Neutron Bragg Diffraction Research Articles

Bragg diffraction by a magnetic all-in–all-out configuration with application to a cubic cerium pyrochlore oxide

The Bragg diffraction of neutrons and x rays are well suited to the task of determining the distribution of magnetization in crystals. Applications of the two techniques proceed by contrasting observed intensities with intensities calculated with a specific model, and changing the model as need be to achieve satisfactory agreement. An all-in--all-out (AIAO) magnetic configuration of magnetic dipoles on a cubic face-centered lattice with networks of corner-sharing tetrahedra is often mentioned in the context of pyrochlore oxides, for example, but the corresponding neutron and x-ray-diffraction patterns appear to not have been calculated. Our results for patterns of Bragg spots from an AIAO magnetic configuration defined by a magnetic space group are symmetry informed and yield exact reflection conditions. Specifically, a long-range order of magnetic dipoles is forbidden in our model. Bulk properties arise from higher-order multipoles that include quadrupoles and octupoles. Bragg spots that exclude all magnetic multipoles other than an octupole have been discovered, and they can be observed by both neutron diffraction and resonant x-ray diffraction. All magnetic multipoles allowed in diffraction by cerium ions $(4{f}^{1})$ are presented in terms of coefficients in a well-documented and unusual magnetic ground state. Symmetry of the cerium site in the cubic structure constrains the coefficients. Our scattering amplitudes have an application in both neutron- and x-ray diffraction experiments on ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$, for example, and searches for the sought-after cerium octupole. Also presented for future use is a result for the total, energy-integrated magnetic neutron-scattering intensity by a powder sample.

Magnetic order and 5d1 multipoles in a rhenate double perovskite Ba2MgReO6

Structural and magnetic transitions in a double perovskite hosting 5d1 Re ions are discussed on the basis of recently published high-resolution x-ray diffraction patterns [D. Hirai, et al., Phys. Rev. Res. 2, 022063(R) (2020)]. A reported structural transition below room temperature, from cubic to tetragonal symmetry, appears not to be driven by T2g-type quadrupoles, as suggested. A magnetic motif at lower temperature is shown to be composed of two order parameters, associated with propagation vectors k = (0, 0, 1) and k = (0, 0, 0). Findings from our studies, for structural and magnetic properties of Ba2MgReO6, surface in predicted amplitudes for x-ray diffraction at rhenium L2 and L3 absorption edges, and magnetic neutron Bragg diffraction. Specifically, entanglement of anapole and spatial degrees of freedom creates a quadrupole in the neutron scattering amplitude. It would be excluded in an unexpected scenario whereby the rhenium atomic state is a manifold. Also, a chiral signature visible in resonant x-ray diffraction will be one consequence of predicted electronic quadrupole and magnetic dipole orders. A model Re wave function consistent with all current knowledge is a guide to electronic and magnetic multipoles engaged in x-ray and neutron diffraction investigations.

Lone octupole and bulk magnetism in osmate 5d2 double perovskites

Cubic double perovskites that host heavy ions with total angular momentum J = 2 can exhibit a singular magnetic state epitomized by a lone octupole and bulk ferro-type magnetism. It exists in the Chen - Balents Hamiltonian with a quadrupole interaction and competing exchange forces between the ions. Our symmetry inspired analysis mirrors the Dzyaloshinskii - Man'ko theory of latent antiferromagnetic ordering, and a 3-k collinear structure. Experimental tests of the singular state include neutron and x-ray Bragg diffraction.

