Reciprocal Space Research Articles

Laue-DIALS: Open-source software for polychromatic x-ray diffraction data.

Most x-ray sources are inherently polychromatic. Polychromatic ("pink") x-rays provide an efficient way to conduct diffraction experiments as many more photons can be used and large regions of reciprocal space can be probed without sample rotation during exposure-ideal conditions for time-resolved applications. Analysis of such data is complicated, however, causing most x-ray facilities to discard >99% of x-ray photons to obtain monochromatic data. Key challenges in analyzing polychromatic diffraction data include lattice searching, indexing and wavelength assignment, correction of measured intensities for wavelength-dependent effects, and deconvolution of harmonics. We recently described an algorithm, Careless, that can perform harmonic deconvolution and correct measured intensities for variation in wavelength when presented with integrated diffraction intensities and assigned wavelengths. Here, we present Laue-DIALS, an open-source software pipeline that indexes and integrates polychromatic diffraction data. Laue-DIALS is based on the dxtbx toolbox, which supports the DIALS software commonly used to process monochromatic data. As such, Laue-DIALS provides many of the same advantages: an open-source, modular, and extensible architecture, providing a robust basis for future development. We present benchmark results showing that Laue-DIALS, together with Careless, provides a suitable approach to the analysis of polychromatic diffraction data, including for time-resolved applications.

Fast generation of spectrally shaped disorder.

Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by means of the nonuniform fast Fourier transform, thus arriving at an algorithm capable of generating systems with arbitrary spectral properties, with a computational cost that scales O(NlogN) with system size. The method is extended to accommodate arbitrary real-space interactions, such as short-range repulsion, to simultaneously control short- and long-range correlations. We thus generate the largest-ever stealthy hyperuniform configurations in 2d (N=10^{9}) and 3d (N>10^{7}) and demonstrate the flexibility of the approach by generating structures with designed spectral features at scale. By an Ewald sphere construction we link the spectral and optical properties at the single-scattering level and show that stealthy hyperuniform structures generically display transmission gaps, providing a concrete example of fine-tuning of a physical property. We also show that large 3d power-law hyperuniformity in particle packings leads to single-scattering properties nearly identical to those of simple hard spheres. Finally, we demonstrate generalizations of the approach to impose features in either continuous or discrete real space, using constraints in either continuous or discrete reciprocal space. In particular, enforcing large spectral power at peaks with the right symmetry leads to the nondeterministic generation of quasicrystalline structures in 2d and 3d. This technique should become an essential tool to embed, and understand the role of, long-range correlations in disordered metamaterials.

Study of Crystallography and Reciprocal Space of Higher Oxides of Lanthanides Using Electron and Neutron Diffraction

Abstract: This study explains uses electron and neutron diffraction techniques to study the crystallography and reciprocal space of higher oxides of lanthanides. The significance of crystallography in comprehending the geometric configuration and bonding of atoms in solids is discussed at the outset of the study. The comprehensive analysis of the crystal structures using accelerated electrons and neutrons highlights the tremendous penetration power of these particles. While neutron diffraction is concerned with plane incidence waves and their scattered counterparts, electron diffraction is concerned with electron generation pulsed by a laser.Important findings show how experimental data may be used to validate Bragg's equation and show how scattering angles, interplanar distance, and order of wavelength are related. To display the relationship between electron energy and electron radiation per electron volt, energy distribution curves are displayed. Additionally, several crystal systems, such as hexagonal, monoclinic, and cubic face-centered structures, are revealed by structural investigation of higher oxides of lanthanides, such as terbium dioxide (Tb2O3).The talk emphasizes how, in contrast to other elements in the series, lanthanides have special qualities that enable them to produce higher oxides with oxidation states greater than +3. The outcomes highlights the improved precision and in-depth structural insights that come from combining electron and neutron diffraction methods. This opens the door for more studies in the crystallography of complicated materials in the future.

Investigating the missing-wedge problem in small-angle X-ray scattering tensor tomography across real and reciprocal space.

