Defects and nanostrain gradients control phase transition mechanisms in single crystal high-voltage lithium spinel

Lithiation dynamics and phase transition mechanisms in most battery cathode materials remain poorly understood, because of the challenge in differentiating inter- and intra-particle heterogeneity. In this work, the structural evolution inside Li1-xMn1.5Ni0.5O4 single crystals during electrochemical delithiation is directly resolved with operando X-ray nanodiffraction microscopy. Metastable domains of solid-solution intermediates do not appear associated with the reaction front between the lithiated and delithiated phases, as predicted by current phase transition theory. Instead, unusually persistent strain gradients inside the single crystals suggest that the shape and size of solid solution domains are instead templated by lattice defects, which guide the entire delithiation process. Morphology, strain distributions, and tilt boundaries reveal that the (Ni2+/Ni3+) and (Ni3+/Ni4+) phase transitions proceed through different mechanisms, offering solutions for reducing structural degradation in high voltage spinel active materials towards commercially useful durability. Dynamic lattice domain reorientation during cycling are found to be the cause for formation of permanent tilt boundaries with their angular deviation increasing during continuous cycling.

Bragg coherent diffraction imaging with the CITIUS charge-integrating detector

The CITIUS detector is a next-generation high-speed X-ray imaging detector. It has integrating-type pixels and is designed to show a consistent linear response at a frame rate of 17.4 kHz, which results in a saturation count rate of over 30 Mcps pixel-1 when operating at an acquisition duty cycle close to 100%, and up to 20 times higher with special extended acquisition modes. Here, its application for Bragg coherent diffraction imaging is demonstrated by taking advantage of the fourth-generation Extremely Brilliant Source of the European Synchrotron (ESRF-EBS, Grenoble, France). The CITIUS detector outperformed a photon-counting detector, similar spatial resolution being achieved (20 ± 6 nm versus 22 ± 9 nm) with greatly reduced acquisition times (23 s versus 200 s). It is also shown how the CITIUS detector can be expected to perform during dynamic Bragg coherent diffraction imaging measurements. Finally, the current limitations of the CITIUS detector and further optimizations for coherent imaging techniques are discussed.

Imaging the strain evolution of a platinum nanoparticle under electrochemical control

Surface strain is widely employed in gas phase catalysis and electrocatalysis to control the binding energies of adsorbates on active sites. However, in situ or operando strain measurements are experimentally challenging, especially on nanomaterials. Here we exploit coherent diffraction at the new fourth-generation Extremely Brilliant Source of the European Synchrotron Radiation Facility to map and quantify strain within individual Pt catalyst nanoparticles under electrochemical control. Three-dimensional nanoresolution strain microscopy, together with density functional theory and atomistic simulations, show evidence of heterogeneous and potential-dependent strain distribution between highly coordinated ({100} and {111} facets) and undercoordinated atoms (edges and corners), as well as evidence of strain propagation from the surface to the bulk of the nanoparticle. These dynamic structural relationships directly inform the design of strain-engineered nanocatalysts for energy storage and conversion applications.

Anomalous Glide Plane in Platinum Nano- and Microcrystals

At the nanoscale, the properties of materials depend critically on the presence of crystal defects. However, imaging and characterizing the structure of defects in three dimensions inside a crystal remain a challenge. Here, by using Bragg coherent diffraction imaging, we observe an unexpected anomalous {110} glide plane in two Pt submicrometer crystals grown by very different processes and having very different morphologies. The structure of the defects (type, associated glide plane, and lattice displacement) is imaged in these faceted Pt crystals. Using this noninvasive technique, both plasticity and unusual defect behavior can be probed at the nanoscale.

