Abstract
Ferroelectric materials rely on some type of non-centrosymmetric displacement correlations to give rise to a macroscopic polarisation. These displacements can show short-range order (SRO) that is reflective of the local chemistry, and so studying it reveals important information about how the structure gives rise to the technologically useful properties. A key means of exploring this SRO is diffuse scattering. Conventional structural studies use Bragg peak intensitiesto determine the average structure. In a single crystal diffuse scattering (SCDS) experiment, the coherent scattered intensity is measured at non-integer Miller indices, and can be used to examine the population of local configurations. This is because the diffuse scattering is sensitive to two-body averages, whereas the Bragg intensity gives single-body averages. This review outlines key results of SCDS studies on several materials and explores the similarities and differences in their diffuse scattering. Random strains are considered, as are models based on a phonon-like picture or a more local-chemistry oriented picture. Limitations of the technique are discussed.
Highlights
Single crystal diffuse scattering (SCDS) has been the subject of study since the earliest days of crystallography [1] and is seen in many patterns collected using film (e.g., [2]), film being an early variant of “area detector” and very good for surveying large regions of reciprocal space—far better than an electronic point counter
It is clear that modelling large windows of reciprocal space and preferably threedimensional volumes are important when the scattering is so anisotropic and extended
Some models work well close to Bragg positions but less well near reciprocal cell boundaries, showing that measuring comprehensive data is necessary if models are to be adequately tested
Summary
Single crystal diffuse scattering (SCDS) has been the subject of study since the earliest days of crystallography [1] and is seen in many patterns collected using film (e.g., [2]), film being an early variant of “area detector” and very good for surveying large regions of reciprocal space—far better than an electronic point counter. The correlation structure is likely to be anisotropic, such that a detailed model of the SRO will often require a threedimensional (3D) dataset [23, 53,54,55,56], in turn implying the need to measure the distribution of weak and delocalised features throughout significant volumes of reciprocal space. This requires long experiments, very carefully characterised instruments, and large crystals—especially for neutron diffuse scattering. How the B-site randomness folds in to this is an interesting question, and it would be interesting to apply this approach to, for example, the PZT materials modelled in [25], in which the Pb-Pb ferroelectric domains were found to be of very different shape, being one-dimensional chains, and in which the static strains due to chemical disorder and B-site cation size mismatch are weaker and should make a thermal-like model more applicable
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