Defects In Crystalline Materials Research Articles

Enabling quantitative analysis of in situ TEM experiments: A high-throughput, deep learning-based approach tailored to the dynamics of dislocations

In situ TEM is by far the most commonly used microscopy method for imaging dislocations, i.e., line-like defects in crystalline materials. However, quantitative image analysis so far was not possible, implying that also statistical analyses were strongly limited. In this work, we created a deep learning-based digital twin of an in situ TEM straining experiment, additionally allowing to perform matching simulations. As application we extract spatio-temporal information of moving dislocations from experiments carried out on a Cantor high entropy alloy and investigate the universality class of plastic strain avalanches. We can directly observe “stick–slip motion” of single dislocations and compute the corresponding avalanche statistics. The distributions turn out to be scale-free, and the exponent of the power law distribution exhibits independence on the driving stress. The introduced methodology is entirely generic and has the potential to turn meso-scale TEM microscopy into a truly quantitative and reproducible approach.

Characterization of extended defects in 2D materials using aperture-based dark-field STEM in SEM

Quantitative diffraction contrast analysis with defined diffraction vectors is a well-established method in TEM for studying defects in crystalline materials. A comparable transmission technique is however not available in the more widely used SEM platforms. In this work, we transfer the aperture-based dark-field imaging method from the TEM to the SEM, thus enabling quantitative diffraction contrast studies at lower voltages in SEM. This is achieved in STEM mode by inserting a custom-made aperture between the sample and the STEM detector and centering the hole on a desired reflection. To select individual reflections for dark-field imaging, we use our Low Energy Nanodiffraction (LEND) setup [Schweizer et al., Ultramicroscopy 213, 112956 (2020)], which captures transmission diffraction patterns from a fluorescent screen positioned below the sample. The aperture-based dark-field STEM method is particularly useful for studying extended defects in 2D materials, where (i) stronger diffraction at the lower voltages used in SEM is advantageous, but (ii) two-beam conditions cannot be established, making quantitative diffraction contrast analysis with standard bright-field and annular dark-field detectors impossible. We demonstrate the method by studying basal plane dislocations in bilayer graphene, which have attracted considerable research interest due to their exceptional structural and electronic properties. Direct comparison of results obtained on identical dislocations by the established TEM method and by the new aperture-based dark-field STEM method in SEM shows that a reliable Burgers vector analysis is possible by applying the well-known g·b=0 invisibility criterion. We further use the LEND setup to acquire 4D-STEM data and show that the virtual dark-field images match well with those in aperture-based dark-field STEM images for reliable Burgers vector analysis.

Simulating charged defects at database scale

Point defects have a strong influence on the physical properties of materials, often dominating the electronic and optical behavior in semiconductors and insulators. The simulation and analysis of point defects is, therefore, crucial for understanding the growth and operation of materials, especially for optoelectronics applications. In this work, we present a general-purpose Python framework for the analysis of point defects in crystalline materials as well as a generalized workflow for their treatment with high-throughput simulations. The distinguishing feature of our approach is an emphasis on a unique, unit cell, structure-only, definition of point defects which decouples the defect definition, and the specific supercell representation used to simulate the defect. This allows the results of first-principles calculations to be aggregated into a database without extensive provenance information and is a crucial step in building a persistent database of point defects that can grow over time, a key component toward realizing the idea of a “defect genome” that can yield more complex relationships governing the behavior of defects in materials. We demonstrate several examples of the approach for three technologically relevant materials and highlight current pitfalls that must be considered when employing these methodologies as well as their potential solutions.

Focused and coherent X-ray beams for advanced microscopies

The use of focused X-ray beams in the micron and sub-micron range has fostered the progress of a wide range of scanning microscopy approaches that exploit the numerous interactions of X-rays with matter. These methods are becoming crucial for an increasing number of research fields, such as energy materials, electronic devices, biology, to cite a few. Nanobeams produced at 4th generation synchrotrons have coherence properties that make them ideal for a 3D diffraction-based microscopy with unique sensitivity to strain and defects in crystalline materials and allow delving into materials heterogeneities. We provide here a short overview on the use of nanobeams for diffraction experiments, and perspectives for their use in spectroscopy studies.