In Situ Nano-Indentation of a Gold Sub-Micrometric Particle Imaged by Multi-Wavelength Bragg Coherent X-ray Diffraction

The microstructure of a sub-micrometric gold crystal during nanoindentation is visualized by in situ multi-wavelength Bragg coherent X-ray diffraction imaging. The gold crystal is indented using a custom-built atomic force microscope. A band of deformation attributed to a shear band oriented along the (221) lattice plane is nucleated at the lower left corner of the crystal and propagates towards the crystal center with increasing applied mechanical load. After complete unloading, an almost strain-free and defect-free crystal is left behind, demonstrating a pseudo-elastic behavior that can only be studied by in situ imaging while it is invisible to ex situ examinations. The recovery is probably associated with reversible dislocations nucleation/annihilation at the side surface of the particle and at the particle-substrate interface, a behavior that has been predicted by atomistic simulations. The full recovery of the particle upon unloading sheds new light on extraordinary mechanical properties of metal nanoparticles obtained by solid-state dewetting.

Gwaihir: Jupyter Notebook graphical user interface for Bragg coherent diffraction imaging

In a world where data are steadily made more available, Gwaihir is a tool that overcomes multiple issues by bridging remote access, cluster computing and a user-friendly interface, consequentially improving the link between synchrotrons and their users for Bragg coherent diffraction imaging.

Bragg coherent X-ray diffraction is a nondestructive method for probing material structure in three dimensions at the nanoscale, with unprecedented resolution in displacement and strain fields. This work presents Gwaihir, a user-friendly and open-source tool to process and analyze Bragg coherent X-ray diffraction data. It integrates the functionalities of the existing packages bcdi and PyNX in the same toolbox, creating a natural workflow and promoting data reproducibility. Its graphical interface, based on Jupyter Notebook widgets, combines an interactive approach for data analysis with a powerful environment designed to link large-scale facilities and scientists.

Imaging the facet surface strain state of supported multi-faceted Pt nanoparticles during reaction

Nanostructures with specific crystallographic planes display distinctive physico-chemical properties because of their unique atomic arrangements, resulting in widespread applications in catalysis, energy conversion or sensing. Understanding strain dynamics and their relationship with crystallographic facets have been largely unexplored. Here, we reveal in situ, in three-dimensions and at the nanoscale, the volume, surface and interface strain evolution of single supported platinum nanocrystals during reaction using coherent x-ray diffractive imaging. Interestingly, identical {hkl} facets show equivalent catalytic response during non-stoichiometric cycles. Periodic strain variations are rationalised in terms of O₂ adsorption or desorption during O₂ exposure or CO oxidation under reducing conditions, respectively. During stoichiometric CO oxidation, the strain evolution is, however, no longer facet dependent. Large strain variations are observed in localised areas, in particular in the vicinity of the substrate/particle interface, suggesting a significant influence of the substrate on the reactivity. These findings will improve the understanding of dynamic properties in catalysis and related fields.

Understanding strain dynamics and their relationship with crystallographic facets have been largely unexplored. Here the authors demonstrate how the 3D lattice displacement and strain evolution depend on the crystallographic facets of Pt nanoparticles during CO oxidation reaction, providing new insights in the relationship between facet-related surface strain and chemistry.

Electrostatically Driven Polarization Flop and Strain-Induced Curvature in Free-Standing Ferroelectric Superlattices

The combination of strain and electrostatic engineering in epitaxial heterostructures of ferroelectric oxides offers many possibilities for inducing new phases, complex polar topologies, and enhanced electrical properties. However, the dominant effect of substrate clamping can also limit the electromechanical response and often leaves electrostatics to play a secondary role. Releasing the mechanical constraint imposed by the substrate can not only dramatically alter the balance between elastic and electrostatic forces, enabling them to compete on par with each other, but also activates new mechanical degrees of freedom, such as the macroscopic curvature of the heterostructure. In this work, an electrostatically driven transition from a predominantly out-of-plane polarized to an in-plane polarized state is observed when a PbTiO₃ /SrTiO₃ superlattice with a SrRuO₃ bottom electrode is released from its substrate. In turn, this polarization rotation modifies the lattice parameter mismatch between the superlattice and the thin SrRuO₃ layer, causing the heterostructure to curl up into microtubes. Through a combination of synchrotron-based scanning X-ray diffraction imaging, Raman scattering, piezoresponse force microscopy, and scanning transmission electron microscopy, the crystalline structure and domain patterns of the curved superlattices are investigated, revealing a strong anisotropy in the domain structure and a complex mechanism for strain accommodation.

