Detailed total scattering analysis of disorder in ZIF-8
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Metz, Peter C.↗
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Illustrated formalisms for total scattering data: a guide for new practitioners
The total scattering method is the simultaneous study of both the real- and reciprocal-space representations of diffraction data. While conventional Bragg-scattering analysis (employing methods such as Rietveld refinement) provides insight into the average structure of the material, pair distribution function (PDF) analysis allows for a more focused study of the local atomic arrangement of a material. Generically speaking, a PDF is generated by Fourier transforming the total measured reciprocal-space diffraction data (Bragg and diffuse) into a real-space representation. However, the details of the transformation employed and, by consequence, the resultant appearance and weighting of the real-space representation of the system can vary between different research communities. As the worldwide total scattering community continues to grow, these subtle differences in nomenclature and data representation have led to conflicting and confusing descriptions of how the PDF is defined and calculated. This paper provides a consistent derivation of many of these different forms of the PDF and the transformations required to bridge between them. Some general considerations and advice for total scattering practitioners in selecting and defining the appropriate choice of PDF in their own research are presented. This contribution aims to benefit people starting in the field or trying to compare their results with those of other researchers.
36 MATERIALS SCIENCE↗
Toxic, radioactive, and disordered: a total scattering study of TlTcO 4
Neutron total scattering reveals that the phase transition in TlTcO 4 is driven by disordering of the Tl + 6s 2 lone pairs.
Mullens, Bryce G. [School of Chemistry, The Univer↗
Structural evolution during solution-based synthesis of Li 7 P 3 S 11 solid electrolyte by synchrotron X-ray total scattering
Solution-based synthesis has emerged as a promising approach for scalable and efficient synthesis of solid electrolytes (SEs). However, the ionic conductivity of solution-synthesized SEs is much lower than that of SEs synthesized by solid state approaches. The structural evolution during the synthesis of SEs is crucial to explaining the decreased ionic conductivities but has not been well understood. Here, in this work, we use synchrotron X-ray total scattering combined with pair distribution function (PDF) analysis to understand the structural evolution during annealing of the solution-processed precursor for the synthesis of Li 7 P 3 S 11 SEs. Combining Bragg diffraction and diffuse scattering, X-ray total scattering enables detection of structural information including phase transition and crystallinity. The results show that the formation of Li 7 P 3 S 11 glass-ceramic starts at 230 °C. Increasing the annealing temperature helps to improve the crystallinity, but the degree of crystallization is still lower than 70.3% even after annealing at 290 °C when thermal decomposition of Li 7 P 3 S 11 to Li 4 P 2 S 6 has occurred. PDF analysis also revealed the existence of acetonitrile used in the solution-based synthesis in the SEs after annealing at high temperatures. The results rationalize the synthesis–property relationship, explain why annealing at 290 °C provides the highest ionic conductivity at the studied temperatures due to an optimal balance for achieving a high crystallinity while suppressing severe decomposition of Li 7 P 3 S 11 , and provide novel insights to develop approaches for synthesizing superior Li 7 P 3 S 11 SEs on a large scale.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
In situ synchrotron X-ray total scattering measurements and analysis of colloidal CsPbX 3 nanocrystals during flow synthesis
In situ X-ray scattering measurements of CsPbX 3 (X = Cl, Br, I) nanocrystal formation and halide exchange at NSLS-II beamlines were performed in an automated flow reactor. Total scattering measurements were performed at the 28-ID-2 (XPD) beamline and small-angle X-ray scattering at the 16-ID (LiX) beamline. Nanocrystal structural parameters of interest, including size, size distribution and atomic structure, were extracted from modeling the total scattering data. The results highlight the potential of these beamlines and the measurement protocols described in this study for studying dynamic processes of colloidal nanocrystal synthesis in solution with timescales on the order of seconds.
