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Bragg coherent diffraction imaging (BCDI) experiments have been carried out at the Advanced Photon Source using a new cryostat system developed to achieve high mechanical stability and low vibrations. We measured the (012)LTO Bragg peak which is unique to the low-temperature orthorhombic (LTO) phase of micron-sized crystals of the high-temperature superconductor La2−xBaxCuO4 (LBCO) to study the formation of structural domains. Each time the sample was cooled into the orthorhombic phase, the diffraction pattern of domains was different. This confirms the interpretation of pinning of the lower-temperature charge density Wave domains observed in coherent resonant X-ray speckle correlation analysis experiments.

The quest for understanding the structural mechanisms of material properties and biological cell functions has led to the active development of coherent diffraction imaging (CDI) and its variants in the hard X-ray regime. Herein, we propose multiple-shot CDI, a full-field CDI technique dedicated to the visualisation of local nanostructural dynamics in extended objects at a spatio-temporal resolution beyond that of current instrumentation limitations. Multiple-shot CDI reconstructs a “movie” of local dynamics from time-evolving diffraction patterns, which is compatible with a robust scanning variant, ptychography. We developed projection illumination optics to produce a probe with a well-defined illumination area and a phase retrieval algorithm, establishing a spatio-temporal smoothness constraint for the reliable reconstruction of dynamic images. The numerical simulations and proof-of-concept experiment using synchrotron hard X-rays demonstrated the capability of visualising a dynamic nanostructured object at a frame rate of 10 Hz or higher. Coherent diffraction imaging (CDI) is a lensless technique for 2D or 3D reconstruction of nanoscale structure images, where a highly coherent beam of x-rays, electrons or other wavelike particle or photon is incident on an object. The authors present a phase retrieval algorithm that takes advantage of the continuity of physical phenomena and uses it as a temporal constraint for CDI, and also present an illumination optics suitable for the method, which allow them to follow dynamic processes, as demonstrate in their proof-of-principle experiment.

X-ray ptychographic microscopy combines the advantages of raster scanning X-ray microscopy with the more recently developed techniques of coherent diffraction imaging. It is limited neither by the fabricational challenges associated with X-ray optics nor by the requirements of isolated specimen preparation, and offers in principle wavelength-limited resolution, as well as stable access and solution to the phase problem. In this Review, we discuss the basic principles of X-ray ptychography and summarize the main milestones in the evolution of X-ray ptychographic microscopy and tomography over the past ten years, since its first demonstration with X-rays. We also highlight the potential for applications in the life and materials sciences, and discuss the latest advanced concepts and probable future developments.

In coherent diffraction imaging systems, mulplex measurement on unknown object can enhance the quality of output image. We apply angular mulplexing scheme to capture several diffracting images. A tilt diffraction model is used for addressing the illumination beam in the imaging process. And an iterative phase retrieval algorithm is desingend and adopted to recover the image of sample. Numerical simulation results are provied to test the imaging method. This approach can be used to enhance the quality of reconstructed images in coherent diffraction imaging.

A dynamic theory of coherent x-radiation emitted by a divergent beam of relativistic electrons traversing a thin single-crystal plate is developed which takes into account multiple scattering of the electrons on the target atoms. The case is considered in which the target is quite thin, so that it is not necessary to take absorption of radiation into account, but the electron path in the target is quite long, so that it is necessary to take multiple scattering into account. Expressions are obtained which describe the spectral–angular characteristics of parametric x-radiation and diffracted transient radiation under these conditions. Conditions are described under which diffracted bremsstrahlung radiation can be neglected. The possibility of manifesting the effects of dynamic diffraction is investigated.