Twin boundary migration in an individual platinum nanocrystal during catalytic CO oxidation

At the nanoscale, elastic strain and crystal defects largely influence the properties and functionalities of materials. The ability to predict the structural evolution of catalytic nanocrystals during the reaction is of primary importance for catalyst design. However, to date, imaging and characterising the structure of defects inside a nanocrystal in three-dimensions and in situ during reaction has remained a challenge. We report here an unusual twin boundary migration process in a single platinum nanoparticle during CO oxidation using Bragg coherent diffraction imaging as the characterisation tool. Density functional theory calculations show that twin migration can be correlated with the relative change in the interfacial energies of the free surfaces exposed to CO. The x-ray technique also reveals particle reshaping during the reaction. In situ and non-invasive structural characterisation of defects during reaction opens new avenues for understanding defect behaviour in confined crystals and paves the way for strain and defect engineering.

Bragg coherent imaging of nanoprecipitates: role of superstructure reflections

Coherent precipitation of ordered phases is responsible for providing exceptional high-temperature mechanical properties in a wide range of compositionally complex alloys. Ordered phases are also essential to enhance the magnetic or catalytic properties of alloyed nanoparticles. The present work aims to demonstrate the relevance of Bragg coherent diffraction imaging (BCDI) for studying bulk and thin-film samples or isolated nanoparticles containing coherent nanoprecipitates/ordered phases. The structures of crystals of a few tens of nanometres in size are modelled with realistic interatomic potentials and are relaxed after introduction of coherent ordered nanoprecipitates. Diffraction patterns from fundamental and superstructure reflections are calculated in the kinematic approximation and used as input to retrieve the strain fields using algorithmic inversion. First, the case of single nanoprecipitates is tackled and it is shown that the strain field distribution from the ordered phase is retrieved very accurately. Then, the influence of the order parameter S on the strain field retrieved from the superstructure reflections is investigated. A very accurate strain distribution can be retrieved for partially ordered phases with large and inhomogeneous strains. Subsequently, the relevance of BCDI is evaluated for the study of systems containing many precipitates, and it is demonstrated that the technique is relevant for such systems. Finally, the experimental feasibility of using BCDI to image ordered phases is discussed in the light of the new possibilities offered by fourth-generation synchrotron sources.

Mapping Inversion Domain Boundaries along Single GaN Wires with Bragg Coherent X-ray Imaging

Gallium nitride (GaN) is of technological importance for a wide variety of optoelectronic applications. Defects in GaN, like inversion domain boundaries (IDBs), significantly affect the electrical and optical properties of the material. We report, here, on the structural configurations of planar inversion domain boundaries inside n-doped GaN wires measured by Bragg coherent X-ray diffraction imaging. Different complex domain configurations are revealed along the wires with a 9 nm in-plane spatial resolution. We demonstrate that the IDBs change their direction of propagation along the wires, promoting Ga-terminated domains and stabilizing into {11̅00}, that is, m-planes. The atomic phase shift between the Ga- and N-terminated domains was extracted using phase-retrieval algorithms, revealing an evolution of the out-of-plane displacement (∼5 pm, at maximum) between inversion domains along the wires. This work provides an accurate inner view of planar defects inside small crystals.

Continuous scanning for Bragg coherent X-ray imaging

We explore the use of continuous scanning during data acquisition for Bragg coherent diffraction imaging, i.e., where the sample is in continuous motion. The fidelity of continuous scanning Bragg coherent diffraction imaging is demonstrated on a single Pt nanoparticle in a flow reactor at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$400\,^\circ \hbox {C}$$\end{document}400∘C in an Ar-based gas flowed at 50 ml/min. We show a reduction of 30% in total scan time compared to conventional step-by-step scanning. The reconstructed Bragg electron density, phase, displacement and strain fields are in excellent agreement with the results obtained from conventional step-by-step scanning. Continuous scanning will allow to minimise sample instability under the beam and will become increasingly important at diffraction-limited storage ring light sources.