nucleation↗
Total-scattering pair-distribution function analysis of zinc from high-energy synchrotron data
The crystal structure of zinc metal deviates from the ideal hexagonal close packing structure by a significantly increased axial ratio (c/a). The local atomic structure of zinc metal is investigated using the total scattering atomic pair distribution function (PDF) analysis based on X-ray powder diffraction data collected at ambient conditions. The X-ray total scattering PDF analysis confirms that the crystal structure of zinc can be described in terms of wurtzite structure, but with an anomalously atomic displacement parameters U 33 , indicating a significant displacement disorder along the c-axis. For the long r-range PDF refinements, the thermal motion of zinc shows a notable anisotropy as expressed by the ratio U 33 /U 11 of 2.5 at ambient conditions. This average distortion level along the c-axis, was not reflected locally for the features below 5.0 Å as it fits the high r region. Based on PDF refinements over different r-ranges, we measure an interesting increase of the U 33 value with decreasing the r-range of the refinement. Finally, this suggests that the local structure features in zinc metal differ from the average structure ones.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
In situ electric field X-ray total scattering reveals composition-dependent electromechanical strain mechanisms in (1 − x )BiFe 2/8 Ti 3/8 Mg 3/8 O 3 – x PbTiO 3 ceramics
Ferroelectric materials find many applications in energy and aerospace industries. A major challenge for ferroelectric materials is maintaining their properties at elevated temperatures. The (1 − x )BiFe 2/8 Ti 3/8 Mg 3/8 O 3 – x PbTiO 3 (BFTM–xPT) ferroelectric solid solution is a promising candidate for high-temperature applications as it has a high piezoelectric response while also maintaining its ferroelectric phase until a high Curie temperature (T C ) of 650 °C. In this work, we investigate the piezoelectric mechanism in BFTM–xPT, a novel high-T C ferroelectric ceramic. To elucidate the origin of its enhanced piezoelectric performance, relative to other piezoceramics of similar T C , in situ electric field X-ray total scattering experiments were performed. Total scattering combines Bragg scattering (diffraction) and diffuse scattering (pair distribution function), providing insight on various length scales. With information spanning different length scales, extrinsic contributions (i.e., domain wall motion and interphase boundary motion) can be separated from intrinsic contributions (i.e., piezoelectric lattice strain). We show that, for compositions within the morphotropic phase boundary (MPB, x = 0.325), the piezoelectric response is dominated by intrinsic piezoelectric lattice strain, whereas outside the MPB (x = 0.375) the major component of the piezoelectric response is from extrinsic mechanisms including an electric-field-induced phase transition and tetragonal domain wall motion. This article reveals that the origin of piezoelectric response in BFTM–xPT is composition-dependent and shows that high-performance materials may also be located outside the MPB. These findings can help guide material design to optimize properties for specific applications.
Richtik, Brooke N. [University of Calgary, AB (Can↗
Systematic study of short- and long-range correlations in RE 3 TaO 7 weberite-type compounds by neutron total scattering and X-ray diffraction
The atomic structures of the lanthanide tantalates, Ln 3 TaO 7 , series (Ln = Pr, Tb, Dy, Ho, Tm, Yb) were systematically investigated using total scattering techniques. High-energy X-ray and neutron diffraction analysis revealed that the long-range structures can be grouped into three distinct families: (1) ordered Cmcm (Ln = Pr), (2) ordered Ccmm (Ln = Tb, Dy, Ho), and (3) disordered, defect-fluorite Fm$\bar{3}$m (Ln = Ho, Tm, Yb). These findings help to clarify the symmetry discrepancy for the already reported long-range structures in the literature. The short-range analysis of neutron total scattering data via pair distribution functions reveals a high degree of structural heterogeneity across length scales for all compounds, with distinct local atomic arrangements that are not fully captured by the average, long-range structure. The short-range structures at the level of coordination polyhedra are better captured by a set of alternative non-centrosymmetric structural models: (1) C2cm, (2) C222 1 , and (3) C2mm. This establishes a short-range multiferroic character for weberite-type tantalates because ferroelectric interactions compete with magnetic correlations. These ferroelectric interactions are particularly pronounced for the disordered compounds Tm 3 TaO 7 and Yb 3 TaO 7 . In conclusion, the structural differences among the three families are the result of changes in TaO 6 polyhedral tilt (transition between families 1 and 2) and dipolar interactions of off-centered Ta cations (transition between families 2 and 3).
