Structural Unit Model Research Articles

Atomistic Modelling of Structures of Tilt Grain Boundaries and Antiphase Boundaries in ?-Silicon Carbide

Structures of symmetrical tilt grain boundaries and antiphase boundaries in β-silicon carbide are investigated by means of classical molecular dynamics simulations using the Tersoff potential. A structural unit model is used to classify the possible interface structures. Structures and energies are given for 〈001〉 tilt grain boundaries in the angular range 0° ≤ θ ≤ 53.15° and for 〈110〉 tilt grain boundaries in the range 0° ≤ θ ≤ 70.53° of tilt angles. It is found that among 〈110〉 boundaries, those containing antiphase boundaries are the most stable ones in an intermediate angular range.

Role of bismuth and titanium in Na 2O–Bi 2O 3–TiO 2–P 2O 5 glasses and a model of structural units

0.60Na 2O–0.40P 2O 5 and (0.55− z)Na 2O–0.05Bi 2O 3– zTiO 2–0.40P 2O 5 glasses (0≤ z≤0.15) were prepared by melting at 1000°C mixtures of Na 2CO 3, Bi 2O 3, TiO 2 and (NH 4) 2HPO 4. Differential Scanning Calorimetry (DSC) measurements give the variation of glass transition temperature ( T g) from 269°C (for 0.60Na 2O–0.40P 2O 5) to 440°C (for z=0.15). The density measurements increases from 2.25 to 3.01 g/cm 3. FTIR spectroscopy shows the evolution of the phosphate skeleton: (PO 3) ∞ chains for 0.60Na 2O–0.40P 2O 5 to P 2O 7 4− groups in the glasses containing Bi 2O 3 or both Bi 2O 3 and TiO 2. When bismuth oxide and titania are added to sodium phosphate glass, phosphate chains are depolymerized by the incorporation of distorted Bi(6) and Ti(6) units through POBi and POTi bonds. Bi 2O 3 and TiO 2 are assumed to be present as six co-ordinated octahedral [BiO 6/2] 3−and [TiO 6/2] 2− units again with shared corners. This is accompanied by the simultaneous conversion of [POO 3/2] into [PO 4/2] + units which achieves charge neutrality in the glasses.

Experimental and computer simulation study of the vibrational spectra of vermiculite

Infrared and Raman spectra of vermiculite clay have been recorded, and an assignment of the observed features in the spectra is proposed on the basis of molecular dynamics calculations. For this purpose, a force field yielding a structure and vibrational spectra in good agreement with the experimental data was developed with the help of ab initio calculations of models of vermiculite structural units. The calculated spectra of the periodic clay model are analysed in terms of symmetry adapted internal coordinates of the building units of the clay structure.

Role of titanium in sodium titanophosphate glasses and a model of structural units

Glasses with composition 50 Na 2 O–x TiO 2–(50−x) P 2 O 5 (0≤x≤15) have been studied. Their density, molar volume, glass transition temperature and infrared spectroscopy have been investigated. The evolution of infrared spectra with the different constituents is studied and the oxide-forming character of TiO 2 is discussed. In sodium titanophosphate glasses, the structures consist of distorted Ti octahedra linked to metaphosphate and pyrophosphate units through P–O–Ti bonds. The metaphosphate (P 2O 6 2−) and pyrophosphate (P 2O 7 4−) units coexist. Metaphosphate groups are the predominant structural units in glasses with the lowest TiO 2 content. For TiO 2-rich glasses, the pyrophosphate groups become the predominant structural units. A structural model is proposed to explain the experimental results. According to this model TiO 2 is assumed to be present as six coordinated octahedral [TiO 6/2] 2− units, again with shared corners.

Structure and energetics of long-period tilt grain boundaries using an effective Hamiltonian

We have investigated the atomic structures of 44 〈110〉 symmetric tilt grain boundaries (GB's) with atomistic simulations using an embedded-atom method (EAM) potential for aluminum. The focus has been on examining the efficacy of the structural unit model in the context of very long period boundaries. Our studies, which have been carried out using two EAM potentials, of both the equilibrium and metastable structures of a number of boundaries, reveal that geometric arguments inherent in the structural unit model must be supplemented by energetic considerations. An effective Hamiltonian is introduced to this end which computes the energy of a string of structural units using two-body potentials between individual units. The potentials are calculated via a least-squares fit to the results of full atomistic represented by the effective Hamiltonian. Results based on as few as 16 inputs are very encouraging and clearly demonstrate the effectiveness of this method. This scheme lends itself to a straightforward extension to GB structure calculations at finite temperatures using Monte Carlo techniques.

