Simulated Diffraction Patterns Research Articles

On the role of the second-order derivative term in the calculation of convergent beam diffraction patterns

The simulation of (scanning) transmission electron microscopy images and diffraction patterns is most often performed using the forward-scattering approximation where the second-order derivative term in z is assumed to be small with respect to the first-order derivative term in the modified Schrödinger equation. This assumption is very good at high incident electron energies, but breaks down at low energies. In order to study the differences between first- and second-order methods, convergent beam electron diffraction patterns were simulated for silicon at the [111] zone-axis orientation at 20 keV and compared using electron intensity difference maps and integrated intensity profiles. The geometrical differences in the calculated diffraction patterns could be explained by an Ewald surface analysis. Furthermore, it was found that solutions based on the second-order derivative equation contained small amplitude oscillations that need to be resolved in order to ensure numerical integration stability. This required the use of very small integration steps resulting in significantly increased computation time compared to the first-order differential equation solution. Lastly, the efficiency of the numerical integration technique is discussed.

Semimetallic carbon allotrope with a topological nodal line in mixed sp2-sp3 bonding networks

Graphene is known as a two-dimensional Dirac semimetal, in which electron states are described by the Dirac equation of relativistic quantum mechanics. Three-dimensional analogs of graphene are characterized by Dirac points or lines in momentum space, which are protected by symmetry. Here, we report a novel 3D carbon allotrope belonging to a class of topological nodal line semimetals, discovered using an evolutionary structure search method. The new carbon phase in the monoclinic C2/m space group, termed m-C8, consists of five-membered rings with sp3 bonding interconnected by sp2-bonded carbon networks. Enthalpy calculations reveal that m-C8 is more favorable than recently reported topological semimetallic carbon allotropes, and the dynamic stability of m-C8 is verified by phonon spectra and molecular dynamics simulations. Simulated X-ray diffraction patterns indicate that m-C8 could be one of the unidentified carbon phases observed in detonation shoot. The analysis of electronic properties indicates that m-C8 exhibits a nodal line protected by both inversion and time-reversal symmetries in the absence of spin-orbit coupling and the surface band connecting the projected nodal points. Our results may help design new carbon allotropes with exotic electronic properties.

Ion-irradiation-induced structural evolution in Ti4AlN3

The microstructural evolutions of Ti4AlN3 induced by 1MeV Au+ ions irradiation over a wide fluence range were investigated by transmission electron microscopy (TEM). The high-resolution TEM (HRTEM) images and selected area electron diffraction (SAED) results clearly reveal the process of irradiation-induced partial phase transitions from the original hexagonal-close-packed (hcp) structure into face-centered-cubic (fcc) structure, with the formation of stacking faults. The mechanism for the phase transitions of Ti4AlN3 is proposed based on the phase contrast images and electron diffraction pattern (EDP) simulation. The remained hcp structure without amorphization after high fluences irradiation suggest that Ti4AlN3 exhibits excellent radiation tolerance.

Non-spectroscopic composition measurements of SrTiO3-La0.7Sr0.3MnO3 multilayers using scanning convergent beam electron diffraction

The local atomic structure of a crystalline sample aligned along a zone axis can be probed with a focused electron probe, which produces a convergent beam electron diffraction pattern. The introduction of high speed direct electron detectors has allowed for experiments that can record a full diffraction pattern image at thousands of probe positions on a sample. By incoherently summing these patterns over crystalline unit cells, we demonstrate that in addition to crystal structure and thickness, we can also estimate the local composition of a perovskite superlattice sample. This is achieved by matching the summed patterns to a library of simulated diffraction patterns. This technique allows for atomic-scale chemical measurements without requiring a spectrometer or hardware aberration correction.

