The bonding electron density in aluminum

Large-Angle Rocking Beam Electron Diffraction of Large Unit Cell Crystals Using Direct Electron Detector

We report a large-angle rocking beam electron diffraction (LARBED) technique for electron diffraction analysis. Diffraction patterns are recorded in a scanning transmission electron microscope (STEM) using a direct electron detector with large dynamical range and fast readout. We use a nanobeam for diffraction and perform the beam double rocking by synchronizing the detector with the STEM scan coils for the recording. Using this approach, large-angle convergent beam electron diffraction (LACBED) patterns of different reflections are obtained simultaneously. By using a nanobeam, instead of a focused beam, the LARBED technique can be applied to beam-sensitive crystals as well as crystals with large unit cells. This paper describes the implementation of LARBED and evaluates the performance using silicon and gadolinium gallium garnet crystals as test samples. We demonstrate that our method provides an effective and robust way for recording LARBED patterns and paves the way for quantitative electron diffraction of large unit cell and beam-sensitive crystals.

Current opinion on the prospect of mapping electronic orbitals in the transmission electron microscope: State of the art, challenges and perspectives

The concept of electronic orbitals has enabled the understanding of a wide range of physical and chemical properties of solids through the definition of, for example, chemical bonding between atoms. In the transmission electron microscope, which is one of the most used and powerful analytical tools for high-spatial-resolution analysis of solids, the accessible quantity is the local distribution of electronic states. However, the interpretation of electronic state maps at atomic resolution in terms of electronic orbitals is far from obvious, not always possible, and often remains a major hurdle preventing a better understanding of the properties of the system of interest. In this review, the current state of the art of the experimental aspects for electronic state mapping and its interpretation as electronic orbitals is presented, considering approaches that rely on elastic and inelastic scattering, in real and reciprocal spaces. This work goes beyond resolving spectral variations between adjacent atomic columns, as it aims at providing deeper information about, for example, the spatial or momentum distributions of the states involved. The advantages and disadvantages of existing experimental approaches are discussed, while the challenges to overcome and future perspectives are explored in an effort to establish the current state of knowledge in this field. The aims of this review are also to foster the interest of the scientific community and to trigger a global effort to further enhance the current analytical capabilities of transmission electron microscopy for chemical bonding and electronic structure analysis.

Dynamical refinement with multipolar electron scattering factors

Dynamical refinement is a well established method for refining crystal structures against 3D electron diffraction (ED) data and its benefits have been discussed in the literature [Palatinus, Petříček & Corrêa, (2015). Acta Cryst. A71, 235-244; Palatinus, Corrêa et al. (2015). Acta Cryst. B71, 740-751]. However, until now, dynamical refinements have only been conducted using the independent atom model (IAM). Recent research has shown that a more accurate description can be achieved by applying the transferable aspherical atom model (TAAM), but this has been limited only to kinematical refinements [Gruza et al. (2020). Acta Cryst. A76, 92-109; Jha et al. (2021). J. Appl. Cryst. 54, 1234-1243]. In this study, we combine dynamical refinement with TAAM for the crystal structure of 1-methyluracil, using data from precession ED. Our results show that this approach improves the residual Fourier electrostatic potential and refinement figures of merit. Furthermore, it leads to systematic changes in the atomic displacement parameters of all atoms and the positions of hydrogen atoms. We found that the refinement results are sensitive to the parameters used in the TAAM modelling process. Though our results show that TAAM offers superior performance compared with IAM in all cases, they also show that TAAM parameters obtained by periodic DFT calculations on the refined structure are superior to the TAAM parameters from the UBDB/MATTS database. It appears that multipolar parameters transferred from the database may not be sufficiently accurate to provide a satisfactory description of all details of the electrostatic potential probed by the 3D ED experiment.

Observations of specimen morphology effects on near-zone-axis convergent-beam electron diffraction patterns

This work presents observations of symmetry breakages in the intensity distributions of near-zone-axis convergent-beam electron diffraction (CBED) patterns that can only be explained by the symmetry of the specimen and not the symmetry of the unit cell describing the atomic structure of the material. The specimen is an aluminium-copper-tin alloy containing voids many tens of nanometres in size within continuous single crystals of the aluminium host matrix. Several CBED patterns where the incident beam enters and exits parallel void facets without the incident beam being perpendicular to these facets are examined. The symmetries in their intensity distributions are explained by the specimen morphology alone using a geometric argument based on the multislice theory. This work shows that it is possible to deduce nanoscale morphological information about the specimen in the direction of the electron beam - the elusive third dimension in transmission electron microscopy - from the inspection of CBED patterns.