In-situtransmission electron microscopy study of the dislocation accommodation in [101] tilt grain boundaries in nickel bicrystals

The relaxation of stresses associated to extrinsic grain-boundary dislocations (EGBDs) in singular Σ = 3, {111}, in vicinal Σ = 11, {311} and in general Σ = 11, {332} grain boundaries (GBs) has been investigated by in-situ transmission electron microscopy (TEM) using weak-beam conditions. In a singular Σ = 3, {111} GB, reactions of combination and annihilation occur between extrinsic and intrinsic dislocations when they initially intersect each other. These reactions yield the parallelism of the two types of dislocation which is the preliminary configuration for any of the existing incorporation models to operate, but further evolution by decomposition of the EGBDs in glissile and sessile components, which can move away, as depicted by theory, was observed once only at a very high temperature. Furthermore, the rearrangement of all the sessile dislocations, extrinsic and intrinsic, in a periodic network was not observed, even after maintaining the thin foil at 930°C = 0.6T m (T m is the melting temperature) for a long time. In vicinal Σ = 11, {311} GBs, the continuous spreading of EGBD contrasts, previously observed by TEM in bright-field conditions, has been proved to be a decomposition process. Indeed, owing to the weak-beam technique, the wide image of a relaxed EGBD has been resolved in a set of small segments resulting from the interaction between the EGBD and the intrinsic dislocations. After annealing the thin foil at temperatures up to 0.4T m , all the GBDs had rearranged themselves in a quasiperiodic network, indicating that equilibration is almost achieved. In general Σ = 11, {332} GBs, the widening of the EGBD contrasts has never been associated with a decomposition phenomenon. No discrete product of EGBD decomposition has ever been observed by TEM, even in weak-beam conditions. The differences between the accommodation processes according to the GB type are discussed by referring to the GB atomic structure as described by the structural unit model.

Atomic and Electronic Structure Analysis of Σ=3, 9 and 27 Boundary, and Multiple Junction in β-SiC

AbstractThe atomic structures of σ=3, 9 and 27 boundaries, and multiple junctions in β-SiC were studied by high-resolution electron microscopy (HREM). Especially, the existence of the variety of structures of σ=3 incoherent twin boundaries and σ=27 boundary was shown by HREM. The structures of σ=3, 9 and 27 boundary were explained by structural unit models. Electron energy-loss spectroscopy (EELS) was used to investigate the electronic structure of grain boundaries. The spectra recorded from bulk, {111}σ=3 coherent twin boundary (CTB) and {1211}σ=3 incoherent twin boundary (ITB) did not show significant differences. Especially, the energy-loss corresponding to carbon 1s-to Φ* transition was not found. It indicates that C atoms exist at grain boundary on the similar condition of bulk

Quasiperiodic tilt boundaries in polycrystalline and nanocrystalline materials: energy and stress fields

Abstract The structural geometry of quasiperiodic tilt boundaries (modeled as sequences of structural units) in polycrystalline and nanocrystalline materials is discussed. The energy density of finite-length quasiperiodic tilt boundaries is calculated in a dislocation–structural-unit model. It is shown that usually the energy density changes when rearrangements of structural units of a quasiperiodic grain boundary with finite extent occur. However, some special rearrangements leave the energy density unchanged.

Atomistic structure of high-index surfaces in metals and alloys

Interatomic potentials of the embedded atom (EAM) type were used to study the atomistic structure of high-index surfaces in metals and ordered alloys. The results show that a structural unit model can be developed for the structure of the high-index surfaces on the basis of the structure of a few low-energy surfaces. The model can predict the structural features and also give an estimate of the energies of the higher-index surfaces. We present examples in pure metals, Fe and Al and in the intermetallic alloys FeAl, NiAl and TiAl. The energies of alloy surfaces that present different possible terminations depend on the composition of the bulk. We show that this effect can be significant for low-index surfaces, and decreases in magnitude for higher-index surfaces.

