The Three-Dimensional Morphology of Growing Dendrites

Accurate real space iterative reconstruction (RESIRE) algorithm for tomography

Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at  https://zenodo.org/record/7273314 .

Controlling Li Dendritic Growth in Graphite Anodes by Potassium Electrolyte Additives for Li-Ion Batteries

Fast charging promotes Li dendrite formation and its growth on graphite anodes, which affects cell performance in Li-ion batteries (LIBs). This work reports the formation of a robust SEI layer by introducing a KPF₆ inorganic additive into the electrolyte. An optimal concentration of 0.001 M KPF₆ effectively inhibits the growth of Li dendrites at 2C charging rates, compared with a commercial electrolyte. Electrolytes containing a KPF₆ additive are shown here to deliver dual effects to mitigate the growth of dendrites. A thin LiF-rich SEI layer is formed on graphite, which blocks the electron leakage pathways. Additionally, K⁺ resides at defect sites (such as particle boundaries) due to its faster diffusion rate and blocks the incoming Li⁺ and restricts the growth of Li dendrites. The electrolyte with optimum concentration of KPF₆, i.e., 0.001 M, effectively directs Li⁺ transport through the thin, durable, and low resistance LiF-rich SEI layer. This has implications for fast charging through optimization of the electrode/electrolyte interphase by controlling additive concentrations.

Sparse ab initio x-ray transmission spectrotomography for nanoscopic compositional analysis of functional materials

The performance of functional materials is either driven or limited by nanoscopic heterogeneities distributed throughout the material's volume. To better our understanding of these materials, we need characterization tools that allow us to determine the nature and distribution of these heterogeneities in their native geometry in 3D. Here, we introduce a method based on x-ray near-edge spectroscopy, ptychographic x-ray computed nanotomography, and sparsity techniques. The method allows the acquisition of quantitative multimodal tomograms of representative sample volumes at sub-30 nm half-period spatial resolution within practical acquisition times, which enables local structure refinements in complex geometries. To demonstrate the method's capabilities, we investigated the transformation of vanadium phosphorus oxide catalysts with industrial use. We observe changes from the micrometer to the atomic level and the formation of a location-specific defect so far only theorized. These results led to a reevaluation of these catalysts used in the production of plastics.

Electrochemical synthesis of tin plasmonic dendritic nanostructures with SEF capability through in situ replacement

Dendrite nanostructures with noble metals, such as Au and silver, act as plasmonic substrates with excellent potential in enhanced fluorescence technology. However, tin dendritic nanostructures are poorly investigated. In this study, we proposed a method of in situ electrochemical synthesis replacement to fabricate highly branched tin dendritic nanostructures on aluminum substrates. The surface enhanced fluorescence performance of the tin dendrites was tested for the detection of rhodamine 6G as probe molecules, and the result showed that the enhancement factors can reach to 36.5-fold that of an aluminum substrate. The fabricated tin dendrites have numerous nanogaps between the stratified and adjacent ones, thereby creating many plasmon-active “hotspots” dedicated to enhanced fluorescence. Electrical field simulation results for the tin dendritic nanostructures proved that its nanogaps can enhance the nearby local electromagnetic field. As a result, tin dendritic nanostructures exhibit outstanding surface enhanced fluorescence and promising application in biomolecule detection and sensor devices.

Dendrite nanostructures with noble metals, such as Au, silver and tin, act as plasmonic substrates with excellent potential in enhanced fluorescence technology.

Versatile compact heater design for in situ nano-tomography by transmission X-ray microscopy

A versatile, compact heater designed at National Synchrotron Light Source-II for in situ X-ray nano-imaging in a full-field transmission X-ray microscope is presented. Heater design for nano-imaging is challenging, combining tight spatial constraints with stringent design requirements for the temperature range and stability. Finite-element modeling and analytical calculations were used to determine the heater design parameters. Performance tests demonstrated reliable and stable performance, including maintaining the exterior casing close to room temperature while the heater is operating at above 1100°C, a homogenous heating zone and small temperature fluctuations. Two scientific experiments are presented to demonstrate the heater capabilities: (i) in situ 3D nano-tomography including a study of metal dealloying in a liquid molten salt extreme environment, and (ii) a study of pore formation in icosahedral quasicrystals. The progression of structural changes in both studies were clearly resolved in 3D, showing that the new heater enables powerful capabilities to directly visualize and quantify 3D morphological evolution of materials under real conditions by X-ray nano-imaging at elevated temperature during synthesis, fabrication and operation processes. This heater design concept can be applied to other applications where a precise, compact heater design is required.