36 MATERIALS SCIENCE↗
Distinguishing isotropic and anisotropic signals for X-ray total scattering using machine learning
Understanding structure–property relationships is essential for advancing technologies based on thin films. X-ray pair distribution function (PDF) analysis can access relevant atomic structure details spanning local-, mid- and long-range structure. While X-ray PDF has been adapted for thin films on amorphous substrates, measurements on single-crystal substrates are necessary to accurately determine structure origins for some thin film materials, especially those for which the substrate changes the accessible structure and properties. However, when measuring films on single-crystal substrates, high-intensity anisotropic Bragg spots saturate 2D detector images, overshadowing the thin films' isotropic scattering signal. This renders previous data processing methods for films on amorphous substrates unsuitable for films on single-crystal substrates. To address this measurement need, we developed IsoDAT2D, an innovative data processing approach using unsupervised machine learning algorithms. The program combines dimensionality reduction and clustering algorithms to separate thin film and single-crystal substrate X-ray scattering signals. We use SimDAT2D , a program we developed to generate simulated thin film data, to validate IsoDAT2D . Here we also use IsoDAT2D to isolate X-ray total scattering signal from a thin film on a single-crystal substrate. The resulting PDF data are compared with similar data processed using previous methods, especially substrate subtraction for single-crystal and amorphous substrates. PDF data from IsoDAT2D -identified X-ray total scattering data are significantly better than from single-crystal substrate subtraction, but not as reliable as PDF data from amorphous substrate subtraction. With IsoDAT2D , there are new opportunities to expand PDF to a wider variety of thin films, including those on single-crystal substrates, with which new structure–property relationships can be elucidated to enable fundamental understanding and technological advances.
36 MATERIALS SCIENCE↗
Lorentz factor for time-of-flight neutron Bragg and total scattering
We report the three fundamental origins of the Lorentz factor for neutron time-of-flight powder diffraction are revisited. A detailed derivation of the Lorentz factor is presented in the context of diffuse scattering modelling in reciprocal space when perfect periodicity is assumed, and the total scattering pattern is constructed in its discrete form – the factor in this case becomes 1/Q 2 (or d 2 ). Discussion is also presented with respect to practical data reduction where a vanadium measurement is usually taken as the normalization factor (to account for various factors such as detector efficiency), and it is shown that the existence of the Lorentz factor is independent of such a normalization process.
36 MATERIALS SCIENCE↗
Local order of orthorhombic weberite-type Y 3 TaO 7 as determined by neutron total scattering and density functional theory calculations
Weberite-type oxides are a family of oxides with A 3 BO 7 stoichiometry that can adopt different space groups depending on chemical composition. There is a discrepancy in previous studies as to whether Y 3 TaO 7 is the orthorhombic C222 1 or the Ccmm space group. Here, we describe the short- and long-range structural properties of weberite-type Y 3 TaO 7 using neutron total scattering data, which has a high sensitivity to the oxygen sublattice. Simultaneous analysis of both short- and long-range structural data via conventional Rietveld and small box modelling demonstrates that Y 3 TaO 7 is best modeled as C222 1 . While the Ccmm describes equally well the long-range structure, pair distribution function analysis revealed that the local atomic configuration can be best modelled as C222 1 . This is corroborated by first-principles calculations that confirm the energetic preference of the C222 1 over Ccmm. Further, neutron total scattering data are reported for the first time for the Y 3 TaO 7 weberite-type ceramics.
