The interpretation and analysis of diffuse scattering using Monte Carlo simulation methods

Abstract

Studies of diffuse scattering had a prominent place in the first issue of Acta Crystallographica 60 years ago at a time when conventional crystallography (determination of the average structure from Bragg peaks) was in its infancy. Since that time, conventional crystallography has developed enormously while diffuse-scattering analysis has seemingly lagged well behind. The paper highlights some of the extra difficulties involved in the measurement, interpretation and analysis of diffuse scattering and plots the progress that has been made. With the advent of the latest X-ray and neutron sources, area detectors and the ever-increasing power of computers, most disorder problems are now tractable. Two recent contrasting examples are described which highlight what can be achieved by current methods.

Lead-free and lead-basedABO3perovskite relaxors with mixed-valenceA-site andGe1, Devreugd2, Phelan3 et al. 2013Phys. Rev. B624490View full textAdd to dashboardCite

“…[25][26][27][28] The diffuse scattering in these compounds has been extensively studied and many different models have been proposed to explain the experimental data. Among these models, some assume (a) the presence of thin, pancake-shaped PNR, 21,[29][30][31] (b) three-dimensional PNR for which the domain walls are parallel to {110} crystallographic planes, 32 (c) correlated Pb displacements oriented along 110 , 29,30,33 or (d) correlations between PNR embedded in an atomically disordered matrix (ADM). 34 But to date there is little consensus on its origin.…”

“…34 But to date there is little consensus on its origin. 21,29,30,[32][33][34][35] In 2006, Matsuura et al made the interesting observation that the compositional dependence of the diffuse scattering in PMN-xPT correlates with that of the longitudinal piezoelectric coefficient d 33 . 36 More specifically, the peak diffuse scattering intensity at the Brillouin-zone center (q = 0), the q-integrated diffuse scattering intensity, and the associated correlation length measured along [11 0] all increase rapidly as the system is doped towards the MPB, 36 which is where the piezoelectric coefficient d 33 is largest.…”

Origin of diffuse scattering in relaxor ferroelectrics

“…The ferroelectric phase shows weak streaks similar to BaTiO 3 and KNbO 3 , but rotated by 45-degrees. The paraelectric phase only shows radial diffuse scattering.Several hypotheses previously advanced to explain the characteristic shapes [6,10,11,12], invoke some type of artificial anisotropic features such as anisotropic strain, correlated atomic shifts, or domain boundaries to generate the experimentally observed anisotropic diffuse scattering features. Fitting the shapes of diffuse scattering features is not sufficient to uniquely determine the nature of the microstructural feature that give rise to them.…”

Analyzing diffuse scattering with supercomputers

“…Here we focus on static disorder associated with local structural variations. Qualitative DS analysis can show general aspects of disorder, but only a quantitative analysis can reveal details of the deviations from the average (or Bragg) structure and provide a basis for explaining the origin of the functional properties (Welberry & Goossens, 2008;Aebischer et al, 2006). Only the disordered atoms or molecules within the overall structure contribute to diffuse scattering, which, being distributed over extensive volumes of reciprocal space, is usually orders of magnitude weaker per unit volume of scattering space than Bragg diffraction.…”