Conventional Neutron Diffraction Research Articles

Neutron Bragg edge imaging for strain characterization in powder bed additive manufacturing environments

Spatially resolved studies of crystalline structures, e.g. lattice spacings, are enabled by recording the transmitted spectra in neutron Bragg edge imaging. The recorded signals are, however, a result of through-thickness averaging of the probed specimen in the beam direction. Therefore, it is challenging to extract the strain distribution when the strain varies across the thickness, which applies for studies on different materials or material states along the beam. Here we introduce the approach to disentangle contributions to the recorded signals, i.e. separating the transmission spectra of two different material states. This is particularly applicable to powder bed additive manufacturing environments where operando strain characterization of the printed specimen using neutrons is intended. In this work, Laser Powder Bed Fusion (PBF-LB/M)-built 316L and IN718 samples embedded in their corresponding powders are used, extracting the desired spectra of the printed specimen. The disentanglement is proven to be satisfactory by obtaining coinciding strain maps of identical specimens embedded in powder layers of different thicknesses. Furthermore, the obtained residual strain distributions of 316L samples were verified by conventional neutron diffraction with lower spatial resolution due to the gauge volume averaging.

Cascade of magnetic-field-driven quantum phase transitions in Ce3Pd20Si6

Magnetically hidden order is a hypernym for electronic ordering phenomena that are visible to macroscopic thermodynamic probes but whose microscopic symmetry cannot be revealed with conventional neutron or x-ray diffraction. In a handful of f-electron systems, the ordering of odd-rank multipoles leads to order parameters with a vanishing neutron cross-section. Among them, Ce$_3$Pd$_{20}$Si$_6$ is known for its unique phase diagram exhibiting two distinct multipolar-ordered ground states (phases II and II'), separated by a field-driven quantum phase transition associated with a putative change in the ordered quadrupolar moment from $O_2^0$ to $O_{xy}$. Using torque magnetometry at subkelvin temperatures, here we find another phase transition at higher fields above 12 T, which appears only for low-symmetry magnetic field directions $\mathbf{B} \parallel \langle11L\rangle$ with $1 < L \leq 2$. While the order parameter of this new phase II'' remains unknown, the discovery renders Ce$_3$Pd$_{20}$Si$_6$ a unique material with two field-driven phase transitions between distinct multipolar phases. They are both clearly manifested in the magnetic-field dependence of the field-induced (111) Bragg intensities measured with neutron scattering for $\mathbf{B} \parallel [112]$. We also find from inelastic neutron scattering that the number of nondegenerate collective excitations induced by the magnetic field correlates with the number of phases in the magnetic phase diagram for the same field direction. Furthermore, the magnetic excitation spectrum suggests that the new phase II'' may have a different propagation vector, revealed by the minimum in the dispersion that may represent the Goldstone mode of this hidden-order phase.

Atomic resolution imaging of cation ordering in niobium\u2013tungsten complex oxides

Energy dispersive X-ray emission imaging at atomic resolution is a powerful tool to solve order–disorder problems in complex metal oxide crystals, supplementing conventional X-ray or neutron diffraction. Here, we use this method, based on scanning transmission electron microscopy, to investigate cation ordering in ternary metal oxides 4Nb2O5·9WO3 and 2Nb2O5·7WO3, which have recently attracted attention as energy storage materials in lithium-ion batteries. Their crystal structures are a tetragonal tungsten bronze-type and its hybrid with a ReO3-type ‘block structure’, respectively. Our study reveals the presence of chemical ordering of metal ions in these materials, which have previously been assumed to be solid-solutions. In particular, we show that the two types of cations, Nb and W, are well ordered in their lattices, and that the Nb ions tend to occupy one third of the pentagonal channel sites. These results demonstrate that atomic resolution X-ray emission imaging is an effective alternative approach for the study of locally ordered crystal structures.