36 MATERIALS SCIENCE↗
Elucidating the local structure of Li 1+ x Al x Ti 2– x (PO 4 ) 3 and Li 3 Al x Ti 2– x (PO 4 ) 3 ( x = 0, 0.3) via total scattering
Li 1+x Al x Ti 2–x (PO 4 ) 3 (LATP) and Li 3 Al x Ti 2–x (PO 4 ) 3 (x = 0, 0.3) are promising candidates in all-solid-state batteries due to their high room temperature conductivity of 10 –3 S cm –1 and air- and moisture-stability. They also exhibit unusual thermal expansion properties, with Li 1+x Al x Ti 2–x (PO 4 ) 3 showing near-zero thermal expansion along the a axis while Li 3 Al x Ti 2–x (PO 4 ) 3 exhibits polynomial positive thermal expansion along the a axis and polynomial negative thermal expansion along the c axis. A crucial component to understanding these properties is understanding the local structure. Total scattering is a powerful analytical technique as it provides information on the long-range, average structure as well as the local structure. Here, we report the first X-ray and neutron total scattering experiments performed on Li 1+x Al x Ti 2–x (PO 4 ) 3 and Li 3 Al x Ti 2–x (PO 4 ) 3 (x = 0, 0.3). We show that the PO 4 and TiO 6 polyhedra experience very little expansion of the P/Ti–O bonds up to 800 °C, nor is there much expansion when the Li content increases significantly. The minor thermal expansion of the nearest-neighbor bonds of the polyhedra is revealed to be the reason behind the unusual thermal expansion properties, causing the near-zero thermal expansion along a in Li 1+x Al x Ti 2–x (PO 4 ) 3 and moving as whole units in Li 3 Al x Ti 2–x (PO 4 ) 3 . The structural robustness of the framework is also the reason for the increased conductivity as Li content increases, as the framework remains undistorted as Li content increases, permitting Li-ion mobility as the number of charge carriers increases. Finally, this suggests that phosphate-based framework materials beyond LATP would also be a good material space to explore for new Li-ion (and other ion-) conducting materials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Simulating and benchmarking neutron total scattering instrumentation from inception of events to reduced and fitted data
In the design and realization of modern neutron scattering instrumentation, particularly when designing beamline concepts from the ground up, it is desirable to fully benchmark against realistically simulated data. This is especially true for total scattering beamlines, where the future deliverable data is to be analysed in both reciprocal- and real-space representations, and needs must be carefully balanced to ensure sufficient range, resolution and flux of the instrument. An approach to optimize the design of neutron scattering instrumentation via a workflow including ray-tracing simulations, event-based data reduction, heuristic analysis and fitting against realistically simulated spectra is demonstrated here. The case of the DISCOVER beamline concept at the Spallation Neutron Source is used as an example. The results of the calculations are benchmarked through simulation of existing instrumentation and subsequent direct comparison with measured data. Finally, on the basis of the validated models, the ability to explore design characteristics for future beamline concepts or future instrument improvements is demonstrated through the examples of detector tube size and detector layout.
47 OTHER INSTRUMENTATION↗
The local structure of 0.5Ba(Zr 0.2 Ti 0.8 )O 3 -0.5(Ba 0.7 Ca 0.3 )TiO 3 from neutron total scattering measurements and multi-edge X-ray absorption analysis
Neutron total scattering measurements and multi-edge X-ray absorption analysis were performed on a 0.5Ba(Zr 0.2 Ti 0.8 )O 3 -0.5(Ba 0.7 Ca 0.3 )TiO 3 powder sample. The TiIII-II edges showed that titanium is distorted in the rhombohedral [111] direction (in a BaTiO 3 -like chemical and bonding environment). Extended X-ray fine structure analysis (EXAFS) was performed on the zirconium K-edge and it was found that zirconium resides in the center of the ZrO 6 octahedra in cubic symmetry. Furthermore, the local structure was initially modelled with the orthorhombic Amm2 space group with unsatisfactory results. To better model the local structure, the results from the EXAFS analysis were incorporated into the small-box pair distribution function (PDF) refinements and the best fit of the observed data was a combination of barium calcium titanate (BCT) and barium calcium zirconate (BCZ) phases.
