Atomic Displacements Research Articles

The importance of definitions in crystallography.

This paper was motivated by the articles `Same or different - that is the question' in CrystEngComm (July 2020) and `Change to the definition of a crystal' in the IUCr Newsletter (June 2021). Experimental approaches to crystal comparisons require rigorously defined classifications in crystallography and beyond. Since crystal structures are determined in a rigid form, their strongest equivalence in practice is rigid motion, which is a composition of translations and rotations in 3D space. Conventional representations based on reduced cells and standardizations theoretically distinguish all periodic crystals. However, all cell-based representations are inherently discontinuous under almost any atomic displacement that can arbitrarily scale up a reduced cell. Hence, comparison of millions of known structures in materials databases requires continuous distance metrics.

Synthesis and in-depth structure determination of a novel metastable high-pressure CrTe3 phase

This study reports the synthesis and crystal structure determination of a novel CrTe3 phase using various experimental and theoretical methods. The average stoichiometry and local phase separation of this quenched high-pressure phase were characterized by ex situ synchrotron powder X-ray diffraction and total scattering. Several structural models were obtained using simulated annealing, but all suffered from an imperfect Rietveld refinement, especially at higher diffraction angles. Finally, a novel stoichiometrically correct crystal structure model was proposed on the basis of electron diffraction data and refined against powder diffraction data using the Rietveld method. Scanning electron microscopy–energy-dispersive X-ray spectrometry (EDX) measurements verified the targeted 1:3 (Cr:Te) average stoichiometry for the starting compound and for the quenched high-pressure phase within experimental errors. Scanning transmission electron microscopy (STEM)–EDX was used to examine minute variations of the Cr-to-Te ratio at the nanoscale. Precession electron diffraction (PED) experiments were applied for the nanoscale structure analysis of the quenched high-pressure phase. The proposed monoclinic model from PED experiments provided an improved fit to the X-ray patterns, especially after introducing atomic anisotropic displacement parameters and partial occupancy of Cr atoms. Atomic resolution STEM and simulations were conducted to identify variations in the Cr-atom site-occupancy factor. No significant variations were observed experimentally for several zone axes. The magnetic properties of the novel CrTe3 phase were investigated through temperature- and field-dependent magnetization measurements. In order to understand these properties, auxiliary theoretical investigations have been performed by first-principles electronic structure calculations and Monte Carlo simulations. The obtained results allow the observed magnetization behavior to be interpreted as the consequence of competition between the applied magnetic field and the Cr–Cr exchange interactions, leading to a decrease of the magnetization towards T = 0 K typical for antiferromagnetic systems, as well as a field-induced enhanced magnetization around the critical temperature due to the high magnetic susceptibility in this region.

Theuerdankite, Ag3AsO4, a new mineral from the Alter Theuerdank Mine, St. Andreasberg, Germany

Abstract The new mineral theuerdankite, ideally Ag3AsO4, was found in the Alter Theuerdank Mine, Beerberg, St. Andreasberg, Goslar District, Lower Saxony, Germany. Theuerdankite occurs as aggregates of anhedral grains up to 3 mm in size, growing in cavities of strongly supergene-weathered material consisting of native silver and chlorargyrite (but with calcite present). It is dark violet, changing to reddish and black when exposed to the air and light. It has a grey to violet grey streak; when readily fresh, its streak is brownish-red. The Mohs hardness is ~2. It is brittle with no observable cleavage or parting and with a conchoidal fracture. The calculated density is 6.620 g⋅cm–3. In reflected light, theuerdankite is dark grey with a pinkish tint, with no observable bireflectance, pleochroism, or anisotropy. It shows dark red internal reflections. The reflectance values for wavelengths recommended by the Commission on Ore Mineralogy of the International Mineralogical Association are (R, %): 13.3 (470 nm), 12.8 (546 nm), 12.7 (589 nm) and 12.5 (650 nm). The empirical formula (based on 4 apfu) is Ag3.00As1.00O4. Theuerdankite is cubic, space group P $\bar{4}$ 3n, a = 6.144(2) Å, V = 231.93(13) Å3 and Z = 2. The six strongest powder X-ray diffraction lines are [dobs in Å, (I) hkl]: 3.0736, (22) 200; 2.7502, (100) 210; 2.5106, (55) 211; 1.7050, (36) 320; 1.6249, (44) 321; and 1.3412, (17) 421. The crystal structure of theuerdankite (R1 = 1.69% for 519 reflections having I > 3σ(I)), is isotypic to those of synthetic Ag3AsO4 and Ag3PO4. The Gram–Charlier development describing the higher-order tensors representing the atomic displacement parameters of the silver atom was implemented, documenting that silver tends to behave anharmonically in the theuerdankite structure at room temperature.