Measurement of charges and chemical bonding in a cryo-EM structure

Hydrogen bonding, bond polarity, and charges in protein molecules play critical roles in the stabilization of protein structures, as well as affecting their functions such as enzymatic catalysis, electron transfer, and ligand binding. These effects can potentially be measured in Coulomb potentials using cryogenic electron microscopy (cryo-EM). We here present charges and bond properties of hydrogen in a sub-1.2 Å resolution structure of a protein complex, apoferritin, by single-particle cryo-EM. A weighted difference map reveals positive densities for most hydrogen atoms in the core region of the complex, while negative densities around acidic amino-acid side chains are likely related to negative charges. The former positive densities identify the amino- and oxo-termini of asparagine and glutamine side chains. The latter observations were verified by spatial-resolution selection and a dose-dependent frame series. The average position of the hydrogen densities depends on the parent bonded-atom type, and this is validated by the estimated level of the standard uncertainties in the bond lengths.

Structure Factors and Charge Density Description of Aluminum: A Quantum Crystallographic Study

Static structure factors and charge density for metallic aluminum were investigated by periodic calculations using atom-centered Gaussian-type basis sets with the Perdew-Burke-Ernzerhof (PBE) functional implemented in the CRYSTAL14 package and X-ray constrained wave function (XCW) fitting. The effects of additional diffuse d and f basis functions on structure factors were compared with synchrotron powder X-ray diffraction and quantitative convergent electron beam diffraction data. Changes in structure factors from an independent atom model at 022, 113, and 222 reflections introduced d and f basis functions similar to those of the experimental data. The XCW fitting was applied to different sizes of aluminum clusters. The charge density features for a 50-atom cluster clearly demonstrated electron accumulation at tetrahedral sites and electron depletion at octahedral sites. The resolution dependence of the XCW study suggests that structure factors of the five lowest resolution reflections with 0.1% accuracy were indispensable for determining the detailed bonding description in the case of metallic aluminum.

Imaging the Spatial Distribution of Electronic States in Graphene Using Electron Energy-Loss Spectroscopy: Prospect of Orbital Mapping

The spatial distributions of antibonding π^{*} and σ^{*} states in epitaxial graphene multilayers are mapped using electron energy-loss spectroscopy in a scanning transmission electron microscope. Inelastic channeling simulations validate the interpretation of the spatially resolved signals in terms of electronic orbitals, and demonstrate the crucial effect of the material thickness on the experimental capability to resolve the distribution of unoccupied states. This work illustrates the current potential of core-level electron energy-loss spectroscopy towards the direct visualization of electronic orbitals in a wide range of materials, of huge interest to better understand chemical bonding among many other properties at interfaces and defects in solids.

Predicted Stable Electrides in Mg-Al System under High Pressure

Magnesium and aluminum, as the adjacent light metal elements, are difficult to form the stable stoichiometries compounds under ambient conditions. In this work, using evolutionary ab initio structural prediction approaches,...

Lattice distortion-enhanced superlubricity of (Mo, X)S2 (X = Al, Ti, Cr and V) with moiré superlattice

Two-dimensional (2D) materials with the advantage of low interlayer shear strain are ultilized as lubricants in aerospace and precision manufacturing. Moiré superlattices (MSL), with attractive physical properties of electronic structures, interlayer hybridization and atomic forces, have been widely investigated in superlubricity, which is caused by elimination of interlayer lock-in by incommensurate atomic reconstruction. Although the foundations of superlubricity and the development of 2D lubricants via vanishing friction have been investigated, it is still important to comprehensively reveal the influence of MSL on the interlayer van der Waals (vdW) interactions of 2D lubricants. Here, the contributions of lattice distortions of solute-doped twisted bilayers (Mo, X)S₂ (X = Al, Ti, V and Cr) to superlubricity are comprehensively investigated by high-throughput modelling and DFT-D2 calculations. It is revealed that the lattice distortion not only breaks the interlayer balance of repulsion and van der Waals interactions but also yields layer corrugation. These layer-corrugation-induced changes of the interlayer interactions and spacing distances are utilized to optimize lubricity, which matches with the experimental friction coefficients in the order of (Mo, Al)S₂ > (Mo, Cr)S₂ > MoS₂ >(Mo, V)S₂ >(Mo, Ti)S₂. The evolutions of the band structures show an exponential relationship of the band edge width and layer deformations, paving a path to accelerate the development of advanced superlubricity materials via lattice distortions.

