Maximum-entropy-method charge densities based on structure-factor extraction with the commonly used Rietveld refinement programs GSAS, FullProf and Jana2006

Structure-factor extractions in commonly used Rietveld refinement programs (FullProf, Jana2006 and GSAS) were examined with respect to subsequent calculation of electron-density distributions (EDDs) using the maximum entropy method (MEM). As a test case, 90 K synchrotron powder X-ray diffraction data were collected on the potential hydrogen storage material, NaGaH₄, at SPring-8, Japan. To support the model, neutron powder diffraction data were collected on the fully deuterated sample at PSI, Switzerland. Firstly, it was established whether the programs can produce observed structure factors, F_obs, corrected for anomalous dispersion and scaled to the scattering power of one unit cell. Secondly, different models for background and peak-shape description were investigated with respect to the extracted F_obs, and the effect on the subsequent MEM EDDs was analysed within the quantum theory of atoms in molecules. Substantial differences are observed in the estimated standard deviations, σ_obs, produced by the different programs. Since σ_obs is a vital parameter in the calculation of MEM EDDs this leads to substantial variation between the MEM EDDs obtained with different Rietveld programs even in cases with similar F_obs. A new approach for selecting an optimized MEM EDD and thereby minimizing the effect of variation in σ_obs is suggested.