Small-angle-scattering tensor tomography is a technique for studying anisotropic nanostructures of millimetre-sized samples in a volume-resolved manner. It requires the acquisition of data through repeated tomographic rotations about an axis which is subjected to a series of tilts. The tilt that can be achieved with a typical setup is geometrically constrained, which leads to limits in the set of directions from which the different parts of the reciprocal space map can be probed. Here, we characterize the impact of this limitation on reconstructions in terms of the missing wedge problem of tomography, by treating the problem of tensor tomography as the reconstruction of a three-dimensional field of functions on the unit sphere, represented by a grid of Gaussian radial basis functions. We then devise an acquisition scheme to obtain complete data by remounting the sample, which we apply to a sample of human trabecular bone. Performing tensor tomographic reconstructions of limited data sets as well as the complete data set, we further investigate and validate the missing wedge problem by investigating reconstruction errors due to data incompleteness across both real and reciprocal space. Finally, we carry out an analysis of orientations and derived scalar quantities, to quantify the impact of this missing wedge problem on a typical tensor tomographic analysis. We conclude that the effects of data incompleteness are consistent with the predicted impact of the missing wedge problem, and that the impact on tensor tomographic analysis is appreciable but limited, especially if precautions are taken. In particular, there is only limited impact on the means and relative anisotropies of the reconstructed reciprocal space maps.

Mixed higher-order topology, and nodal and nodeless flat band topological phases in a superconducting multiorbital model

We investigate the topological phases that appear in an orbital version of the Benalcazar-Bernevig-Hughes (BBH) model in the presence of conventional spin-singlet s-wave superconductivity and with the possibility of tuning an in-plane magnetic field. We chart out the phase diagram by considering different boundary conditions, with the topology of the individual phases further examined by considering both the Wannier and entanglement spectra, as well as the Majorana polarization. For weak to moderate values of magnetic field and superconducting pairing amplitude, we find a second-order topological superconductor phase with eight zero-energy corner modes. Further increasing field or pairing, half of the corner states can be turned into zero-energy edge-localized modes, thus forming what we name hybrid-order phase. Then, we find two different putative first-order topological phases, a nodal and a nodeless phase, both with zero-energy flat bands localized along mirror-symmetric open edges. For the nodal phase, the flat bands are, as expected, localized between the nodes in reciprocal space, while in the nodeless phase, the zero-energy boundary flat band instead spans the whole Brillouin zone and appears disjoint from the fully gapped bulk spectrum. As a consequence, this model present several unexpected phases with unusual surface states that can be tuned via an external magnetic field. Published by the American Physical Society 2024

A quantitative theory and atomistic simulation study on the soft-sphere crystal-melt interfacial properties. I. Kinetic coefficients.

By employing non-equilibrium molecular dynamics (NEMD) simulations and time-dependent Ginzburg-Landau (TDGL) theory for solidification kinetics [Cryst. Growth Des. 20, 7862 (2020)], we predict the kinetic coefficients of FCC(100) crystal-melt interface (CMI) of soft-spheres modeled with an inverse-sixth-power repulsive potential. The collective dynamics of the local interfacial liquid phase at the equilibrium FCC(100) CMIs are calculated based on a recently proposed algorithm [J. Chem. Phys. 157, 084 709 (2022)] and are employed as the resulting parameter that eliminates the discrepancy between the predictions of the kinetic coefficient using the NEMD simulations and the TDGL solidification theory. A speedup of the two modes of the interfacial liquid collective dynamics (at wavenumbers equal to the principal and the secondary reciprocal lattice vector of the grown crystal) is observed. With the insights provided by the quantitative predictive theory, the variation of the solidification kinetic coefficient along the crystal-melt coexistence boundary is discussed. The combined methodology (simulation and theory) presented in this study could be further applied to investigate the role of the inter-atomic potential (e.g., softness parameter s = 1/n of the inverse-power repulsive potential) in the kinetic coefficient.

Integrating Newton's equations of motion in the reciprocal space.

We here present the normal dynamics technique, which recasts the Newton's equations of motion in terms of phonon normal modes by exploiting a proper sampling of the reciprocal space. After introducing the theoretical background, we discuss how the reciprocal space sampling enables us to (i) obtain a computational speedup by selecting which and how many wave vectors of the Brillouin zone will be considered and (ii) account for distortions realized across large atomic distances without the use of large simulation cells. We implemented the approach into an open-source code, which we used to present three case studies: in the first one, we elucidate the general strategy for the sampling of the reciprocal space; in the second one, we illustrate the potential of the approach by studying the stabilization effect of temperature in α-uranium; and in the last one, we investigate the characterization of Raman spectra at different temperatures in MoS2/MX2 transition metal dichalcogenide heterostructures. Finally, we discuss how the procedure is general and can be used to simulate periodic, semiperiodic, and finite systems such as crystals, slabs, nanoclusters, or molecules.

Experimental demonstration of merging quasi-BICs in photonic crystal slabs

Merging bound states in the continuum (BICs) and avoided crossing of resonances (ACR) are promising theoretical approaches to greatly enhance the quality (Q) factors of quasi-BICs in reciprocal space. We observe the phenomena of merging BICs and ACR in millimeter-sized C4v symmetry photonic crystal structures. The ACR at Γ point is obtained in the variation of the structural parameter. In off-Γ region, the merging BICs at arbitrary locations are observed in the experimental measurements. The findings offer a pathway to high-performance photonic devices with potential applications in optoelectronics and microwave experimentation.

