X-ray Laue Microdiffraction Research Articles

In-situ characterization of highly reversible phase transformation by synchrotron X-ray Laue microdiffraction

The alloy Cu25Au30Zn45 undergoes a huge first-order phase transformation (6% strain) and shows a high reversibility under thermal cycling and an unusual martensitc microstructure in sharp contrast to its nearby compositions. This alloy was discovered by systematically tuning the composition so that its lattice parameters satisfy the cofactor conditions (i.e., the kinematic conditions of compatibility between phases). It was conjectured that satisfaction of these conditions is responsible for the enhanced reversibility as well as the observed unusual fluid-like microstructure during transformation, but so far, there has been no direct evidence confirming that these observed microstructures are those predicted by the cofactor conditions. To verify this hypothesis, we use synchrotron X-ray Laue microdiffraction to measure the orientations and structural parameters of variants and phases near the austenite/martensite interface. The areas consisting of both austenite and multi-variants of martensite are scanned by microLaue diffraction. The cofactor conditions have been examined from the kinematic relation of lattice vectors across the interface. The continuity condition of the interface is precisely verified from the correspondent lattice vectors between two phases.

Measurements of stress fields near a grain boundary: Exploring blocked arrays of dislocations in 3D

The interaction between dislocation pile-ups and grain boundaries gives rise to heterogeneous stress distributions when a structural metal is subjected to mechanical loading. Such stress heterogeneity leads to preferential sites for damage nucleation and therefore is intrinsically linked to the strength and ductility of polycrystalline metals. To date the majority of conclusions have been drawn from 2D experimental investigations at the sample surface, allowing only incomplete observations. Our purpose here is to significantly advance the understanding of such problems by providing quantitative measurements of the effects of dislocation pile up and grain boundary interactions in 3D. This is accomplished through the application of differential aperture X-ray Laue micro-diffraction (DAXM) and high angular resolution electron backscatter diffraction (HR-EBSD) techniques. Our analysis demonstrates a similar strain characterization capability between DAXM and HR-EBSD and the variation of stress intensity in 3D reveals that different parts of the same grain boundary may have different strengths in resisting slip transfer, likely due to the local grain boundary curvature.

Laue-DIC: a new method for improved stress field measurements at the micrometer scale.

A better understanding of the effective mechanical behavior of polycrystalline materials requires an accurate knowledge of the behavior at a scale smaller than the grain size. The X-ray Laue microdiffraction technique available at beamline BM32 at the European Synchrotron Radiation Facility is ideally suited for probing elastic strains (and associated stresses) in deformed polycrystalline materials with a spatial resolution smaller than a micrometer. However, the standard technique used to evaluate local stresses from the distortion of Laue patterns lacks accuracy for many micromechanical applications, mostly due to (i) the fitting of Laue spots by analytical functions, and (ii) the necessary comparison of the measured pattern with the theoretical one from an unstrained reference specimen. In the present paper, a new method for the analysis of Laue images is presented. A Digital Image Correlation (DIC) technique, which is essentially insensitive to the shape of Laue spots, is applied to measure the relative distortion of Laue patterns acquired at two different positions on the specimen. The new method is tested on an in situ deformed Si single-crystal, for which the prescribed stress distribution has been calculated by finite-element analysis. It is shown that the new Laue-DIC method allows determination of local stresses with a strain resolution of the order of 10(-5).

A look-up table based approach to characterize crystal twinning for synchrotron X-ray Laue microdiffraction scans.

An automated method has been developed to characterize the type and spatial distribution of twinning in crystal orientation maps from synchrotron X-ray Laue microdiffraction results. The method relies on a look-up table approach. Taking into account the twin axis and twin plane for plausible rotation and reflection twins, respectively, and the point group symmetry operations for a specific crystal, a look-up table listing crystal-specific rotation angle-axis pairs, which reveal the orientation relationship between the twin and the parent lattice, is generated. By comparing these theoretical twin-parent orientation relationships in the look-up table with the measured misorientations, twin boundaries are mapped automatically from Laue microdiffraction raster scans with thousands of data points. Taking advantage of the high orientation resolution of the Laue microdiffraction method, this automated approach is also applicable to differentiating twinning elements among multiple twinning modes in any crystal system.

Tensile strained germanium nanowires measured by photocurrent spectroscopy and X-ray microdiffraction.