Coherent 3D nanostructure of γ-Al2O3: Simulation of whole X-ray powder diffraction pattern

The structure and nanostructure features of nanocrystalline γ-Al2O3 obtained by dehydration of boehmite with anisotropic platelet-shaped particles were investigated. The original models of 3D coherent nanostructure of γ-Al2O3 were constructed. The models of nanostructured γ-Al2O3 particles were first confirmed by a direct simulation of powder X–Ray diffraction (XRD) patterns using the Debye Scattering Equation (DSE) with assistance of high-resolution transmission electron microscopy (HRTEM) study. The average crystal structure of γ-Al2O3 was shown to be tetragonally distorted. The experimental results revealed that thin γ-Al2O3 platelets were heterogeneous on a nanometer scale and nanometer-sized building blocks were separated by partially coherent interfaces. The XRD simulation results showed that a specific packing of the primary crystalline blocks in the nanostructured γ-Al2O3 particles with formation of planar defects on {001}, {100}, and {101} planes nicely accounted for pronounced diffuse scattering, anisotropic peak broadening and peak shifts in the experimental XRD pattern. The identified planar defects in cation sublattice seem to be described as filling cation non-spinel sites in existing crystallographic models of γ-Al2O3 structure. The overall findings provided an insight into the complex nanostructure, which is intrinsic to the metastable γ-Al2O3 oxide.

Thermal evolution of Mg-Al and Ni-Al layered double hydroxides: the structure of the dehydrated phase.

Simulation of X-ray diffraction patterns on the basis of the models of one-dimensional disordered crystals was used to investigate the structure of the dehydrated phase produced by dehydration of Mg-Al and Ni-Al layered double hydroxides at a temperature of ∼473-498 K. It was found that the removal of water molecules transforms the initial structure, which is a mixture of 3R1 and 2H1 polytypes, into a structure that comprises preferentially fragments of 3R2 and 1H polytypes and has some turbostratic disorder.

Package of double helical bromine chains inside single-walled carbon nanotubes

The helicity of stable double helical bromine chains inside single-walled carbon nanotubes (SWCNTs) was studied through the calculation of systematic interaction energy, using the van der Waals interaction potential. The results presented clear images of stable double helical structures inside SWCNTs. The optimal helical radius and helical angle of chain structure increase and decrease, respectively, with the increase of tube radius. The detailed analysis indicated that some metastable structures in SWCNTs may also co-exist with the optimal structures, but not within the same tubes. In addition, a detailed simulation of X-ray diffraction patterns was performed for the obtained optimal helical structures.

Diffraction pattern simulation of cellulose fibrils using distributed and quantized pair distances

Intensity simulation of X-ray scattering from large twisted cellulose molecular fibrils is important in understanding the impact of chemical or physical treatments on structural properties such as twisting or coiling. This paper describes a highly efficient method for the simulation of X-ray diffraction patterns from complex fibrils using atom-type-specific pair-distance quantization. Pair distances are sorted into arrays which are labelled by atom type. Histograms of pair distances in each array are computed and binned and the resulting population distributions are used to represent the whole pair-distance data set. These quantized pair-distance arrays are used with a modified and vectorized Debye formula to simulate diffraction patterns. This approach utilizes fewer pair distances in each iteration, and atomic scattering factors are moved outside the iteration since the arrays are labelled by atom type. This algorithm significantly reduces the computation time while maintaining the accuracy of diffraction pattern simulation, making possible the simulation of diffraction patterns from large twisted fibrils in a relatively short period of time, as is required for model testing and refinement.

Orientational distribution functions and order parameters in "de Vries"-type smectics: A simulation study.

Simple smectic A liquid crystal phases with different types of prescribed orientational distribution functions have been simulated and compared in order to study the possibility to distinguish between the Maier-Saupe type and cone-like orientational distributions using the popular method of Davidson et al. [J. Phys. II 5, 113 (1995)]. This method has been used to extract the orientational distribution functions from simulated diffraction patterns, and the results have been compared with actual distribution functions which have been prescribed during simulations. It has been shown that it is indeed possible to distinguish between these two qualitatively different types of orientational distribution already from the shape of the 2D diffraction pattern. Moreover, typical experimental diffraction patterns for "de Vries"-type smectic liquid crystals appear to be close to the ones which have been simulated using the prescribed Maier-Saupe orientational distribution function.