Unambiguous determination of the commensurate antiferromagnetic structure of HoNi2B2C in the superconducting ground state

Crystal and magnetic structures of the intermetallic ${\mathrm{HoNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ have been investigated using different single-crystal diffraction techniques at both room and low temperatures (superconducting phase). Combined refinement of the neutron and x-ray diffraction data performed at room temperature shows that the crystal structure of ${\mathrm{HoNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ is well described in the tetragonal space group $I4/mmm$, in agreement with the literature. The magnetic ordering at low temperatures is accompanied by a structural phase transition to the orthorhombic space group $Fmmm$. However, only noncharacteristic orbits are occupied in this space group, and the symmetry reduction is entirely due to a lifting of the symmetry-induced restrictions on the anisotropic displacement parameters. Based on magnetic symmetry analysis, two types of commensurate antiferromagnetic structures with different magnetic space groups (MSGs) are found below ${T}_{\mathrm{N}}\ensuremath{\approx}5.2$ K: MSG ${P}_{I}nnm$ (Ho spins are along the [100] direction of the parent structure) and MSG ${C}_{A}mca$ (Ho spins are along [110] of the parent structure). Both models agree well with conventional unpolarized neutron diffraction data at low temperature (2.4 K) with ordered magnetic moments of 9.16(9) ${\ensuremath{\mu}}_{\mathrm{B}}$/${\mathrm{Ho}}^{3+}$ atom. Spherical neutron polarimetry, on the other hand, allowed us to unambiguously solve the magnetic structure (MSG ${C}_{A}mca$) as well as to determine the population of two types of ${90}^{\ensuremath{\circ}}$ antiferromagnetic domains (0.45/0.55).

Mapping residual strain induced by cold working and by laser shock peening using neutron transmission spectroscopy

This paper presents 2D mapping of residual strains, induced by cold expansion and laser shock peening processing of aluminium alloy samples, by using Bragg edge neutron transmission. Neutron transmission uses information contained in the neutron beam transmitted through a sample. It is shown that neutron transmission strain mapping with high spatial resolution can provide important insights into the distribution of residual strains associated with processing of materials. The residual strain field around a cold-expanded hole can be revealed in detail, as can be the residual strain profile associated with laser peening. Results are correlated with measurements obtained by conventional neutron diffraction and incremental hole drilling. The residual strain variation around the cold-expanded hole and the depth of compressive residual strain generated by the peening process were captured with high spatial resolution, showing the advantages of neutron transmission over other well-established strain measurement methods by non-destructively generating a map of residual strains over a large area.

Neutron Strain Tomography using the Radon Transform

Determining bulk residual elastic strains is a topic of critical importance for predictive modelling and materials testing. Although there are numerous approaches to obtaining this information the process is often time-consuming and frequentlyinvolves destructive sectioning of the sample. This paper presents the latest developments in Bragg-edge neutron strain tomography which offers a rapid, non-destructive means of determining residual elastic strains in polycrystalline materials with high spatial resolution.Neutron strain tomography utilises the fact that the energy-resolved transmission spectrum of thermal neutrons froma polycrystalline sample displays well-defined, sudden jumps in intensity known as ‘Bragg-edges’, which reveal information about the average residual elastic strain throughout the sample volume. By measuring the spatially resolved transmission spectrum for a number of different sample orientations it is possible to recover the underlying three-dimensional residual elastic strain profile. This process is analogous to conventional absorption tomography where a three-dimensional map of the sample density is recovered from a lower order two-dimensional set of integral absorption measurements. Using the newly developed microchannel plate TimePixneutron detectorin time-of-flight experiments, elastic strains can in principle be recovered with 10 um spatial resolution. The current work demonstrates a model-free method for direct inversion of the average strain profiles obtained from Bragg-edge measurements using results from linear elasticity theory and the Radon transform, which is the basis for absorption tomography reconstructions. We demonstrate this method in simulation on an axisymmetric sample with analytic strain profile before applying it to a ‘real-world’ sample where the results are validated against conventional neutron diffraction and hole drilling measurements.

