Burgers Vectors Of Dislocations Research Articles

Scattering of phonons by quantum-dislocation segments in an elastic continuum

A canonical quantization procedure is applied to elastic waves interacting with pinned dislocation segments (``strings'') of length $L$ via the Peach-Koehler force. The interaction Hamiltonian, derived from an action principle that classically generates the Peach-Koehler force, is a power series of creation and annihilation operators. The leading term is quadratic, and keeping only this term the observable quantities of scattering processes are computed to all orders in perturbation theory. The resulting theory is characterized by the magnitude of $kL$, with $k$ the wave number of an incident phonon. The theory is solved for arbitrary $kL$, and different limits are explored. A significant result at this level is the scattering cross section for phonons by dislocation segments. As a function of frequency, this cross section has a much richer structure than the linear-in-frequency behavior that is inferred from scattering by an infinite, static, dislocation. The rate of spontaneous phonon emission by an excited dislocation is computed as well. When many dislocations are present, an effective mass operator is computed in the weak and independent scattering approximation. The contribution of the cubic terms is computed to leading order in perturbation theory. They allow for a comparison of the scattering of a phonon by a string and the three-phonon scattering, as well as studying the dependence of scattering amplitudes on the temperature of the solid. It is concluded that the effect of dislocations of Burgers vector 0.5 nm and length 50 nm will dominate for relatively modest dislocation densities: ${10}^{8}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. Finally, the full power series of the interaction Hamiltonian is considered. The effects of quantum corrections, i.e., contributions proportional to Planck's constant, are estimated, and found to be controlled by another wave-number-dependent parameter $k{d}_{q}$, where ${d}_{q}$ is a length proportional to $\sqrt{\ensuremath{\hbar}}$. The possibility of using the results of this paper in the study of the phononic thermal properties of two- and three-dimensional materials is noted and discussed.

Solute precipitation on a screw dislocation and its effects on dislocation mobility in bcc Fe

Reactor pressure vessel steels are well-known to harden and embrittle under neutron irradiation. The primary mechanism of radiation embrittlement for these bainitic steels is the obstruction of dislocation motion, mainly due to clusters or precipitates of solute atoms such as Cu, Ni, Mn, Si and P. Microstructural examinations reveal that these clusters or precipitates are often preferentially formed at dislocation lines, which are sometimes completely surrounded by segregated solute clusters. Evidence of this is provided in this work, too, which extends a previous one dedicated to edge dislocations, by studying the effect of this segregation around screw dislocations (Burgers vector b = 1/2 [111]) on the critical stress for dislocation motion. A Monte Carlo algorithm in a variance-constrained semi-grand canonical (VC-SGC) ensemble is applied to study the decoration of atoms around dislocations, by minimizing the free energy. Next, the critical stress for dislocation unpinning from the clusters is evaluated by standard molecular dynamics to analyze the effect of Cu, Ni, Mn, and P segregation in the Fe matrix. Consistently with expectations and in agreement with previous work, our results highlight that the required stress for triggering dislocation motion drastically increases due to the presence of segregated solutes. Our finding is that solute-decorated screw dislocations may be considered as practically immobile because of the strong segregation around them.

Identification of dislocation characteristics in Na-flux-grown GaN substrates using bright-field X-ray topography under multiple-diffraction conditions

Basal-plane and threading dislocations in multipoint-seed Na-flux-grown GaN single crystals are characterized in terms of Burgers vectors mainly by using bright-field X-ray topography under multiple-diffraction conditions. The technique, combined with a CMOS camera system with high spatial resolution, can provide topographic images of the dislocations with a relatively high dislocation density (up to approximately 5×105cm−2). It is possible to directly determine the Burgers vector of individual dislocations based on invisibility criteria. From the present experiment, it is found that almost all basal-plane dislocations have a-type Burgers vectors, and threading dislocations have a- and (a + c)-type Burgers vectors.

Slip transmission for dislocations across incoherent twin boundary

We performed molecular dynamic simulations to elucidate the transmission mechanisms of ½〈110〉 dislocation across a Σ3{112} incoherent twin boundary (ITB). There are the certain relations between incoming and outcoming dislocations, determined by the dislocation structure of the ITB and the character of incoming dislocation. A screw dislocation can cross-slip onto the ITB and push out the pre-existing interface dislocation into the twin. The Burgers vector of the incoming dislocation determines the emitted dislocation and corresponding glide plane. A mixed dislocation can only directly cross the ITB when its leading partial reacts with pre-existing interface dislocation to produce a full dislocation.