Simulation tools for detector and instrument design

The high performance requirements at the European Spallation Source have been driving the technological advances on the neutron detector front. Now more than ever is it important to optimize the design of detectors and instruments, to fully exploit the ESS source brilliance. Most of the simulation tools the neutron scattering community has at their disposal target the instrument optimization until the sample position, with little focus on detectors. The ESS Detector Group has extended the capabilities of existing detector simulation tools to bridge this gap. An extensive software framework has been developed, enabling efficient and collaborative developments of required simulations and analyses – based on the use of the Geant4 Monte Carlo toolkit, but with extended physics capabilities where relevant (like for Bragg diffraction of thermal neutrons in crystals). Furthermore, the MCPL (Monte Carlo Particle Lists) particle data exchange file format, currently supported for the primary Monte Carlo tools of the community (McStas, Geant4 and MCNP), facilitates the integration of detector simulations with existing simulations of instruments using these software packages. These means offer a powerful set of tools to tailor the detector and instrument design to the instrument application.

Electronic and magnetic properties of multiferroic ScFeO3 available from diffraction experiments

Electronic and magnetic properties of ferric ions (3d5) in multiferroic ScFeO3 are puzzling, in part because they are different from the only other multiferroic known to possess the same polar chemical structure, BiFeO3. Open questions about ScFeO3 can be addressed by confronting observations with results for G-type antiferromagnetism allowed by the lithium niobate (LiNbO3)-like parent R3c structure. Calculated structure factors for resonant x-ray diffraction include all charge-like quadrupoles allowed by symmetry, and if experimental results for ScFeO3 subsequently imply they are different from zero then ferric ions cannot be in the high-spin 6S state. The same type of experiment can reveal the moment direction in the G-type antiferromagnetism, according to our calculations, and thereby contribute to understanding magnetic anisotropy. Furthermore, structure factors for magnetic neutron diffraction by ScFeO3 include Dirac multipoles that are time-odd and parity-odd, e.g. dipoles that are often called anapoles or toroidal moments. Apart from Dirac multipoles, the conventional approach to the interpretation of neutron Bragg diffraction data will be inadequate if ferric ions (Fe3+) are not in the high-spin 6S state, because the scattering amplitude includes more than simple dipole moments in the general case.

Advanced Synchrotron Radiation and Neutron Scattering Techniques for Microstructural Characterization in Industrial Research

The rapid development of new materials and their application in an extremely wide variety of research and technological fields has lead to the request of increasingly sophisticated characterization methods. In particular residual stress measurements by neutron diffraction, small angle scattering of X-rays and neutrons, as well as 3D imaging techniques with spatial resolution at the micron or even sub-micron scale, like micro-and nano-computerized tomography, have gained a great relevance in recent years.Residual stresses are autobalancing stresses existing in a free body not submitted to any external surface force. Several manufacturing processes, as well as thermal and mechanical treatments, leave residual stresses within the components. Bragg diffraction of X-rays and neutrons can be used to determine residual elastic strains (and then residual stresses by knowing the material elastic constants) in a non-destructive way. Small Angle Scattering of neutrons or X-rays, complementary to Transmission Electron Microscopy, allows the determination of structural features such as volume fraction, specific surface and size distribution of inhomogeneities embedded in a matrix, in a huge variety of materials of industrial interest. X-ray microtomography is similar to conventional Computed Tomography employed in Medicine, allowing 3D imaging of the investigated samples, but with a much higher spatial resolution, down to the sub-micron scale. Some examples of applications of the experimental techniques mentioned above are described and discussed.

Neutron scattering by Dirac multipoles

Scattering by magnetic charge formed by Dirac multipoles that are magnetic and polar is examined in the context of materials with properties that challenge conventional concepts. An order parameter composed of Dirac quadrupoles has been revealed in the pseudo-gap phase of ceramic, high-Tc superconductors on the basis of Kerr effect and magnetic neutron Bragg diffraction measurements. Construction of Dirac quadrupoles that emerge from centrosymmetric sites used by Cu ions in the ceramic superconductor Hg1201 is illustrated, together with selection rules for excitations that will feature in neutron inelastic scattering, and RIXS experiments. We report magnetic scattering amplitudes for diffraction by polar multipoles that have universal value, because they are not specific to ceramic superconductors. To illustrate this attribute, we consider neutron Bragg diffraction from a magnetically ordered iridate (Sr2IrO4) and discuss shortcomings in published interpretations of diffraction data.

