Journal of Applied Crystallography最新文献

This paper analyzes the Hasse diagram, or family tree, of the 3D crystal classes, also called geometric crystal classes. The 32 point-group classes are partitioned into seven crystal systems. In this paper, the structures of these systems are analyzed, leading to a new understanding of the relationships among and within them. The point groups, including their subgroups up to conjugacy, appear in six structural motifs in the Hasse diagram or family tree. Each motif has a parity - even or odd - that determines its structure. In three dimensions, the odd motifs are called monads, trigonals and cubics, and the even motifs are called dyads, tetragonals and hexagonals. Of the 32 classes of 3D point groups, 29 have a well defined parity, in that they appear in either an even or an odd motif. In contrast, the three monoclinic point groups are 'ambidextrous', in that they appear in two motifs, one of each parity. An analysis of the ten 2D point groups reveals an analogous structure, except for the presence of an ambidextrous crystal system. The striking structural uniformity of the motifs across the Hasse diagram confirms that they are essential building blocks of the crystallographic point groups.

A method to determine the strain tensor and local lattice rotation with dark-field X-ray microscopy is presented. Using a set of at least three non-coplanar symmetry-equivalent Bragg reflections, the illuminated volume of the sample can be kept constant for all reflections, facilitating easy registration of the measured lattice variations. This requires an oblique diffraction geometry, i.e. the diffraction plane is neither horizontal nor vertical. We derive a closed analytical expression that allows determination of the strain and lattice rotation from the deviation of experimental observables (e.g. goniometer angles) from their nominal values for an unstrained lattice.

We present a novel experimental approach employing high-energy X-ray scattering in ultra-small-angle grazing-incidence geometry to investigate local atomic structures in single-crystalline thin films. This non-destructive and non-invasive method overcomes the limitations of conventional moderate-energy grazing-incidence diffraction, achieving both high reciprocal-space resolution and coverage and high surface sensitivity. By leveraging high-energy X-ray diffraction, we enable quantitative analysis of local structures in the model system of ferroelectric PbTiO₃ and dielectric SrTiO₃ superlattices through three-dimensional difference pair distribution function analysis. The approach provides detailed insights into atomic structures in single-crystalline thin films with local order, capturing information on spatial correlations within and across unit cells.

During the past few years, serial electron crystallography (serial electron diffraction) has been gaining attention for the structure determination of crystalline compounds that are sensitive to irradiation by an electron beam. By recording a single electron diffraction pattern per crystal, indexing thousands to tens of thousands of such patterns and merging the reflection intensities of the successfully indexed patterns, one can retrieve crystal structure models with strongly mitigated beam damage contributions. However, one of the technique's bottlenecks is the need to obtain so many well indexed diffraction patterns, which leads to the collection of raw diffraction data in an automated way that usually yields low indexing rates. This work demonstrates how to overcome this limitation by performing the serial crystallography experiment following a semi-automated routine with a precessed electron beam (serial precession electron diffraction). The precession movement increases the number of reflections present in the diffraction patterns, and dynamical effects related to specific orientations of the crystals with respect to the electron beam are greatly minimized. This leads to more uniform reflection intensities across the serial data set, and a smaller number of patterns are required to merge the reflection intensities for good statistics. Furthermore, structure refinements based on the dynamical diffraction theory become possible due to the diffraction volume integration of beam precession, providing a novel approach for more accurate structure models. In this context, the use of beam precession is presented as an advantageous tool for serial electron crystallography, as it enables reliable crystal structure analysis with a lower amount of diffraction data.

The X-ray restrained wavefunction (XRW) method is a quantum crystallographic technique that enables the determination of wavefunctions compatible with experimental X-ray diffraction data. Extensive research has demonstrated that this strategy inherently captures electron correlation and polarization effects on the electron density, while also providing consistent electron distributions. These findings suggest that the approach could be valuable in the development of new exchange-correlation (xc) functionals for density functional theory (DFT) calculations. This is particularly relevant in light of recent observations and recommendations by Medvedev et al. [Science (2017), 355, 49-52], who stressed the importance that xc functionals give both accurate energy values and exact electron densities, in line with the original spirit of DFT. Motivated by this perspective, this paper presents a preliminary investigation that aims at extracting and visualizing for the first time the perturbation potentials arising from the use of X-ray diffraction data as restraints in XRW calculations. In the present work, these potentials are simply obtained as orbital-averaged potentials through straightforward inversions of the XRW equations, where theoretical or high-quality experimental X-ray structure factors are employed in XRW computations at the restricted Hartree-Fock level for atoms (neon, argon and krypton) and simple molecules (dilithium and urea). Features and limitations of the resulting preliminary potentials are illustrated, while future perspectives on the use of the XRW method for the development of xc functionals are also discussed.