High-performance powder diffraction pattern simulation for large-scale atomistic modelsviafull-precision pair distribution function computation

A new full-precision algorithm to solve the Debye scattering equation has been developed for high-performance computing of powder diffraction line profiles from large-scale atomistic models of nanomaterials. The Debye function was evaluated using a pair distribution function computed with high accuracy, exploiting the series expansion of the error between calculated and equispace-sampled pair distances of atoms. The intensity uncertainty (standard deviation) of the computed diffraction profile was estimated as a function of the algorithm-intrinsic approximations and coordinate precision of the atomic positions, confirming the high accuracy of the simulated pattern. Based on the propagation of uncertainty, the new algorithm provides a more accurate powder diffraction profile than a brute-force calculation. Indeed, the precision of floating-point numbers employed in brute-force computations is worse than the estimated accuracy provided by the new algorithm. A software application,ROSE-X, has been implemented for parallel computing on CPU/GPU multi-core processors and distributed clusters. The computing performance is directly proportional to the total processor speed of the devices. An average speed of ∼30 × 109computed pair distances per second was measured, allowing simulation of the powder diffraction pattern of an ∼23 million atom microstructure in a couple of hours. Moreover, the pair distribution function was recorded and reused to evaluate powder diffraction profiles of the same system with different properties (i.e.Qrather than 2θ range, step and wavelength), avoiding additional pair distance computations. This approach was used to investigate a large collection of monoatomic and polyatomic microstructures, isolating the contribution from atoms belonging to different moieties (e.g.different species or crystalline domains).

Van der Waals effects on grazing-incidence fast-atom diffraction for H on LiF(001)

We theoretically address grazing incidence fast atom diffraction (GIFAD) for H atoms impinging on a LiF(001) surface. Our model combines a description of the H-LiF(001) interaction obtained from Density Functional Theory calculations with a semi-quantum treatment of the dynamics. We analyze simulated diffraction patterns in terms of the incidence channel, the impact energy associated with the motion normal to the surface, and the relevance of Van der Waals (VdW) interactions. We then contrast our simulations with experimental patterns for different incidence conditions. Our most important finding is that, for normal energies lower than 0.5 eV and incidence along the <100> channel, the inclusion of Van der Waals interactions in our potential energy surface yields a greatly improved accord between simulations and experiments. This agreement strongly suggests a non-negligible role of Van der Waals interactions in H/LiF(001) GIFAD in the low-to-intermediate normal energy regime.

Influence of the goethite (α-FeOOH) surface on the stability of distorted PuO2 and PuO2–x phases

