Coincidence Site Lattice Model Research Articles

Twisting two-dimensional iron sulfide layers into coincident site superlattices via intercalation chemistry.

Layered van der Waals (vdW) materials are susceptible not only to various stacking polymorphs through translations but also twisted structures due to rotations between layers. Here, we study the influence of such layer-to-layer twisting through the intercalation of ethylenediamine (EDA) molecules into tetragonal iron sulfide (Mackinawite FeS). Selected area electron diffraction patterns of intercalated FeS display reflections corresponding to multiple square lattices with a fixed angle between them, contrary to a single square lattice seen in the unintercalated phase. The observed twist angles of 49.13° and 22.98° result from a superstructure formation well described by the coincident site lattice (CSL) theory. According to the CSL theory, these measured twist angles lead to the formation of larger coincident site supercells. We build these CSL models for FeS using crystallographic group-subgroup transformations and find simulated electron diffraction patterns from the model to agree with the experimentally measured data.

Strain and atomic stacking of bismuth thin film in its quasi-van der Waals epitaxy on (111) Si substrate.

We report on the structural properties of Bi thin films grown on (111) Si substrates with a thickness of 22-30 BL. HRXRD and EBSD measurements show that these Bi films are mainly composed of twinning grains in the (0003) direction. The grain size can be as large as tens of microns. From a double-peak (01[Formula: see text]4) φ-scan, we found two pairs of twinning phases coexisting with a rotation angle of ~ 3.6°. We proposed a coincidence site lattice model based on preferential close-packed sites for Bi atoms on Si (111) surface to explain the coexistence of the rotation phases in the quasi-van der Waals epitaxy. From the measured lattice constants c and a of our samples, along with the data from the literature, we derived a c-a relation: (c-c0) = - 2.038(a-a0), where c0 and a0 are the values of bulk Bi. The normalized position of the second basis atom in the unit cell x, in these strained Bi films is found very close to that of bulk Bi, indicating that the strain does not disturb the Peierls distortion of the lattice. The fixed ratio of bilayer thickness to lattice constant c, reveals that the elastic properties of covalent-bonded bilayer dominate those of Bi crystal.

Solubility and segregation of B in paramagnetic fcc Fe

Boron solubility and segregation in paramagnetic (PM) fcc iron have been investigated by means of DFT calculations. The results focus on the Boron site preference in both bulk and coincidence site lattice model $\mathrm{\ensuremath{\Sigma}}5$ (012) GB in fcc Fe and evaluate the validity of different model approaches for modeling the PM state. Boron and PM fcc iron are predicted to form an interstitial solid solution. The PM state model and pressure correction have been introduced into the 0 K DFT calculations to evaluate Boron solubility in fcc Fe as a function of its thermal lattice expansion within the temperature range of 0--1670 K. The relatively high segregation energy of Boron of about $\ensuremath{-}$1.57 eV to both interstitial and substitutional GB sites at 0 K is predicted to substantially decrease with thermal lattice expansion, reaching the value of about $\ensuremath{-}$0.3 eV at the lattice parameter of fcc Fe corresponding to 1670 K. The contribution of the PM state to the segregation energy was found to be of the order of 0.1 eV compared to the nonmagnetic calculations.

Atomistic study of the structure and deformation behavior of symmetric tilt grain boundaries in [formula omitted]-zirconium

We have investigated the structure, energetics and mechanical deformation of symmetric tilt grain boundaries (STGB) in hexagonal close-packed Zr (α-Zr). Molecular dynamics (MD) simulations are performed to determine the equilibrium structures of STGBs with [0001], [11¯00] and [112¯0] tilt axes with respect to the misorientation angle. We characterized the atomic structure and energy of STGBs, determined within the coincidence site lattice model, for the tilt axes considered. Subsequently, we performed simulations of uniaxial tensile loading to evaluate their mechanical response under mechanical deformation. Our results provide a comprehensive characterization of STGBs in α-Zr in a wide variety of conditions, and therefore substantially contributing to the understanding of the mechanical properties of α-Zr-based materials.

