Effects of Voigt diffraction peak profiles on the pair distribution function

Abstract

Powder diffraction and pair distribution function (PDF) analysis are well established techniques for investigation of atomic configurations in crystalline materials, and the two are related by a Fourier transformation. In diffraction experiments, structural information, such as crystallite size and microstrain, is contained within the peak profile function of the diffraction peaks. However, the effects of the PXRD (powder X-ray diffraction) peak profile function on the PDF are not fully understood. Here, all the effects from a Voigt diffraction peak profile are solved analytically, and verified experimentally through a high-quality X-ray total scattering measurement on Ni powder. The Lorentzian contribution to the microstrain broadening is found to result in Voigt-shaped PDF peaks. Furthermore, it is demonstrated that an improper description of the Voigt shape during model refinement leads to overestimation of the atomic displacement parameter.

Structural Analysis of Molecular Materials Using the Pair Distribution Function

“…The lower is the resolution in Q -space, the more damped is the PDF signal, which effectively reduces the total distance over which the structure can be analyzed and greatly affects the ability to estimate domain sizes (section ) when the structural damping is larger than the instrumental damping. This has been discussed systematically, ,, and for practical use-cases. ,, Improved descriptions of the damping effects are being developed for cases where the peak profile cannot be considered Gaussian …”

“…32,139,177 Improved descriptions of the damping effects are being developed for cases where the peak profile cannot be considered Gaussian. 759 Another consideration is that the resolution of the detector is often not constant with respect to Q, rather a function of Q. This can be due to different effects, such as beam divergence, 760 or due to the nonconstant sample-to-detector distance with increasing angle for flat detectors.…”

Sub-second pair distribution function using a broad bandwidth monochromator

“…The Gaussian and Lorentzian components of the Voigt profile width can be separated into two terms each, Q-independent terms K G and K L , and Q-dependent terms G and L . The Q-independent terms lead to damping of the PDF, whereas the Q-dependent terms impact the broadening of the PDF peaks (Beyer et al, 2022). Surprisingly, although the simple model used above indicated a Q broad contribution of the same order of magnitude as Q damp in the MLM data, the former is this time an order of magnitude smaller than the latter in the advanced model.…”

“…To further characterize the difference in PDF peak profile between the DCM and MLM, we apply the analysis recently proposed by Beyer et al (2022). Here the individual Gaussian and Lorentzian contributions of a Voigt profile in Q space are used to describe the PDF in real space.…”

“…a more rapid damping of the PDF at high r) hinders a large scale factor. In the case of the approach of Beyer et al (2022) [Figs. S3(c)-S3(d)], a strong anti-correlation of the Gaussian broadening factor arises with several parameters for the MLM data, notably the Gaussian damping, Lorentzian broadening and scale factors, and the La ADP.…”