Abstract Experiments by [Powell, B. A., Dai, Z. R., Zavarin, M., Zhao, P. H., Kersting, A. B.: Stabilization of plutonium nano-colloids by epitaxial distortion on mineral surfaces. Environ. Sci. Technol. 45, 2698 (2011).] deduced the heteroepitaxial growth of a bcc Pu4O7 phase when sorbed onto goethite from d-spacing measurements obtained from selected-area electron diffraction (SAED) patterns. The structural and/or chemical modification of Pu(IV) oxide (PO) nanocolloids upon sorption to goethite, in turn, affects colloidal-transport of Pu in the subsurface. In this study, molecular simulations were applied to investigate mechanisms affecting the formation of non-fcc PO phases and to understand the influence of goethite in stabilizing the non-fcc PO phase. Analyses of the structure, chemistry, and formation energetics for several bulk PuO2 and PuO2–x phases, using ab initio methods, show that the formation of a non-fcc PO can occur from the lattice distortion (LD) of fcc PuO2 upon sorption and formation of a PO–goethite interface. To strain and non-uniformly distort the PuO2 lattice to match that of the goethite substrate at ambient conditions would require 88 kJ/mol Pu4O8. The formation of a hypostoichiometric PuO2–x phase, such as the experimentally-deduced bcc, Ia3̅ Pu4O7 phase, requires more O-poor conditions and/or high energetic inputs (&gt; +365 kJ/mol Pu4O7 at O-rich conditions). Empirical methods were also applied to study the effect of lattice distortion on sorption energetics and adsorbate particle growth using simple heterointerfaces between cubic salts, where KCl clusters (notated as KClLD) of varying size and lattice mismatch (LM) were sorbed to a NaCl cluster. When the lattice of a KClLD cluster has &lt;15% LM with that of a NaCl substrate, the sorption of KClLD onto NaCl is exothermic (&lt;–80 kJ/mol) and the KClLD cluster can reach sizes of ~2–5 nm on the NaCl substrate. These models suggest that the lattice of a fcc PuO2 particle can distort upon formation of a heterointerface with goethite to lower LM, in turn better enabling the growth of the PO adsorbates and yielding more exothermic adsorption energies. A more detailed understanding of the interfacial environment between PO and goethite is obtained through structural, chemical, and energetic analyses on modeled PuO2 (110)– and PuO2–x (110)–goethite (001) heterointerfaces. Structural analyses of the heterointerfaces continue to support that the lattice of PO is strained to better match that of goethite and thus lead to the formation of a non-fcc PO phase. When the lattice of the PO (110) surface is distorted to match that of the goethite (001) surface, the alignment and d-spacings from simulated electron diffraction patterns for the PO–goethite heterointerfaces reproduce experimental observations. Non-fcc PO thin-films are also found to be stabilized through the formation of an interface with goethite, as the work of adhesion for the PuO2– and PuO2–x–goethite interfaces are 1.4 J/m2 and 2.0 J/m2, respectively. Analyses of electron and charge density of the heterointerfaces also show that covalent- to polar-covalent bonding at the interface promotes the stabilization of a PO–goethite interface. The results from these models contribute to experimental observations, providing further understanding of how the goethite substrate influences the formation and stabilization of a non-fcc PO phase. Furthermore, the information from this study aids in better understanding processes at mineral–water interfaces that influence actinide transport.

Combining experiment and optical simulation in coherent X-ray nanobeam characterization of Si/SiGe semiconductor heterostructures

The highly coherent and tightly focused x-ray beams produced by hard x-ray light sources enable the nanoscale characterization of the structure of electronic materials but are accompanied by significant challenges in the interpretation of diffraction and scattering patterns. X-ray nanobeams exhibit optical coherence combined with a large angular divergence introduced by the x-ray focusing optics. The scattering of nanofocused x-ray beams from intricate semiconductor heterostructures produces a complex distribution of scattered intensity. We report here an extension of coherent x-ray optical simulations of convergent x-ray beam diffraction patterns to arbitrary x-ray incident angles to allow the nanobeam diffraction patterns of complex heterostructures to be simulated faithfully. These methods are used to extract the misorientation of lattice planes and the strain of individual layers from synchrotron x-ray nanobeam diffraction patterns of Si/SiGe heterostructures relevant to applications in quantum electronic devices. The systematic interpretation of nanobeam diffraction patterns from semiconductor heterostructures presents a new opportunity in characterizing and ultimately designing electronic materials.

Effect of electron irradiation on different crystal planes of titanium aluminum carbide

Ti3AlC2 is irradiated by electron-beams at the energy of 200keV for different times. For the first time, the electron irradiation resistance of Ti3AlC2 of two crystal planes ((0001) and (112¯0)) is studied. It is found that the sputtering of atoms occurs in both morphologies of the two selected planes by performing high-resolution transmission electron microscopy (HRTEM). There’s no amorphous ring observed on their selected area electron diffraction (SAED) patterns. Some weakened diffraction spots on their SAED patterns are observed. Structure transformation from α to β phase is attributed to the weakened diffraction spots on (112¯0) plane by simulated electron diffraction patterns (EDPs), indicating the high irradiation resistance of Ti3AlC2.

