Ross E. Whitfield

Event-mode data collection presents remarkable new opportunities for time-of-flight neutron scattering studies of collective excitations, diffuse scattering from short-range atomic and magnetic structures, and neutron crystallography. In these experiments, large volumes of the reciprocal space are surveyed, often using different wavelengths and counting times. These data then have to be added together, with accurate propagation of the counting errors. This paper presents a statistically correct way of adding and histogramming the data for single-crystal time-of-flight neutron scattering measurements. In order to gain a broader community acceptance, particular attention is given to improving the efficiency of calculations.

The pyRS (Python residual stress) analysis software was designed to address the data reduction and analysis needs of the High Intensity Diffractometer for Residual Stress Analysis (HIDRA) user community. pyRS implements frameworks for the calibration and reduction of measured 2D data into intensity versus scattering vector magnitude and subsequent single-peak-fitting analysis to facilitate texture and residual strain/stress analysis. pyRS components are accessible as standalone user interfaces for peak-fitting and stress/strain analysis or as Python scripts. The scripting interface facilitates automated data reduction and peak-fitting analysis using an autoreduction protocol. Details of the implemented functionality are discussed.

Diffuse scattering occurring in the Bragg diffraction pattern of a long-range-ordered structure represents local deviation from the governing regular lattice. However, interpreting the real-space structure from the diffraction pattern presents a significant challenge because of the dramatic difference in intensity between the Bragg and diffuse components of the total scattering function. In contrast to the sharp Bragg diffraction, the diffuse signal has generally been considered to be a weak expansive or continuous background signal. Herein, using 1D and 2D models, it is demonstrated that diffuse scattering in fact consists of a complex array of high-frequency features that must not be averaged into a low-frequency background signal. To evaluate the actual diffuse scattering effectively, an algorithm has been developed that uses robust statistics and traditional signal processing techniques to identify Bragg peaks as signal outliers which can be removed from the overall scattering data and then replaced by statistically valid fill values. This method, described as a `K-space algorithmic reconstruction' (KAREN), can identify Bragg reflections independent of prior knowledge of a system's unit cell. KAREN does not alter any data other than that in the immediate vicinity of the Bragg reflections, and reconstructs the diffuse component surrounding the Bragg peaks without introducing discontinuities which induce Fourier ripples or artifacts from underfilling `punched' voids. The KAREN algorithm for reconstructing diffuse scattering provides demonstrably better resolution than can be obtained from previously described punch-and-fill methods. The superior structural resolution obtained using the KAREN method is demonstrated by evaluating the complex ordered diffuse scattering observed from the neutron diffraction of a single plastic crystal of CBr₄ using pair distribution function analysis.

Wide Angle Neutron Diffractometer Squared is a high-flux versatile diffractometer with a 2-Dimensional Position Sensitive Detector at the High Flux Isotope Reactor. The instrument has strengths in both powder and single crystal diffraction. It is a unique instrument in the neutron scattering landscape of North America, and its capabilities are at least equal to similar instruments in the world.

The CORELLI instrument at Oak Ridge National Laboratory is a statistical chopper spectrometer designed and optimized to probe complex disorder in crystalline materials through diffuse scattering experiments. On CORELLI, the high efficiency of white-beam Laue diffraction combined with elastic discrimination have enabled an unprecedented data collection rate to obtain both the total and the elastic-only scattering over a large volume of reciprocal space from a single measurement. To achieve this, CORELLI is equipped with a statistical chopper to modulate the incoming neutron beam quasi-randomly, and then the cross-correlation method is applied to reconstruct the elastic component from the scattering data. Details of the implementation of the cross-correlation method on CORELLI are given and its performance is discussed.

Diffuse neutron scattering has become a valuable tool for investigating local structure in materials ranging from organic molecular crystals containing only light atoms to piezo-ceramics that frequently contain heavy elements. Although neutron sources will never be able to compete with X-rays in terms of the available flux the special properties of neutrons, viz. the ability to explore inelastic scattering events, the fact that scattering lengths do not vary systematically with atomic number and their ability to scatter from magnetic moments, provides strong motivation for developing neutron diffuse scattering methods. In this paper, we compare three different instruments that have been used by us to collect neutron diffuse scattering data. Two of these are on a spallation source and one on a reactor source.

The ability of the pair distribution function (PDF) analysis of total scattering (TS) from a powder to determine the local ordering in ferroelectric PZN (PbZn_1/3Nb_2/3O₃) has been explored by comparison with a model established using single-crystal diffuse scattering (SCDS). While X-ray PDF analysis is discussed, the focus is on neutron diffraction results because of the greater extent of the data and the sensitivity of the neutron to oxygen atoms, the behaviour of which is important in PZN. The PDF was shown to be sensitive to many effects not apparent in the average crystal structure, including variations in the B-site—O separation distances and the fact that 〈110〉 Pb²⁺ displacements are most likely. A qualitative comparison between SCDS and the PDF shows that some features apparent in SCDS were not apparent in the PDF. These tended to pertain to short-range correlations in the structure, rather than to interatomic separations. For example, in SCDS the short-range alternation of the B-site cations was quite apparent in diffuse scattering at (½ ½ ½), whereas it was not apparent in the PDF.

This work extends previous efforts to model diffuse scattering from PZN (PbZn_1/3Nb_2/3O₃). Earlier work [Welberryet al.(2005).J. Appl. Cryst.38, 639–647; Welberryet al.(2006).Phys. Rev. B,74, 224108] is highly prescriptive, using Monte Carlo simulation with very artificial potentials to induce short-range-order structures which were deduced as necessary from inspection of the data. While this gives valid results for the nature of the local structure, it does not strongly relate these structures to underlying crystal chemistry. In that work, the idea of the bond-valence sum was used as a guide to the expected behaviour of the atoms. This paper extends the use of the bond-valence sum from a qualitative guide to becoming a key aspect of the potential experienced by the atoms, through the idea of the global instability index, whose square has been shown to be proportional to the density functional theory energy of some systems when close to the minimum energy configuration.