Variable-Wavelength Quick Scanning Nanofocused X-Ray Microscopy for In Situ Strain and Tilt Mapping

Compression of micropillars is followed in situ by a quick nanofocused X-ray scanning microscopy technique combined with 3D reciprocal space mapping. Compared to other attempts using X-ray nanobeams, it avoids any motion or vibration that would lead to a destruction of the sample. The technique consists of scanning both the energy of the incident nanofocused X-ray beam and the in-plane translations of the focusing optics along the X-ray beam. Here, the approach by imaging the strain and lattice orientation of Si micropillars and their pedestals during in situ compression is demonstrated. Varying the energy of the incident beam instead of rocking the sample and mapping the focusing optics instead of moving the sample supplies a vibration-free measurement of the reciprocal space maps without removal of the mechanical load. The maps of strain and lattice orientation are in good agreement with the ones recorded by ordinary rocking-curve scans. Variable-wavelength quick scanning X-ray microscopy opens the route for in situ strain and tilt mapping toward more diverse and complex materials environments, especially where sample manipulation is difficult.

Towards a quantitative determination of strain in Bragg Coherent X-ray Diffraction Imaging: artefacts and sign convention in reconstructions

Bragg coherent X-ray diffraction imaging (BCDI) has emerged as a powerful technique to image the local displacement field and strain in nanocrystals, in three dimensions with nanometric spatial resolution. However, BCDI relies on both dataset collection and phase retrieval algorithms that can induce artefacts in the reconstruction. Phase retrieval algorithms are based on the fast Fourier transform (FFT). We demonstrate how to calculate the displacement field inside a nanocrystal from its reconstructed phase depending on the mathematical convention used for the FFT. We use numerical simulations to quantify the influence of experimentally unavoidable detector deficiencies such as blind areas or limited dynamic range as well as post-processing filtering on the reconstruction. We also propose a criterion for the isosurface determination of the object, based on the histogram of the reconstructed modulus. Finally, we study the capability of the phasing algorithm to quantitatively retrieve the surface strain (i.e., the strain of the surface voxels). This work emphasizes many aspects that have been neglected so far in BCDI, which need to be understood for a quantitative analysis of displacement and strain based on this technique. It concludes with the optimization of experimental parameters to improve throughput and to establish BCDI as a reliable 3D nano-imaging technique.

The Nanodiffraction beamline ID01/ESRF: a microscope for imaging strain and structure

The ID01 beamline has been built to combine Bragg diffraction with imaging techniques to produce a strain and mosaicity microscope for materials in their native or operando state. A scanning probe with nano-focused beams, objective-lens-based full-field microscopy and coherent diffraction imaging provide a suite of tools which deliver micrometre to few nanometre spatial resolution combined with 10-5 strain and 10-3 tilt sensitivity. A detailed description of the beamline from source to sample is provided and serves as a reference for the user community. The anticipated impact of the impending upgrade to the ESRF - Extremely Brilliant Source is also discussed.

Crystallographic orientation of facets and planar defects in functional nanostructures elucidated by nano-focused coherent diffractive X-ray imaging

The physical and chemical properties of nanostructures depend on their surface facets. Here, we exploit a pole figure approach to determine the three-dimensional orientation matrix of a nanostructure from a single Bragg reflection measured with a coherent nano-focused X-ray beam. The signature of any truncated (faceted) crystal produces a crystal truncation rod, which corresponds to a streak of intensity in reciprocal space normal to the surface. When two or more non-parallel facets are present, both the crystal orientation and the crystal facets can be identified. This enables facets to be rapidly indexed and uncommon facets, and planar defects, that have been difficult to study before to be identified. We demonstrate the technique with (i) epitaxial core-shell InGaN/GaN multiple quantum-wells grown on GaN nanowires, where surface facets and planar defects are determined, and (ii) single randomly oriented highly faceted tetrahedrahexal Pt nanoparticles. The methodology is applicable to a broad range of nanocrystals and provides a unique insight into the connection between structure and properties of nanomaterials.