Zeeman spectrum, magnetic neutron diffraction pattern, and Dirac multipoles for a multiferroic materialCuB2O4

Zeeman spectra, dichroic signals, and neutron Bragg diffraction patterns generated by copper ions in magnetically ordered copper metaborate $(\mathrm{Cu}{\mathrm{B}}_{2}{\mathrm{O}}_{4})$ are investigated within a minimal model of Cu atomic states. A theory platform, common to understanding optical spectra and neutron diffraction patterns, affords the immediate benefit of a unified description of the experimental probes in terms of electronic multipoles. Results for dichroic signals illustrate a nontrivial use of a general, quantum mechanical theory of photon absorption couched in terms of Dirac multipoles that are magnetic and polar. Anapoles (Dirac dipoles) are predicted to generate Bragg spots in magnetic neutron diffraction that are not indexed by the motif of conventional (axial) magnetic-dipole moments. The minimal model of Cu states is informed by magnetic symmetry, derived from an established commensurate antiferromagnetic order, with a sparse number of parameters that comply with available empirical evidence.

High-resolution 2-D Bragg diffraction reveal heterogeneous domain transformation behavior in a bulk relaxor ferroelectric

In-situ measurement of fine-structure of neutron Bragg diffraction peaks from a relaxor single-crystal using a time-of-flight instrument reveals highly heterogeneous mesoscale domain transformation behavior under applied electric fields. It is observed that only ∼25% of domains undergo reorientation or phase transition contributing to large average strains, while at least 40% remain invariant and exhibit microstrains. Such insights could be central for designing new relaxor materials with better performance and longevity. The current experimental technique can also be applied to resolve complex mesoscale phenomena in other functional materials.

Ferro-type order of magneto-electric quadrupoles as an order-parameter for the pseudo-gap phase of a cuprate superconductor

There is general agreement within the community of researchers that investigate high-Tc materials that it is most important to understand the pseudo-gap phase. To this end, many experiments on various cuprates have been reported. Two prominent investigations—Kerr effect and neutron Bragg diffraction—imply that underdoped YBCO samples possess long-range magnetic order of an unusual kind. However, other measurements do not support the existence of magnetic order. Here we show that the Kerr effect and magnetic Bragg diffraction data are individual manifestations of ordered magneto-electric quadrupoles at Cu sites. While the use of magneto-electric multipoles is new in studies of the electronic properties of cuprates, they are not unknown in other materials, including an investigation with x-rays of the parent compound CuO. We exploit the recent prediction that neutrons are deflected by magneto-electric multipoles. The outcome of our study is a theory for the order-parameter of the pseudo-gap phase without the aforementioned conflict with other measurements, and the first experimental evidence that neutrons interact with multipoles belonging to a state of magnetic charge.

Symmetry-protected hidden order and magnetic neutron Bragg diffraction by URu2Si2

We investigate how the order parameter of a continuous phase transition can be protected from view by symmetry in a magnetic crystal. The symmetry in question forbids atomic displacements and formation of magnetic dipoles, rendering the order parameter invisible in standard x-ray and magnetic neutron Bragg diffraction. Analysis of the allowed magnetic space-groups reveals exact properties of the hidden order parameter. We demonstrate that Bragg spots forbidden by the chemical structure can unveil magnetic hidden order. The method is applied to URu2Si2, which has been thoroughly investigated in the past few decades using all manner of experimental techniques. Starting from the established chemical structure of URu2Si2, we have performed a critical analysis of available data for magnetic neutron Bragg diffraction.

