Accuracy of pair distribution function analysis applied to crystalline and non-crystalline materials

Abstract

Pair distribution function (PDF) analysis of neutron or X-ray powder diffraction data is a useful technique for analysis of short-range structure in both amorphous and crystalline materials. Errors in PDF determinations may arise from several sources: termination of the Fourier transform, lack of instrument resolution, counting statistics and inaccurate corrections for experimental artifacts. Estimates of the amount of error from termination and instrument resolution are computed using a model structure. A general method for estimating the expected contribution of statistical error to the PDF is introduced for the first time. The effect of termination varies with the type of material and with the amplitude of lattice vibrations but, in general, termination with Q > 30 produces minimal errors. Broadening of the diffraction pattern produces negligible effect for conventional instrumentation. With moderate data-collection times, the statistical errors can be reduced to reasonable levels. Pulsed-neutron diffraction can provide accurate and precise PDF measurements, as is demonstrated in this work by the agreement between model and experimental results for polycrystalline aluminium.

Charge Fluctuations in the NdO1−xFxBiS2 Superconductors

“…3(b), overall, the average model ρ mod (r) for the x=0.2 in the blue dashed line is in good agreement with the experimental PDF, ρ exp , except in the 2.5-3.5Å region where the model peak intensity is higher. The agreement factor, A, calculated [22] is 0.181 where ρ 0 is the atomic density of the unit cell. On the other hand, a local model, ρ mod , involving in-plane displacements at both sulfur S1 and S2 atoms, reproduces the data well as seen in the figure.…”

Surface Chemistry Controls Crystallinity of ZnS Nanoparticles

“…The magnitude of the diffraction vector smooth atomic scattering contribution to the intensity is removed to produce the structure factors for each sample, which possess all the structural information. The structure factors were multiplied by the q scattering axis and Fourier transformed to give the real-space pair distribution functions (PDF) (32). Figure 2 shows the q-weighted structure factors and associated PDFs for each sample.…”

Y1−xLaxVO3: Effects of doping on orbital ordering

“…The Rietveld refinement provides a description of the average or long-range atomic arrangement, with reliable information of the unit cell parameters, while the PDF provides information on the nature of local distortions that do not follow the lattice periodicity. This method has been applied successfully in many oxide systems [33][34][35]. The PDF is a real space representation of the atomic correlations [32].…”