Topics in Catalysis 10 (2000) 221–230 221 Asymmetric pair distribution functions in catalysts Bjerne S. Clausen a and Jens K. Nørskov b a Haldor Topsøe Research Laboratories, DK-2800 Lyngby, Denmark b Center for Atomic-scale Materials Physics, Department of Physics, Technical University of Denmark, DK-2800 Lyngby, Denmark The structural parameters, i.e., coordination numbers, bond distances and disorder obtained from the analysis of EXAFS spectra may sometimes be significantly influenced by errors introduced due to the inadequacy of the analysis method applied. Especially in the case of heterogeneous catalysts it has been realized that often there is a need to use an improved EXAFS data analysis compared to the simple harmonic approach which works well for well-defined bulk structures. This is due to the fact that catalysts contain highly dispersed or disordered structures with pair distribution functions quite different from well-crystalline bulk materials. In addition, the increased interest for in situ studies, which typically imply high temperatures, makes the influence from anharmonic vibrations on the shape of the pair distribution a significant factor. In this paper, we discuss the importance of asymmetric pair distribution functions for nano-sized particles and how they influence the structural parameters obtained from the standard data analysis. An alternative method, which takes into account deviations from the Gaussian pair distribution function typically used in the analysis of EXAFS spectra, will be described. The method is based on an analysis of the pair distribution functions derived from molecular dynamics simulations of small metal particles and its reliability is demonstrated by comparing structural parameters obtained from independent X-ray diffraction experiments. Keywords: EXAFS, catalysis, XRD, molecular dynamics, asymmetric pair distribution, anharmonic, in situ studies 1. Introduction The unique potential of X-ray absorption spectroscopy for the study of catalysts was recognized after the formu- lation of the first successful theory of the origin of the extended fine structure part (EXAFS) of the X-ray absorp- tion spectrum by Sayers, Stern and Lyttle [1]. Earlier, Van Nordstrand [2] pointed out in a qualitative manner the ad- vantages of X-ray absorption spectroscopy as a useful tech- nique for the study of catalytic materials. The success of the technique is related to the fact that since it only probes the local atomic environment, it is particularly useful for the study of amorphous structures and nano-sized particles. Only a few other structural techniques have these capabili- ties, and commonly applied techniques, such as for example XRD or TEM, cannot elucidate structures with a dimen- sion less than about 2 nm. In addition, X-ray absorption spectroscopy is easily adopted in in situ experiments pro- vided appropriate reaction cells are available. This opens the possibility to apply EXAFS to determine the structure of a catalyst during preparation [3,4] or under reaction con- ditions [3,5]. With the increased availability of synchrotron radiation facilities, EXAFS has become a more or less rou- tine technique in studies of catalysts and important new insight in their structural properties has been obtained (see, e.g., [5]). EXAFS has been reported to be capable of determining parameters, like bond lengths and coordination numbers, quite accurately in most systems [6,7]. However, there are several examples in the literature of studies of highly dispersed or disordered systems where the EXAFS results are in apparent disagreement with results obtained by other techniques (see, e.g., [8–11]). Of course, one possible ex- planation for these discrepancies is that different techniques may not probe the various structural properties of a system in a comparable way, making a direct comparison of num- bers questionable. Another explanation may be related to the fact that the EXAFS formulae typically used to analyze the experimental data are based on bulk structural proper- ties, i.e., it assumes that the pair distribution function has a Gaussian shape. Hence, it may be expected that these EXAFS formulae have some limitations when applied to nano-size clusters and amorphous structures, which due to their special structures may have non-Gaussian pair dis- tribution functions. This was, for example, discussed in an analysis of EXAFS spectra of supported 1 nm large Pt particles recorded at various temperatures [12] where an apparent bond contraction was observed. The contraction was attributed to the incomplete theoretical treatment of EXAFS spectra for structures with non-Gaussian pair dis- tribution functions. Eisenberger and Brown [13] and several other re- searchers [6,7,12,14–19] have pointed out the serious lim- itations of the EXAFS technique for studying systems in which the pair distribution function is non-Gaussian. The problems arise from two related sources. The first is the problem of a correct treatment of EXAFS spec- tra of systems with complicated pair distribution func- tions (non-transferability of amplitude functions). One attempt to minimize this problem is to use the cumu- lant expansion approach [20] instead of the standard har- monic approach. The second source is originating from the loss of information at low k values in experimental EXAFS spectra, a problem not easy to solve without re- lying on model-dependent descriptions of the actual sys- tem.  J.C. Baltzer AG, Science Publishers