Cryogenic Electron Microscopy on Strongly Correlated Quantum Materials

ConspectusQuantum materials refers to a class of materials with exotic properties that arise from the quantum mechanical nature of their constituent electrons, exhibiting, for example, high-temperature superconductivity, colossal magnetoresistivity, multiferroicity, and topological behavior. Quantum materials often have incompletely filled d- or f-electron shells with narrow energy bands, and the conduct of their electrons is strongly correlated. One distinct characteristic of the materials is that their electronic states are often spatially inhomogeneous and thus well suited for study using a spatially resolved electron beam with its great scattering power and sensitivity to atomic ionicity. Furthermore, most of these exotic properties only manifest at very low temperatures, posing a challenge to modern electron microscopy. It requires extraordinarily instrument stabilities at cryogenic temperatures with critical spatial, temporal, and energy resolutions in both static and dynamic manner to probe these materials. On the other hand, the ability to directly visualize the atomic, electronic and spin structures and inhomogeneities of quantum materials and correlate them to their functionalities creates enormous opportunities. At the most elementary levels of condensed matter physics, understanding the competing order of electron, spin, orbital, and lattice and their degrees of freedom, the impacts of defects and interfaces, and the site-specific quantum phenomena and phase transitions that give rise to the emergent behaviors allows us to discover and control novel materials for quantum information science and technologies.In this Account, several of our research examples are selected to highlight the use of cryogenic electron microscopy (cryo-EM) to study strongly correlated quantum materials. We focus on the critical roles of heterogeneity, interfaces, defects, and disorder in crystal structure, magnetic structure, and electronic structure to understand the physical properties of the materials that cryo-EM enables. We show how electron crystallography coupled with Bragg diffraction and diffuse scattering analysis empowers us to reveal the nature of structural modulations, lattice distortion, and phonons and how quantitative electron diffraction can be used to map the distributions of the valence electrons that bond atoms together. We exploit transformative advances in imaging capabilities including the use of femtosecond laser and ultrafast electron diffraction to probe electron-lattice interactions and photoinduced transitions beyond equilibrium of matter. We review our Lorentz phase microscopy studies to illustrate the intriguing transformations among various topological chiral spin states under applied magnetic field at various cryogenic temperatures. Finally, we show that atomically resolved imaging and electron energy-loss spectroscopy at 10 K can be used to understand interface-enhanced superconductivity. The wide range of research and progress on quantum materials at low temperature reported here may inspire and attract more researchers in this ever-expanding field of cryo-EM.

Refinements on electron diffraction data of β-glycine in MoPro: a quest for an improved structure model

The advancement in 3D electron diffraction (3D ED) techniques that lead to a revolution in molecular structure determination using nano-sized crystals is now achieving atomic resolution. The structures can be obtained from 3D ED data with tools similar to those used for X-ray structure determination. In this context, the MoPro software, originally designed for structure and charge density refinements using X-ray diffraction data, has been adapted. Structure refinement on 3D ED data was achieved via implementation of electron scattering factors available in the literature and by application of the Mott–Bethe equation to X-ray scattering factors computed from the multipolar atom model. The multipolar model was parametrized using the transferable pseudoatom databanks ELMAM2 and UBDB. Applying the independent atom model (IAM), i.e. spherical neutral atom refinement, to 3D ED data on β-glycine in MoPro resulted in structure and refinement statistics comparable to those obtained from other well known software. Use of the transferred aspherical atom model (TAAM) led to improvement of the refinement statistics and a better fit of the model to the 3D ED data as compared with the spherical atom refinement. The anisotropic displacement parameters of non-H atoms appear underestimated by typically 0.003 Å2 for the non-H atoms in IAM refinement compared with TAAM. Thus, MoPro is shown to be an effective tool for crystal structure refinement on 3D ED data and allows use of a spherical or a multipolar atom model. Electron density databases can be readily transferred with no further modification needed when the Mott–Bethe equation is applied.

Correlation analysis of materials properties by machine learning: illustrated with stacking fault energy from first-principles calculations in dilute fcc-based alloys