Near-surface small-angle neutron scattering (NS-SANS) is a highly versatile, yet under-utilized, technique in condensed matter research. It addresses the shortcomings of transmission SANS to enable the characterization of nano-structures within extremely small sample volumes in the thin-film limit. NS-SANS stands out in its capacity to resolve 1D, 2D or 3D structural, chemical and magnetic correlations beneath the surfaces of thin films with nanometre resolution. By varying the incident angle above the critical angle of reflection, NS-SANS delivers tuneable depth sensitivity across nano-confined volumes, effectively minimizing noise contributions from substrates while surpassing the surface-sensitive capabilities of grazing-incidence SANS. This perspective highlights the future potential of NS-SANS to study condensed matter thin films and heterostructures, with a special focus on nanoscale magnetic phenomena, such as topological skyrmion lattices, superconducting vortex lattices and chiral domain walls, which are of timely interest to the magnetism and quantum materials communities.

Neutron reflectivity is a powerful technique for probing density profiles in films, with applications across physics, chemistry and biology. However, challenges arise when dealing with samples characterized by high roughness, unknown scattering length density (SLD) with low contrast, very thin layers or complex multi-layered structures that cannot be uniquely resolved due to the phase problem. Incorporating a magnetic reference layer (MRL) and using polarized neutron reflectivity improves the sensitivity and modelling accuracy by providing complementary information. In this study, we introduce a quantitative means of comparing MRL systems in a model-free way. We apply this approach to demonstrate that CoTi alloys offer a superior solution as MRLs compared with the commonly used Fe or Ni MRLs. The low nuclear and magnetic scattering length densities of CoTi significantly enhance sensitivity, making it particularly advantageous for soft-matter research. Furthermore, the tunable Co versus Ti ratio allows for optimization of the SLD to achieve maximum sensitivity, establishing CoTi as a highly effective choice for MRL applications. The applied simulation framework for optimizing MRL sensitivity to a specific materials system and research question is a generic approach that can be used prior to growing the MRL for a given experiment.

We share personal experience in the fields of materials science and high-pressure research, discussing which parameters, in addition to positions of peak maxima and intensities, may be important to control and to document in order to make deposited powder diffraction data reusable, reproducible and replicable. We discuss, in particular, which data can be considered as 'raw' and some challenges of revisiting deposited powder diffraction data. We consider procedures such as identifying ('fingerprinting') a known phase in a sample, solving a bulk crystal structure from powder data, and analyzing the size of coherently scattering domains, lattice strain, the type of defects or preferred orientation of crystallites. The specific case of characterizing a multi-phase multi-grain sample following in situ structural changes during mechanical treatment in a mill or on hydrostatic compression is also examined. We give examples of when revisiting old data adds a new knowledge and comment on the challenges of using deposited data for machine learning.

Grazing-incidence X-ray diffraction (GIXD) is widely used for the structural characterization of thin films, particularly for analyzing phase composition and the orientation distribution of crystallites. While various tools exist for qualitative evaluation, a widely applicable systematic procedure to obtain quantitative information has not yet been developed. This work presents a first step in that direction, allowing accurate quantitative information to be obtained through the evaluation of radial line profiles from GIXD data. An algorithm is introduced for computing radial line profiles based on the crystal structure of known compounds. By fitting experimental data with calculated line profiles, accurate quantitative information about orientation distribution and phase composition is obtained, along with additional parameters such as mosaicity and total crystal volume. The approach is demonstrated using three distinct thin film systems, highlighting the broad applicability of the algorithm. This method provides a systematic and general approach to obtaining quantitative information from GIXD data.

The use of Hermite functions to describe pair distribution functions (PDFs) from total scattering data was previously proposed by Krylov & Vvedenskii [J. Non-Cryst. Solids (1995), 192-193, 683-687]. Hermite functions have a suitable form for describing both the total scattering data and the PDF, and have the useful feature that they are eigenfunctions of the Fourier transform operation. We demonstrate that, by fitting Hermite functions to total scattering data, it is possible to take into account the effects of experimental resolution when deriving the PDF from the scattering data. This is particularly advantageous for neutron time-of-flight data, where different banks of detectors have different resolution functions and the resolution widths vary with the size of the scattering vector. A number of technical points are discussed and illustrated using examples of synthetic data, including both amorphous and crystalline materials. These include a solution to the problem of handling the sharp Bragg peaks, and how to scale the scattering function and PDF to match the scale of the Hermite functions. A number of examples using real scattering data, both synchrotron X-ray and spallation neutron data, are also shown. To account for uncertainties in the levels of the scattering functions, we have modified a method of Billinge & Farrow [J. Phys. Condens. Matter (2013), 25, 454202] to remove backgrounds by fitting with low-order orthogonal (Chebyshev) functions.