Observations on the crystal structures of lueshite

Laboratory powder XRD patterns of the perovskite-group mineral lueshite from the type locality (Lueshe, Kivu, DRC) and pure NaNbO3 demonstrate that lueshite does not adopt the same space group (Pbma; #57) as the synthetic compound. The crystal structures of lueshite (2 samples) from Lueshe, Mont Saint-Hilaire (Quebec, Canada) and Sallanlatvi (Kola, Russia) have been determined by single-crystal CCD X-ray diffraction. These room temperature X-ray data for all single-crystal samples can be satisfactorily refined in the orthorhombic space group Pbnm (#62). Cell dimensions, atomic coordinates of the atoms, bond lengths and octahedron tilt angles are given for four crystals. Conventional neutron diffraction patterns for Lueshe lueshite recorded over the temperature range 11–1,000 K confirm that lueshite does not adopt space group Pbma within these temperatures. Neutron diffraction indicates no phase changes on cooling from room temperature to 11 K. None of these neutron diffraction data give satisfactorily refinements but suggest that this is the space group Pbnm. Time-of-flight neutron diffraction patterns for Lueshe lueshite recorded from room temperature to 700 °C demonstrate phase transitions above 550 °C from Cmcm through P4/mbm to $$Pm\overline{3} m$$ above 650 °C. Cell dimensions and atomic coordinates of the atoms are given for the three high-temperature phases. The room temperature to 400 °C structures cannot be satisfactorily resolved, and it is suggested that the lueshite at room temperature consists of domains of pinned metastable phases with orthorhombic and/or monoclinic structures. However, the sequence of high-temperature phase transitions observed is similar to those determined for synthetic NaTaO3, suggesting that the equilibrated room temperature structure of lueshite is orthorhombic Pbnm.

Residual strain measurement for arc welding and localised high-pressure rolling using resistance strain gauges and neutron diffraction

Neutron diffraction and foil resistance strain gauges have been used to study the state of residual stress introduced by localised high-pressure rolling of structural steel plates, and compare it to that caused by gas metal arc welding. Rolling creates a region in which the residual stress state is highly compressive in the rolling direction. Furthermore, this region is sharply defined, making it potentially very suitable for cancelling out the tensile residual stresses caused by welding. It is also demonstrated that non-destructive strain measurements made during the welding and rolling processes can be used to indicate residual elastic strain and stress, and that this method shows good agreement with conventional neutron diffraction measurements. Determination of residual stresses in this way requires consideration of the effect of curvature on the values of strain measured at the surface of the object.

Minimization of spurious strains by using a Si bent-perfect-crystal monochromator: neutron surface strain scanning of a shot-peened sample

Neutron strain measurements are critical at the surface. When scanning close to a sample surface, aberration peak shifts arise due to geometrical and divergence effects. These aberration peak shifts can be of the same order as the peak shifts related to residual strains. In this study it will be demonstrated that by optimizing the horizontal bending radius of a Si (4 0 0) monochromator, the aberration peak shifts from surface effects can be strongly reduced. A stress-free sample of fine-grained construction steel, S690QL, was used to find the optimal instrumental conditions to minimize aberration peak shifts. The optimized Si (4 0 0) monochromator and instrument settings were then applied to measure the residual stress depth gradient of a shot-peened SAE 4140 steel sample to validate the effectiveness of the approach. The residual stress depth profile is in good agreement with results obtained by x-ray diffraction measurements from an international round robin test (BRITE-EURAM-project ENSPED). The results open very promising possibilities to bridge the gap between x-ray diffraction and conventional neutron diffraction for non-destructive residual stress analysis close to surfaces.

Microstructural Evolution during the Novel Quenching and Partitioning (Q&amp;P) Heat Treatment of Steel

The novel non-equilibrium heat treatment procedure known as Quenching and Partitioning (Q&amp;P) may offer the prospect of higher strength steel products with enhanced formability based upon martensitic microstructures containing controlled quantities of carbon-enriched retained austenite. The Q&amp;P process requires an interrupted quench and isothermal annealing (partitioning) step at intermediate temperatures, whereby untransformed austenite can be thermodynamically stabilised by carbon migration from supersaturated martensite regions. The concept is comparable to that producing carbide-free bainite, for example, in TRIP-assisted steel, although Q&amp;P allows separation of the ferrite formation and austenite enrichment stages of the process. However, although the Q&amp;P concept is readily understood, evolution of the microstructure during interrupted quenching and partitioning has been inferred indirectly from dilatometer studies and metallographic examination after final quenching to room temperature. Consequently, a model alloy was developed in which the sequential steps of heat treatment could be separated for direct inspection by conventional metallography, X-ray diffraction and neutron diffraction techniques.