Temperature dependence of tribological properties in NiTi shape memory alloy: A nanoscratching study

The molecular dynamics method was used to simulate nanoscratching of a monocrystalline NiTi shape memory alloy (SMA) under various temperatures. Parameters, including the normal force, tangential force, friction coefficient, contact area, scratching hardness, atomic displacement, atomic structure, and surface morphology, were comprehensively studied to understand the friction mechanism of the NiTi SMA during operation. It was verified that the temperature dependence of the tribological properties of the NiTi SMA is mainly attributed to the temperature dependence of the tangential force.The beginning temperature of the reverse martensitic transition (As) is the critical temperature for the transition of tribological properties. Below this temperature, the sliding contact region exhibits good normal/tangential projection symmetry, with the atoms on the contact surface arranged in order. A wide range of martensitic strain coordination occurs in the contact region, leading to a low friction coefficient and minimal wear. When the temperature exceeds this threshold, the asymmetry of the contact surface projection gradually increases. The atoms on the contact surface exhibit amorphous atomic characteristics, causing the influence domain of martensitic transformation of scratches to gradually decrease and the friction coefficient to increase. This study offers insights into the atomic-scale perspective for analyzing the temperature-dependent friction behavior of NiTi SMA induced by phase transition.

Unraveling the dynamic slowdown in supercooled water: The role of dynamic disorder in jump motions.

When a liquid is rapidly cooled below its melting point without inducing crystallization, its dynamics slow down significantly without noticeable structural changes. Elucidating the origin of this slowdown has been a long-standing challenge. Here, we report a theoretical investigation into the mechanism of the dynamic slowdown in supercooled water, a ubiquitous yet extraordinary substance characterized by various anomalous properties arising from local density fluctuations. Using molecular dynamics simulations, we found that the jump dynamics, which are elementary structural change processes, deviate from Poisson statistics with decreasing temperature. This deviation is attributed to slow variables competing with the jump motions, i.e., dynamic disorder. The present analysis of the dynamic disorder showed that the primary slow variable is the displacement of the fourth nearest oxygen atom of a jumping molecule, which occurs in an environment created by the fluctuations of molecules outside the first hydration shell. As the temperature decreases, the jump dynamics become slow and intermittent. These intermittent dynamics are attributed to the prolonged trapping of jumping molecules within extended and stable low-density domains. As the temperature continues to decrease, the number of slow variables increases due to the increased cooperative motions. Consequently, the jump dynamics proceed in a higher-dimensional space consisting of multiple slow variables, becoming slower and more intermittent. It is then conceivable that with further decreasing temperature, the slowing and intermittency of the jump dynamics intensify, eventually culminating in a glass transition.

Single-Atom Substituents in Copper Surfaces May Adsorb Multiple CO Molecules.