Applying tensile strain in a single germanium crystal is a very promising way to tune its bandstructure and turn it into a direct band gap semiconductor. In this work, we stress vapor-liquid-solid grown germanium nanowires along their [111] axis thanks to the strain tranfer from a silicon nitride thin film by a microfabrication process. We measure the Γ-LH direct band gap transition by photocurrent spectrometry and quantify associated strain by X-ray Laue microdiffraction on beamline BM32 at the European Synchrotron Radiation Facility. Nanowires exhibit up to 1.48% strain and an absorption threshold down to 0.73 eV, which is in good agreement with theoretical computations for the Γ-LH transition, showing that the nanowire geometry is an efficient way of applying tensile uniaxial stress along the [111] axis of a germanium crystal.

Effect of surface microstructure on electrochemical performance of garnet solid electrolytes.

Cubic garnet phases based on Al-substituted Li7La3Zr2O12 (LLZO) have high ionic conductivities and exhibit good stability versus metallic lithium, making them of particular interest for use in next-generation rechargeable battery systems. However, high interfacial impedances have precluded their successful utilization in such devices until the present. Careful engineering of the surface microstructure, especially the grain boundaries, is critical to achieving low interfacial resistances and enabling long-term stable cycling with lithium metal. This study presents the fabrication of LLZO heterostructured solid electrolytes, which allowed direct correlation of surface microstructure with the electrochemical characteristics of the interface. Grain orientations and grain boundary distributions of samples with differing microstructures were mapped using high-resolution synchrotron polychromatic X-ray Laue microdiffraction. The electrochemical characteristics are strongly dependent upon surface microstructure, with small grained samples exhibiting much lower interfacial resistances and better cycling behavior than those with larger grain sizes. Low area specific resistances of 37 Ω cm(2) were achieved; low enough to ensure stable cycling with minimal polarization losses, thus removing a significant obstacle toward practical implementation of solid electrolytes in high energy density batteries.

Crystal Structure of an Indigo@Silicalite Hybrid Related to the Ancient Maya Blue Pigment

The structure of the indigo@silicalite pigment, an analog of ancient Maya Blue, has been determined by combining X-ray Laue microdiffraction and powder diffraction techniques. After the adsorption of indigo into the calcined (monoclinic) silicalite sample, the powder diffraction pattern contained peaks from both orthorhombic (major phase) and monoclinic (minor phase) silicalite. Assuming that the orthorhombic phase was induced by the adsorption of indigo, Laue microdiffraction was used to map the unit cell changes (and thereby the indigo distribution) within a single crystal. It was found to be highly heterogeneous with empty monoclinic and indigo-induced orthorhombic domains. The Laue diffraction data indicated that the space group of the orthorhombic domains was Pnma rather than P212121. With this information, the indigo@silicalite structure could be solved and refined from the powder diffraction data. The starting positions for two independent indigo molecules, described as rigid bodies, were obtained by simulated annealing, with a first molecule positioned in the straight channel and the second one in the sinusoidal channel. The positions and occupancies of these molecules and the positions of the framework atoms were then refined using the Rietveld method. Approximately four indigo molecules per unit cell were found, two per independent site, and possible local arrangements are suggested. The size of the indigo molecule prevents the structure from being fully ordered.

A tunable multicolour `rainbow' filter for improved stress and dislocation density field mapping in polycrystals using X-ray Laue microdiffraction

White-beam X-ray Laue microdiffraction allows fast mapping of crystal orientation and strain fields in polycrystals, with a submicron spatial resolution in two dimensions. In the well crystallized parts of the grains, the analysis of Laue-spot positions provides the local deviatoric strain tensor. The hydrostatic part of the strain tensor may also be obtained, at the cost of a longer measuring time, by measuring the energy profiles of the Laue spots using a variable-energy monochromatic beam. A new `rainbow' method is presented, which allows measurement of the energy profiles of the Laue spots while remaining in the white-beam mode. It offers mostly the same information as the latter monochromatic method, but with two advantages: (i) the simultaneous measurement of the energy profiles and the Laue pattern; (ii) rapid access to energy profiles of a larger number of spots, for equivalent scans on the angle of the optical element. The method proceeds in the opposite way compared to a monochromator-based method, by simultaneously removing several sharp energy bands from the incident beam, instead of selecting a single one. It uses a diamond single crystal placed upstream of the sample. Each Laue diffraction by diamond lattice planes attenuates the corresponding energy in the incident spectrum. By rotating the crystal, the filtered-out energies can be varied in a controlled manner, allowing one to determine the extinction energies of several Laue spots of the studied sample. The energies filtered out by the diamond crystal are obtained by measuring its Laue pattern with another two-dimensional detector, at each rotation step. This article demonstrates the feasibility of the method and its validation through the measurement of a known lattice parameter.