Domain Wall Orientations in Ferroelectric Superlattices Probed with Synchrotron X-Ray Diffraction

Ferroelectric domains in PbTiO_{3}/SrTiO_{3} superlattices are studied using synchrotron x-ray diffraction. Macroscopic measurements reveal a change in the preferential domain wall orientation from {100} to {110} crystallographic planes with increasing temperature. The temperature range of this reorientation depends on the ferroelectric layer thickness and domain period. Using a nanofocused beam, local changes in the domain wall orientation within the buried ferroelectric layers are imaged, both in structurally uniform regions of the sample and near defect sites and argon ion-etched patterns. Domain walls are found to exhibit a preferential alignment with the straight edges of the etched patterns as well as with structural features associated with defect sites. The distribution of out-of-plane lattice parameters is mapped around one such feature, showing that it is accompanied by inhomogeneous strain and large strain gradients.

Ultrafast Three-Dimensional Integrated Imaging of Strain in Core/Shell Semiconductor/Metal Nanostructures

Visualizing the dynamical response of material heterointerfaces is increasingly important for the design of hybrid materials and structures with tailored properties for use in functional devices. In situ characterization of nanoscale heterointerfaces such as metal-semiconductor interfaces, which exhibit a complex interplay between lattice strain, electric potential, and heat transport at subnanosecond time scales, is particularly challenging. In this work, we use a laser pump/X-ray probe form of Bragg coherent diffraction imaging (BCDI) to visualize in three-dimension the deformation of the core of a model core/shell semiconductor-metal (ZnO/Ni) nanorod following laser heating of the shell. We observe a rich interplay of radial, axial, and shear deformation modes acting at different time scales that are induced by the strain from the Ni shell. We construct experimentally informed models by directly importing the reconstructed crystal from the ultrafast experiment into a thermo-electromechanical continuum model. The model elucidates the origin of the deformation modes observed experimentally. Our integrated imaging approach represents an invaluable tool to probe strain dynamics across mixed interfaces under operando conditions.

Reactor for nano-focused x-ray diffraction and imaging under catalytic in situ conditions

A reactor cell for in situ studies of individual catalyst nanoparticles or surfaces by nano-focused (coherent) x-ray diffraction has been developed. Catalytic reactions can be studied in flow mode in a pressure range of 10^-2-10³ mbar and temperatures up to 900 °C. This instrument bridges the pressure and materials gap at the same time within one experimental setup. It allows us to probe in situ the structure (e.g., shape, size, strain, faceting, composition, and defects) of individual nanoparticles using a nano-focused x-ray beam. Here, the setup was used to observe strain and facet evolution of individual model Pt catalysts during in situ experiments. It can be used for heating other (non-catalytically active) nanoparticles (e.g., nanowires) in inert or reactive gas atmospheres or vacuum as well.

Characterization of individual stacking faults in a wurtzite GaAs nanowire by nanobeam X-ray diffraction

Coherent X-ray diffraction was used to measure the type, quantity and the relative distances between stacking faults along the growth direction of two individual wurtzite GaAs nanowires grown by metalorganic vapour epitaxy. The presented approach is based on the general property of the Patterson function, which is the autocorrelation of the electron density as well as the Fourier transformation of the diffracted intensity distribution of an object. Partial Patterson functions were extracted from the diffracted intensity measured along the [000\bar{1}] direction in the vicinity of the wurtzite 00\bar{1}\bar{5} Bragg peak. The maxima of the Patterson function encode both the distances between the fault planes and the type of the fault planes with the sensitivity of a single atomic bilayer. The positions of the fault planes are deduced from the positions and shapes of the maxima of the Patterson function and they are in excellent agreement with the positions found with transmission electron microscopy of the same nanowire.