36 MATERIALS SCIENCE↗
On single-crystal total scattering data reduction and correction protocols for analysis in direct space
Data reduction and correction steps and processed data reproducibility in the emerging single-crystal total-scattering-based technique of three-dimensional differential atomic pair distribution function (3D-ΔPDF) analysis are explored. All steps from sample measurement to data processing are outlined using a crystal of CuIr 2 S 4 as an example, studied in a setup equipped with a high-energy X-ray beam and a flat-panel area detector. Computational overhead as pertains to data sampling and the associated data-processing steps is also discussed. Various aspects of the final 3D-ΔPDF reproducibility are explicitly tested by varying the data-processing order and included steps, and by carrying out a crystal-to-crystal data comparison. Situations in which the 3D-ΔPDF is robust are identified, and caution against a few particular cases which can lead to inconsistent 3D-ΔPDFs is noted. Although not all the approaches applied herein will be valid across all systems, and a more in-depth analysis of some of the effects of the data-processing steps may still needed, the methods collected herein represent the start of a more systematic discussion about data processing and corrections in this field.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Pressure cells for in situ neutron total scattering: time and real-space resolution during deuterium absorption
In situ gas-loading sample holders for two-dimensionally arranged detectors in time-of-flight neutron total scattering experiments have been developed to investigate atomic arrangements during deuterium absorption using time and real-space resolution. A single-crystal sapphire container was developed that allows conditions of 473 K and 10 MPa hydrogen gas pressure. High-resolution transient measurements detected deuterium absorption by palladium that proceeded within a few seconds. A double-layered container with thick- and thin-walled vanadium allowed conditions of 423 K and 10 MPa hydrogen gas pressure. The deuterium occupation sites of a lanthanum–nickel–aluminium alloy are discussed in detail on the basis of real-space high-resolution data obtained from in situ neutron scattering measurements and reverse Monte Carlo structural modeling.
08 HYDROGEN↗
Bibliometric review and recent advances in total scattering pair distribution function analysis: 21 years in retrospect
Global research activities have been driven by the quest to develop and characterize novel materials for technological advancements. The total scattering pair distribution function (TSPDF) is a powerful and versatile characterization technique for examining the structural details of diverse complex materials including liquid, amorphous, disordered crystalline, and nanostructured materials. Thus, it is critical to keep track of research progress, identify research gaps, and future research directions of the application of the TSPDF technique in materials development and discovery. In this work, a bibliometric analysis of literature regarding the TSPDF technique between 2000 and 2021 was conducted using datasets retrieved from the Web of Science database. The research trends based on publication outputs, research subject distribution, co-authorships among institutions, countries/regions, co-citation of referenced sources, and keyword co-occurrence are evaluated and discussed herein. The impact of the TSPDF technique is projected to increase due to its importance in probing emerging functional materials, and the advances in specialized facilities and instrumentation among the scientific communities engaged with it. Finally, current and emerging research hotspots related to TSPDF technique such as catalysis, computer modeling and simulation, pharmaceutics, machine learning, hydrogen storage, battery materials, and layered structured materials are also identified and discussed.
36 MATERIALS SCIENCE↗
The total scattering cross sections for H2 + H2, D2 + D2, and HD + HD for relative collision energies below 10 meV
Relative total scattering cross sections for normal H2 + normal H2, para-H2 + para-H2, normal D2 + normal D2, ortho-D2 + ortho-D2, and HD + HD were measured at energy below 10 meV by colliding particles from two inclined nozzle beams. Cross sections for the H2 + H2 pairs were measured over a relative velocity range of 200-1450 m/s; the normal H2 + normal H2 results suggest a l = 3 orbiting resonance near 375 m/s while the para-H2 + para-H2 results have a l = 4 orbiting resonance near 585 m/s. This latter resonance has a peak energy of 1.79 meV and a FWHM of 1.05 meV. The D2 + D2 cross sections were measured over the velocity range of 190 to 1000 m/s and a minimum between the l = 4 and l = 5 orbiting resonances was observed. Some preliminary measurements on HD + HD over the range of 250-1250 m/s indicate a possible l = 4 orbiting resonance near 300 m/s. The experimental work compares favorably to cross sections calculated from a theoretical potential.
Johnson, D. L.↗