Mapping the full lattice strain tensor of a single dislocation by high angular resolution transmission Kikuchi diffraction (HR-TKD)

The full lattice strain tensor and lattice rotations induced by a dislocation in pure tungsten were mapped using high-resolution transmission Kikuchi diffraction (HR-TKD) in a SEM. The HR-TKD measurement agrees very well with a forward calculation using an elastically isotropic model of the dislocation and its Burgers vector. Our results demonstrate that the spatial and angular resolution of HR-TKD in SEM is sufficiently high to resolve the details of lattice distortions near individual dislocations. This capability opens a number of new interesting opportunities, for example determining the Burgers vector of an unknown dislocation in a fast and straightforward way.

First-principles study on solute-basal dislocation interaction in Mg alloys

To better understand the influence of alloying elements on the mechanical properties of Mg-X (Al, Sn, Ca, Y, Sc, Er, Gd, and Nd) binary alloys, the local interactions between the solute atoms and basal screw dislocation cores were investigated using first-principles calculations. It is revealed that Rare Earth (Y, Sc, Er, Gd, and Nd) and Ca solute atoms can hinder the dissociation behavior of the full basal dislocation core to different extents. Moreover, Y, Sc, and Er tend to stabilize the perfect Burgers vector of basal dislocations. Furthermore, Sn, Y, and Nd were selected to access the interactions between solute atoms and partial <a> dislocations. It is found that Y and Nd can alter the structure of partial dislocation and reduce the width of the stacking fault at specific locations. By comparison, Al and Sn solutes slightly influence the width of the stacking fault. The energies of relaxed basal dislocation cores decorated by Rare Earth and Ca are significantly lower than those decorated by Al and Sn, which suggests that a stronger binding is present between Rare Earth elements, Ca solute atoms, and basal dislocation cores. Moreover, non-planar basal dislocation cores would be induced by Rare Earth solutes. Finally, the physical factors of alloying elements influencing dislocation core structures and the implications of the diverse geometries of dislocation cores to mechanical properties of Mg alloys are discussed.

Caution in building a Burgers circuit for studying secondary dislocations

As the Burgers vector of a secondary dislocation may not conform to the translation vectors in the periodic pattern in a high-resolution transmission electron microscope (HRTEM) image, a Burgers circuit directly constructed according to an HRTEM image may render a wrong Burgers vector. The HRTEM images of the habit plane (HP) of δ precipitate in an Inconel 718 alloy were re-examined by using different Burgers circuits, as an example. Evidence is found for predicted secondary dislocation associated with a down step. The Burgers vector of the dislocation is 1/6[112¯]γ/1/3[001¯]δ, determined with the Burgers circuit built on the reference of the displacement shift completely lattice (DSCL). It is consistent with both the calculated and the measured result of the major defects in the habit plane. Different Burgers vectors due to different Burgers circuits were explained quantitatively. The present study has a general implication for the determination of the Burgers vectors of secondary interfacial dislocations in other systems.

Grain boundary structure and migration in graphene via the displacement shift complete lattice

We describe grain boundary structure and migration in graphene using the concept of dislocations in the displacement shift complete lattice. The equivalence of displacement shift complete lattice dislocations and grain boundary kinks in graphene is shown both topologically and energetically. Topologically, a grain boundary kink and a displacement shift complete lattice dislocation both translate the coincident site lattice. The energetic equivalence is established through comparison of atomistic and continuum elasticity models of metastable states to show that DSC dislocations are well-described by elasticity theory. The continuum results are fitted to the atomistic results with one adjustable parameter, the DSC dislocation core radius. The atomistic results reveal that low sigma boundaries have large energy barriers to grain boundary motion, which match continuum results obtained for smaller core radii dislocations. The larger energy barriers for low sigma boundaries are consistent with experimental results reporting isolated, low sigma boundaries in grown graphene. The trends in the dislocation Burgers vector and fitted core radii across grain boundaries of different misorientation are expressed in a unified model. The analysis provides a framework for understanding grain boundary motion in graphene and can serve as a basis for engineering the atomic structure of graphene.

Temperature and exposure-dependent interfacial fracture toughness model for thermal barrier coatings

An interfacial fracture toughness model for thermal barrier coatings (TBCs) is proposed in which model parameters not only include the effect of high temperature and exposure period of TBCs but also demonstrate the mode mixity characteristics. The model is expressed in terms of the Arrhenius-type form showing a temperature-dependent feature and also exhibits a dependence of microcrack density distributed along the coating interface. Two scaling parameters are used in formulating the model, one is introduced to link dislocation Burgers vector to the crack tip opening displacement (CTOD), the other is utilized to describe the crack tip energy release rate associated with the P-N force responsible for dislocation movement. These scaling parameters can be obtained by fitting to the interfacial fracture toughness data at ambient temperature and the CTOD, respectively. Since the experimentally measured microcrack density exhibits thermal cycle dependent behavior, an attempt is made to explain the experimentally obtained toughness values using the proposed interfacial crack toughness model. The model predicts an increase in fracture toughness with exposure temperature and mode mixity. The limitation of the model and possible improvement scheme are discussed.

