Estimation of radial distribution functions in electron diffraction experiments: physical, mathematical and numerical aspects

Radial distribution functions (RDFs) can be obtained from transmission electron diffraction experiments. Polycrystalline gold specimens have been used to study how different mathematical methods extract the RDF information from electron diffraction data. Fourier transform (FT) and a maximum-entropy (ME) algorithm have been used in these calculations. Results obtained by the two methods are very similar and reproduce the interatomic distances accurately. Between the two methods, FT and ME, no significant difference could be found. ME calculations are very sensitive towards input parameters whereas the FT is a very robust algorithm. Calculations on reduced sets of experimental data with little error margin showed no improvement of resolution in the RDF calculated by ME.