The in situ physicochemical analysis of nanostructured functional materials is crucial for advances in their design and production. X-ray coherent diffraction imaging (CDI) methods have recently demonstrated impressive potential for characterizing such materials with a high spatial resolution and elemental sensitivity; however, moving from the current ex situ static regime to the in situ dynamic one remains a challenge. By combining soft X-ray ptychography and single-shot keyhole CDI, we performed the first in situ spatiotemporal study on an electrodeposition process in a sealed wet environment, employed for the fabrication of oxygen-reduction catalysts, which are key components for alkaline fuel cells and metal-air batteries. The results provide the first experimental demonstration of theoretically predicted Turing–Hopf electrochemical pattern formation resulting from morphochemical coupling, adding a new dimension for the in-depth in situ characterization of electrodeposition processes in space and time.

Atomic level defects such as dislocations play key roles in determining the macroscopic properties of crystalline materials. Their effects are important and wide-reaching, and range from increased chemical reactivity to enhanced mechanical properties to vastly increased rates of crystal growth. Dislocations have therefore been widely studied using traditional techniques such as X-ray diffraction (XRD) and optical imaging. More recently, advances in microscopy have allowed their direct visualization. Atomic force microscopy (AFM) has enabled the 2D study of single dislocations while transmission electron microscopy (TEM), which was initially limited to 2D projections of thin specimens, can now visualize strain fields in 3D with near atomic resolution. However, these techniques can- not offer in situ, 3D imaging of the formation or movement of dislocations during dynamic processes such as crystal growth and dissolution. Here, we describe how Bragg Coherent Diffraction Imaging (BCDI) can be used to visualize in 3D the entire network of dislocations present within an individual crystal. Using calcite (CaCO3) single crystals, we also use BCDI to monitor the propagation of the dislocation network during repeated growth and dissolution cycles, and show how this is intimately linked to the growth and dissolution mechanisms. These investigations demonstrate the potential of BCDI for studying the mechanisms underlying the response of crystalline materials to external stimuli.

Coherent reflection imaging is a new imaging technology allowing X-ray study of upper surface layers of thick and opaque samples or nanostructures and thin samples fixed on a reflecting substrate. We develop the diffraction theory and calculations relevant to coherent reflection imaging of tilted objects illuminated below critical angles of X-ray reflection.

Coherent diffraction imaging (CDI) in the extreme ultraviolet has become an important tool for nanoscale investigations. Laser-driven high harmonic generation (HHG) sources allow for lab scale applications such as cancer cell classification and phase-resolved surface studies. HHG sources exhibit excellent coherence but limited photon flux due poor conversion efficiency. In contrast, table-top soft X-ray lasers (SXRL) feature excellent temporal coherence and extraordinary high flux at limited transverse coherence. Here, the performance of a SXRL pumped at moderate pump energies is evaluated for CDI and compared to a HHG source. For CDI, a lower bound for the required mutual coherence factor of |μ12| ≥ 0.75 is found by comparing a reconstruction with fixed support to a conventional characterization using double slits. A comparison of the captured diffraction signals suggests that SXRLs have the potential for imaging micron scale objects with sub-20 nm resolution in orders of magnitude shorter integration time compared to a conventional HHG source. Here, the low transverse coherence diameter limits the resolution to approximately 180 nm. The extraordinary high photon flux per laser shot, scalability towards higher repetition rate and capability of seeding with a high harmonic source opens a route for higher performance nanoscale imaging systems based on SXRLs.

Ptychography is a diffraction-based X-ray microscopy technique in which an extended sample is scanned by a coherent beam with overlapped illuminated areas and complex transmission function of the sample is obtained by applying iterative phase retrieval algorithms to the diffraction patterns recorded at each scanned position. It permits quantitatively imaging of non-crystalline specimens at a resolution limited only by the X-ray wavelength and the maximal scattering angle detected. In this paper, the development of soft X-ray ptychography method at the BL08U1A beamline of Shanghai Synchrotron Radiation Facility is presented. The experimental setup, experimental parameters selection criteria, and post-experimental data analyzing procedures are presented in detail with a prospect of high-resolution image reconstruction in real time. The performance of this newly implemented method is demonstrated through the measurements of a resolution test pattern and two real samples: Pt–Co alloy nanoparticles and a breast cancer cell. The results indicate that strong scattering specimens can be reconstructed to sub-20 nm resolution, while a sub-25 nm resolution for biological specimens can be achieved.