Copper is a good CO2 electroreduction catalyst as products beyond CO form, but efficiency and selectivity is low. Experiments have shown that an admixture of other elements can help, and computational screening studies have pointed out various promising candidates based on the adsorption of a single CO molecule as a descriptor. Our calculations of CO adsorption on surfaces where a first row transition metal atom replaces a Cu atom show that multiple CO molecules, not just one, bind to the substitutional atom. For Fe, Co, and Ni atoms, a decrease in binding energy is found, but the reverse trend, namely, increasing bond strength, is found for V, Cr, and Mn and the first three CO molecules. Magnetic moment, charge, and position of the substitutional atom are also strongly affected by the CO adsorption in most cases. Magnetic moment is stepwise reduced to zero, and the outward displacement of the substitutional atom increased.

Measurement of atomic dispersion on buried Ag nanoparticles decomposed by Ne[formula omitted] ion irradiation

The effects of room temperature 200keV Ne+ ion irradiation on Ag nanoparticles (NPs) embedded in a silicon nitride film have been studied via Medium Energy Ion Scattering (MEIS), Scanning Transmission Electron Microscopy (STEM), and the results are discussed in comparison with Monte Carlo TRI3DYN simulations. The experiment was designed to test the mechanisms controlling the room temperature irradiation-induced microstructure evolution of individual NPs and the overall system. We present an innovative MEIS approach capable of quantitatively determining Ag’s content and spatial distribution in solution. The STEM observations demonstrate the nucleation of smaller Ag NPs distributed within the solute field. The TRI3DYN simulations suggest that a fraction of the solute content is reincorporated within the NPs. These results are discussed considering that room-temperature thermal diffusion processes are significantly retarded in silicon nitride substrates, which leads to an interpretation primarily based on the irradiation-induced atomic displacements that render a microstructure evolution driven by the minimization of chemical potential as an elemental thermodynamic force. Our findings are of applied interest concerning the application of ion beams to manipulate NP ensembles.

Van der Waals Engineering of Charge Density Waves in One-Dimensional Nb6Te6 Nanowires.

One-dimensional (1D) systems have played a crucial role in the development of fundamental physics and practical applications. Recently, transition metal monochalcogenide (TMM) wires based on molybdenum (Mo) and tungsten (W) have emerged as promising platforms for investigating 1D physics in pure van der Waals (vdW) platforms. Here, we report on the bottom-up fabrication of Nb6Te6 wires down to the single-wire limit. The unique properties of Nb6Te6 single wire enable the realization of 1D charge density wave (CDW) phases in an isolated single TMM wire. Moreover, we revealed the appealing regulation of 1D CDW orders by van der Waals interactions at either the 1D-2D interface (i.e., rotation of a single wire along its wire axis) or the 1D-1D interface. Two rotation angles (30° and 0°) give rise to 3 × 1 and zigzag chain CDW morphologies, respectively, which exhibit pronounced differences in atomic displacement by a factor of 2. The interwire vdW coupling overwhelms its counterpart at the 1D-2D interface, thus locking the rotation angle (at 0°) as well as the interwire atomic registries. In contrast, interestingly, the phases of the charge oscillations are independent of the adjacent wires. The ability to tailor 1D charge orders provides a crucial addition to the toll set of vdW integrations beyond two-dimensional materials.

Detection of dislocation motion in atomistic simulations of nanocrystalline materials

A method for identifying dislocation motion in atomistic simulations is presented. While identifying static and moving dislocations within a single crystal or a combination of such is well established, the method described here is tailored to identify dislocation motion by correlating the displacements of individual atoms. This facilitates the identification of dislocation motion in complex structural arrangements, and allows the specific contribution to plastic deformation, due to dislocation motion, to be separated from that of other mechanisms. The method is applied to test cases in crystals and grain boundaries (GBs), in which irradiation-induced creep (IIC) was induced. It is shown that the method singles out the moving dislocations from among the dislocation forest at GBs, thus identifying the specific reactions driving the distortion at any given time. This enables the study of dislocation processes in the presence of realistic obstacles, and the study of the effects of microstructure on dislocation mobility. As an example of such a study, the method is applied to rule out intragranular slip, and to estimate the contribution of dislocation motion to strain, in a NC undergoing IIC.

