Burgers Vector Component Research Articles

The Green's functions of two-dimensional piezoelectric quasicrystal semi-infinite crack and finite crack

This paper investigates the interactions of a semi-infinite crack / finite crack with multiple loadings in a two-dimensional piezoelectric quasicrystal under different boundary conditions. Utilizing the Stroh formalism and conformal mapping, Green's functions of generalized displacements and stresses are obtained for two general cases: a semi-infinite crack and a finite crack subject to free-free or fixed-fixed boundary conditions. The stress and electric displacement intensity factors at the crack tip and the image forces on how dislocations are affected by the crack surfaces are given explicitly. The results are analyzed and compared with special cases documented in the scholarly literature. At the same time, the effects of the Burgers vector components on the generalized stresses and image forces numerically illustrate as well as the impacts of line forces on generalized stress intensity factors.

Stable nanofacets in [111] tilt grain boundaries of face-centered cubic metals

Grain boundaries can dissociate into facets if that reduces their excess energy. This, however, introduces line defects at the facet junctions, which present a driving force to grow the facets in order to reduce the total number of junctions and thus the system's energy. Often, micrometer-sized facet lengths are observed and facet growth only arrests for kinetic reasons. So far, energetically stable, finite-sized facets have not been observed, even though theoretical stability conditions have already been proposed. Here, we show a case where nanometer-sized facets are indeed stable compared to longer facets in [111¯] tilt grain boundaries in Cu by atomistic simulation and transmission electron microscopy. The facet junctions lack a Burgers vector component, which is unusual, but which removes the main energy cost of facet junctions. Only attractive interactions via line forces remain, which result from a discontinuity of grain boundary excess stress at the junction. Atomistic simulations predict that the same phenomenon also occurs in at least Al and Ag. Published by the American Physical Society 2024

Effective Penetration Depth Investigation for Frank Type Dislocation (Deflected TSDs/TMDs) on Grazing Incidence Synchrotron X-Ray Topographs of 4H-SiC Wafers

In 4H-SiC crystals, Frank type dislocations are created through the deflection of threading screw/mixed dislocations onto the basal plane. Grazing-incidence X-ray topographs are often used to evaluate the density of such dislocations and a knowledge of the effective penetration depth is therefore essential. In this study, a systematic analysis is performed to investigate the effective penetration depth, which is the depth from which contrast from the dislocation is still discernible. This is achieved by comparison between observed topographic images and detailed ray tracing simulations. Simulations shows no significant contrast difference between a deflected TSD and a deflected TMD with the same line direction since the large c component is the dominant contributor to the effective misorientation, whereas the effect of a component is rather negligible. Therefore, this effective penetration depth study uses ray tracing simulation images of deflected TSDs with photoelectric absorption applied to compare with all topographically observed Frank type dislocations. Analysis first reveals that the effective penetration depth varies with the line direction of a Frank type dislocation, and the effective penetration depth is significantly deeper compared to that of a BPD. Further, the effective penetration depth on ray tracing simulations with absorption applied matches well with experimentally measured depth. The study also evaluated the effectiveness of a simplified model based on an approximate expression for the effective misorientation of a dislocation modulated by photoelectric absorption. This was also found to yield satisfactory results and can be used as a universal method to determine the effective penetration depth for Frank type dislocations with c component of Burgers vector.

Strain Field Development of a Rectangular Dislocation Loop in a Semi-Infinite Medium with Verification

This paper considers a rectangular Volterra dislocation loop lying beneath and parallel to a free surface in a semi-infinite material. The paper utilizes the displacement field of an infinitesimal dislocation loop to obtain the strain field and then integrate over a finite rectangular area. For the loop, it can have three non-zero Burgers vector components. The stress field is also obtained from Hooke’s law for isotropic materials. Analytical and numerical verifications of the strain and stress fields are performed. In addition, the effect of the free surface on stresses is displayed versus depth from the surface. Verification includes satisfaction of the zero-traction boundary condition, the stress equilibrium equations and the strain compatibility equations.

Populations and propagation behaviors of pure and mixed threading screw dislocations in physical vapor transport grown 4H-SiC crystals investigated using X-ray topography

The populations and propagation behaviors of pure and mixed threading screw dislocations (TSDs) in physical vapor transport (PVT) grown 4H-SiC crystals were investigated using X-ray topography. The X-ray topography studies revealed that mixed TSDs, which have a Burgers vector component within the basal plane in addition to the c-component, were dominant in PVT-grown 4H-SiC crystals, even though they have a higher energy contained in the elastic field around them compared to pure TSDs. The studies also revealed that mixed TSDs tended to propagate in a specific direction inclined from the c-axis, whereas pure TSDs were often converted into helical dislocations during the PVT growth. Based on these results, we discussed the nature and propagation behavior of pure and mixed TSDs in PVT-grown 4H-SiC crystals and suggested an importance of the interaction between TSDs and point defects during PVT growth of 4H-SiC.

Direct evaluation of threading dislocations in 4H-SiC through large-angle convergent beam electron diffraction

ABSTRACTIn this study, the structures of threading dislocations (TDs) in a 4H-SiC epilayer were directly characterised using large-angle convergent beam electron diffraction (LACBED) via transmission electron microscopy (TEM), by examining the splitting of reflections due to the presence of dislocation lines. Previously, X-ray topography (XRT) mapping in combination with ray-tracing simulations has been shown to be an efficient method for imaging and differentiating common TD types and variants in 4H-SiC. In this work, the validity of XRT-based results was verified by LACBED through direct evaluation and differentiation of the Burgers vectors and physical crystallographic features of all threading edge, threading screw, and threading mixed dislocations variants. The LACBED results agreed with the XRT-based results with respect to TD type and variant. The screw-sense or half-plane orientation and Burgers vector determined from LACBED analysis for each TD were self-consistent. For the case of -TEDs, atomic-resolution analysis of the core structure, through high-angle annular dark field scanning TEM, directly revealed two half-planes, each with a Burgers vector component, and the sum of these components was confirmed to be . Finally, an algorithm for efficient LACBED analysis of TDs in 4H-SiC was discussed.

