We describe the development of an atom-based Monte Carlo simulation model which gives rise to a nanoscale polar domain structure as envisaged to occur in Pb͑Zn 1/3 Nb 2/3 ͒O 3 ͑PZN͒ and similar relaxor ferroelectric materials. Individual domains are essentially thin platelike domains normal to each of the six ͗110͘ directions. Calculated diffuse scattering patterns have been obtained from the simulations, and these are in good agreement with observed neutron scattering data. Nanoscale domain formation is driven by the need for the Pb atoms to satisfy their valence requirements; within a planar domain, the Pb atoms are displaced in a concerted fashion away from the center of their 12-fold coordination polyhedra with an in-plane displacement along ͗110͘ towards one of the coordinating O atoms. The B-site cations Zn and Nb display a strong tendency to alternate in the ͗100͘ directions but complete order is frustrated by the 2:1 stoichiometry. No diffraction evidence has been found that this B-site ordering is directly linked to the nanoscale polar domain ordering. Such a linkage cannot be completely ruled out, but if it does exist, its effect on the diffraction pattern must be quite subtle. The B-site ordering does play an indirect role in establishing the average cell dimension, which in turn dictates the magnitude of the Pb displacements. The effect of applying an external electric field is modeled, and the results are found to be consistent with experiment.

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Full three‐dimensional diffuse neutron scattering data have been recorded from a single crystal of Pb(Zn1/3Nb2/3)O3 (PZN) at 300 K using the time‐of‐flight Laue technique on the SXD single‐crystal instrument at ISIS. The data show a series of diffuse rods of scattering oriented parallel to each of the six 〈1 1 0〉 crystal directions. Monte Carlo simulation has been used to demonstrate that the diffuse rods are caused by planar nanodomains oriented normal to the 〈1 1 0〉 directions. Within these domains, there are correlated displacements of the atoms away from their average site positions. In order to explain the systematic absence of some rods of scattering in the (h k 1) data but the presence of all rods in the (h k 0) data, it is necessary that the displacement of an O atom is of opposite sign to that of its neighbouring Pb atoms. This is explained in terms of a model based on the fact that Pb2+ possesses a lone pair of electrons, giving the Pb ion directionality.

Full three-dimensional diffuse scattering data have been recorded for both polymorphic forms [(I) and (II)] of aspirin and these data have been analysed using Monte Carlo computer modelling. The observed scattering in form (I) is well reproduced by a simple harmonic model of thermally induced displacements. The data for form (II) show, in addition to thermal diffuse scattering (TDS) similar to that in form (I), diffuse streaks originating from stacking fault-like defects as well as other effects that can be attributed to strain induced by these defects. The present study has provided strong evidence that the aspirin form (II) structure is a true polymorph with a structure quite distinct from that of form (I). The diffuse scattering evidence presented shows that crystals of form (II) are essentially composed of large single domains of the form (II) lattice with a relatively small volume fraction of intrinsic planar defects or faults comprising misoriented bilayers of molecular dimers. There is evidence of some local aggregation of these defect bilayers to form small included regions of the form (I) structure. Evidence is also presented that shows that the strain effects arise from the mismatch of molecular packing between the defect region and the surrounding form (II) lattice. This occurs at the edges of the planar defects in the b direction only.

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