The last decade has seen a remarkable surge in x-ray characterization methods (Willmott, An Introduction to Synchrotron Radiation, John Wiley & Sons, Inc., New York, 2011). Imaging with x-rays has evolved from simple radiography, to image internal structure and diagnose injury, to a full-fledged tool for nanoscale characterization (Holt et al., Annu Rev Mater Res 43:1, 2013). Central to this development has been the advent of high-brilliance synchrotron and free electron laser sources of x-rays. The high degree of spacial coherence of the resulting beams has enabled novel imaging methods. Of these, coherent diffraction imaging has proven highly successful at imaging the structure in nano materials (Miao et al., Nature 400:342, 1999). In addition, this imaging method can be combined with Bragg diffraction to image strain with high sensitivity (Pfeifer et al., Nature 442:63, 2006; Robinson and Harder, Nat Mater 8:291, 2009).

High-resolution imaging offers one of the most promising approaches for exploring and understanding the structure and function of biomaterials and biological systems. X-ray free-electron lasers (XFELs) combined with coherent diffraction imaging can theoretically provide high-resolution spatial information regarding biological materials using a single XFEL pulse. Currently, the application of this method suffers from the low scattering cross-section of biomaterials and X-ray damage to the sample. However, XFELs can provide pulses of such short duration that the data can be collected using the “diffract and destroy” approach before the effects of radiation damage on the data become significant. These experiments combine the use of enhanced coherent diffraction imaging with single-shot XFEL radiation to investigate the cellular architecture of Staphylococcus aureus with and without labeling by gold (Au) nanoclusters. The resolution of the images reconstructed from these diffraction patterns were twice as high or more for gold-labeled samples, demonstrating that this enhancement method provides a promising approach for the high-resolution imaging of biomaterials and biological systems.

The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called ‘diffraction before destruction' experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing the phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects., Short X-ray pulses from free-electron lasers enable coherent diffractive imaging of noncrystalline objects such as single molecules. Here, the authors reconstructing full image information from a single-shot diffraction pattern by using two sufficiently separated objects to act as references for each other.

High-resolution X-ray imaging techniques using optical elements such as zone plates are widely used for viewing the internal structure of samples in exquisite detail. The resolution attainable is ultimately limited by the manufacturing tolerances for the optics. Combining ideas from crystallography and holography, this limit may be surpassed by the method of coherent diffractive imaging (CDI) 1 . Although CDI shows particular promise in applications involving X-ray free-electron lasers 2 , it is also emerging as an important new technique for imaging at third-generation synchrotrons. The limited coherent output of these sources, however, is a significant barrier to obtaining shorter exposure times. A fundamental assumption of coherent diffractive imaging is that the incident light is well-approximated by a single optical frequency. In this Letter, we demonstrate the first experimental realization of ‘polyCDI’, using a broadband source to achieve a factor of 60 reduction in the exposure time over quasi-monochromatic coherent diffractive imaging. Over the past decade, the extension of crystallographic techniques to the high-resolution imaging of non-crystalline objects 3 has proved enormously successful in a wide variety of applications 4 . Iterative retrieval of the phase of the far-field diffraction pattern permits reconstruction of the diffracting object with a spatial resolution that is limited, in principle, only by the wavelength of the incident illumination. In crystallography, the periodic arrangement of atoms amplifies the signal diffracted from the unit cell, making detection of the Bragg peaks straightforward. A main goal for coherent diffractive imaging (CDI) is to develop it into a form of highspatial-resolution microscopy that can be routinely applied using synchrotron sources. In this endeavour it must compete with the very successful results obtained using zone-plate-based full-field transmission X-ray microscopy 5 . A fundamental issue for both forms of imaging is that higher spatial resolution requires that the sample be illuminated with a greater number of photons per resolution element, scaling approximately as the fourth power of the desired spatial resolution 6 . Although it has been asserted that CDI is able to achieve equivalent resolution to zone plate microscopy, but with fewer photons 7 , the two techniques are limited to precisely the same degree by the spectral bandwidth (longitudinal coherence length) of the incident light. Significant increases in the spatial resolution require brighter sources, much longer exposure times or the capacity to increase the acceptable limits on the bandwidth. A pathway to achromatic zone plates has been proposed 8 that