The two-step nucleation of G-phase in ferrite

By combining atom probe tomography (APT) with transmission electron microscopy (TEM) we have attempted to identify the stage at which solute clusters transform into compounds crystallographically distinct from the matrix, in the precipitation of the G-phase (Ni16Si7Mn6) from ferrite solid solution subjected to isothermal annealing at 673 K. Based on a systematic analysis on the number density, size, composition and structure of solute clusters as a function of annealing time, the nucleation of the G-phase was found to occur via a two-step process: spontaneous growth of solute clusters first, followed by a structural change transforming into the G-phase. Moreover, the structural change was found to occur via another two-step process. There was a time lag between the end of cluster growth to become a critical size (mean diameter: ∼2.6 nm) and the start of the structural change. During the incubation period solute enrichment occurred inside the clusters without further size growth, indicating that the nucleation of the G-phase occurs at the critical size with a critical composition. Judging from the results of APT, TEM and the simulation of electron diffraction patterns, the critical composition was estimated to be Ni16Si3.5(Fe,Cr)3.5Mn6.

Modeling Powder X-ray Diffraction Patterns of the Clay Minerals Society Kaolinite Standards: KGa-1, KGa-1b, and KGa-2

AbstractThree kaolinite reference samples identified as KGa-1, KGa-1b, and KGa-2 from the Source Clays Repository of The Clay Mineral Society (CMS) are used widely in diverse fields, but the defect structures have still not been determined with certainty. To solve this problem, powder diffraction patterns of the KGa-1, KGa-1b, and KGa-2 samples were modeled. In a kaolinite layer among three symmetrically independent octahedral sites named as A, B, and C and separated from each other by b/3 along the b parameter, the A and B sites are occupied by Al cations, whereas, the C sites located along the long diagonal of the oblique kaolinite unit cell are vacant. The layer displacement vectors t1 and t2 are related by a pseudo-mirror plane from defect-free 1Tc kaolinite enantiomorphs, whereas, the random interstratification within individual kaolinite crystallites creates right-hand and left-hand layer sub-sequences producing structural disorder. A third layer displacement vector, t0, located along the long diagonal of the oblique layer unit cell that contains the vacant octahedral site and coincides with the layer pseudo-mirror plane may exist. Thus, a structural model should be defined by the probability of t1, t2, and t0 layer displacement translations Wt1, Wt2, and Wt0, respectively, determined by simulated experimental X-ray diffraction (XRD) patterns. X-ray diffraction patterns were calculated for structures with a given content of randomly interstratified displacement vectors, and other XRD patterns were calculated for a physical mixture of crystallites having contrasting structural order with only C-vacant layers. The samples differ from each other by the content of high- and low-ordered phases referred to as HOK and LOK. The HOK phase has an almost defect-free structure in which 97% of the layer pairs are related by just the layer displacement vector t1 and only 3% of the layer pairs form the enantiomorphic fragments. In contrast, the LOK phases in the KGa-1, KGa-1b, and KGa-2 samples differ from HOK phases by the occurrence probabilities for the t1, t2, and t0 layer displacements. In addition, the LOK phases contain stacking faults that displace adjacent layers in arbitrary lengths and directions. Low XRD profile factors (Rp = 8-11%) support the defect structure models. Additional structural defects and previously published models are discussed.

Body-Centered Orthorhombic C_{16}: A Novel Topological Node-Line Semimetal.

We identify by abinitio calculations a novel topological semimetal carbon phase in all-sp^{2} bonding networks with a 16-atom body-centered orthorhombic unit cell, termed bco-C_{16}. Total-energy calculations show that bco-C_{16} is comparable to solid fcc-C_{60} in energetic stability, and phonon and molecular dynamics simulations confirm its dynamical stability. This all-sp^{2} carbon allotrope can be regarded as a three-dimensional modification of graphite, and its simulated x-ray diffraction (XRD) pattern matches well a previously unexplained diffraction peak in measured XRD spectra of detonation and chimney soot, indicating its presence in the specimen. Electronic band structure calculations reveal that bco-C_{16} is a topological node-line semimetal with a single nodal ring. These findings establish a novel carbon phase with intriguing structural and electronic properties of fundamental significance and practical interest.