Unambiguous indexing of trigonal crystals from white-beam Laue diffraction patterns: application to Dauphiné twinning and lattice stress mapping in deformed quartz

Synchrotron X-ray Laue microdiffraction is used to investigate the microstructure of deformed quartz, which has trigonal symmetry. The unambiguous indexing of a Laue diffraction pattern can only be achieved by taking the intensities of the diffraction peaks into account. The intensities are compared with theoretical structure factors after correction for the incident X-ray beam flux, X-ray beam polarization, air absorption, detector response and Lorentz factor. This allows mapping of not only the grain orientation but also the stress tensor. The method is applicable for correct orientation determination of all crystals with trigonal symmetry and is indispensable for structure refinements of such materials from Laue diffraction data.

Plasticity of indium nanostructures as revealed by synchrotron X-ray microdiffraction

Indium columnar structures with diameters near 1 μm were deformed by uniaxial compression at strain rates of approximately 0.01 and 0.001 s−1. Defect density evolution in the nanopillars was evaluated by applying synchrotron Laue X-ray microdiffraction (μSLXRD) on the same specimens before and after deformation. Results of the μSLXRD measurements indicate that the dislocation density increases as a result of mechanical deformation and is a strong function of strain rate. These results suggest that the rate of defect generation during the compression tests exceeds the rate of defect annihilation, implying that plasticity in these indium nanostructures commences via dislocation multiplication rather than nucleation processes. This is in contrast with the behaviors of other materials at the nanoscale, such as, gold, tin, molybdenum, and bismuth. A hypothesis based on the dislocation mean-free-path prior to the multiplication process is proposed to explain this variance.

Plasticity in the nanoscale Cu/Nb single-crystal multilayers as revealed by synchrotron Laue x-ray microdiffraction

Abstract

Combining Laue Microdiffraction and Digital Image Correlation for Improved Measurements of the Elastic Strain Field with Micrometer Spatial Resolution

The X-ray Laue microdiffraction technique, available at beamline BM32 on the synchrotron ESRF, is ideally suited for probing the field of elastic strain (and associated stress) in deformed polycrystalline materials with a micrometric spatial resolution. We show that using Digital Image Correlation for measuring Laue pattern distortions between two mechanical states improves significantly the estimate of elastic strain increment. The potentiality of this new Laue-DIC method is illustrated on an elastically bent Si single crystal, for which the measured elastic strain deviates not more than 10-5 from the theoretical strain distribution provided by standard solutions.

In situ synchrotron analysis of lattice rotations in individual grains during stress-induced martensitic transformations in a polycrystalline CuAlBe shape memory alloy

Two synchrotron diffraction techniques, three-dimensional X-ray diffraction and Laue microdiffraction, are applied to studying the deformation behaviour of individual grains embedded in a Cu 74Al 23Be 3 superelastic shape memory alloy. The average lattice rotation and the intragranular heterogeneity of orientations are measured during in situ tensile tests at room temperature for four grains of mean size ∼1 mm. During mechanical loading, all four grains rotate and the mean rotation angle increases with austenite deformation. As the martensitic transformation occurs, the rotation becomes more pronounced, and the grain orientation splits into several sub-domains: the austenite orientation varies on both sides of the martensite variant. The mean disorientation is ∼1°. Upon unloading, the sub-domains collapse and reverse rotation is observed.