The understanding and management of strain is of fundamental importance in the design and implementation of materials. The strain properties of nanocrystalline materials are different from those of the bulk because of the strong influence of their surfaces and interfaces, which can be used to augment their function and introduce desirable characteristics. Here we explain how new X-ray diffraction techniques, which take advantage of the latest synchrotron radiation sources, can be used to obtain quantitative three-dimensional images of strain. These methods will lead, in the near future, to new knowledge of how nanomaterials behave within active devices and on unprecedented timescales.

Techniques for reconstructing an object’s microstructure from its diffraction pattern have substantially improved the future imaging potential of next-generation X-ray sources. Yet the same techniques can already be applied to conventional electron microscopes, to extend their resolution to below an angstrom.

This issue of MRS Bulletin focuses on the rapid progress that is ongoing in the development of hard x-ray microscopies with three-dimensional spatial resolutions ranging from micrometers to nanometers. The individual articles provide a crosscut of developments in hard x-ray projection tomography microscopy for imaging density and chemical fluctuations in crystalline and noncrystalline materials; large-angle diffractionbased, spatially resolved imaging of local structure, orientation, and strain distributions in crystalline materials; and emerging coherent diffraction imaging for nanometer-range Fourier transform imaging of crystalline and noncrystalline materials.

Lensless X-ray imaging techniques such as coherent diffraction imaging and ptychography, and Fourier transform holography can provide time-resolved, diffraction-limited images. Nearly all examples of these techniques have focused on transmission geometry, restricting the samples and reciprocal spaces that can be investigated. We report a lensless X-ray technique developed for imaging in Bragg and small-angle scattering geometries, which may also find application in transmission geometries. We demonstrate this by imaging a nanofabricated pseudorandom binary structure in small-angle reflection geometry. The technique can be used with extended objects, places no restriction on sample size, and requires no additional sample masking. The realization of X-ray lensless imaging in reflection geometry opens up the possibility of single-shot imaging of surfaces in thin films, buried interfaces in magnetic multilayers, organic photovoltaic and field-effect transistor devices, or Bragg planes in a single crystal.

The requirement for an object to be surrounded by empty space when imaged by coherent X-ray diffraction was once thought to be a fundamental limitation. A variant of coherent diffractive imaging proves this not to be the case, and substantially widens its potential use.

Mineral inclusions in biomass are attracting increased scrutiny due to their potential impact on processing methods designed to provide renewable feedstocks for the production of chemicals and fuels. These inclusions are often sculpted by the plant into shapes required to support functional roles that include the storage of specific elements, strengthening of the plant structure and providing a defense against pathogens and herbivores. In situ characterization of these inclusions faces substantial challenges since they are embedded in an opaque, complex polymeric matrix. Here we describe the use of Bragg coherent diffraction imaging (BCDI) to study mineral inclusions within intact maize stalks. Three-dimensional BCDI data sets were collected and used to reconstruct images of mineral inclusions at 50–100 nm resolution. Asymmetries in the intensity distributions around the Bragg peaks provided detailed information about the deformation fields within these crystal particles revealing lattice defects that result in distinct internal crystal domains.