Dislocation absorption and transmutation at [formula omitted] twin boundaries in deformation of magnesium

How matrix dislocations, i.e. basal, prismatic and pyramidal, interact with {101¯2}101¯1¯ twin boundaries in hexagonal close-packed metals has been discussed extensively in the literature. However, so far no systematic investigation has been reported. In this work, we performed atomistic simulations to study interaction between matrix dislocations in pure Mg with a {101¯2} twin boundary. Our results show that for the basal and the prismatic slip, when the Burgers vector is parallel to the zone axis of the twins, a matrix basal dislocation can be transmuted to a twin prismatic dislocation and vice versa. However, when the Burgers vector of the matrix dislocation is non-parallel to the zone axis, no transmutation occurs and the dislocation is absorbed by the twin boundary which acts as a dislocation sink. For a matrix pyramidal dislocation, the dislocation is absorbed by the twin boundary and no transmutation occurs either. It appears that if the product dislocation is a real slip system, transmutation may occur during twin-slip interaction. Otherwise the matrix dislocation will be shredded by atomic shuffling and then absorbed by the twin boundary. If the core structure of the product dislocation is complex, transmutation may not occur as well and dislocation absorption will occur. Lattice correspondence in deformation twinning was applied in explaining the interaction mechanisms. Our results can be well correlated to macroscopic experimental observations which show twin-slip interaction only contributes negligibly to work hardening in deformation of hcp metals.

Strain Transfer across the Ferrite/Cementite Interface in Carbon Steels with Coarse Lamellar Pearlite

A crystal geometry analysis was performed of strain transfer mechanisms across the ferrite/cementite interface in coarse lamellar pearlite. The possibility of strain transfer was evaluated using LRB criteria, which were developed by Lee, Robertson, and Birnbaum to describe the slip transfer mechanism across grain boundaries. Dislocation reactions at the Fe/Fe3C interface were studied according to the Pitsch–Petch orientation relationships between ferrite and cementite, which are valid for coarse lamellar pearlite. Slip planes and Burgers vectors of partial and full dislocations in cementite were proposed based on the results of atomistic simulation of stacking faults in close-packed planes of cementite. It was determined that the strain transfer across the Fe/Fe3C interface is possible only for two slip systems 1/2〈111〉{110}F and one slip system 1/2〈111〉{112}F of ferrite. The other slip systems of ferrite do not cross the interface and are involved in the hardening of the ferrite phase of pearlite.

Crystalline Defects Induced during MPCVD Lateral Homoepitaxial Diamond Growth.

The development of new power devices taking full advantage of the potential of diamond has prompted the design of innovative 3D structures. This implies the overgrowth towards various crystallographic orientations. To understand the consequences of such growth geometries on the defects generation, a Transmission Electron Microscopy (TEM) study of overgrown, mesa-patterned, homoepitaxial, microwave-plasma-enhanced, chemical vapor deposition (MPCVD) diamond is presented. Samples have been grown under quite different conditions of doping and methane concentration in order to identify and distinguish the factors involved in the defects generation. TEM is used to reveal threading dislocations and planar defects. Sources of dislocation generation have been evidenced: (i) doping level versus growth plane, and (ii) methane concentration. The first source of dislocations was shown to generate <110> Burgers vector dislocations above a critical boron concentration, while the second induces <112> type Burgers vector above a critical methane/hydrogen molar ratio. The latter is attributed to partial dislocations whose origin is related to the dissociation of perfect ones by a Shockley process. This dissociation generated stacking faults that likely resulted in penetration twins, which were also observed on these samples. Lateral growth performed at low methane and boron content did not exhibit any dislocation.

The Sizes of Jumps and Levels of Deformation of Metals

It is proposed to characterize levels of deformation by a size of its jumps, which can be observed when the strain rate is accurately measured in experiments with load that is constant or defined according a certain law. At the micro- and nanometer scales, the strain rate was measured and the deformation jumps were computed for copper, lead, and tin using a precision interferometric method. A correlation of the size of jumps with the Burgers vector of dislocations in metals was shown, and hypotheses about ensembles of dislocations participating in the formation of a deformation jump are made.