Advances in machine learning (ML), especially in the cooperation between ML predictions, density functional theory (DFT) based first-principles calculations, and experimental verification are emerging as a key part of a new paradigm to understand fundamentals, verify, analyze, and predict data, and design and discover materials. Taking stacking fault energy (γ_SFE) as an example, we perform a correlation analysis ofγ_SFEin dilute Al-, Ni-, and Pt-based alloys by descriptors and ML algorithms. Theseγ_SFEvalues were predicted by DFT-based alias shear deformation approach, and up to 49 elemental descriptors and 21 regression algorithms were examined. The present work indicates that (i) the variation ofγ_SFEaffected by alloying elements can be quantified through 14 elemental attributes based on their statistical significances to decrease the mean absolute error (MAE) in ML predictions, and in particular, the number of p valence electrons, a descriptor second only to the covalent radius in importance to model performance, is unexpected; (ii) the alloys with elements close to Ni and Co in the periodic table possess higherγ_SFEvalues; (iii) the top four outliers of DFT predictions ofγ_SFEare for the alloys of Al₂₃La, Pt₂₃Au, Ni₂₃Co, and Al₂₃Be based on the analyses of statistical differences between DFT and ML predictions; and (iv) the best ML model to predictγ_SFEis produced by Gaussian process regression with an average MAE < 8 mJ m^-2. Beyond detailed analysis of the Al-, Ni-, and Pt-based alloys, we also predict theγ_SFEvalues using the present ML models in other fcc-based dilute alloys (i.e., Cu, Ag, Au, Rh, Pd, and Ir) with the expected MAE < 17 mJ m^-2and observe similar effects of alloying elements onγ_SFEas those in Pt₂₃X or Ni₂₃X.

Improvement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditions

A local structure analysis method based on convergent-beam electron diffraction (CBED) has been used for refining isotropic atomic displacement parameters and five low-order structure factors with sin θ/λ ≤ 0.28 Å^-1 of potassium tantalate (KTaO₃). Comparison between structure factors determined from CBED patterns taken at the zone-axis (ZA) and Bragg-excited conditions is made in order to discuss their precision and sensitivities. Bragg-excited CBED patterns showed higher precision in the refinement of structure factors than ZA patterns. Consistency between higher precision and sensitivity of the Bragg-excited CBED patterns has been found only for structure factors of the outer zeroth-order Laue-zone reflections with larger reciprocal-lattice vectors. Correlation coefficients among the refined structure factors in the refinement of Bragg-excited patterns are smaller than those of the ZA ones. Such smaller correlation coefficients lead to higher precision in the refinement of structure factors.

A new electron diffraction approach for structure refinement applied to Ca3Mn2O7

The digital large-angle convergent-beam electron diffraction (D-LACBED) technique is applied to Ca3Mn2O7 for a range of temperatures. Bloch-wave simulations are used to examine the effects that changes in different parameters have on the intensity in D-LACBED patterns, and atomic coordinates, thermal atomic displacement parameters and apparent occupancy are refined to achieve a good fit between simulation and experiment. The sensitivity of the technique to subtle changes in structure is demonstrated. Refined structures are in good agreement with previous determinations of Ca3Mn2O7 and show the decay of anti-phase oxygen octahedral tilts perpendicular to the c axis of the A21am unit cell with increasing temperature, as well as the robustness of oxygen octahedral tilts about the c axis up to ∼400°C. The technique samples only the zero-order Laue zone and is therefore insensitive to atom displacements along the electron-beam direction. For this reason it is not possible to distinguish between in-phase and anti-phase oxygen octahedral tilting about the c axis using the [110] data collected in this study.

Measuring Density Functional Parameters from Electron Diffraction Patterns

We integrate density functional theory (DFT) into quantitative convergent-beam electron diffraction (QCBED) to create a synergy between experiment and theory called QCBED-DFT. This synergy resides entirely in the electron density which, in real materials, gives rise to the experimental CBED patterns used by QCBED-DFT to refine DFT model parameters. We use it to measure the Hubbard energy U for two strongly correlated electron systems, NiO and CeB_{6} (U=7.4±0.6  eV for d orbitals in NiO and U=3.0±0.6  eV for f orbitals in CeB_{6}), and the boron position parameter x for CeB_{6} (x=0.1992±0.0003). In verifying our measurements, we demonstrate an accuracy test for any modeled electron density.

ab initio description of bonding for transmission electron microscopy

The simulation of transmission electron microscopy (TEM) images or diffraction patterns is often required to interpret their contrast and extract specimen features. This is especially true for high-resolution phase-contrast imaging of materials, but electron scattering simulations based on atomistic models are widely used in materials science and structural biology. Since electron scattering is dominated by the nuclear cores, the scattering potential is typically described by the widely applied independent atom model. This approximation is fast and fairly accurate, especially for scanning TEM (STEM) annular dark-field contrast, but it completely neglects valence bonding and its effect on the transmitting electrons. However, an emerging trend in electron microscopy is to use new instrumentation and methods to extract the maximum amount of information from each electron. This is evident in the increasing popularity of techniques such as 4D-STEM combined with ptychography in materials science, and cryogenic microcrystal electron diffraction in structural biology, where subtle differences in the scattering potential may be both measurable and contain additional insights. Thus, there is increasing interest in electron scattering simulations based on electrostatic potentials obtained from first principles, mainly via density functional theory, which was previously mainly required for holography. In this Review, we discuss the motivation and basis for these developments, survey the pioneering work that has been published thus far, and give our outlook for the future. We argue that a physically better justified ab initio description of the scattering potential is both useful and viable for an increasing number of systems, and we expect such simulations to steadily gain in popularity and importance.