Universal prediction of strain footprints via simulation, statistics, and machine learning: low-Σ grain boundaries

Interface engineering usually imposes a trade-off between catalytic activity, product selectivity, and property tunability, facilitating multiple product yields. Due to their structural disorder, metal grain boundaries (GBs) can be constructed to satisfy all of these conditions. Though experiments show GB catalytic footprints are determined by dislocation-induced elastic strain, the atomistic structural and energetic origins of GB catalytic performance are not currently known. In former models solely reviewing metastable GBs defined by macroscopic degrees of freedom (DOFs), exceptional low-Σ GBs anticipated by the coincident site lattice model cannot be consistently discerned. Herein, a structure-energy correlation linking changes in atomistic properties to physical models is developed, distinguishing exceptional GBs from unexceptional high-angle GBs over structural DOFs. This work constructs particular GB elastic responses by varying three microscopic DOFs, comparing low-Σ distinguished and other GB responses via a directed statistical approach. Such elastic properties successfully distinguish low-Σ GBs from high-angle grain boundaries (HAGBs) by their strain-related footprints without failure of a single unique GB structure and composition combination. A priori application of machine learning classification is completed using metastable GB and elastic response related properties. This classification not only validates distinguished strain footprints, but also identifies GB subgroups with footprints unexpected by former models.

AB INITIO МОДЕЛИРОВАНИЕ ВЗАИМОДЕЙСТВИЯ P, H, C, S С ГРАНИЦАМИ ЗЕРЕН В α-ЖЕЛЕЗЕ

The results of modeling from the first principles of interaction of nonmetallic impurities of interstitial (H, C) and substitutional (P, S) with grain boundaries in α-iron are presented. The modeling has been conducted within the framework of the density functional theory (DFT) by the full-potential linearized augmented plane waves (FP LAPW) method with consideration to the generalized gradient approximation (GGA'96) in the WIEN2k software package. Three grain boundaries of the slope Σ3 (111), Σ5 (210) and Σ5 (310) are studied. The supercells of the tilt grain boundaries using the coincidence site lattice model is constructed. The values of the energy characteristics of various grain boundaries with impurities are influenced by a number of factors, namely, the volume of the Voronoi polyhedron per impurity, magnetic moments, and the symmetry of the surrounding matrix. The results show that symmetric grain boundaries Σ3 (111) and Σ5 (310) are embrittled by phosphorus, hydrogen, and sulfur, while carbon strengthens interatomic bonds at the grain boundary, which coincides with the data available in the work. In the case of an asymmetric grain boundary Σ5 (210), phosphorus and hydrogen weaken bonds at the grain boundary, while sulfur strengthens them. This is primarily explained by the geometry of the surrounding matrix. The magnetic moments at the impurity atoms are very small and, in most cases, are antiparallel to the magnetic moments at the neighboring Fe atoms.

Geometrical constraints on the bending deformation of Penta-twinned silver nanowires

Penta-twinned and single crystal silver nanowires were bent in-situ for TEM structural analysis using high spatial resolution scanning precession electron diffraction. Machine learning methods were used to determine the structure of the localised bends in the wires. Single crystal nanowires showed both dispersed large radius bend deformation and abrupt, angular bends with narrow deformation zones accommodated by a high angle boundary plane. The penta-twinned wires were found to display simple in-plane bends with narrow deformation zones in all 5 sub-crystals of the wire, with a common boundary plane. A coincident site lattice model has been developed to explain the bending angles seen in individual nanowires and the observed distribution of angles in a population of penta-twinned nanowires. The geometrical constraints of the model explain the difference in this distribution when compared to that from a population of single crystal nanowires.