Nanoscopic analysis of rapid thermal annealing effects on InGaN grown over Si(111)

This study explores the impact of rapid thermal annealing (RTA) on InxGa1-xN grown over Si(111) by molecular beam epitaxy (MBE). Through X-ray diffraction (XRD) and reciprocal space map (RSM) characterization, notable shifts in diffraction peaks were observed post-annealing, suggesting alterations of the Indium content in the nanostructures. Morphological assessments using scanning electron microscopy (SEM) and atomic force microscopy (AFM) indicated that RTA could smooth the surface of the samples, though some instances of degradation were also noted. Energy-dispersive X-ray spectroscopy (EDS) showed further stoichiometric modification following annealing. Photoluminescence spectroscopy (PL) revealed notable shifts and increases in the intensity of the InxGa1-xN peaks, indicating the formation of regions with high Indium or Gallium concentration. The presence of these enriched regions was particularly evident from the peaks at around 540 nm and 433 nm, suggesting significant changes in the material's composition. Transmission electron microscopy combined with electron energy loss spectroscopy (TEM-EELS) corroborated the presence of In-rich and Ga-rich areas, affirming the phenomenon of Indium surface segregation. So, this study contributes to understanding the behavior of InxGa1-xN nanostructures under rapid thermal annealing, providing insights for advanced optoelectronic applications.

PyArc: A python package for computing absorption and radiative coefficients from first principles

Light absorption and radiative recombination are two critical processes in optoelectronic materials that characterize the energy conversion efficiency. The absorption and radiative coefficients are thus key properties for device optimization and design. Here, we develop a python package named pyArc that allows rigorous computation of absorption and radiative coefficients from first principles. By integrating several interpolation strategies to augment k-point sampling in reciprocal space, our code is accurate yet highly efficient. In addition to evaluation of the coefficients, our code is capable of intuitive analysis of carrier distribution, facilitating a deeper understanding of the microscopic mechanisms underlying the radiative coefficients. Utilizing GaAs as a prototypical example, we demonstrate how to employ our package to compute absorption and radiative coefficients and to investigate the key features in the electronic structure that give rise to these coefficients. Program SummaryProgram title: PyArcCPC Library link to program files:https://doi.org/10.17632/5x9g9bvhcv.1Licensing provisions: MIT licenseProgramming language: Python 3Nature of problem: Light absorption and radiative recombination processes in semiconductors critically impact the energy conversion efficiency of optoelectronic devices. Developing a method to calculate coefficients of the two processes based on first-principles theory is essential, which not only can help to obtain the key properties of those semiconductor materials and guide the device design, but also can unveil the underlying microscopic mechanisms.Solution method: PyArc, written in the Python language, implements first-principles methodologies for the computation of absorption and radiative coefficients of semiconductors based on Fermi's golden rule. This package takes the electronic eigenvalues and dipole matrix elements of a material computed from first-principles codes such as VASP as input. Dense k-point sampling for the Brillouin zone is achieved through efficient interpolation schemes implemented in our code to acquire well converged results. The functionality of cross-sectional visualization of carrier distribution in our code provides intuitive insights into the fundamental mechanism beneath the charge-carrier radiative recombination process.

Symmetry change in LaNiO3 films caused by epitaxial strain from LaAlO3, SrTiO3, and DyScO3 pseudocubic (001) surfaces

To elucidate the epitaxial strain effect over a wide range of lattice mismatch, we investigated the structures of ∼25 nm thick LaNiO3 films grown on the pseudocubic (001) surfaces of three different substrates, namely, LaAlO3 (LAO), SrTiO3 (STO), and DyScO3 (DSO). Such structural information had been inferred from the intensities of a small number of Bragg reflections that relate to the NiO6 octahedral tilting in previous studies. Here, we measured more than 100 reciprocal lattice points to derive reliable structural information. The procedure of ordinary crystal structure analysis is hampered by the multidomain structure and limited volume of measurable reciprocal space, both caused by a huge, highly symmetric substrate. To overcome this difficulty, we employed the Bayesian inference to obtain the detailed atomic positions in film samples. Octahedral tilting about the c axis was dominant for the compressively strained film grown on LAO, whereas tilting about the a and b axes was dominant for the tensile strained films grown on STO and DSO. The film lattice parameters of the samples grown on STO and DSO were nearly identical, whereas additional twofold lattice modulation, including cation displacement, was only observed in the latter.