Evaluation of accuracy in the determination of crystal structure factors using large-angle convergent-beam electron diffraction patterns

The accuracy of electron density distribution analysis using large-angle convergent-beam electron diffraction (LACBED) patterns is evaluated for different convergence angles. An orbital ordered state of FeCr2O4 is used as an example of the analysis. Ideal orbital-ordered and non-ordered states are simulated by using orbital scattering factors. LACBED patterns calculated for the orbital-ordered state were used as hypothetical experimental data sets. Electron density distribution of the Fe 3d orbitals has been successfully reconstructed with a higher accuracy from LACBED patterns with convergence angles larger than 15.2 mrad, which is 4 times as large as that for conventional convergent-beam electron diffraction patterns. Excitation of particular Bloch waves with the aid of LACBED patterns has a key role in the accurate analysis of electron density distributions.

Characterizing local metallic bonding variation induced by external perturbation

The subtle variation of metallic bonding, induced by external influence, plays an essential role in determining physical, mechanical, and chemical properties of metals. However, it is extremely difficult to describe this variation because of the delocalization nature of metallic bonding. Here, we utilize the reduced density gradient and topological analysis of electron density to capture the local metallic bonding variations (LMBV) caused by lattice distortion and carrier injection in many face-centered cubic (fcc) metals. We find that the LMBV determines the traits of fcc metals such as strength, malleability, and ductility. Moreover, the fcc metals can become more flexible/stronger with the electron/hole injection, providing an important guidance to tune metals for desired mechanical properties.

The Aluminum-Ion Battery: A Sustainable and Seminal Concept?

The expansion of renewable energy and the growing number of electric vehicles and mobile devices are demanding improved and low-cost electrochemical energy storage. In order to meet the future needs for energy storage, novel material systems with high energy densities, readily available raw materials, and safety are required. Currently, lithium and lead mainly dominate the battery market, but apart from cobalt and phosphorous, lithium may show substantial supply challenges prospectively, as well. Therefore, the search for new chemistries will become increasingly important in the future, to diversify battery technologies. But which materials seem promising? Using a selection algorithm for the evaluation of suitable materials, the concept of a rechargeable, high-valent all-solid-state aluminum-ion battery appears promising, in which metallic aluminum is used as the negative electrode. On the one hand, this offers the advantage of a volumetric capacity four times higher (theoretically) compared to lithium analog. On the other hand, aluminum is the most abundant metal in the earth's crust. There is a mature industry and recycling infrastructure, making aluminum very cost efficient. This would make the aluminum-ion battery an important contribution to the energy transition process, which has already started globally. So far, it has not been possible to exploit this technological potential, as suitable positive electrodes and electrolyte materials are still lacking. The discovery of inorganic materials with high aluminum-ion mobility—usable as solid electrolytes or intercalation electrodes—is an innovative and required leap forward in the field of rechargeable high-valent ion batteries. In this review article, the constraints for a sustainable and seminal battery chemistry are described, and we present an assessment of the chemical elements in terms of negative electrodes, comprehensively motivate utilizing aluminum, categorize the aluminum battery field, critically review the existing positive electrodes and solid electrolytes, present a promising path for the accelerated development of novel materials and address problems of scientific communication in this field.

Structure Retrieval at Atomic Resolution in the Presence of Multiple Scattering of the Electron Probe

The projected electrostatic potential of a thick crystal is reconstructed at atomic resolution from experimental scanning transmission electron microscopy data recorded using a new generation fast-readout electron camera. This practical and deterministic inversion of the equations encapsulating multiple scattering that were written down by Bethe in 1928 removes the restriction of established methods to ultrathin (≲50  Å) samples. Instruments already coming on line can overcome the remaining resolution-limiting effects in this method due to finite probe-forming aperture size, spatial incoherence, and residual lens aberrations.

Structure refinement from 'digital' large angle convergent beam electron diffraction patterns

We use semi-automated data acquisition and processing to produce digital large angle CBED (D-LACBED) patterns. We demonstrate refinements of atomic coordinates and isotropic Debye-Waller factors for well-known materials using simulations produced with a neutral, spherical independent atom model. We find that atomic coordinate refinements in Al₂O₃ have sub-pm precision and accuracy. Isotropic DWFs are accurate for Cu, a simple fcc metal, but do not agree with X-ray measurements of GaAs or Al₂O₃. This lack of agreement is probably caused by bonding and change transfer between atoms. While it has long been appreciated that CBED is sensitive to bonding, examination of D-LACBED data shows that some regions exhibit large changes in diffracted intensity from small changes in the periodic crystal potential. Models of bonding will be essential to fully interpret D-LACBED data.