Ultrafast Three-Dimensional X-ray Imaging of Deformation Modes in ZnO Nanocrystals

Imaging the dynamical response of materials following ultrafast excitation can reveal energy transduction mechanisms and their dissipation pathways, as well as material stability under conditions far from equilibrium. Such dynamical behavior is challenging to characterize, especially operando at nanoscopic spatiotemporal scales. In this letter, we use X-ray coherent diffractive imaging to show that ultrafast laser excitation of a ZnO nanocrystal induces a rich set of deformation dynamics including characteristic "hard" or inhomogeneous and "soft" or homogeneous modes at different time scales, corresponding respectively to the propagation of acoustic phonons and resonant oscillation of the crystal. By integrating the 3D nanocrystal structure obtained from the ultrafast X-ray measurements with a continuum thermo-electro-mechanical finite element model, we elucidate the deformation mechanisms following laser excitation, in particular, a torsional mode that generates a 50% greater electric potential gradient than that resulting from the flexural mode. Understanding of the time-dependence of these mechanisms on ultrafast scales has significant implications for development of new materials for nanoscale power generation.

Three Dimensional Variable-Wavelength X-Ray Bragg Coherent Diffraction Imaging

We present and demonstrate a formalism by which three-dimensional (3D) Bragg x-ray coherent diffraction imaging (BCDI) can be implemented without moving the sample by scanning the energy of the incident x-ray beam. This capability is made possible by introducing a 3D Fourier transform that accounts for x-ray wavelength variability. We demonstrate the approach by inverting coherent Bragg diffraction patterns from a gold nanocrystal measured with an x-ray energy scan. Variable-wavelength BCDI will expand the breadth of feasible in situ 3D strain imaging experiments towards more diverse materials environments, especially where sample manipulation is difficult.

Chemistry and structure of homoepitaxial SrTiO3 films and their influence on oxide-heterostructure interfaces

The properties of single-crystal SrTiO3 substrates and homoepitaxial SrTiO3 films grown by pulsed laser deposition have been compared, in order to understand the loss of interfacial conductivity when more than a critical thickness of nominally homoepitaxial SrTiO3 is inserted between a LaAlO3 film and a SrTiO3 substrate. In particular, the chemical composition and the structure of homoepitaxial SrTiO3 investigated by low-energy ion-scattering and surface X-ray diffraction show that for insulating heterointerfaces, a Sr-excess is present between the LaAlO3 and homoepitaxial SrTiO3. Furthermore, an increase in the out-of-plane lattice constant is observed in LaAlO3, indicating that the conductivity both with and without insertion of the SrTiO3 thin film originates from a Zener breakdown associated with the polar catastrophe. When more than a critical thickness of homoepitaxial SrTiO3 is inserted between LaAlO3 and SrTiO3, the electrons transferred by the electronic reconstruction are trapped by the formation of a Sr-rich secondary phase and Sr-vacancies. The migration of Sr towards the surface of homoepitaxial SrTiO3 and accompanying loss of interfacial conductivity can be delayed by reducing the Sr-content in the PLD target.

Cluster method for analysing surface X-ray diffraction data sets using area detectors

An automated cluster algorithm is described, applicable to any image where a signal is to be analysed. The algorithm is employed in the context of surface X-ray diffraction data and extended to automate the data reduction process, which at present limits both the lead time to and the reliability of the retrieved structural information. A detailed evaluation of the constraints used to automate surface X-ray diffraction data analysis is provided. To overcome limitations of the algorithm and the experiment itself in certain geometries, the full field of view of area detectors is exploited to obtain orders of magnitude improvements in data collection. The method extends the surface X-ray diffraction technique to new systems and highlights the often archaic approach to the analysis of data collected with a two-dimensional detector.