Imperfect Battery Materials: A Closer Look at the Role of Defects in Electrochemical Performance

Structural and compositional defects in crystalline materials are unavoidable. Accurately disentangling their role in composition–structure–property correlations is therefore essential but has long been hindered by our inability to precisely identify and quantify certain microstructural features. As a result, deviations from ideal structures have frequently been disregarded or assumed to be detrimental. Nonetheless, today’s structural disorder characterization advancements offer unprecedented insights into defect architectures. Recent models and tools applied to scattering and spectroscopic techniques provide an accessible window for observing and accurately parametrizing microstructural complexity and, if understood and mastered, offer the utmost control for designing better materials. One important field that can greatly benefit from advancement in the understanding and control of structural defects is the development of battery materials, whose performance and cycle life are closely related to structural aspects, including defects. This perspective offers an overview of the progress achieved in this field, with a special focus on cathode materials, and a discussion about opportunities for future developments.

Experimental and numerical verification of anomalous screening theory in granular matter

The concept of mechanical screening is widely applied in solid-state systems. Examples include nucleation of defects in crystalline materials, scars and pleats in curved crystals, wrinkles in strongly confined thin sheets, and cell-rearrangements in biological tissue. Available theories of such screening usually contain a crucial ingredient, which is the existence of an ordered reference state, with respect to which screening elements nucleate to release stresses. In contradistinction, amorphous materials in which a unique reference state does not exist, nevertheless exhibits plastic events that act as screening geometric charges with significant implications on the mechanical response. In a recent paper [Phys. Rev. E 104, 024904] it was proposed that mechanical strains in amorphous solids can be either weakly or strongly screened by the formation of low or high density of plastic events. At low densities the screening effect is reminiscent of the role of dipoles in dielectrics, in only renormalizing the elastic moduli. The effect of high density screening has no immediate electrostatic analog and is expected to change qualitatively the mechanical response, as seen for example in the displacement field. On the basis of experiments and simulations, we show that in granular matter, strong screening results in significant deviation from elasticity theory. The theoretical analysis, which accounts for an emergent inherent length scale, the experimental measurements and the numerical simulations of frictional granular amorphous assemblies are in agreement with each other, and provide a strong support for the novel continuum theory.

Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect

Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work rigorously derives a novel far-field expansion of these fields. The expansion is computable and is expressed as a sum of continuum correctors and discrete multipole terms which decay with increasing algebraic rate as the order of the expansion increases. Truncating the expansion leaves a remainder describing the defect core structure, which is localised in the sense that it decays with an algebraic rate corresponding to the order at which the truncation occurred.

An extended computational approach for point-defect equilibria in semiconductor materials

Concentrations of intrinsic and extrinsic point defects in crystalline materials with a bandgap are typically calculated in a constant-μ approach from defect formation energies based on density functional theory. In this work, calculations of thermal and charge equilibria among point defects are extended to a constant-N approach. The two approaches for point-defect equilibria are comparatively demonstrated in the application to Mg2Si doped with Li, Na, and Ag, which is a lightweight and environmentally friendly thermoelectric candidate material. Our results reveal the systematic behavior of defect and carrier concentrations. The dopant atoms form interstitial defects at similar concentrations to substitutional defects at the Mg sites, resulting in significantly reduced free-carrier concentrations compared to the expected values. The developed procedures could be utilized to find an optimal avenue for achieving higher carrier concentrations, e.g., with regard to annealing temperature and the concentration of dopant atoms, in various semiconductors and insulators.