Circumventing silver oxidation induced performance degradation of silver surface-enhanced Raman scattering substrates

Surface-enhanced Raman scattering (SERS) has been recognized as a promising sensing technique in biomedical/biosensing applications and analytical chemistry. Silver (Ag) nanostructures have the strongest SERS enhancement, but suffer from severe enhancement degradation induced by oxidation. Here, we introduce electrochemical reduction of silver oxide to produce Ag SERS substrates on request to partially circumvent the SERS enhancement degradation problem of Ag SERS substrates. Silver oxide nanostructures were first prepared in pure silver citrate aqueous solutions with controllable morphologies depending on the electrodeposition parameters. The transition process from silver oxide to Ag was investigated by density functional theory calculations. Based on the understanding of the transition mechanism, heating treatment, applying reducing agent, and electrochemical reduction were adopted to transform silver oxide to Ag. Notably, no organic agents were introduced neither in the electrodeposition of silver oxide nor electrochemical transformation of silver oxide to Ag. The electrochemical reduction strategy could produce Ag SERS substrates with a 'clean' surface with outstanding SERS performance in a simple as well as cost and time effective manner. Ag SERS substrates can be used in biomedical/biosensing fields. The approach through electrochemical reduction of silver oxide to generate Ag SERS substrate may push forward practical application process of Ag SERS substrates.

Tightly binding valence electron in aluminum observed through X-ray charge density study

Accurate and high reciprocal resolution experimental structure factors of aluminum were determined from a synchrotron powder X-ray diffraction data measured at 30 K with sin θ/λ < 2.31 Å⁻¹. The structure factors have small deviations from independent atom model in sin θ/λ < 0.83 Å⁻¹. Theoretical structure factors were prepared using density functional theoretical calculations by full potential linearized augmented plane wave method. The deviation between experimental and theoretical data was also observed at around sin θ/λ ≈ 0.4 Å⁻¹. The charge density was determined by an extended Hansen-Coppens multipole modeling using experimental and theoretical structure factors. Charge density maxima at tetrahedral site were observed in both experimental and theoretical deformation density. The charge-density difference peaks indicating directional bonding formation were observed in the difference density between experiment and theory. The present study reveals tight binding like character of valence electron of aluminum. The fact will provide a crucial information for development of high-performance aluminum alloy.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

New Deformation-Induced Nanostructure in Silicon

Nanostructures in silicon (Si) induced by phase transformations have been investigated during the past 50 years. Performances of nanostructures are improved compared to that of bulk counterparts. Nevertheless, the confinement and loading conditions are insufficient to machine and fabricate high-performance devices. As a consequence, nanostructures fabricated by nanoscale deformation at loading speeds of m/s have not been demonstrated yet. In this study, grinding or scratching at a speed of 40.2 m/s was performed on a custom-made setup by an especially designed diamond tip (calculated stress under the diamond tip in the order of 5.11 GPa). This leads to a novel approach for the fabrication of nanostructures by nanoscale deformation at loading speeds of m/s. A new deformation-induced nanostructure was observed by transmission electron microscopy (TEM), consisting of an amorphous phase, a new tetragonal phase, slip bands, twinning superlattices, and a single crystal. The formation mechanism of the new phase was elucidated by ab initio simulations at shear stress of about 2.16 GPa. This approach opens a new route for the fabrication of nanostructures by nanoscale deformation at speeds of m/s. Our findings provide new insights for potential applications in transistors, integrated circuits, diodes, solar cells, and energy storage systems.

Hydrogen positions in single nanocrystals revealed by electron diffraction

The localization of hydrogen atoms is an essential part of crystal structure analysis, but it is difficult because of their small scattering power. We report the direct localization of hydrogen atoms in nanocrystalline materials, achieved using the recently developed approach of dynamical refinement of precession electron diffraction tomography data. We used this method to locate hydrogen atoms in both an organic (paracetamol) and an inorganic (framework cobalt aluminophosphate) material. The results demonstrate that the technique can reliably reveal fine structural details, including the positions of hydrogen atoms in single crystals with micro- to nanosized dimensions.

Quantum crystallography

Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated tool. The development of quantum crystallographic research is reviewed. Some results obtained by quantum crystallography illustrate the potential and limitations of this field.