Atomistic-level analysis of nanoindentation-induced plasticity in arc-melted NiFeCrCo alloys: The role of stacking faults

Concentrated solid solution alloys (CSAs) have attracted attention for their promising properties; however, current manufacturing methods face challenges in complexity, high costs, and limited scalability, raising concerns about industrial viability. The prevalent technique, arc melting, yields high-purity samples with complex shapes. In this study, we explore nanoindentation tests at room temperature where arc-melted samples exhibit larger grain sizes, diminishing the effects of grain boundaries on the results. Motivated by these findings, our investigation focuses on the atomistic-level exploration of plasticity mechanisms, specifically dislocation nucleation and propagation during nanoindentation tests. The intricate chemistry of NiFeCrCo CSA influences pile-ups and slip traces, aiming to elucidate plastic deformation by considering both pristine and pre-existing stacking fault tetrahedra. Our analysis scrutinizes dynamic deformation processes, defect nucleation, and evolution, complemented by stress–strain and dislocation densities–strain curves illustrating the hardening mechanism of defective materials. Additionally, we examine surface morphology and plastic deformation through atomic shear strain and displacement mappings. This integrated approach provides insights into the complex interplay between the material structure and mechanical behavior, paving the way for an enhanced understanding and potential advancements in CSA applications.

B-Factor Rescaling for Protein Crystal Structure Analyses

The B-factor, also known as the atomic displacement parameter, is a fundamental metric in crystallography for quantifying the positional flexibility of atoms within crystal lattices. In structural biology, various developments have expanded the use of B-factors beyond conventional crystallographic analysis, allowing for a deeper understanding of protein flexibility, enzyme manipulation, and an improved understanding of molecular dynamics. However, the interpretation of B-factors is complicated by their sensitivity to various experimental and computational factors, necessitating rigorous rescaling methods to ensure meaningful comparisons across different structures. This article provides an in-depth description of rescaling approaches used for B-factors. It includes an examination of several methods for managing conformational disorder and selecting the atom types required for the analysis.

Bayesian inference of atomic column positions in scanning transmission electron microscopy images

Abstract Atomic-resolution scanning transmission electron microscopy combined with 2D Gaussian fitting enables the accurate and precise identification of atomic column positions within a few picometers. The measurement performance significantly depends on the signal-to-noise ratio of the atomic columns. In areas with low signal-to-noise ratios, such as near surfaces, the measurement performance was lower than that of the bulk. However, previous studies evaluated the accuracy and precision only in bulk areas, underscoring the need for a method that quantitatively evaluates the accuracy and precision of each atomic column position with various signal-to-noise ratios. This study introduced Bayesian inference to assess the accuracy and precision of determining individual atomic column positions under various signals. We applied this method to simulated and experimental images and demonstrated its effectiveness in identifying statistically significant displacements, particularly near surfaces with signal degradation. The use of vector maps and kernel density estimate plots obtained from Bayesian inference provided a probabilistic understanding of the atom displacement. Therefore, this study highlighted the potential benefits of Bayesian inference in high-resolution imaging to reveal material properties.

The Formation and Transformation of Low-Dimensional Carbon Nanomaterials by Electron Irradiation.

Low-dimensional materials based on graphene or graphite show a large variety of phenomena when they are subjected to irradiation with energetic electrons. Since the 1990s, electron microscopy studies, where a certain irradiation dose is unavoidable, have witnessed unexpected structural transformations of graphitic nanoparticles. It is recognized that electron irradiation is not only detrimental but also bears considerable potential in the formation of new graphitic structures. With the availability of aberration-corrected electron microscopes and the discovery of techniques to produce monolayers of graphene, detailed insight into the atomic processes occurring during electron irradiation became possible. Threshold energies for atom displacements are determined and models of different types of lattice vacancies are confirmed experimentally. However, experimental evidence for the configuration of interstitial atoms in graphite or adatoms on graphene remained indirect, and the understanding of defect dynamics still depends on theoretical concepts. This article reviews irradiation phenomena in graphene- or graphite-based nanomaterials from the scale of single atoms to tens of nanometers. Observations from the 1990s can now be explained on the basis of new results. The evolution of the understanding during three decades of research is presented, and the remaining problems are pointed out.