Magnetic symmetries in neutron and resonant x-ray Bragg diffraction patterns of four iridium oxides

The magnetic properties of Sr2IrO4, Na2IrO3, Sr3Ir2O7 and CaIrO3 are discussed, principally in the light of experimental data in recent literature for Bragg intensities measured in x-ray diffraction with enhancement at iridium L-absorption edges. The electronic structure factors we report, which incorporate parity-even and acentric entities, serve the immediate purpose of making full use of crystal and magnetic symmetry to refine our knowledge of the magnetic properties of the four iridates from resonant x-ray diffraction data. They also offer a platform on which to interpret future investigations, using dichroic signals, resonant x-ray diffraction and neutron diffraction, for example, as well as ab initio calculations of electronic structure. Unit-cell structure factors, suitable for x-ray Bragg diffraction enhanced by an electric dipole–electric dipole (E1–E1) event, reveal exactly which iridium multipoles are visible, e.g., a magnetic dipole parallel to the crystal c-axis (z-axis) and an electric quadrupole with yz-like symmetry in the specific case of CaIrO3. Magnetic space-groups are assigned to Sr2IrO4, Sr3Ir2O7 and CaIrO3, namely, PIcca, PAban and Cm′cm′, respectively, in the Belov–Neronova–Smirnova notation. The assignment for Sr2IrO4 is possible because of our new high-resolution neutron diffraction data, gathered on a powder sample. In addition, the new data are used to show that the ordered magnetic moment of an Ir4+ ion in Sr2IrO4 does not exceed 0.29(4) μB. Na2IrO3 has two candidate magnetic space-groups that are not resolved with currently available resonant x-ray data.

Structures of Pd(CN)2 and Pt(CN)2: Intrinsically Nanocrystalline Materials?

Analysis and modeling of X-ray and neutron Bragg and total diffraction data show that the compounds referred to in the literature as "Pd(CN)(2)" and "Pt(CN)(2)" are nanocrystalline materials containing small sheets of vertex-sharing square-planar M(CN)(4) units, layered in a disordered manner with an intersheet separation of ~3.44 Å at 300 K. The small size of the crystallites means that the sheets' edges form a significant fraction of each material. The Pd(CN)(2) nanocrystallites studied using total neutron diffraction are terminated by water and the Pt(CN)(2) nanocrystallites by ammonia, in place of half of the terminal cyanide groups, thus maintaining charge neutrality. The neutron samples contain sheets of approximate dimensions 30 Å × 30 Å. For sheets of the size we describe, our structural models predict compositions of Pd(CN)(2)·xH(2)O and Pt(CN)(2)·yNH(3) (x ≈ y ≈ 0.29). These values are in good agreement with those obtained from total neutron diffraction and thermal analysis, and are also supported by infrared and Raman spectroscopy measurements. It is also possible to prepare related compounds Pd(CN)(2)·pNH(3) and Pt(CN)(2)·qH(2)O, in which the terminating groups are exchanged. Additional samples showing sheet sizes in the range ~10 Å × 10 Å (y ~ 0.67) to ~80 Å × 80 Å (p = q ~ 0.12), as determined by X-ray diffraction, have been prepared. The related mixed-metal phase, Pd(1/2)Pt(1/2)(CN)(2)·qH(2)O (q ~ 0.50), is also nanocrystalline (sheet size ~15 Å × 15 Å). In all cases, the interiors of the sheets are isostructural with those found in Ni(CN)(2). Removal of the final traces of water or ammonia by heating results in decomposition of the compounds to Pd and Pt metal, or in the case of the mixed-metal cyanide, the alloy, Pd(1/2)Pt(1/2), making it impossible to prepare the simple cyanides, Pd(CN)(2), Pt(CN)(2), or Pd(1/2)Pt(1/2)(CN)(2), by this method.

Neutron Bragg diffraction on a thick Ge single crystal excited by ultrasound

The intensities of neutron Bragg diffracted from the front- and back-faces of a 22 mm thick perfect Ge single crystal undergoing on ultrasound excitation has been measured and calculated theoretically. It is shown that at the same time as the acoustic wave amplitude is increased, the main Bragg peaks grow and the back-face peak becomes asymmetric and tends to disappear. Such a back-face scattering was observed for the first time and successfully described within frameworks of the dynamic theory of neutron scattering modified in the presence of ultrasound excitation and Kato’s quasiclassical approximation taking into account new ultrasonic extinction length appearance.