Neutral beam microscopy with a reciprocal space approach using magnetic beam spin encoding

The emerging technique of neutral beam microscopy offers a non-perturbative way of imaging surfaces of various materials which cannot be studied using conventional microscopes. Current neutral beam microscopes use either diffractive focusing or pin-hole scanning to achieve spatial resolution, and are characterised by a strong dependence of the imaging time on the required resolution. In this work we introduce an alternative method for achieving spatial resolution with neutral atom beams which is based on manipulating the magnetic moments of the beam particles in a gradient field, and is characterised by a much weaker dependence of the imaging time on the image resolution. The validity of the imaging approach is demonstrated experimentally by reconstructing one dimensional profiles of the beam which are in good agreement with numerical simulation calculations. Numerical simulations are used to demonstrate the dependence of the signal to noise on the scan resolution and the topography of the sample, and assess the broadening effect due to the spread of velocities of the beam particles. The route towards implementing magnetic encoding in high resolution microscopes is discussed.

Crystal facet/interface anchored Janus activity of BiOBr in driving photocatalytic water splitting

Constructing Janus junctions is expected to provide a novel perspective for analyzing the intrinsic photocatalytic activity of bismuth oxyhalide. Herein, Janus-typed BiOBr(010)/BiOBr(001) homojunction with efficiently photocatalytic H2 evolution has been achieved by a hydrothermal synthesis. The experimental results show that the designed Janus-typed junction can effectively elevate the carrier lifetime, significantly enhance the photocurrent, and prominently reduce the overpotential. The potential difference (0.34 eV) between (010) facet and (001) facet can drive the carrier transport at the interface for Janus junctions. Theoretical calculations indicate that the designed Janus junction has a stable mechanical structure, providing certain support for the long lifetime of the photocatalyst in the photocatalytic process. The carrier distributions in the Janus junction exhibit the typical characteristic distribution. Interestingly, the photo-generated electrons are only localized in BiOBr(001) component, which embodies significantly a role of n-type semiconductor. This essentially activates HER activity (32 µmol/h g−1) of Janus junction. The holes preferentially localize in the BiOBr(010) component of Janus junction. This component undertaking p-type role reduces the free energy of the rate determining step (from OH* to O*) in the oxygen evolution process (0.88 eV). The Janus junction intensively suppresses the carrier recombination probability at the high symmetry point (reciprocal space) in BiOBr. Ab initio molecular dynamics calculations show that the adsorbed water is easy to decompose on the surface of Janus junction. The obtained results of the photocatalytic water splitting further confirm that the designed BiOBr(010)/BiOBr(001) has Janus characteristics, which are consistent with theoretical calculations and tracer tracing results. The diffusion characteristics of hydrogen also evidence that the interaction of the internal electric field in the Janus junction can drive the HER performance. Additionally, these results offer us a unique angle of view to regulate the charge carrier dynamics by the highly oriented facet coupling for the layered semiconductor.

Symmetry-Guided Engineering of Polarization by 2D Moiré Metasurfaces.

Cylindrical vector (CV) beams exhibit spatially varying polarization important in optical communication, super-resolution microscopy, and high-throughput information processing. Compared to radially or azimuthally polarized CV beams that are cylindrically symmetric, hybrid-electric (HE) beams offer increased optical tunability because of their polygonally symmetric polarizations. However, efforts to generate and isolate HE beams have relied on bulky optical assemblies or devices with complex and stringent fabrication requirements. Here, we report a moiré-based metasurface approach to engineer HE polarization states with high degrees of rotational symmetry. Importantly, polarization symmetries can be tailored based only on the reciprocal lattice of the metasurface and not the real-space patterns. Our modular method outlines important design principles for shaping light at the nanoscale.

Indexing neutron transmission spectra of a rotating crystal.

Neutron time-of-flight transmission spectra of mosaic crystals contain Bragg dips, i.e., minima at wavelengths corresponding to diffraction reflections. The positions of the dips are used for investigating crystal lattices. By rotating the sample around a fixed axis and recording a spectrum at each rotation step, the intensity of the transmitted beam is obtained as a function of the rotation angle and wavelength. The questions addressed in this article concern the determination of lattice parameters and orientations of centrosymmetric crystals from such data. It is shown that if the axis of sample rotation is inclined to the beam direction, the reflection positions unambiguously determine reciprocal-lattice vectors, which is not the case when the axis is perpendicular to the beam. Having a set of such vectors, one can compute the crystal orientation or lattice parameters using existing indexing software. The considerations are applicable to arbitrary Laue symmetry. The work contributes to the automation of the analysis of diffraction data obtained in the neutron imaging mode.