Crystallographic and mechanical investigation of intergranular stress corrosion crack initiation in austenitic stainless steel

This study used crystallographic and mechanical analyses to investigate the nucleation of intergranular stress corrosion cracking (IGSCC) on a smooth surface of type 304 austenitic stainless steel. Constant load testing was conducted on thermally sensitized austenitic stainless steel in a tetrathionate solution, and the nucleation behavior of IGSCC on a smooth surface was observed in situ. Then, grain boundaries (GBs) at which stress corrosion cracks occurred were characterized based on the coincidence site lattice model, GB length, and stress acting on GBs. It was found that GBs with the following characteristics exhibited high susceptibility to IGSCC: GBs with little resistance to intergranular corrosion (IGC), long GBs, and GBs subjected to high normal stress. Shear stress acting on GBs seemed to have little effect on the nucleation of IGSCC. Then, a criterion for intergranular stress corrosion crack initiation was developed using the susceptibility of GBs to IGC, GB length, and the stresses acting on GBs.

Point defects at the [formula omitted](012)[100] grain boundary in TiN and the early stages of Cu diffusion: An ab initio study

Diffusion of impurities along grain boundaries of compound materials is of high relevance for multiple practical applications. In this work, we perform a case study of Cu-impurity diffusion along the special coincident site lattice model Σ5(012)[100] GB in stoichiometric and off-stoichiometric TiN. The study includes a thorough investigation of the GB structure, formation of point defects and their interaction with a Cu-impurity at the interface as well as the evaluation of energy barriers for a few plausible impurity migration pathways along TiN grain boundaries. The results show that one of the most probable diffusion mechanisms (with an activation energy of 0.77 eV) is Cu-interstitial migration along a grain boundary channel. For a non-stoichiometric case when nitrogen vacancies can be present at GB, the results show that they can act as trapping centers for Cu atoms and increase the migration energy barrier to 1.2 eV. However, our results also indicate that at equilibrium conditions the effect of trapping may be reduced due to slightly unfavored segregation of N vacancies at TiN grain boundaries.

Structural Stabilities and Electronic Properties of High-Angle Grain Boundaries in Perovskite Cesium Lead Halides

Organometal trihalide perovskites are emerging as very promising photovoltaic materials, which is rivaling that of single crystal silicon solar cells despite their polycrystalline nature with relatively high density of grain boundaries (GBs). There is a lack of understanding of the effects of GBs on halide perovskites as their presence in silicon and other photovoltaic materials is generally detrimental to their photovoltaic properties. Using first-principles calculations, we systematically investigate the geometric structures of high-angle tilt GBs in halide perovskites CsPbX3 (X = Cl, Br, and I) starting from the coincidence site lattice model and refining using crystal shifts and lattice expansion. Electronic density of states calculations reveal that GBs in halides perovskites do not generate midgap states because of the large distance between the unsaturated atoms and the atomic reconstructions in the GB region. However, we show that the GBs can induce different very shallow states near the valence b...

Crystallography of the Mg2Y precipitates in a damping Mg–Cu–Mn–Zn–Y alloy

The crystallography of the Mg2Y precipitates in an Mg–Cu–Mn–Zn–Y damping alloy has been characterized by transmission electron microscopy. The novel orientation relationship between Mg2Y and the α-Mg matrix was determined as [0001]p//[0001]α, 〈10{\overline 1}0〉p//〈2{\overline 1}{\overline 1}0〉α and 〈01{\overline 1}0〉p//〈11{\overline 2}0〉α. The precipitate exhibits a polygonal morphology with four pairs of facets, each of which is normal to a Δg vector in reciprocal space. The secondary constrained coincidence site lattice model was employed to examine the preference of each facet. The results show that a much better degree of lattice matching is realized across each facet than their vicinal orientations, indicating the energetically favoured feature of the interface. The configurations of the misfit-compensating dislocations across each interface were also calculated using the O-lattice model.