Real-space mapping of electronic orbitals

Electronic states are responsible for most material properties, including chemical bonds, electrical and thermal conductivity, as well as optical and magnetic properties. Experimentally, however, they remain mostly elusive. Here, we report the real-space mapping of selected transitions between p and d states on the Ångström scale in bulk rutile (TiO2) using electron energy-loss spectrometry (EELS), revealing information on individual bonds between atoms. On the one hand, this enables the experimental verification of theoretical predictions about electronic states. On the other hand, it paves the way for directly investigating electronic states under conditions that are at the limit of the current capabilities of numerical simulations such as, e.g., the electronic states at defects, interfaces, and quantum dots.

How do specimen preparation and crystal perfection affect structure factor measurements by quantitative convergent-beam electron diffraction?

The effectiveness of tripod polishing and crushing as methods of mechanically preparing transmission electron microscopy specimens of hard brittle inorganic crystalline materials is investigated via the example of cerium hexaboride (CeB6). It is shown that tripod polishing produces very large electron-transparent regions of very high crystal perfection compared to the more rapid technique of crushing, which produces crystallites with a high density of imperfections and significant mosaicity in the case studied here where the main crystallite facets are not along the natural {001} cleavage planes of CeB6. The role of specimen quality in limiting the accuracy of structure factor measurements by quantitative convergent-beam electron diffraction (QCBED) is investigated. It is found that the bonding component of structure factors refined from CBED patterns obtained from crushed and tripod-polished specimens varies very significantly. It is shown that tripod-polished specimens yield CBED patterns of much greater integrity than crushed specimens and that the mismatch error that remains in QCBED pattern matching of data from tripod-polished specimens is essentially nonsystematic in nature. This stands in contrast to QCBED using crushed specimens and lends much greater confidence to the accuracy and precision of bonding measurements by QCBED from tripod-polished specimens.

Discovering a First-Order Phase Transition in the Li-CeO2 System

An in-depth understanding of (de)lithiation induced phase transition in electrode materials is crucial to grasp their structure-property relationships and provide guidance to the design of more desirable electrodes. By operando synchrotron XRD (SXRD) measurement and Density Functional Theory (DFT) based calculations, we discover a reversible first-order phase transition for the first time during (de)lithiation of CeO₂ nanoparticles. The Li_xCeO₂ compound phase is identified to possess the same fluorite crystal structure with FM3M space group as that of the pristine CeO₂ nanoparticles. The SXRD determined lattice constant of the Li_xCeO₂ compound phase is 0.551 nm, larger than that of 0.541 nm of the pristine CeO₂ phase. The DFT calculations further reveal that the Li induced redistribution of electrons causes the increase in the Ce-O covalent bonding, the shuffling of Ce and O atoms, and the jump expansion of lattice constant, thereby resulting in the first-order phase transition. Discovering the new phase transition throws light upon the reaction between lithium and CeO₂, and provides opportunities to the further investigation of properties and potential applications of Li_xCeO₂.

Prediction of Diffusion Coefficients in Liquid and Solids

Our activities in predicting diffusion coefficients in fcc, bcc, and hcp solid solutions using first-principles calculations and in liquid usingabinitiomolecular dynamics are reviewed. These include self-diffusion coefficients [1-4], tracer diffusion coefficients in dilute solutions [5-7], calculation of migration entropy [8], tracer diffusion coefficients in metallic and oxide liquid [9, 10], and effects of vacancy on diffusion of oxygen [11, 12]. The effects of exchange correlation functionals are examined in some cases along with charge transfer between solute and solvent elements. The dominant contribution of diffusion on the effects of Re addition on the creep properties of Ni-base superalloys is discussed [13].

Comparison of convergent beam electron diffraction methods for simultaneous structure and Debye Waller factor determination

The measurement of accurate and precise structure factors and Debye Waller (DW) factors by quantitative convergent beam electron diffraction (QCBED) permits experimental determination of the electron density distribution and probing of interatomic bonding in crystals. The three QCBED methods used successfully for high precision measurements of low order structure factors to date, namely the zone axis pattern (ZAP) method, the excited row ER method and the multi-beam off-zone axis (MBOZA) technique, differ from each other regarding the crystal orientation relative to the incident electron beam. Consequently, the details of their respective dispersion surface representations differ regarding the number, relative amplitudes and phases of excited Bloch wave branches. Under the same experimental setup conditions, the factors most important to the degree of accuracy and precision achievable in electron density determination for crystals with QCBED methods ultimately depend on the sensitivity of the excited Bloch wave branches and the resultant contrast in the respective CBED patterns to changes in both structure and DW factors. In general, a QCBED pattern will be more sensitive to changes in both structure and DW factor, if it contains more and stronger excited Bloch wave branches, as dynamic interactions of the Bloch waves increase the sensitivity of the pattern. In this work we analyzed Bloch wave excitation and dispersion surfaces for the three most popular QCBED methods. The analysis indicates, that the QCBED patterns obtained using the MBOZA orientation generally contain more and stronger excited Bloch wave branches. Hence, MBOZA diffraction patterns are more sensitive than the ZAP and the ER patterns to changes in both DW and structure factors and therefore allow in differences to the other two methods simultaneous refinements effectively and robustly.