Stress field in deformed polycrystals at the micron scale

Theoretical, numerical, and experimental micromechanical approaches have been the subject of significant improvements during the last decade, from the scale of the lattice defect (nanometre) up to the scale of the polycrystal (millimetre). When plastic deformations take place in polycrystals, strong and systematic strain heterogeneities build up between neighbouring grains but also inside individual grains. These heterogeneities have to be (or should be) considered for many issues, e.g. onset of microplasticity, crack propagation, phase transformation, activation of twinning, or simply the prediction of the effective behaviour of the material. From the experimental point of view, Digital Image Correlation (DIC) techniques adapted to images obtained by Scanning Electron Microscopy generally reveal strain localization bands the extent of which is typically 5 to 10 grain sizes. The prediction of such behaviour with theoretical or numerical scale transition models is however most of the time severely limited by the poor knowledge of the local behaviour at the grain or at an even finer scale. Furthermore, although significant progress could be reached by several research groups as for the characterization of the displacement/strain fields by DIC, one has to recognize that similar developments for the characterization of the stress field are far less spectacular. This comes probably from the high accuracy that has to be obtained on elastic strain measurements to get reliable stress estimation. Combining this difficulty with a micrometric spatial resolution as needed for standard micromechanical problems is not simple. The present work is a contribution to the development of an X-ray Laue microdiffraction technique, which is well adapted for the characterization of the stress field in deformed polycrystals at the micron scale. The technique consists in scanning the specimen in front of a focussed white Xray beam with micrometric cross section. The shape of the resulting Laue diffraction patterns reveals many features relative to the specimen deformation and among them the elastic strain of interest here. X-ray Laue microdiffraction setup has been developed and installed on few synchrotron facilities such as ALS-Berkeley and APS-Argonne in the USA, and ESRF in France. However, although the technique is very promising, only very few quantitative results have been published so far, since poorly appropriate data treatment method and software has been proposed so far. We aim at developing and applying an adapted procedure by putting together different experimental and image processing techniques, in particular Laue microdiffraction as available at beamline BM32 of the ESRF, and Digital Image Correlation (DIC) for the precise evaluation of the evolution of the Laue pattern in the form of an apparent heterogeneous displacement related to the lattice distorsion (figure 1). Particular attention is placed on the careful investigation of experimental and image processing uncertainties in order to evaluate precisely the experimental errors on stress evaluation.

Metal plasticity by grain rotation—Microdiffraction case studies

The synchrotron-based X-ray Laue microdiffraction technique has become more and more popular over that last year. In addition to measuring the deviatoric part of the elastic strain tensor this technique is specifically accurate in measuring grain rotations. The current paper illustrates the high rotational sensitivity by three deformation mechanisms that lead to grain rotation; one mechanism is the nearly diffusionless interaction between disclinations and dislocations a mechanism for low homologous temperatures and two mechanisms are interactions between diffusive mechanisms and dislocation motion, namely hillock growth upon thermal cycling and during electromigration. The communalities and differences between these mechanisms are discussed to provide further insight into a special deformation mode.

Texture, residual strain, and plastic deformation around scratches in alloy 600 using synchrotron X-ray Laue micro-diffraction

Deformation around two scratches in Alloy 600 (A600) was studied nondestructively using synchrotron Laue differential aperture X-ray microscopy. The orientation of grains and elastic strain distribution around the scratches were measured. A complex residual deviatoric elastic strain state was found to exist around the scratches. Heavy plastic deformation was observed up to a distance of 20μm from the scratches. In the region 20–30μm from the scratches the diffraction spots were heavily streaked and split indicating misoriented dislocation cell structures.

Spatially Resolved Characterization of Microstructure, Defects and Tilts in GaN Layers Grown on Si(111) Substrates by Maskless Cantilever Epitaxy

ABSTRACTThe spatially resolved distribution of strain, misfit and threading dislocations, and crystallographic orientation in uncoalesced GaN layers grown on Si(111) substrates by maskless cantilever epitaxy was studied by white-beam Laue x-ray microdiffraction, scanning electron microscopy, and orientation imaging microscopy. Tilt boundaries formed at the column/wing interface with the misorientation strongly depending on the growth conditions. A depth-dependent deviatoric strain gradient is found in the GaN. Types and density of misfit dislocations as well as their arrangement within different dislocation arrays was quantified. The results are discussed with respect to the miscut of the Si(111) surface and misfit dislocations formed at the interface.

On the effect of persistent slip band (PSB) parameters on fatigue life: Cao, W.-D. and Conrad, H. Fatigue Fract. Eng. Mater. Struct. June 1992 15, (6), 573–583

We study the mechanisms of slip transfer at a grain boundary, in titanium, using Differential Aperture X-ray Laue Micro-diffraction (DAXM). This 3D characterisation tool enables measurement of the full (9-component) Nye lattice curvature tensor and calculation of the density of geometrically necessary dislocations (GNDs). We observe dislocation pile-ups at a grain boundary, as the neighbour grain prohibits easy passage for dislocation transmission. This incompatibility results in local micro-plasticity within the slipping grain, near to where the slip planes intersect the grain boundary, and we observe bands of GNDs lying near the grain boundary. We observe that the distribution of GNDs can be significantly influenced by the formation of grain boundary ledges that serve as secondary dislocation sources. This observation highlights the non-continuum nature of polycrystal deformation and helps us understand the higher order complexity of grain boundary characteristics.