The Materials Science beamline upgrade at the Swiss Light Source

The Materials Science beamline at the Swiss Light Source has been operational since 2001. In late 2010, the original wiggler source was replaced with a novel insertion device, which allows unprecedented access to high photon energies from an undulator installed in a medium-energy storage ring. In order to best exploit the increased brilliance of this new source, the entire front-end and optics had to be redesigned. In this work, the upgrade of the beamline is described in detail. The tone is didactic, from which it is hoped the reader can adapt the concepts and ideas to his or her needs.

Atomic imaging and direct phase retrieval using anomalous surface x-ray diffraction

The application of multi-wavelength anomalous diffraction to thin films, interfaces and surface structures is presented. The method directly determines the amplitudes and phases of the complex surface structure factors from surface x-ray diffraction data, measured at three different energies around the absorption edge of one of the elements present in the film. Thereby, one is able to directly Fourier transform the data, which immediately provides meaningful and unambiguous electron-density distributions. These serve as a starting point for subsequent structural refinement. The robustness of the algorithm was evaluated on simulated data as a proof of principle. The experimental limitations and their effect on the method will be discussed as well as stability tests for the algorithm, such as the positions of the anomalous scatterers and the interfacial roughness. It will be shown that the method can be applied to real structures. The algorithm was tested on real data from a thin film of SrTiO(3) grown on NdGaO(3)(110).

Electrostriction at the LaAlO3/SrTiO3 interface

We present a direct comparison between experimental data and ab initio calculations for the electrostrictive effect in the polar LaAlO(3) layer grown on SrTiO(3) substrates. From the structural data, a complete screening of the LaAlO(3) dipole field is observed for film thicknesses between 6 and 20 uc. For thinner films, an expansion of the c axis of 2% matching the theoretical predictions for an electrostrictive effect is observed experimentally.

Evolution of the interfacial structure of LaAlO3 on SrTiO3

The evolution of the atomic structure of LaAlO_{3} grown on SrTiO_{3} was investigated using surface x-ray diffraction in conjunction with model-independent, phase-retrieval algorithms between two and five monolayers film thickness. A depolarizing buckling is observed between cation and oxygen positions in response to the electric field of polar LaAlO_{3}, which decreases with increasing film thickness. We explain this in terms of competition between elastic strain energy, electrostatic energy, and electronic reconstructions. Based on these structures, the threshold for formation of a two-dimensional electron system at a film thickness of 4 monolayers is quantitatively explained. The findings are also qualitatively reproduced by density-functional-theory calculations.

Three-dimensional imaging of strain in a single ZnO nanorod

Nanoscale structures can be highly strained because of confinement effects and the strong influence of their external boundaries. This results in dramatically different electronic, magnetic and optical material properties of considerable utility. Third-generation synchrotron-based coherent X-ray diffraction has emerged as a non-destructive tool for three-dimensional (3D) imaging of strain and defects in crystals that are smaller than the coherence volume, typically a few cubic micrometres, of the available beams that have sufficient flux to reveal the material's structure. Until now, measurements have been possible only at a single Bragg point of a given crystal because of the limited ability to maintain alignment; it has therefore been possible to determine only one component of displacement and not the full strain tensor. Here we report key advances in our fabrication and experimental techniques, which have enabled diffraction patterns to be obtained from six Bragg reflections of the same ZnO nanocrystal for the first time. All three Cartesian components of the ion displacement field, and in turn the full nine-component strain tensor, have thereby been imaged in three dimensions.

Longitudinal coherence function in X-ray imaging of crystals

The longitudinal coherence function at the Advanced Photon Source beamline 34-ID-C has been measured by a novel method and the coherence length (xi(L)) determined to be, xi(L) = 0.66 +/- 0.02 microm. Three dimensional Coherent X-ray Diffraction (CXD) patterns were measured for multiple Bragg reflections from two Zinc Oxide (ZnO) nanorods with differing aspect ratios. The visibility of fringes corresponding to the 002 crystal direction for each reflection were found to be different and used to map the coherence function of the incident radiation. Partial coherence was found to be associated with amplitude 'hot' spots in three dimensional reconstructions of the crystal structure.