New measures of sharpness for symmetric powder diffraction peak profiles

Abstract

New measures of sharpness for symmetric powder diffraction peak profiles are proposed. The sharpness parameter is defined through the th-order moment of the Fourier transform of the profile function. Analytical expressions for the sharpness parameter for empirical model profile functions, namely the Gaussian, logistic distribution, hyperbolic secant, Lorentzian, Voigt, Pearson VII and pseudo-Voigt functions, and theoretical size-broadening profiles with statistical size distribution are presented. Theoretical diffraction profiles with complicated formulae can be approximated by empirical model functions assuming equivalent values of the sharpness parameter. The concept of the sharpness parameter provides a simple way to define an approximation for a theoretical diffraction peak profile with empirical model functions.

Calculation of scattering-patterns of ordered nano- and mesoscale materials

“…For larger domain sizes (l l = 300 nm) the peaks develop into sharp arcs (C). This well reproduces the measured scattering pattern of a shearoriented gyroid phase (D)[47].…”

“…The normalized Pearson-VII function can be given in terms of the integral peak width B [47] L ψ ð Þ = 1 where the integral peak width B is related to the peak width δ (FWHM) by…”

Application of a theory for particle statistics to structure refinement from powder diffraction data

“…in measurements involving a counting method because the counting event should follow Poisson statistics when the counting loss is negligible (Ida, 2008). The dependence of the variance caused by particle statistics on the diffraction angle 2Â varies with the geometry of the diffractometer.…”

Impurity dominated thin film growth

“…The XRD peaks were fitted with a Pearson VII peak shape as described by Ida. 29 Based on the determined integral breadth, the domain size was calculated according to the Debye-Scherrer equation. The crosses are used for measurements excluded from the analysis.…”