Limitations of empirical supercell extrapolation for calculations of point defects in bulk, at surfaces, and in two-dimensional materials

The commonly employed supercell approach for defects in crystalline materials may introduce spurious interactions between the defect and its periodic images. A rich literature is available on how the interaction energies can be estimated, reduced, or corrected. A simple and seemingly straightforward approach is to extrapolate from a series of finite supercell sizes to the infinite-size limit, assuming a smooth polynomial dependence of the energy on inverse supercell size. In this work, we demonstrate by means of explict density-functional theory supercell calculations and simplified models that wave-function overlap and electrostatic interactions lead to more complex dependencies on supercell size than commonly assumed. We show that this complexity cannot be captured by the simple extrapolation approaches and that suitable correction schemes should be employed.

Integration of a Wigner effect-based energy storage system with an advanced nuclear reactor

In this work, an innovative energy storage concept based on the purposeful creation of defects in crystalline material by neutron irradiation is presented. Lattice defects are generated when heavy particles collide with the atoms in acrystal structure, i.e., if the incoming particles have enough energy, recoil atoms are displaced from their initial lattice sites. Most of the displaced atoms will eventually combine with nearby vacancies, but some of them will come to rest in non-ideal locations. The energy held by displaced atoms is called Wigner energy. Lattice defects can migrate and form clusters, and the Wigner energy can be released from these groupings if sufficient activation energy is provided. In the nuclear industry, this effect is well-known since it represented an issue for graphite-moderated reactors. This work presents the conceptual design of an engineering system that exploits this physical process to store the energy of neutrons in advanced reactor concepts. In the first part of the paper, the theoretical performance of an energy storage system based on the Wigner effect is described. Given the lattice properties and the compatibility with the harsh reactor environment, graphite was selected as the candidate material for the irradiation targets. Both experimental data and molecular dynamics simulations confirmed that this system can achieve performance comparable with state-of-the-art batteries in terms of stored energy density. In the second part of the paper, the engineering challenges of this innovative technology and the proposed solutions are described. After defining the optimal irradiation conditions, the different steps of the operation of the proposed energy system (from energy storing to energy harvesting) were defined. Finally, the integration of this concept with advanced reactor designs, i.e., a Sodium-cooled Fast Reactor and a Molten Salt-cooled Reactor, was investigated and the corresponding performance was evaluated.

Inspection of defects in crystalline materials

Inspection of defects in crystalline materials

Simulation-based methodology to assess the lattice defects creation as energy storing process

In nuclear industry, damages caused to in-core structural materials by high-energy neutrons have been studied for years. Recently, the possibility of storing energy through the creation of defects in crystalline materials via heavy particle bombardment was investigated. To evaluate the potential of the Wigner effect as energy-storing process, a graphite-moderated Molten Salt Reactor was adopted as a test case. Neutronics simulations performed with OpenMC Monte Carlo code allowed estimating the amount of energy released during fission events, the fraction that is deposited in graphite, and the fraction that has the potential to cause radiation damages. Molecular dynamics simulations were then performed to study the evolution of cascades triggered by high-energy neutrons. As a major outcome, a more accurate estimate of the radiation damage with respect to the traditional approaches was obtained, and the fraction of the deposited neutron energy that can be stored through long-lived defects was quantified.

Dislocation as a bulk probe of higher-order topological insulators

Topological materials occupy the central stage in the modern condensed matter physics because of their robust metallic edge or surface states protected by the topological invariant, characterizing the electronic band structure in the bulk. Higher-order topological (HOT) states extend this usual bulk-boundary correspondence, so they host the modes localized at lower-dimensional boundaries, such as corners and hinges. Here we theoretically demonstrate that dislocations, ubiquitous defects in crystalline materials, can probe higher-order topology, recently realized in various platforms. We uncover that HOT insulators respond to dislocations through symmetry protected finite-energy in-gap electronic modes, localized at the defect core, which originate from an interplay between the orientation of the HOT mass domain wall and the Burgers vector of the dislocation. As such, these modes become gapless only when the Burgers vector points toward lower-dimensional gapless boundaries. Our findings are consequential for the systematic probing of the extended bulk-boundary correspondence in a broad range of HOT crystals and photonic and phononic or mechanical metamaterials through the bulk topological lattice defects.

