Fitting EXAFS data using molecular dynamics outputs and a histogram approach

The estimation of metal nanoparticle diameter by analysis of extended x-ray absorption fine structure (EXAFS) data from coordination numbers is nontrivial, particularly for particles < 5 nm in diameter, for which the undercoordination of surface atoms becomes an increasingly significant contribution to the average coordination number. These undercoordinated atoms have increased degrees of freedom over those within the core of the particle, which results in an increase in the degree of structural disorder with decreasing particle size. This increase in disorder, however, is not accounted for by the standard means of EXAFS analysis, where each coordination shell is fitted with a single bond length and disorder term. In addition, the surface atoms of nanoparticles have been observed to undergo a greater contraction than those in the core, further increasing the range of bond distances. Failure to account for this structural change results in an increased disorder being measured, and therefore, a lower apparent coordination number and corresponding particle size are found. Here, we employ molecular dynamics (MD) simulations for a range of nanoparticle sizes to determine each of the nearest neighbor bond lengths, which were then binned into a histogram to construct a radial distribution function (RDF). Each bin from the histogram was considered to be a single scattering path and subsequently used in fitting the EXAFS data obtained for a series of carbon-supported platinum nanoparticles. These MD-based fits are compared with those obtained using a standard fitting model using Artemis and the standard model with the inclusion of higher cumulants, which has previously been used to account for the non-Gaussian distribution of neighboring atoms around the absorber. The results from all three fitting methods were converted to particle sizes and compared with those obtained from transmission electron microscopy (TEM) and x-ray diffraction (XRD) measurements. We find that the use of molecular dynamics simulations resulted in an improved fit over both the standard and cumulant models, in terms of both quality of fit and correlation with the known average particle size.