Parasitic Small-Moment Antiferromagnetism and Nonlinear Coupling of Hidden Order and Antiferromagnetism inURu2Si2Observed by Larmor Diffraction

We report for the first time simultaneous microscopic measurements of the lattice constants, the distribution of the lattice constants, and the antiferromagnetic moment in high-purity URu(2)Si(2), combining Larmor and conventional neutron diffraction at low temperatures and pressures up to 18 kbar. Our data demonstrate quantitatively that the small moment in the hidden order (HO) of URu(2)Si(2) is purely parasitic. The excellent experimental conditions we achieve allow us to resolve that the transition line between HO and large-moment antiferromagnetism (LMAF), which stabilizes under pressure, is intrinsically first order and ends in a bicritical point. Therefore, the HO and LMAF must have different symmetry, which supports exotic scenarios of the HO such as orbital currents, helicity order, or multipolar order.

Static structure factor of liquid parahydrogen

The single-differential neutron-scattering cross section of liquid parahydrogen has been measured at 15.2 K and 2 bars of applied pressure by means of low-energy neutron diffraction. Our experimental conditions enable the direct observation of the peak of the liquid structure factor and therefore largely improve the signal-to-noise ratio with respect to measurements carried out using higher-energy neutron diffraction. This avoids the need of performing corrections of approximate nature to the measured cross section that is dominated by molecular rotational components if measured by conventional neutron diffraction.

In situdetermination of stresses from time-of-flight neutron transmission spectra

The pulsed neutron transmission diffraction technique exploits the sharp steps in intensity (Bragg edges) appearing in the transmitted spectra of thermal neutrons through polycrystalline materials. In this paper the positions of these edges acquired by the time-of-flight (TOF) technique are used to measure accurately the interplanar lattice distances to a resolution of Δd/d≃ 10−4of specimens subjected toin situuniaxial tensile loading. The sensitivity of the method is assessed for elastically isotropic (b.c.c. ferritic) and anisotropic (f.c.c. austenitic) polycrystalline specimens of negligible and moderately textured steels. For the more anisotropic austenitic steel, the elastic anisotropy is studied with regard to a Pawley refinement, and compared with previous results from conventional neutron diffraction experiments on the same material. It is shown that the method can be used to determine anisotropic strains, diffraction elastic constants, the residual and applied stress state as well as the unstrained lattice parameter by recording transmission spectra at different specimen inclinations, by complete analogy with the sin2ψ technique frequently used in X-ray diffraction. The technique is shown to deliver reliable measures of strain even in the case of moderate texture and elastic anisotropy.

Engineering applications of Bragg-edge neutron transmission

The shape, magnitude and location of the Bragg edges appearing in the transmission spectrum of polycrystalline materials can be accurately determined by the time-of-flight technique, and hence information about the stress state, texture and phases present in the material is readily available. An advantage of Bragg-edge transmission over conventional neutron diffraction is that it can use a pixellated detector to map the strain in plane samples, producing images analogous to neutron radiography. Moreover, maps of the unstressed lattice spacing can be achieved by tilting the sample relative to the direction of the neutron beam. Examples of the application of this technique to typical engineering problems are presented in this work.

High-resolution diffraction using Larmor precession of polarized neutrons

A new Larmor precession device, consisting of two separate precession modules, is introduced. It operates as a high-resolution neutron diffractometer, without the need for a highly collimated beam, necessary in conventional high-resolution neutron diffraction. The same instrument operates in different modes as an effective small-angle scattering device or accurately determines the line profile, the lattice plane orientation or the angular spread in crystal orientations. A dramatic intensity gain can be obtained in all applications discussed, compared with the conventional analogues, owing to the possibility to use a relaxed wavelength and angular resolution. Experiments in the high-resolution diffraction mode on Si and Al are discussed.