The evolution of morphology and internal strain under high pressure fundamentally alters the physical property, structural stability, phase transition and deformation mechanism of materials. Until now, only averaged strain distributions have been studied. Bragg coherent X-ray diffraction imaging is highly sensitive to the internal strain distribution of individual crystals but requires coherent illumination, which can be compromised by the complex high-pressure sample environment. Here we report the successful de-convolution of these effects with the recently developed mutual coherent function method to reveal the three-dimensional strain distribution inside a 400 nm gold single crystal during compression within a diamond-anvil cell. The three-dimensional morphology and evolution of the strain under pressures up to 6.4 GPa were obtained with better than 30 nm spatial resolution. In addition to providing a new approach for high-pressure nanotechnology and rheology studies, we draw fundamental conclusions about the origin of the anomalous compressibility of nanocrystals., Extreme pressure can induce significant changes in a material’s mechanical response, but characterizing the evolution of these changes as they take place is challenging. Yang et al. demonstrate the use of coherent X-ray diffraction imaging to follow changes in the three-dimensional shape and strain fields within gold particles under pressure.

The wave properties of light, particularly its coherence, are responsible for interference effects, which can be exploited in powerful imaging applications. Coherent diffractive imaging relies heavily on coherence and has recently experienced rapid growth. Coherent diffractive imaging recovers an object from its diffraction pattern by computational phasing with the potential of wavelength-limited resolution. Diminished coherence results in reconstructions that suffer from artefacts or fail completely. Here we demonstrate ab initio phasing of partially coherent diffraction patterns in three dimensions, while simultaneously determining the coherence properties of the illuminating wavefield. Both the dramatic improvements in image interpretability and the three-dimensional evaluation of the coherence will have broad implications for quantitative imaging of nanostructures and wavefield characterization with X-rays and electrons.

Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens

Coherent diffraction imaging (CDI) is an emerging technique that is currently used mainly in the field of physics. An opportunity is present for materials scientists to make use of this technique in order to solve current and future materials-centric problems. In addition to introducing the scope of the section in this article, the readers are also given backgrounds for the authors and how each paper fits together. Finally, a brief review of the inaugural symposium held at the TMS 2013 Annual Meeting is provided along with an invitation for the next symposium scheduled for 2015. Although the concept of CDI has been around since the 1950s, experimental realization of this technique occurred only about 15 years ago. Through a combination of the oversampling method and iterative phase retrieval algorithms, high-resolution images can be obtained through the inversion of diffraction patterns from both crystalline and noncrystalline materials. This allows imaging and characterization through the use of x-rays to occur for a broad range of materials including nanoparticles, strained crystals, biomaterials, and cells. Unique characterization abilities such as threedimensional strain mapping and nondestructive three-dimensional tomographic imaging highlight the emerging importance of CDI in the field of materials science. In this series of papers, current and potential applications of CDI techniques to solve problems in materials science are explored as a way to foster increased interaction between materials scientists and physicists, the predominant developers of CDI. The first paper in this series is titled ‘‘From Grain Boundaries to Single Defects: A Review of Coherent Methods for Materials Imaging in the X-ray Sciences.’’ In this paper, Brian Abbey (La Trobe University, Melbourne, Australia, and Melbourne Centre for Nanofabrication, Melbourne, Australia) provides a broad overview of the various techniques within the field of CDI. Brief descriptions of the governing physics as well as limits of the techniques such as phase contrast tomography, plane wave CDI, ptychographic CDI, diverging beam CDI, reduced coherence CDI, coherent x-ray microbeam diffraction, and Bragg CDI are reported. The author also discusses current and potential uses for each technique within the materials science field. Dr. Abbey, in addition to the previously listed appointments, is also a member of the Micro Materials Characterization Beamline development team for the Australian Synchrotron. The second paper in this series is titled ‘‘X-Ray Coherent Diffraction Imaging of Nanomaterials.’’ Ross Harder (Advanced Photon Source, Argonne, IL, USA) and Ian K. Robinson (University College London, London, England) explore the use of Bragg CDI to image structure in nanosized barium titanate crystals in conjunction with local strain measurements with high sensitivity. Harder manages the 34-ID-C beamline at the Advanced Photon Source and welcomes user proposals that will continue to push the envelope in CDI’s abilities and applications, especially in the field of strain mapping. The final paper in this series is titled ‘‘Studies of Materials at the Nanometer Scale using Coherent X-Ray Diffraction Imaging.’’ Richard Sandberg (Los Alamos National Laboratory, Los Alamos, NM, USA), Zhifeng Huang, Rui Xu, Jose Rodriguez, and John Miao (all from the University of California Los Angeles, Los Angeles, CA, USA) explore the use of CDI in imaging materials as varied as biological cells and GaN quantum dot nanoparticles. The use of CDI is discussed in the context of both beamline-based CDI and table-topsource-based CDI. Sandberg’s primary research focus involves the development of table-top sourJohn Carpenter, chair of and JOM advisor for the Materials Characterization Committee of the TMS Extraction & Processing Division, and Richard Sandberg coordinated the topic Coherent X-ray Diffraction Imaging as a Characterization Tool in this issue. JOM, Vol. 65, No. 9, 2013