New method for calculation of intensities of X-rays and thermal neutrons scattered dynamically in defected single crystals

We propose a new method for calculating intensities of X-rays and thermal neutrons, dynamically scattered in defected single crystals by comparing the dynamical theory of Bragg diffraction of X-rays and thermal neutrons in perfect single crystals with the theory of their small-angle scattering.

Ultrasound effect on neutron Bragg diffraction in a perfect and deformed silicon single crystal

The features of neutron Bragg diffraction in a perfect and bent (deformed) silicon single crystal have been studied under ultrasound excitation. In contrast to a perfect crystal where an increase in the diffraction intensity has been observed with an increase in the ultrasound wave’s amplitude, in a deformed silicon crystal the intensity sharply decreases (two times) already at small voltages on a piezoelectric transducer. The depth and position of minima of the total intensity depend on the ultrasound wave’s amplitude and the bending radius of a crystal. To explain the observed effects the modified Penning-Polder-Kato model has been successfully used, in which the role of ultrasound is reduced to the formation of resonance transitions of imaging points between different sheets of dispersion surface. Experimental proofs of validity of the used model are presented. Estimations of the probabilities of one- and multiphonon scattering processes obtained from experimental data have a good agreement with theoretical ones.

Neutron Bragg Diffraction on a Bent Silicon Single Crystal Excited by Ultrasound

Neutron Bragg Diffraction on a Bent Silicon Single Crystal Excited by UltrasoundThe neutron Bragg diffraction on a bent silicon monocrystal excited by ultrasound was investigated. It is shown that for perfect crystal the relative diffraction intensity is proportional to the acoustic wave amplitudew.The calibration parameters between the generator voltage and acoustic wave amplitude were derived assumingw= (2.3±0.3)·10-2Å/V. To explain the results, a modified Penning—Polder—Kato model was applied. In a bent crystal, owing to ultrasound, transitions between the sheets of a dispersion surface take place. This leads to various manifestations of the behaviour of the integral scattering intensity, which drastically differs from the case of a perfect crystal. The observed effects may be used for creating new types of neutron monochromators and choppers governed by the ultrasound wave amplitude as well as by the length and bending radius of the crystal.

Correlated magnetic reversal in periodic stripe patterns

The magnetization reversal in a periodic magnetic stripe array has been studied with a combination of direct and reciprocal space methods: Kerr microscopy and polarized neutron scattering. Kerr images show that during magnetization reversal over a considerable magnetic-field range a ripple domain state occurs in the stripes with magnetization components perpendicular to the stripes. Quantitative analysis of polarized neutron specular reflection, Bragg diffraction, and off-specular diffuse scattering provides a detailed picture of the mean magnetization direction in the ripple domains as well as longitudinal and transverse fluctuations, and reveals a strong correlation of those components over a number of stripes.

Vortex lattice reorientation and anisotropy in MgB 2––effects of two-band superconductivity

We present small-angle neutron scattering (SANS) measurements of the vortex lattice (VL) in single crystal MgB 2––a two-band superconductor. Bragg diffraction of neutrons visualizes the structure and orientation of the VL while the scattered intensity probes the super-carrier density. Superconductivity in the π-band is rapidly suppressed with increasing field with a corresponding decrease in scattered intensity and a re-orientation of the VL between 0.5 and 0.9 T. Both these observations are consistent with superconductivity in the π-band being weaker than in the σ-band ( Δ π< Δ σ), and a changing influence of different parts of the Fermi surface determining the VL orientation. SANS measurements of the VL for fields applied at an angle to the c-axis allow the penetration depth anisotropy, γ λ , to be estimated.

Structure of AuCN Determined from Total Neutron Diffraction.

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