Abstract
Evidence is mounting that potentially exploitable properties of technologically and chemically interesting crystalline materials are often attributable to local structure effects, which can be observed as modulated diffuse scattering (mDS) next to Bragg diffraction (BD). BD forms a regular sparse grid of intense discrete points in reciprocal space. Traditionally, the intensity of each Bragg peak is extracted by integration of each individual reflection first, followed by application of the required corrections. In contrast, mDS is weak and covers expansive volumes of reciprocal space close to, or between, Bragg reflections. For a representative measurement of the diffuse scattering, multiple sample orientations are generally required, where many points in reciprocal space are measured multiple times and the resulting data are combined. The common post-integration data reduction method is not optimal with regard to counting statistics. A general and inclusive data processing method is needed. In this contribution, a comprehensive data analysis approach is introduced to correct and merge the full volume of scattering data in a single step, while correctly accounting for the statistical weight of the individual measurements. Development of this new approach required the exploration of a data treatment and correction protocol that includes the entire collected reciprocal space volume, using neutron time-of-flight or wavelength-resolved data collected at TOPAZ at the Spallation Neutron Source at Oak Ridge National Laboratory.
Highlights
Crystalline materials are primarily characterized by longrange order, which is reflected in the diffraction pattern as a series of delta functions, i.e. Bragg diffraction (BD)
The sparse grid of BD needs to be transformed into a fine grid that covers the modulated diffuse scattering (mDS) volume, with adequate resolution to account for variations in scattering geometry and in wavelength, for the case of time-of-flight Laue data
Subsequent investigation of the local structure arrangement through analysis of the associated diffuse diffraction data supported the spectroscopic findings. This shows that complementary information provided by mDS is needed to allow insight on the true structure–property relationship (Auzel, 2004; Kramer et al, 2004; Aebischer et al, 2005, 2006; Tu et al, 2013), and understanding of the local structure is critical for targeted development and improvement of materials, in this case up-conversion properties
Summary
Crystalline materials are primarily characterized by longrange order, which is reflected in the diffraction pattern as a series of delta functions, i.e. Bragg diffraction (BD). Due to the accumulating nature of most two-dimensional area X-ray detectors, are data overflow, detector dead time and oversaturation of Bragg reflections This necessitates separate individual data collection and data treatment of BD and mDS, and impairs consistent and simultaneous data processing and analysis. The instrument is equipped with state-of-the-art area detectors, with continuous readout of individual neutron events This circumvents limitations of data overflow and oversaturation of Bragg reflections, eliminating the necessity of a separate weighting scheme for the diffuse intensities. The sparse grid of BD needs to be transformed into a fine grid that covers the mDS volume, with adequate resolution to account for variations in scattering geometry and in wavelength, for the case of time-of-flight Laue data Both requirements (dense grid and corrections) can be met simultaneously by processing the volume of reciprocal space as a whole in momentum space.
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