SrAl12O19 thin films by chemical solution deposition and their use as buffer layers for oriented growth of hexagonal ferrites

Thin films of SrAl12O19 were prepared on α-Al2O3(0001) substrates through the chemical solution deposition method and thermal treatment. Two types of precursor systems were used: stoichiometric mixture of strontium methoxyethoxide with aluminium iso-butoxide, and strontium methoxyethoxide topotactically reacting with Al2O3 substrate. Two distinctly different film-substrate orientation relationships were observed. In the latter case the orientation can described as perfect hexagon-on-hexagon epitaxy with 112−0SrAl12O19 || 101−0Al2O3 and (0001)Al2O3 || (0001)SrAl12O19. This relationship has 1.17% lattice misfit in the substrate plane. In the former case SrAl12O19 grains are rotated about the substrate normal and form more orientation variants that can be explained by the coincident-site lattice model for grain boundaries. We demonstrated that both types of SrAl12O19 films can be used as a chemical buffer and structural template layer for the growth of oriented hexagonal ferrite thin films. In both types of films the (BaSr)Fe12O19 phase cope the in-plane orientation of their respective templates.

In situx-ray scattering study of Ag island growth on Si(111)7×7

We report on the epitaxial relationship between Ag and the Si(111)$7\ifmmode\times\else\texttimes\fi{}7$ substrate where the wetting layer and the emergence of islands was investigated using in situ x-ray scattering with a combination of grazing incidence diffraction, specular reflectivity, and crystal truncation rod measurements. The atomic-scale structure of the wetting layer evolves continuously with coverage until a transition where it ceases to change its structure concomitantly with the appearance of islands. The islands are observed to reside on the Si(111)$7\ifmmode\times\else\texttimes\fi{}7$ and, although the minimum average island height is three atomic layers of face-centered-cubic Ag, the average island height depends on the coverage and temperature. The majority of the Ag islands are oriented along the symmetry-equivalent Si crystallographic axes and a minority population of islands are rotated by $15.{7}^{\ensuremath{\circ}}$. A coincidence-site lattice model is used to show that kinetic considerations lead to the observed island orientations.

Special Grain Boundaries in Ultrafine-Grained Tungsten.

Field ion microscopy and computer simulation were used for the study of an atomic structure high-angle grain boundary in hard-drawn ultrafine-grained tungsten wire. These boundaries with special misorientations are beyond the scope of the coincident site lattice model. It was demonstrated that the special non-coincident grain boundaries are the plane-matching boundaries, and rigid-body displacements of adjacent nanograins are normal to the <110> misorientation axis. The vectors of rigid-body translations of grains are described by broad asymmetric statistical distribution. Mathematical modeling showed that special incommensurate boundaries with one grain oriented along the {211} plane have comparatively high cohesive energies. The grain-boundary dislocations ½<110> were revealed and studied at the line of local mismatch of {110} atomic planes of adjacent grains.

Assessment of the CSL and SU models for bcc-Fe grain boundaries from first principles

We present a systematic first principles investigation on a group of representative low-Σ (Σ⩽11) symmetric tilt grain boundaries in bcc-Fe. The grain boundary (GB) structures were constructed using both the coincident site lattice (CSL) and structural unit (SU) models. Calculations are performed to address the relation and applicability of the two models. Results suggest that on some of the GBs, the CSL and SU models may yield different atomistic structures. In these cases, their structures differ only by one vacancy, and the SU model always predicts a much lower GB formation energy than the CSL does. Further calculations on GB vacancy formation suggest that the SU model is more appropriate for describing the low-Σ bcc GBs.