REFLECTED light from a coherent light source such as a laser shows a graininess known as speckle. In general, a speckle pattern is produced whenever randomly distributed regions of a material introduce different phase shifts into the scattering of coherent incident light. If the arrangement of the regions evolves with time, the speckle pattern will also change. Observation of the intensity fluctuations at a single point in the speckle pattern provides a direct measure of the time correlation function of the inhomogeneity. This leads to a technique1,2, alternatively called light-beating spectroscopy, dynamic light scattering or intensity fluctuation spectroscopy, which has been widely used with visible light to study processes such as critical fluctuations near phase transitions in fluids and the diffusion of particles in liquids. But it is not possible to study processes involving length scales less than about 200 nm, or those in opaque materials, using visible light. If intensity fluctuation spectroscopy could be carried out using coherent X-rays, however, one could probe the dynamics of processes involving atomic length scales in a wide range of materials. Here we show that by using a high-brilliance X-ray source it should be possible to perform this type of measurement using radiation of wavelength ∼0.15nm. Specifically, we have observed a speckle pattern in the diffraction of coherent X-rays from randomly arranged antiphase domains in a single crystal of the binary alloy Cu3Au.

It is shown that an x-ray interference phenomenon, Coherent Grating X-ray Diffraction (CGXD), can be used to study lateral nanostructure arrays on crystal surfaces and interfaces. Compared to Fraunhofer grating diffraction of visible light, x-ray grating diffraction contains information not only about geometric profiles of a surface, but also about the internal crystalline structures and lattice strain distributions in grating features. Grating diffraction patterns can also be measured in a white-beam Laue method using highly collimated polychromatic synchrotron radiation. This provides a way for parallel data collection and is useful in in-situ studies of structural evolution of nanostructure arrays.

The study demonstrates that a profile of crystalline diffraction of X-rays is determined by the coherent properties of the radiation. Using the classical theory of coherence a general expression of the intensity of X-ray diffraction on a three dimensional crystal lattice is derived and applied to a concrete calculation of diffraction intensity in the so-called Bragg case. As the calculation indicates only those atoms contribute to the formation of interference patterns which are present in the coherent region and whose magnitude is exactly defined by the coherence function, a quantity dependent on the width of the spectral line of the X-rays, the size of the source of the X-rays, and the source-to-crystal distance. The coherent region is found to be smaller than, or of the same order of magnitude as the region in which the conditions of the Frauenhofer diffraction are satisfied, i.e. of the order of 103 A. A model of X-ray diffraction respecting the coherent properties is also given, which help to explain why it is sufficient to include crystal absorption as late as the calculation of the intensities, and which undoubtedly will influence the existing model used in the interpretation of the diffraction patterns produced by strained metals.

The effect of partial coherency on electron diffraction patterns of Cd1−xMnxTe – Cd1−yMny Te superlattices has been investigated. Observed diffraction patterns are compared with intensity calculations performed using dynamical diffraction theory with a model of an extended incoherent monochromatic source. From this study, a new method of electron diffraction for characterization of multilayer structures can be developed. Under the condition that the lateral coherent distance of the incident beam covers two adjacent layers, diffraction beams arising from the two layers give rise to an interference fringe in a diffraction spot. With this type of diffraction pattern, one can determine the refractive index of a crystal in the multilayer structure.