Асимметричная рентгеновская дифракция ограниченных пучков в кристаллах

Asymmetric dynamic diffraction of confined X-ray beams in crystals has been theoretically studied using Takagi–Taupin equations, including numerical solution using nodal grid and calculations of X-ray fields in Fourier space. We have fulfilled simulation of scattering intensity distribution maps from silicon crystal near reciprocal lattice site depending on size of X-ray beams.

К теории рентгеновской Лауэ дифракции в термомиграционном кристаллическом канале с легирующей примесью

X-ray Laue diffraction in a silicon crystal with Si(Al) thermomigration channels has been theoretically considered. Based on the model of elastic fields of atomic displacements in the channel, expressions for the distribution of strains have been obtained to describe diffraction in the Laue geometry. A numerical calculation of the X-ray scattering intensity distribution near a reciprocal lattice point has been performed. The difference between diffraction in a perfect and strained crystal has been shown.

Dislocation structure evolution during metal additive manufacturing

Abstract Dislocation structures are abundantly present in any additively manufactured alloy and they play a primary role in determining the mechanical response of an alloy. Until recently, it was understood that these structures form due to rapid solidification during AM. However, there was no consensus on whether they evolve due to the subsequent solid-state thermal cycling that occurs with further addition of layers. In order to design alloy microstructures with desired mechanical responses, it is crucial to first answer this outstanding question. This question was answered in a recent work [1] involving a novel experiment employing high resolution reciprocal space mapping, a synchrotron based X-ray diffraction technique, in situ during AM of an austenitic stainless steel. The study revealed that dislocation structures formed during rapid solidification undergo significant evolution during subsequent solid-state thermal cycling, in particular during addition of the first few (up to 5) layers above the layer of interest. A summary of the findings of this study are presented in this work. A possible pathway (involving experiment and modelling synergy) to better understanding dislocation structure formation during AM is presented.

Pinpointing lattice-matched conditions for wurtzite ScxAl1−xN/GaN heterostructures with x-ray reciprocal space analysis

Using comprehensive x-ray reciprocal space mapping, we establish the precise lattice-matching composition for wurtzite ScxAl1−xN layers on (0001) GaN to be x = 0.14 ± 0.01. 100 nm thick ScxAl1−xN films (x = 0.09–0.19) were grown in small composition increments on c-plane GaN templates by plasma-assisted molecular beam epitaxy. The alloy composition was estimated from the fit of the (0002) x-ray peak positions, assuming the c-lattice parameter of ScAlN films coherently strained on GaN increases linearly with Sc-content determined independently by Rutherford backscattering spectrometry [Dzuba et al., J. Appl. Phys. 132, 175701 (2022)]. Reciprocal space maps obtained from high-resolution x-ray diffraction measurements of the (101¯5) reflection reveal that ScxAl1−xN films with x = 0.14 ± 0.01 are coherently strained with the GaN substrate, while the other compositions show evidence of relaxation. The in-plane lattice-matching with GaN is further confirmed for a 300 nm thick Sc0.14Al0.86N layer. The full-width-at-half-maximum of the (0002) reflection rocking curve for this Sc0.14Al0.86N film is 106 arc sec and corresponds to the lowest value reported in the literature for wurtzite ScAlN films.

Texture tomography, a versatile framework to study crystalline texture in 3D.

Crystallographic texture is a key organization feature of many technical and biological materials. In these materials, especially hierarchically structured ones, the preferential alignment of the nano constituents heavily influences the macroscopic behavior of the material. To study local crystallographic texture with both high spatial and angular resolution, we developed Texture Tomography (TexTOM). This approach allows the user to model the diffraction data of polycrystalline materials using the full reciprocal space of the crystal ensemble and describe the texture in each voxel via an orientation distribution function, hence it provides 3D reconstructions of the local texture by measuring the probabilities of all crystal orientations. The TexTOM approach addresses limitations associated with existing models: it correlates the intensities from several Bragg reflections, thus reducing ambiguities resulting from symmetry. Further, it yields quantitative probability distributions of local real space crystal orientations without further assumptions about the sample structure. Finally, its efficient mathematical formulation enables reconstructions faster than the time scale of the experiment. This manuscript presents the mathematical model, the inversion strategy and its current experimental implementation. We show characterizations of simulated data as well as experimental data obtained from a synthetic, inorganic model sample: the silica-witherite biomorph. TexTOM provides a versatile framework to reconstruct 3D quantitative texture information for polycrystalline samples; it opens the door for unprecedented insights into the nanostructural makeup of natural and technical materials.