Visualizing the Internal Nanocrystallinity of Calcite Due to Nonclassical Crystallization by 3D Coherent X-Ray Diffraction Imaging.

The internal crystallinity of calcite is investigated for samples synthesized using two approaches: precipitation from solution and the ammonium carbonate diffusion method. Scanning electron microscopy (SEM) analyses reveal that the calcite products precipitated using both approaches have a well-defined rhombohedron shape, consistent with the euhedral crystal habit of the mineral. The internal structure of these calcite crystals is characterized using Bragg coherent diffraction imaging (BCDI) to determine the 3D electron density and the atomic displacement field. BCDI reconstructions for crystals synthesized using the ammonium carbonate diffusion approach have the expected euhedral shape, with internal strain fields and few internal defects. In contrast, the crystals synthesized by precipitation from solution have very complex external shapes and defective internal structures, presenting null electron density regions and pronounced displacement field distributions. These heterogeneities are interpreted as multiple crystalline domains, created by a nonclassical crystallization mechanism, where smaller nanoparticles coalescence into the final euhedral particles. The combined use of SEM, X-ray diffraction (XRD), and BCDI allows for structurally differentiating calcite crystals grown with different approaches, opening new opportunities to understand how grain boundaries and internal defects alter calcite reactivity.

Unzipping hBN with ultrashort mid-infrared pulses.

Manipulating the nanostructure of materials is critical for numerous applications in electronics, magnetics, and photonics. However, conventional methods such as lithography and laser writing require cleanroom facilities or leave residue. We describe an approach to creating atomically sharp line defects in hexagonal boron nitride (hBN) at room temperature by direct optical phonon excitation with a mid-infrared pulsed laser from free space. We term this phenomenon "unzipping" to describe the rapid formation and growth of a crack tens of nanometers wide from a point within the laser-driven region. Formation of these features is attributed to the large atomic displacement and high local bond strain produced by strongly driving the crystal at a natural resonance. This process occurs only via coherent phonon excitation and is highly sensitive to the relative orientation of the crystal axes and the laser polarization. Its cleanliness, directionality, and sharpness enable applications such as polariton cavities, phonon-wave coupling, and in situ flake cleaving.

Pseudomagnetic fields in fully relaxed twisted bilayer and trilayer graphene

We present simple models to describe the in-plane and the out-of-plane lattice relaxation in twisted bilayer and symmetrically twisted trilayer graphene. Analytical results and series expansions show that for twist angles θ>1.4∘ , the in-plane atomic displacements lead to pseudomagnetic fields weakly dependent on θ. In symmetrically twisted trilayer graphene, the central layer in-plane relaxation is greatly enhanced. The joint effect of the relaxation-induced pseudoscalar potentials and the associated energy difference between interlayer dimer and non-dimer pairs resulted in a significant electron–hole asymmetry both in twisted bilayer and trilayer graphene.

Three-dimensional domain identification in a single hexagonal manganite nanocrystal

The three-dimensional domain structure of ferroelectric materials significantly influences their properties. The ferroelectric domain structure of improper multiferroics, such as YMnO3, is driven by a non-ferroelectric order parameter, leading to unique hexagonal vortex patterns and topologically protected domain walls. Characterizing the three-dimensional structure of these domains and domain walls has been elusive, however, due to a lack of suitable imaging techniques. Here, we present a multi-peak Bragg coherent x-ray diffraction imaging determination of the domain structure in single YMnO3 nanocrystals. We resolve two ferroelectric domains separated by a domain wall and confirm that the primary atomic displacements occur along the crystallographic c-axis. Correlation with atomistic simulations confirms the Mexican hat symmetry model of domain formation, identifying two domains with opposite ferroelectric polarization and adjacent trimerization, manifesting in a clockwise arrangement around the hat’s brim.