New software protocols for enabling laboratory based temporal CT

Temporal micro-computed tomography (CT) allows the non-destructive quantification of processes that are evolving over time in 3D. Despite the increasing popularity of temporal CT, the practical implementation and optimisation can be difficult. Here, we present new software protocols that enable temporal CT using commercial laboratory CT systems. The first protocol drastically reduces the need for periodic intervention when making time-lapse experiments, allowing a large number of tomograms to be collected automatically. The automated scanning at regular intervals needed for uninterrupted time-lapse CT is demonstrated by analysing the germination of a mung bean (vigna radiata), whilst the synchronisation with an in situ rig required for interrupted time-lapse CT is highlighted using a shear cell to observe granular segregation. The second protocol uses golden-ratio angular sampling with an iterative reconstruction scheme and allows the number of projections in a reconstruction to be changed as sample evolution occurs. This overcomes the limitation of the need to know a priori what the best time window for each scan is. The protocol is evaluated by studying barite precipitation within a porous column, allowing a comparison of spatial and temporal resolution of reconstructions with different numbers of projections. Both of the protocols presented here have great potential for wider application, including, but not limited to, in situ mechanical testing, following battery degradation and chemical reactions.

Motion compensated micro-CT reconstruction for in-situ analysis of dynamic processes

This work presents a framework to exploit the synergy between Digital Volume Correlation (DVC) and iterative CT reconstruction to enhance the quality of high-resolution dynamic X-ray CT (4D-µCT) and obtain quantitative results from the acquired dataset in the form of 3D strain maps which can be directly correlated to the material properties. Furthermore, we show that the developed framework is capable of strongly reducing motion artifacts even in a dataset containing a single 360° rotation.

Extracting shape from curvature evolution in moving surfaces

Shape is a crucial geometric property of surfaces, interfaces, and membranes in biology, colloidal and interface science, and many areas of physics. This paper presents theory, simulation and scaling of local shape and curvedness changes in moving surfaces and interfaces, under uniform normal motion, as in phase ordering transitions in liquid crystals. Previously presented measures of shape and curvedness are introduced in quantities and equations used in colloidal science and interfacial transport phenomena to separate shape effects from those of curvedness. Considering in parallel the new shape formalism with the classical curvature formalism, this paper sheds new light on what effects originate only from shape. The new shape evolution equations are solved under uniform normal surface flow. It is found that the solutions obey the so-called "astigmatism equation" fixing the linear relation between the radii of curvature. Astigmatic trajectories in the shape-curvedness phase plane, can be clearly classified into two modes: (i) constant shape evolution, and (ii) variable shape-variable curvedness. Shapes between spheres and cylinders follow the former mode for large curvedness and transition at smaller curvedness into the latter. Shapes' transitions between cylinder and saddles only follow the second mode. Under geometry-driven stagnation (i.e. zero normal velocity) shapes can be frozen. Evolving spheres and cylinders freeze into the same original shape, but perturbed cylinders can freeze into a variety of shapes including saddles. The results provide a useful complementary view on how to describe and control shape evolution in surfaces and interfaces, of wide interest in soft matter materials.

Packing of sedimenting equiaxed dendrites

The packing of free-floating crystal grains during solidification has a strong impact on the phase-change process as well as on the structure and the defects in the solidified material. The packing fraction is affected by the particular dendritic morphology of the grains and by their low inertia resulting from the small density difference between solid and liquid. Understanding the grain packing phenomenon during metal alloy solidification is not experimentally possible since packing is coupled to many other phenomena. We therefore investigate the packing of equiaxed dendrites on a model system, consisting of fixed-shape nonconvex model particles sedimenting in conditions hydrodynamically similar to those encountered in solidifying metals. We perform numerical simulations by a discrete-element model and experiments with transparent liquids in a sedimentation column. The combination of experiments and simulations enables us to determine the packing fraction as a function of (i) the grain morphology, expressed by a shape parameter, and (ii) the hydrodynamic conditions, expressed by the particle Stokes number.

Simulation of temperature, stress and microstructure fields during laser deposition of Ti-6Al-4V

We study the evolution of prior columnar β phase, interface L phase, and α phase during directional solidification of a Ti-6Al-4V melt pool. Finite element simulations estimate the solidification temperature and velocity fields in the melt pool and analyze the stress field and thermal distortions in the solidified part during the laser powder bed fusion process. A phase-field model uses the temperature and velocity fields to predict the formation of columnar prior-β(Ti) phase. During the solidification of β phase from an undercooled liquid, the residual liquid below the solidus temperature within the β columns results in α phase. The finite element simulated stress and strain fields are correlated with the length scales and volume fractions of the microstructure fields. Finally, the coalescence behavior of the β(Ti) cells during solidification is illustrated. The above analyses are important as they can be used for proactive control of the subsequent modeling of the heat treatment processes.

GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging

Tomography has made a radical impact on diverse fields ranging from the study of 3D atomic arrangements in matter to the study of human health in medicine. Despite its very diverse applications, the core of tomography remains the same, that is, a mathematical method must be implemented to reconstruct the 3D structure of an object from a number of 2D projections. Here, we present the mathematical implementation of a tomographic algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE), for high-resolution 3D reconstruction from a limited number of 2D projections. GENFIRE first assembles a 3D Fourier grid with oversampling and then iterates between real and reciprocal space to search for a global solution that is concurrently consistent with the measured data and general physical constraints. The algorithm requires minimal human intervention and also incorporates angular refinement to reduce the tilt angle error. We demonstrate that GENFIRE can produce superior results relative to several other popular tomographic reconstruction techniques through numerical simulations and by experimentally reconstructing the 3D structure of a porous material and a frozen-hydrated marine cyanobacterium. Equipped with a graphical user interface, GENFIRE is freely available from our website and is expected to find broad applications across different disciplines.