Atomistic simulation of [001] symmetrical tilt grain boundaries in NiAl

We study the atomic structure of [001] symmetrical tilt grain boundaries (GBs) with stoichiometric composition in the B2 compound NiAl using molecular statics with an embedded-atom potential. The simulations are performed in the misorientation range 0° ⩽ θ 90° in every 3° in average. The multiplicity of stable GB structures is addressed by using the γ-surface technique combined with full atomic relaxation. The GBs typically have only a few nonidentical stable structures. All other structures either are symmetrically related to those few structures or are their strained variants and reduce to one of them if relative translations of the grains are allowed. All ground-state structures are composed of only four types of structural unit, or their variants obtained by site substitution. Many structural features of the GBs can be understood in terms of the significant atomic size effect peculiar to NiAl. The ground-state Σ = 5, (310), θ = 36.87° and Σ = 5,(210),θ = 53.13° GBs, as well as all GBs with intermediate orientations, show a relative shift of the grains by 1/2[001]. All such GBs follow the structural unit model with the two Σ = 5 GBs being the delimiting boundaries. For all other orientations, the ground-state GB structures have no shift along the tilt axis and are consistent with the structural unit model only at θ< 30° and θ> 65°. In some GBs, the primary or secondary GB dislocations are observed to dissociate in partials associated with GB steps. Many GBs contain regions of antiphase boundaries on (100) and (110) planes. The behaviour of GBs under applied shear stress parallel to the GB plane is discussed.

Atomistic Studies of Generic Tilt Grain Boundary Structures

AbstractWe investigate the atomic-scale structures of high-sigma (∑) tilt grain boundaries in aluminum using lattice statics calculations. In particular, we examine the efficacy of the structural unit model (SUM) in the context of long-period boundaries. Our investigation of both the equilibrium and metastable structures for certain high ∑ boundaries may necessitate a revision of the SUM formalism. We also consider further departures from high symmetry boundaries by considering the structural rearrangements induced by steps on boundaries.

Structural Characteristics and Quantum Chemistry Calculation of Si-Doped Boron Carbides

AbstractStructural characteristics, chemical bonds and thermoelectric properties of Si-doped boron carbides are studied through calculations of various structural unit models by using a self-consistent-field discrete variation Xα method. The calculations show that Si atom doped in boron carbide is in preference to substituting B or C atoms on the end of boron carbide chain, and then may occupy interstitial sites, but it is difficult for Si to substitute B or C atom in the centers of chain or in the icosahedra. A representative structural unit containing a Si atom is [C-B-Si]ε+ [B11C]ε-, while the structural unit without Si is [C-B-B(C)]δ--[B11C]δ+, and the coexistence of these two different structural units makes the electrical conductivity increases. As the covalent bond of Si-B or Si-C is weaker than that of B-B or B-C, the thermal conductivity decreases when Si is added into boron carbides. With the electrical conductivity increases and the thermal conductivity decreases, Si doping has significant effect on thermoelectric properties of boron carbides.

〈110〉 symmetric tilt grain-boundary structures in fcc metals with low stacking-fault energies

Twenty-one {l_angle}110{r_angle} symmetric tilt grain boundaries (GB{close_quote}s) are investigated with atomistic simulations, using an embedded-atom method (EAM) potential for a low stacking-fault energy fcc metal. Lattice statics simulations with a large number of initial configurations are used to identify both the equilibrium and metastable structures at 0 K. The level of difficulty in finding the equilibrium structures is quantitatively assessed. The stability of the structures at an elevated temperature is investigated by Monte Carlo annealing. A form of GB dissociation is identified in a number of the boundaries. These structures are used to develop a dislocation model of GB dissociation by stacking-fault emission. Also, an attempt is made to apply the structural unit model (SUM) to the simulated boundaries and problems that are encountered for GB structures in low stacking-fault energy metals are enumerated and discussed. {copyright} {ital 1996 The American Physical Society.}

TEM Characterization of Invariant Line Interfaces and Structural Ledges in a Mo-Si Alloy

Two distinct lath morphologies of Mo{sub 5}Si{sub 3} precipitates observed in MoSi{sub 2} differ in their cross-sectional shape and lattice orientation. Type I laths exhibit a rectangular cross section, with interfaces parallel to low-index planes, while Type II laths are parallelogram-shaped, with their major interface at 13{degree} to the Type I precipitate. The corresponding orientation relationships differ by a 1.8{degree} rotation around the lath axis. In this study, the difference between the two characteristic morphologies and orientation relationships is shown to be the formation of an invariant line strain for Type II precipitates. On an atomic scale, both interfaces have a terrace and ledge structure but differ in the stacking sequence of interfacial ledges associated with partial dislocations. The structural unit model and the invariant line model predict identical interface geometries which agree closely with the observations.

Limitations of the Structural Unit Model

Limitations of the Structural Unit Model

Atomistic Structure of High Index Surfaces

AbstractInteratomic potentials of the embedded atom (EAM) type were used to study the atomistic structure of high index surfaces in metals and ordered alloys. The results show that a structural unit model can be developed to model the structure of the high index surfaces on the basis of the structure of a few low energy surfaces. The model can predict the structural features and give an estimate of the energies of the higher index surfaces. We present examples of Fe, B2 FeAl and NiAl.