Quantitative Atomic-Site Analysis of Functional Dopants/Point Defects in Crystalline Materials by Electron-Channeling-Enhanced Microanalysis.

A novel elemental and chemical analysis scheme based on electron-channeling phenomena in crystalline materials is introduced, where the incident high-energy electron beam is rocked with the submicrometric pivot point fixed on a specimen. This method enables us to quantitatively derive the site occupancies and site-dependent chemical information of impurities or intentionally doped functional elements in a specimen, using energy-dispersive X-ray spectroscopy and electron energy-loss spectroscopy attached to a scanning transmission electron microscope, which is of significant interest to current materials science, particularly related to nanotechnologies. This scheme is applicable to any combination of elements even when the conventional Rietveld analysis by X-ray or neutron diffraction occasionally fails to provide the desired results because of limited sample sizes and close scattering factors of neighboring elements in the periodic table. In this methodological article, we demonstrate the basic experimental procedure and analysis method of the present beam-rocking microanalysis.

Quantitative Atomic-Site Analysis of Functional Dopants/Point Defects in Crystalline Materials by Electron-Channeling-Enhanced Microanalysis

A novel elemental and chemical analysis scheme based on electron-channeling phenomena in crystalline materials is introduced, where the incident high-energy electron beam is rocked with the submicrometric pivot point fixed on a specimen. This method enables us to quantitatively derive the site occupancies and site-dependent chemical information of impurities or intentionally doped functional elements in a specimen, using energy-dispersive X-ray spectroscopy and electron energy-loss spectroscopy attached to a scanning transmission electron microscope, which is of significant interest to current materials science, particularly related to nanotechnologies. This scheme is applicable to any combination of elements even when the conventional Rietveld analysis by X-ray or neutron diffraction occasionally fails to provide the desired results because of limited sample sizes and close scattering factors of neighboring elements in the periodic table. In this methodological article, we demonstrate the basic experimental procedure and analysis method of the present beam-rocking microanalysis.

Distinct pathways of solid-to-solid phase transitions induced by defects: the case of dl-me-thio-nine.

Understanding of solid-to-solid phase transition mechanisms in polymorphic systems is of critical importance for rigorous control over polymorph purity in the pharmaceutical industry to achieve the desired bioavailability and efficacy of drugs. Ubiquitous defects in crystals may play an important role in the pathways of phase transitions. However, such effects remain poorly understood. Here, the effects of crystal defects on the solid-to-solid phase transformations between dl-me-thio-nine polymorphs α and β are investigated by means of experimental and computational approaches. Thermal analyses of polycrystalline powders show two endothermic peaks in the α-to-β phase transition (and two exothermic peaks for the reverse transition), in contrast with one thermal event observed for single crystals. Variable-temperature 1D and 2D Raman spectra, as well as powder X-ray diffraction patterns, reveal the appearance of two peaks that can attributed to a two-step phase transition, and the extent of the second-step phase transition increases with milling time (or defect density). Quantification of transition kinetics unveils a remarkably higher energy barrier in the second-step phase transition than in the first, proceeding by the cooperative molecular motion pathway. The good linear fitting on the kinetic data by the Jeziorny model suggests that the second-step transition follows the nucleation and growth mechanism. Molecular dynamics simulations were also conducted to understand the role of crystal defects in the solid-state phase transition by tracking the atomic distribution and hydrogen bond lifetime during the transition. It was found that the increasing defect density hinders the propagation of cooperative molecular motion, leading to a combined transition mechanism involving both cooperative motion and nucleation and growth. This study highlights the significant impact of crystal defects on solid-state phase transitions, and the two-step transition mechanism postulated may be universal given the ubiquitous presence of defects in crystalline materials.