Influence of Dislocations in Transition Metal Oxides on Selected Physical and Chemical Properties

Studies on dislocations in prototypic binary and ternary oxides (here TiO2 and SrTiO3) using modern TEM and scanning probe microscopy (SPM) techniques, combined with classical etch pits methods, are reviewed. Our review focuses on the important role of dislocations in the insulator-to-metal transition and for redox processes, which can be preferentially induced along dislocations using chemical and electrical gradients. It is surprising that, independently of the growth techniques, the density of dislocations in the surface layers of both prototypical oxides is high (109/cm2 for epipolished surfaces and up to 1012/cm2 for the rough surface). The TEM and locally-conducting atomic force microscopy (LCAFM) measurements show that the dislocations create a network with the character of a hierarchical tree. The distribution of the dislocations in the plane of the surface is, in principle, inhomogeneous, namely a strong tendency for the bundling and creation of arrays or bands in the crystallographic &lt;100&gt; and &lt;110&gt; directions can be observed. The analysis of the core of dislocations using scanning transmission electron microscopy (STEM) techniques (such as EDX with atomic resolution, electron-energy loss spectroscopy (EELS)) shows unequivocally that the core of dislocations possesses a different crystallographic structure, electronic structure and chemical composition relative to the matrix. Because the Burgers vector of dislocations is per se invariant, the network of dislocations (with additional d1 electrons) causes an electrical short-circuit of the matrix. This behavior is confirmed by LCAFM measurements for the stoichiometric crystals, moreover a similar dominant role of dislocations in channeling of the current after thermal reduction of the crystals or during resistive switching can be observed. In our opinion, the easy transformation of the chemical composition of the surface layers of both model oxides should be associated with the high concentration of extended defects in this region. Another important insight for the analysis of the physical properties in real oxide crystals (matrix + dislocations) comes from the studies of the nucleation of dislocations via in situ STEM indentation, namely that the dislocations can be simply nucleated under mechanical stimulus and can be easily moved at room temperature.

Atomic simulations to evaluate effects of stacking fault energy on interactions between edge dislocation and spherical void in face-centred cubic metals

In this study, molecular dynamics simulations were performed to elucidate the effects of stacking fault energy (SFE) on the physical interactions between an edge dislocation and a spherical void in the crystal structure of face-centred cubic metals at various temperatures and for different void sizes. Four different types of interaction morphologies were observed, in which (1) two partial dislocations detached from the void separately, and the maximum stress corresponded to the detachment of the trailing partial; (2) two partial dislocations detached from the void separately, and the maximum stress corresponded to the detachment of the leading partial; (3) the partial dislocations detached from the void almost simultaneously without jog formation; and (4) the partial dislocations detached from the void almost simultaneously with jog formation. With an increase in void size or SFE, the interaction morphology changed in the above-mentioned order. It was observed that the magnitude of the critical resolved shear stress (CRSS) and its dependence on the SFE were determined by these interaction morphologies. The value of the CRSS in the case of interaction morphology (1) is almost equal to an analytical one based on the linear elasticity by employing the Burgers vector of a single partial dislocation. The maximum value of the CRSS is also obtained by the analytical model with the Burgers vector of the two partial dislocations.

Observation of Threading Dislocations in Ammonothermal Gallium Nitride Single Crystal Using Synchrotron X-ray Topography

Synchrotron monochromatic-beam x-ray topography observation has been performed on high-quality ammonothermal gallium nitride single crystal to evaluate threading dislocations (TD) in a nondestructive manner. Asymmetric diffractions with six equivalent g-vectors of 11–26, in addition to a symmetric diffraction with g = 0008, were applied to determine the Burgers vectors (b) of dislocations. It was found that pure edge-type TDs with \( {\varvec b} = \left\langle {11 - 20} \right\rangle /3 \) did not exist in the sample. A dominant proportion of TDs were of mixed type with \( {\varvec b} = \left\langle {11 - 20} \right\rangle /3 + \left\langle {0001} \right\rangle \), i.e., so-called c + a dislocations. Pure 1c screw dislocations with \( {\varvec b} = \left\langle {0001} \right\rangle \) and TDs with c-component larger than 1c were also observed.