Study on four polymorphs of bifendate based on X-ray crystallography

Bifendate, a synthetic anti-hepatitis drug, exhibits polycrystalline mode phenomena with 2 polymorphs reported (forms A and B). Single crystals of the known crystalline form B and 3 new crystallosolvates involving bifendate solvated with tetrahydrofuran (C), dioxane (D), and pyridine (E) in a stoichiometric ratio of 1:1 were obtained and characterized by X-ray crystallography, thermal analysis, and Fourier transform infrared (FT-IR) spectroscopy. The differences in molecular conformation, intermolecular interaction and crystal packing arrangement for the four polymorphs were determined and the basis for the polymorphisms was investigated. The rotation of single bonds resulted in different orientations for the biphenyl, methyl ester and methoxyl groups. All guest solvent molecules interacted with the host molecule via an interesting intercalative mode along the [1 0 0] direction in the channel formed by the host molecules through weak aromatic stacking interactions or non-classical hydrogen bonds, of which the volume and planarity played an important role in the intercalation of the host with the guest. The incorporation of solvent-augmented rotation of the C–C bond of the biphenyl group had a striking effect on the host molecular conformation and contributed to the formation of bifendate polymorphs. Moreover, the simulated powder X-ray diffraction (PXRD) patterns for each form were calculated on the basis of the single-crystal data and proved to be unique. The single-crystal structures of the four crystalline forms are reported in this paper.

Structure determination of a pseudo-decagonal quasicrystal approximant by the strong-reflections approach and rotation electron diffraction

The structure of a complicated pseudo-decagonal (PD) quasicrystal approximant in the Al–Co–Ni alloy system, denoted as PD1, was solved by the strong-reflections approach on three-dimensional rotation electron diffraction (RED) data, using the phases from the known PD2 structure. RED shows that the PD1 crystal is primitive and orthorhombic, witha= 37.3,b= 38.8,c= 8.2 Å. However, as with other approximants in the PD series, the superstructure reflections (corresponding toc= 8.2 Å) are much weaker than those of the main reflections (corresponding toc= 4.1 Å), so it was decided to solve the PD1 structure in the smaller primitive unit cell first,i.e.with unit-cell parametersa= 37.3,b= 38.8,c= 4.1 Å and space groupPnam. A density map of PD1 was calculated from only the 15 strongest unique reflections. It contained all 31 Co/Ni atoms and many weaker peaks corresponding to Al atoms. The structure obtained from the strong-reflections approach was confirmed by applying direct methods to the complete RED data set. Successive refinement using the RED data set resulted in 108 unique atoms (31 Co/Ni and 77 Al). This is one of the most complicated approximant structures ever solved by electron diffraction. As with other approximants in the PD series, PD1 is built of characteristic 2 nm wheel clusters with fivefold rotational symmetry, which agrees with results from high-resolution electron microscopy images. The simulated electron diffraction patterns for the structure model are in good agreement with the experimental electron diffraction patterns obtained by RED.

Reconstructing three-dimensional helical structure with an X-ray free electron laser

Recovery of three-dimensional structure from single-particle X-ray scattering of completely randomly oriented diffraction patterns as predicted a few decades ago has been realized owing to the advent of the new emerging X-ray free electron laser (XFEL) technology. Since the world's first XFEL started operation in June 2009 at SLAC National Laboratory at Stanford, the first few experiments have been conducted on larger objects such as viruses. Many of the important structures of nature such as helical viruses or DNA consist of helical repetition of biological subunits. Hence development of a method for reconstructing helical structure from collected XFEL data has been a top research priority. This work describes the development of a method for solving helical structures such as tobacco mosaic virus from a set of randomly oriented simulated diffraction patterns exploiting the symmetry and Fourier space constraint of the diffraction volume.