X-ray ptychographic topography: A robust nondestructive tool for strain imaging

Strain and defects in crystalline materials are responsible for the distinct mechanical, electric and magnetic properties of a desired material, making their study an essential task in material characterization, fabrication and design. Existing techniques for the visualization of strain fields, such as transmission electron microscopy and diffraction, are destructive and limited to thin slices of the materials. On the other hand, non-destructive X-ray imaging methods either have a reduced resolution or are not robust enough for a broad range of applications. Here we present X-ray ptychographic topography, a new method for strain imaging, and demonstrate its use on an InSb micro-pillar after micro-compression, where the strained region is visualized with a spatial resolution of 30 nm. Thereby, X-ray ptychographic topography proves itself as a robust non-destructive approach for the imaging of strain fields within bulk crystalline specimens with a spatial resolution of a few tens of nanometers.

Analysis of nanoscale fluid inclusions in geomaterials by atom probe tomography: Experiments and numerical simulations

The spatial correlation between defects in crystalline materials and trace element segregation plays a fundamental role in determining the physical and mechanical properties of a material, which is particularly important in naturally deformed materials. Herein, we combine electron backscatter diffraction, electron channelling contrast imaging, scanning transmission electron microscopy and atom probe tomography on a naturally occurring metal sulphide in an attempt to document mechanisms of element segregation in a brittle-dominated deformation regime. Within APT reconstructions, features with a high point density comprising O-rich discs stacked over As-rich spherules are observed. The combined microscopy data allow us to interpret these as nanoscale fluid inclusions. Our observations are confirmed by simulated APT experiments of core-shell particles with a core exhibiting a very low evaporation field and the shell emulating a segregated layer at the inclusion interface. Our data has significant trans-disciplinary implications to the geosciences, the material sciences, and analytical microscopy.

Quick-start guide for first-principles modelling of point defects in crystalline materials

Defects influence the properties and functionality of all crystalline materials. For instance, point defects participate in electronic (e.g. carrier generation and recombination) and optical (e.g. absorption and emission) processes critical to solar energy conversion. Solid-state diffusion, mediated by the transport of charged defects, is used for electrochemical energy storage. First-principles calculations of defects based on density functional theory have been widely used to complement, and even validate, experimental observations. In this ‘quick-start guide’, we discuss the best practice in how to calculate the formation energy of point defects in crystalline materials and analysis techniques appropriate to probe changes in structure and properties relevant across energy technologies.

Plasma Model of Generation and Slip of Linear Defects in Crystalline Materials

In dielectrics and semiconductors, a plasma model of the generation and slip of dislocations is considered, where under shock loads in a generalized space of rectangular pulses an alternating field forms a distribution of pairs of photoelectrons and cations; these electrons with velocities Ve create δ-collisions with cold plasma from free electrons and holes with masses me and mh (mh ≫ me), they emit and absorb longitudinal electron plasma waves whose phase velocities wpw / kpw are close to or are equal to the velocities Ve, while the frequencies wpw and wave numbers kpw of the wave packet of plasma waves are complex, the short-wave components of this wave packet at kpw ⋅ ae ≫ 1 (ae -Debye screening radius) decay in the core linear defect, and its long-wavelength components propagate in the region of the medium surrounding the core of the defect at kpw ⋅ ae ≅ 1. When a defect is generated, the distribution of cations under the influence of the internal Coulomb field shifts to the region of the first peak (protrusion) of the electron plasma wave, thereby forming a vacancy valley. When sliding under the influence of an external electric field, a cationic plasma wave consisting of a vacancy valley and two cationic protrusions moves against the background of an additional potential relief created by an electron plasma wave near the core of the defect. It has been shown that δ-collisions create flows of dynamic large-scale correlations of plasma fluctuations in the form of asymptotics of different-time correlators of density and potential fluctuations as t → +∞.