Atomistic simulation of shear-coupled motion of [1 1 0] symmetric tilt grain boundary in α-iron

Shear-coupled grain boundary (GB) motion (SCGBM) is an important and efficacious plasticity mechanism in the deformation of metals, especially nanocrystalline metals. In this work, molecular dynamic (MD) simulation has been performed to investigate the SCGBM of two [1 1 0] symmetric tilt GBs, Σ9[1 1 0](2 2 1) and Σ17[1 1 0](2 2 3), in α-iron, and the effects of temperature and strain rate on SCGBM have been studied. The coupling factor β which is defined as the ratio of the velocities of GB lateral translation and migration was calculated, and a geometric model of β depending on the misorientation angle was constructed in [1 1 0] symmetric tilt GBs of BCC metals. The model was branched into two modes (〈1 0 0〉 and 〈1 1 1〉) corresponding to the perfect dislocation Burgers vectors in BCC metals. The β values calculated in the 〈1 1 1〉 mode were in good agreement with the MD simulation results for both the GBs. Further, the atomistic mechanisms of the SCGBM processes were also investigated. A same structural unit transformation was observed for the two GBs, which confirmed that both Σ9[1 1 0](2 2 1) and Σ17[1 1 0](2 2 3) GBs moved in the 〈1 1 1〉 mode during the SCGBM process.

Dynamics and Removal Pathway of Edge Dislocations in Imperfectly Attached PbTe Nanocrystal Pairs: Toward Design Rules for Oriented Attachment.

Using in situ high-resolution TEM, we study the structure and dynamics of well-defined edge dislocations in imperfectly attached PbTe nanocrystals. We identify that attachment of PbTe nanocrystals on both {100} and {110} facets gives rise to b = a/2⟨110⟩ edge dislocations. Based on the Burgers vector of individual dislocations, we can identify the glide plane of the dislocations. We observe that defects in particles attached on {100} facets have glide planes that quickly intersect the surface, and HRTEM movies show that the defects follow the glide plane to the surface. For {110} attached particles, the glide plane is collinear with the attachment direction, which does not provide an easy path for the dislocation to reach the surface. Indeed, HRTEM movies of dislocations for {110} attached particles show that defect removal is much slower. Further, we observe conversion from pure edge dislocations in imperfectly attached particles to dislocations with mixed edge and screw character, which has important implications for crystal growth. Finally, we observe that dislocations initially closer to the surface have a higher speed of removal, consistent with the strong dislocation free surface attractive force. Our results provide important design rules for defect-free attachment of preformed nanocrystals into epitaxial assemblies.

Morphology of single Shockley-type stacking faults generated by recombination enhanced dislocation glide in 4H–SiC

Morphology of single Shockley-type stacking faults (SFs) generated by recombination enhanced dislocation glide (REDG) in 4H–SiC are discussed and analysed. A complete set of the 12 different dissociated states of basal-plane dislocation loops is obtained using the crystallographic space group operations. From this set, six different double rhombic-shaped SFs are derived. These tables indicate the rules that connect shapes of SFs with the locations of partial dislocations having different core structures, the positions of slip planes in a unit cell, and the Burgers vectors of partial dislocations. We applied these tables for the analysis of SFs generated by the REDG effect reported in the past articles. Shapes, growing process of SFs and perfect dislocations for origins of SFs were well analysed systematically.

Influence of spinodal decomposition structures on the strength of Fe-Cr alloys: A dislocation dynamics study

This paper presents a numerical analysis of the influence of spinodal decomposition on the strength of Fe-Cr alloys using the dislocation dynamics (DD) method. In the DD simulations, the structure of a spinodally decomposed chromium distribution is approximated using a cosine function. Using the equation for internal stress distribution, the interaction between a dislocation and the internal stress distribution is precisely accounted for in the DD simulations. The structure of the spinodally decomposed chromium distribution is parameterized using four variables, including the magnitude of chromium concentration, wave length of chromium distribution, position of the slip plane of dislocation, and the dislocation character (angle between the dislocation line and Burgers vector). Using these variables, the influence of the structure of chromium distribution on the critical resolved shear stress (CRSS) is studied. Furthermore, we focused on two major slip systems of the BCC structure, {110}〈111〉 and {112}〈111〉, and discuss the difference in the influence between the different slip systems. In the {110}〈111〉 slip system, the ΔCRSS appears only for a mixed dislocation with θ = 54.7°, because of the stripe pattern of the resolved shear stress distribution. On the other hand, in the {112}〈111〉 slip system, the dislocations with θ = 39.2° and 90° have a large ΔCRSS. There is a plateau of ΔCRSS in a range of 39.2∘<θ<90∘. The slip plane position does not change the ΔCRSS. There is a dependence of ΔCRSS on the wave-length of the chromium distribution. The dependence of ΔCRSS on the wave-length can be found not with a straight dislocation but with a curved dislocation using the DD simulations. The information is a new finding, and is meaningful in understanding the relationship between the material strength and the structure of spinodal decomposition.