Effect of F− doping on structural, elastic, and electronic properties of SmO1−xFxBiS2: A first principles investigation

Structural, elastic, and electronic properties of SmO1−xFxBiS2 were studied using first principles method, and effects of F− doping were clearly observed. By increasing x, the increase of lattice parameter ‘a’ and decrease of ‘c’ are mainly due to the displacement of S1 and Sm atoms respectively. For x = 0.3, new (Bi–S1)2 bonds formation was observed. The gap between Bi- and S1-planes decreases and disappeared at x = 0.9. Cauchy pressures, B/G, and ν indicate ductile nature having metallic bonds with small ionic contribution. B, G, and E are highly anisotropic and show anomaly at x = 0.3, 0.5, and 0.8. Sm 4f states are mainly responsible for metallicity. For x = 0.3, total DOS decreases due to new bonds formation. Anomalous displacement of Sm-sites by doping at O- or Sm-sites induces anomalous displacement of S1 atoms which may be the main reason for change of different properties of SmO1-xFxBiS2.

Static and dynamic atom displacements in nanocrystalline powders from diffraction analysis at finite temperature

We evaluate the accuracy of x-ray diffraction analysis performed by Rietveld refinement in extracting the static and dynamic atomic displacement parameters of spherical gold nanocrystals with sizes of 30 nm and below and within a temperature interval of 10–300 K. A self-consistent computational workflow composed of real- and reciprocal- space analyses is designed for this purpose. We obtain average lattice parameters, static and thermal atomic displacements as well as their temperature and particle size dependence in an ideally monodispersed and realistic nanocrystalline powder generated by molecular dynamics simulations. Then, we compare crystallographic parameters obtained from real- and reciprocal- space analyses to evaluate the accuracy of diffraction analysis. We also extend the comparison to local variations of crystallographic parameters in the nanocrystals and show how Rietveld refinement relates to the average parameters of the core and surface regions separately. We show that 1) average lattice parameters obtained from Rietveld refinement are greater than the mean lattice parameter of small nanocrystals and converge to the core lattice parameter with increasing particle size, 2) Rietveld refinement significantly underestimates static atom displacements of surface atoms in small nanocrystals, 3) dynamic atomic displacements in nanocrystalline gold powders are reliably obtained within 5 % error by Rietveld refinement, provided that thermal diffuse scattering is adequately removed from the diffraction data, 4) the discrepancy between real- and reciprocal-space analysis increases for the smallest gold nanocrystal.

Study of the Surface-Layer Softening Effects in xLi2ZrO3–(1−x)Li4SiO4 Ceramics under Irradiation with He2+ Ions

The study investigates alterations in the mechanical and thermophysical properties of ceramics composed of xLi2ZrO3–(1−x)Li4SiO4 as radiation damage accumulates, mainly linked to helium agglomeration in the surface layer. This research is motivated by the potential to develop lithium-containing ceramics characterized by exceptional strength properties and a resistance to the accumulation of radiation damage and ensuing deformation distortions in the near-surface layer. The study of the radiation damage accumulation processes in the near-surface layer was conducted through intense irradiation of ceramics using He2+ ions at a temperature of 700 °C, simulating conditions closely resembling operation conditions. Following this, a correlation between the accumulation of structural modifications (value of atomic displacements) and variations in strength and thermophysical characteristics was established. During the research, it was observed that two-component ceramics exhibit significantly greater resistance to external influences and damage accumulation related to radiation exposure compared to their single-component counterparts. Furthermore, the composition that provides the highest resistance to softening in two-component ceramics is an equal ratio of the components of 0.5Li2ZrO3–0.5Li4SiO4 ceramics.