Atomic structure and electronic properties of the ?37(610) and ?29(520) [001] tilt grain boundaries in Ge

400 kV high resolution electron microscopy (HREM), deep level transient spectroscopy (DLTS) and steady state electrical measurements have been applied to ∑37(610) and ∑29(520) [001] tilt grain boundaries (GBs) in germanium bicrystals. The atomic boundary structures were revealed by experimental HREM images taken under different defocus conditions. Later, structure models were refined by means of a trial-and-error method applying alternatively the image simulation and the molecular static calculation of relaxed structures. The structures were shown to be consistent with the modified structural unit model. Although the structures are different for the two GBs studied, DLTS data and steady state measurements were found to be quite similar for both GBs. Thus, the results point to the extrinsic origin of localized deep states at the GBs. The analysis of DLTS spectra indicates the impurity segregation at the boundary, e.g., the formation of vacancy-type oxygen complexes of a donor-like state at Ec-0.21 eV, which results in the fluctuation of the potential barrier. Defects in the GBs—like facets, atomic steps and secondary grain boundary dislocations—which are characteristic of both boundaries can act as nuclei to the impurity segregation.

Grain-boundary structures in hexagonal materials: Coincident and near coincident grain boundaries

Embedded atom method (EAM) simulations of the structure of grain boundaries in hexagonal metals are presented. The simulations use recently developed interatomic potentials for Ti and Co. Structures were calculated for various symmetrical tilt boundaries with the [1¯100] tilt axis. The structures obtained for both metals are very similar. The energies for the Co boundaries are higher than those for Ti by a factor of 2. The structural unit model was applied to the computed grain-boundary structures in these hexagonal materials. As in cubic materials, the structural unit model can describe a series of symmetrical tilt coincident boundaries. In addition, when the coincidence ratio in the grain-boundary plane varies with thec/a ratio, a structural unit-type model can describe the variation of grain-boundary structure withc/a ratio. This model is adequate for describing series of symmetrical tilt boundaries with the grain-boundary plane oriented perpendicular to a fixed crystallographic direction and varyingc/a ratios. For the structures of the so-called near coincident boundaries that appear in these materials, it was concluded that near coincident boundaries behave similarly to exact coincidence boundaries if there is a coincident periodic structure in the grain-boundary plane. This may occur even without a three-dimensional (3-D) coincident site lattice.

Segregation to and structure of [001] twist grain boundaries in CuNi alloys

The segregation, thermodynamic, and structural properties of [001] twist boundaries in CuNi alloys have been examined within a wide range of misorientations and temperatures. Cu always segregates to the boundary. The concentration of the first layer adjacent to the boundary increases monotonically with misorientation and no obvious cusps are observed. All other thermodynamic properties vary smoothly with the misorientation, with the exception of the vibrational entropy of the boundaries without segregation. The unsegregated vibrational entropy shows a large peak at the misorientation corresponding to the Σ17 boundary and two minima around the Σ13 and Σ5 boundary orientations. The concentration distribution within the plane of the grain boundaries can be described by the same structural unit model established for [001] twist boundaries in pure materials. Regions of large tensile stress show greater segregation than do regions of compressive stress. Regions of large shear stress tend to show reduced segragation compared with regions of small shear stress.

High-resolution transmission electron microscopy study of twin-boundary structures in epitaxial NiSi2thin films

Abstract Symmetric, asymmetric and overlapped twins were observed in epitaxial NiSi2 thin films. These twin structures were studied by high-resolution electron microscopy. The twin-boundary planes of the observed symmetrical twins were found to be (1―11―)1-(1―11)2, while those of the asymmetrical twins were (1―11)1-(11―5)2 and (001)1-(22―1)2. The structural unit model was applied to explain the observed twin-boundary structures. The summetrical twin boundary is comprised of a uniform array of six-atom ring structural units, while the asymmetrical twins contained a mixture of structural units of the (1―11―)1-(1―11)2 and (1―12)1-(11―2)2 symmetrical twins. The {111} lattice plane containing Si was found to be the terminating lattice plane at the boundary core of the symmetrical twin in which case the bond length between Si atoms of two grains was determined to be the same as that of Si-Si bonds in bulk Si crystal, and the Ni atoms are sevenfold coordinated. High-resolution images of overlapped twins show triple periodicity along the directions of {111} plane normal which is dependent not only on the defocus, the total foil thickness and the thickness ratio of twins, but also on the stacking order of the two grains.