The sin2 ψ-method in pulsed neutron transmission

Abstract The transmission spectrum of thermal neutrons through polycrystalline samples as a function of wavelength displays sudden increases in intensity known as Bragg edges. These edges occur whenever the wavelength ceases to fulfil the Bragg condition for coherent scattering at Bragg angle 2Θ = 180°. The shape and position of these edges contain information about the stress state present in the sample. The transmission method has two key advantages over conventional neutron diffraction. For samples with essentially one or two-dimensional stress-fields the use of pixellated detector arrays enables simultaneous, therefore very fast, spatial imaging of strains. At the same time it allows for the determination of the unstrained lattice spacing as well as stresses in the sample by evaluating a set of strain images taken at different sample inclinations, similar to the sin2 ψ-technique of X-ray diffraction. We show how this technique has been successfully employed to determine accurately the unstrained latti...

Synchrotron X-ray study of bulk lattice strains in externally loaded Cu-Mo composites

A synchrotron X-ray transmission technique was applied to study the internal load transfer and micromechanical damage in molybdenum particle-reinforced copper matrix composites during plastic deformation. Mechanically loaded, 1.5-mm-thick specimens were irradiated with a monochromatic beam of 65 keV X-rays. Low-index diffraction rings of both phases were recorded with a high-resolution two-dimensional detector. By means of newly developed data processing routines, we could quantify as a function of applied stress both the ring distortion (from which the volume-averaged elastic strains in the two phases were calculated), and the ring graininess (which is related to the Bragg peak broadening). Based on this information, the deformation and damage processes in these alloys were studied in detail. As compared to conventional neutron diffraction methods, the photon transmission technique yielded similar precision but at much reduced measurement times. The main sources of experimental errors were identified and strategies to minimize these errors were developed.

Novel instrumentation concepts using polarised neutrons

A new Larmor precession device, consisting of two separate precession modules, is introduced. It operates as a high-resolution neutron diffractometer, without the need of a highly collimated beam, necessary in conventional high-resolution neutron diffraction. A spin-echo mode of the same instrument, operates in different modes as an effective small-angle scattering device or accurately determines the line profile, the lattice plane orientation or the angular spread. A dramatic intensity gain in all applications discussed can be obtained, due to the possibility to use a relaxed wavelength and angular resolution.

Partial Structural Functions of Molten AgBr Estimated from the Anomalous X-Ray Scattering Data Coupled with Neutron Diffraction

The three partial structural functions of molten AgBr have been determined by using a combination of the anomalous X-ray scattering (AXS) data and conventional neutron diffraction result. This data processing includes the help of the reverse Monte Carlo (RMC) simulation technique. The partial structure factor of a AgAg ( Q ) in molten AgBr was rather broad than that found in molten alkali halides such as RbBr. The resultant structural parameters suggest that the structure of molten AgBr is quite likely described by disordered close packing of Br ions where Ag ions are distributed in both octahedral and tetrahedral holes.

Crystal alignment of carbonated apatite in bone and calcified tendon: results from quantitative texture analysis

Calcified tissue contains collagen associated with minute crystallites of carbonated apatite. In this study, methods of quantitative X-ray texture analysis were used to determine the orientation distribution and texture strength of apatite in a calcified turkey tendon and in trabecular and cortical regions of osteonal bovine ankle bone (metacarpus). To resolve local heterogeneity, a 2 or 10 μm synchrotron microfocus X-ray beam (λ = 0.78 Å) was employed. Both samples revealed a strong texture. In the case of turkey tendon, 12 times more c axes of hexagonal apatite were parallel to the fibril axis than perpendicular, and a axes had rotational freedom about the c axis. In bovine bone, the orientation density of the c axes was three times higher parallel to the surface of collagen fibrils than perpendicular to it, and there was no preferential alignment with respect to the long axis of the bone (fiber texture). Whereas half of the apatite crystallites were strongly oriented, the remaining half had a random orientation distribution. The synchrotron X-ray texture results were consistent with previous analyses of mineral orientation in calcified tissues by conventional X-ray and neutron diffraction and electron microscopy, but gave, for the first time, a quantitative description.