Four dimensional material movies: High speed phase-contrast tomography by backprojection along dynamically curved paths

We present an approach towards four dimensional (4d) movies of materials, showing dynamic processes within the entire 3d structure. The method is based on tomographic reconstruction on dynamically curved paths using a motion model estimated by optical flow techniques, considerably reducing the typical motion artefacts of dynamic tomography. At the same time we exploit x-ray phase contrast based on free propagation to enhance the signal from micron scale structure recorded with illumination times down to a millisecond (ms). The concept is demonstrated by observing the burning process of a match stick in 4d, using high speed synchrotron phase contrast x-ray tomography recordings. The resulting movies reveal the structural changes of the wood cells during the combustion.

Improved tomographic reconstruction of large-scale real-world data by filter optimization

In advanced tomographic experiments, large detector sizes and large numbers of acquired datasets can make it difficult to process the data in a reasonable time. At the same time, the acquired projections are often limited in some way, for example having a low number of projections or a low signal-to-noise ratio. Direct analytical reconstruction methods are able to produce reconstructions in very little time, even for large-scale data, but the quality of these reconstructions can be insufficient for further analysis in cases with limited data. Iterative reconstruction methods typically produce more accurate reconstructions, but take significantly more time to compute, which limits their usefulness in practice. In this paper, we present the application of the SIRT-FBP method to large-scale real-world tomographic data. The SIRT-FBP method is able to accurately approximate the simultaneous iterative reconstruction technique (SIRT) method by the computationally efficient filtered backprojection (FBP) method, using precomputed experiment-specific filters. We specifically focus on the many implementation details that are important for application on large-scale real-world data, and give solutions to common problems that occur with experimental data. We show that SIRT-FBP filters can be computed in reasonable time, even for large problem sizes, and that precomputed filters can be reused for future experiments. Reconstruction results are given for three different experiments, and are compared with results of popular existing methods. The results show that the SIRT-FBP method is able to accurately approximate iterative reconstructions of experimental data. Furthermore, they show that, in practice, the SIRT-FBP method can produce more accurate reconstructions than standard direct analytical reconstructions with popular filters, without increasing the required computation time.

The mechanism of eutectic growth in highly anisotropic materials

In the past 50 years, there has been increasing interest—both theoretically and experimentally—in the problem of pattern formation of a moving boundary, such as a solidification front. One example of pattern formation is that of irregular eutectic solidification, in which the solid–liquid interface is non-isothermal and the interphase spacing varies in ways that are poorly understood. Here, we identify the growth mode of irregular eutectics, using reconstructions from four-dimensional (that is, time and space resolved) X-ray microtomography. Our results show that the eutectic growth process can be markedly different from that seen in previously used model systems and theories based on the ex situ analysis of microstructure. In light of our experimental findings, we present a coherent growth model of irregular eutectic solidification.

The origins of non-periodic growth features observed in irregular eutectics have been a source of controversy. Here authors use time-resolved X-ray microtomography during eutectic growth of an alloy to show how competing models can be extended and reconciled.

Twin-mediated crystal growth: an enigma resolved

During crystal growth, faceted interfaces may be perturbed by defects, leading to a rich variety of polycrystalline growth forms. One such defect is the coherent Σ3 {111} twin boundary, which is widely known to catalyze crystal growth. These defects have a profound effect on the properties of many materials: for example, electron-hole recombination rates strongly depend on the character of the twin boundaries in polycrystalline Si photovoltaic cells. However, the morphology of the twinned interface during growth has long been a mystery due to the lack of four-dimensional (i.e., space and time resolved) experiments. Many controversial mechanisms have been proposed for this process, most of which lack experimental verification. Here, we probe the real-time interfacial dynamics of polycrystalline Si particles growing from an Al-Si-Cu liquid via synchrotron-based X-ray tomography. Our novel analysis of the time evolution of the interfacial normals allows us to quantify unambiguously the habit plane and grain boundary orientations during growth. This, when combined with direct measurements of the interfacial morphology provide the first confirmation of twin-mediated growth, proposed over 50 years ago. Using the insights provided by these experiments, we have developed a unified picture of the phenomena responsible for the dynamics of faceted Si growth.

Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data

The processing of tomographic synchrotron data requires advanced and efficient software to be able to produce accurate results in reasonable time. In this paper, the integration of two software toolboxes, TomoPy and the ASTRA toolbox, which, together, provide a powerful framework for processing tomographic data, is presented. The integration combines the advantages of both toolboxes, such as the user-friendliness and CPU-efficient methods of TomoPy and the flexibility and optimized GPU-based reconstruction methods of the ASTRA toolbox. It is shown that both toolboxes can be easily installed and used together, requiring only minor changes to existing TomoPy scripts. Furthermore, it is shown that the efficient GPU-based reconstruction methods of the ASTRA toolbox can significantly decrease the time needed to reconstruct large datasets, and that advanced reconstruction methods can improve reconstruction quality compared with TomoPy's standard reconstruction method.