Исследование взаимодействия водорода с границами зерен в α-Fe

The article presents results of first-principles modeling of the interaction of hydrogen with grain boundaries in α-iron. The simulation was performed in the framework of density functional theory (DFT) method of the full-potential linearised augmented-plane wave (FP LAPW) with generalised gradient approximation (GGA’96) in WIEN2k package. Three tilt grain boundaries Σ3 (111), Σ5(210) and Σ5(310) were studied. The calculated tilt grain boundaries were constructed using the coincidence site lattice model. The supercells contained 40–48 atoms, i.e. 20–24 atoms in each of the two grains. Calculated formation energies of grain boundaries are 1.46, 1.83 and 1.44 J/m 2 and maximum binding energies of hydrogen to the boundaries are 0.39, 0.81 and 0.43 eV, respectively. These data are in good agreement with the results shown in other studies. The high value of trapping energy of the Σ5(210) boundary is probably due to the asymmetrical structure resulting from mutual rigid shift of the two grains, that was necessary to be introduced to provide optimum distance between Fe atoms, in contrast to the other two types of boundaries.

Crystallography Analysis of the β-Mg17Al12 Precipitates by the Secondary Constrained Coincident Site Lattice Model

Crystallography Analysis of the β-Mg17Al12 Precipitates by the Secondary Constrained Coincident Site Lattice Model

Growth of BaIn2S4 layers through the hot-wall-epitaxy method and their electric/optical properties

The epitaxial growth of photoconductive BaIn2S4 layers was first achieved through the hot-wall-epitaxy method. In spite of an existing large lattice mismatch between the substrate and layer, BaIn2S4 layers were epitaxially grown along the (440) direction onto a GaAs (100) substrate. Thus, the lattice mismatch was well interpreted through a coincidence site lattice model. From the relationship between the reciprocal temperature and the carrier concentration, the three donor levels were found to be 1.3, 20.2, and 78.3meV below the conduction band. These donor levels are caused by the native defects originating from slight stoichiometric deviations. From the temperature dependence of the Hall mobility, two specific scatterings were observed. One, at high temperatures ranging over 180K, is mainly due to the acoustic phonon mode of lattice vibrations through a deformation potential. The other, at low temperatures ranging below 100K, is ascribed to the dislocation scattering. From the photocurrent (PC) measurement, three PC peaks due to band-to-band transitions were observed. Also, based on the analysis of optical absorption and PC spectra, the optical band gap has been compared and matched well with Eg(T)=Eg(0)−3.95×10−3T2/(T+499), where Eg(0) is estimated to be 3.0597, 3.2301, and 3.2606eV for the transitions corresponding to the valence band states of peaks A, B and C, respectively.

Characterization of commercially cold sprayed copper coatings and determination of the effects of impacting copper powder velocities

Copper coated steel containers are being developed for the disposal of high level nuclear waste using processes such as cold spray and electrodeposition. Electron Back-Scatter Diffraction has been used to determine the microstructural properties and the quality of the steel-copper coating interface. The influence of the nature of the cold-spray carrier gas as well as its temperature and pressure (velocity) on the coating's plastic strain and recrystallization behaviour have been investigated, and one commercially-produced electrodeposited coating characterized. The quality of the coatings was assessed using the coincident site lattice model to analyse the properties of the grain boundaries. For cold spray coatings the grain size and number of coincident site lattice grain boundaries increased, and plastic strain decreased, with carrier gas velocity. In all cases annealing improved the quality of the coatings by increasing texture and coincidence site-lattices, but also increased the number of physical voids, especially when a low temperature cold spray carrier gas was used. Comparatively, the average grain size and number of coincident site-lattices was considerably larger for the strongly textured electrodeposited coating. Tensile testing showed the electrodeposited coating was much more strongly adherent to the steel substrate.

Characterization and interpretation of interfacial structure of the Mg2Sn laths in an Mg–Sn–Mn–Ag–Zn alloy

Interfacial structures in facets of the basal Mg2Sn lath approximately along were characterized using high-resolution transmission electron microscopy. A set of periodic misfit-compensating ledges is observed along the irrational major facet, which deviates from by an angle of around 5°. The observation is interpreted quantitatively using a constrained secondary coincidence-site lattice model. The calculation results reveal a favourable singular structure with a specific configuration of steps, showing good agreement with the experimental observations.