it is reasonable to expect that comparable conclusions can be drawn for other fcc-metals such as Al, Ca, Ni, Pd or Ag. Moonen et al. [6] already pointed out that fcc clusters of 147 atoms in vacuum have the same amount of atoms in the first and second shell (8.9 and 4) like a combination of clusters composed of 13 (32%) and 1415 atoms (68%), and, according to this study, experimental EXAFS data analysis cannot solve this issue. The first detectable difference appears in the 3rd shell where the linear composition shows 13.8 atoms and the 147 atoms cluster 13.0 atoms. However, this difference is hard to detect even if high quality experimental data is available. Here, a new approach based on EXAFS simulations followed by linear combination (LC) of EXAFS spectra is presented. The simulations were performed for pure Cu clusters and binary clusters composed of Cu in the inner core surrounded