Effects of alloying element and temperature on the stacking fault energies of dilute Ni-base superalloys

A systematic study of stacking fault energy (γ(SF)) resulting from induced alias shear deformation has been performed by means of first-principles calculations for dilute Ni-base superalloys (Ni(23)X and Ni(71)X) for various alloying elements (X) as a function of temperature. Twenty-six alloying elements are considered, i.e., Al, Co, Cr, Cu, Fe, Hf, Ir, Mn, Mo, Nb, Os, Pd, Pt, Re, Rh, Ru, Sc, Si, Ta, Tc, Ti, V, W, Y, Zn, and Zr. The temperature dependence of γ(SF) is computed using the proposed quasistatic approach based on a predicted γ(SF)-volume-temperature relationship. Besides γ(SF), equilibrium volume and the normalized stacking fault energy (Γ(SF) = γ(SF)/Gb, with G the shear modulus and b the Burgers vector) are also studied as a function of temperature for the 26 alloying elements. The following conclusions are obtained: all alloying elements X studied herein decrease the γ(SF) of fcc Ni, approximately the further the alloying element X is from Ni on the periodic table, the larger the decrease of γ(SF) for the dilute Ni-X alloy, and roughly the γ(SF) of Ni-X decreases with increasing equilibrium volume. In addition, the values of γ(SF) for all Ni-X systems decrease with increasing temperature (except for Ni-Cr at higher Cr content), and the largest decrease is observed for pure Ni. Similar to the case of the shear modulus, the variation of γ(SF) for Ni-X systems due to various alloying elements is traceable from the distribution of (magnetization) charge density: the spherical distribution of charge density around a Ni atom, especially a smaller sphere, results in a lower value of γ(SF) due to the facility of redistribution of charges. Computed stacking fault energies and the related properties are in favorable accord with available experimental and theoretical data.

Extra-electron induced covalent strengthening and generalization of intrinsic ductile-to-brittle criterion

Traditional strengthening ways, such as strain, precipitation, and solid-solution, come into effect by pinning the motion of dislocation. Here, through first-principles calculations we report on an extra-electron induced covalent strengthening mechanism, which alters chemical bonding upon the introduction of extra-valence electrons in the matrix of parent materials. It is responsible for the brittle and high-strength properties of Al(12)W-type compounds featured by the typical fivefold icosahedral cages, which are common for quasicrystals and bulk metallic glasses (BMGs). In combination with this mechanism, we generalize ductile-to-brittle criterion in a universal hyperbolic form by integrating the classical Pettifor's Cauchy pressure with Pugh's modulus ratio for a wide variety of materials with cubic lattices. This study provides compelling evidence to correlate Pugh's modulus ratio with hardness of materials and may have implication for understanding the intrinsic brittleness of quasicrystals and BMGs.

On the charge transfer between conventional cations: the structures of ternary oxides and chalcogenides of alkali metals

The structures of ternary oxides and chalcogenides of alkali metals are dissected in light of the extended Zintl-Klemm concept. This model, which has been successfully extended to other compounds different to the Zintl phases, assumes that crystal structures can be better understood if the cation substructures are contemplated as Zintl polyanions. This implies the occurrence of charge transfer between cations, even if they are of the same kind. In this article, the charge transfer between cations is even more illustrative because the two alkali atoms have different electronegativity, so that the less electropositive alkali metal and the O/S atom always form skeletons characteristic of the group 14 elements. Thus, partial structures of the zincblende-, wurtzite-, PbO- and SrAl(2)-type are found in the oxides/sulfides. In this work, such an interpretation of the structures remains at a topological level. The analysis also shows that this interpretation is complementary to the model developed by Andersson and Hyde which contemplates the structures as the intergrowth of structural slabs of more simple compounds.

In situ quantification of noise as a function of signal in digital images

An efficient and accurate algorithm for determining the magnitude of noise as a function of signal in an arbitrary digital image is presented and demonstrated. The algorithm is robust and largely independent of the form of the image, returning the noise function with subcount error across the full dynamic range of a synthetic test image where noise of a known form has been added. The noise performance of a CCD under different image recording and processing conditions is examined using the algorithm. The effect of different noise functions on pattern-matching measurements of electronic structure by quantitative convergent beam electron diffraction is investigated.