V-shaped dislocations in a GaN epitaxial layer on GaN substrate

In this study, V-shaped dislocations in a GaN epitaxial layer on a free-standing GaN substrate were observed. Our investigation further revealed that the V-shaped dislocations were newly generated at the interface in the epilayer rather than propagated from the GaN substrate. V-shaped dislocations consist of two straight parts. The straight parts of the V-shaped dislocations were separated from each other in the m-direction and tilted toward the step-flow direction of the GaN epitaxial layer. The V-shaped dislocations are continuous single dislocations having a Burgers vector component of 1a and an intrinsic stacking fault between their straight parts.

Change of Deformation Mechanisms Leading to High Strength and Large Ductility in Mg-Zn-Zr-Ca Alloy with Fully Recrystallized Ultrafine Grained Microstructures

Recently, we have found that fully recrystallized ultrafine-grained (UFG) microstructures could be realized in a commercial precipitation-hardened Magnesium (Mg) alloy. The UFG specimens exhibited high strength and large ductility under tensile test, but underlying mechanisms for good mechanical properties remained unclear. In this study, we have carried out systematic observations of deformation microstructures for revealing the influence of grain size on the change of dominant deformation modes. We found that plastic deformation of conventionally coarse-grained specimen was predominated by {0001} <11–20> slip and {10–12} <10–11> twinning, and the quick decrease of work-hardening rate was mainly due to the early saturation of deformation twins. For the UFG specimens, {10–12} <10–11> twinning was dramatically suppressed, while non-basal slip systems containing <c> component of Burgers vector were activated, which contributed significantly to the enhanced work-hardening rate leading to high strength and large ductility. It was clarified by this study that limited ductility of hexagonal Mg alloys could be overcome by activating unusual slip systems (<c + a> dislocations) in fully recrystallized UFG microstructures.

The features of moiré pattern on electron-microscope images of free-standing quantum dots containing dislocations

Simulation of moiré pattern arising on plan-view transmission electron-microscope image of nanoisland (quantum dot) containing dislocations was performed on the base of finite-element method. The presence of dislocations with a screw component of Burgers vector in the nanoisland is shown to be energetically unfavourable. On the contrary, edge dislocations allow relieving mismatch stress most effectively. The simulation results provide a means to determine the type of dislocation inside quantum dot by the specific features of the moiré pattern on transmission electron microscope image.

Comparison of cross-sectional transmission electron microscope studies of thin germanium epilayers grown on differently oriented silicon wafers.

We compare transmission electron microscopical analyses of the onset of islanding in the germanium-on-silicon (Ge/Si) system for three different Si substrate orientations: (001), (11¯0) and (11¯1)Si. The Ge was deposited by reduced pressure chemical vapour deposition and forms islands on the surface of all Si wafers; however, the morphology (aspect ratio) of the deposited islands is different for each type of wafer. Moreover, the mechanism for strain relaxation is different for each type of wafer owing to the different orientation of the (111) slip planes with the growth surface. Ge grown on (001)Si is initially pseudomorphically strained, yielding small, almost symmetrical islands of high aspect ratio (clusters or domes) on top interdiffused SiGe pedestals, without any evidence of plastic relaxation by dislocations, which would nucleate later-on when the islands might have coalesced and then the Matthews-Blakeslee limit is reached. For (11¯0)Si, islands are flatter and more asymmetric, and this is correlated with plastic relaxation of some islands by dislocations. In the case of growth on (11¯1)Si wafers, there is evidence of immediate strain relaxation taking place by numerous dislocations and also twinning. In the case of untwined film/substrate interfaces, Burgers circuits drawn around certain (amorphous-like) regions show a nonclosure with an edge-type a/4[1¯12] Burgers vector component visible in projection along [110]. Microtwins of multiples of half unit cells in thickness have been observed which occur at the growth interface between the Si(11¯1) buffer layer and the overlying Ge material. Models of the growth mechanisms to explain the interfacial configurations of each type of wafer are suggested.

Crystallographic tilt and in-plane anisotropies of an a-plane InGaN/GaN layered structure grown by MOCVD on r-plane sapphire using a ZnO buffer

High-resolution x-ray diffraction (HRXRD) was used to investigate the crystallographic tilts and structural anisotropies in epitaxial nonpolar a-plane InGaN/GaN grown by metal–organic chemical vapor deposition on r-plane sapphire using a ZnO buffer. The substrate had an unintentional miscut of 0.14° towards its [–4 2 2 3] axis. However, HRXRD revealed a tilt of 0.26° (0.20°) between the ZnO (GaN) (11-20) and the Al2O3 (1-102) atomic planes, with the (11-20) axis of ZnO (GaN) tilted towards its c-axis, which has a difference of 163° in azimuth from that of the substrate’s miscut. Excess broadenings in the GaN/ZnO (11-20) rocking curves (RCs) were observed along its c-axis. Specific analyses revealed that partial dislocations and anisotropic in-plane strains, rather than surface-related effects, wafer curvature or stacking faults, are the dominant factors for the structural anisotropy. The orientation of the partial dislocations is most likely affected by the miscut of the substrate, e.g. via tilting of the misfit dislocation gliding planes created during island coalescences. Their Burgers vector components in the growth direction, in turn, gave rise to crystallographic tilts in the same direction as that of the excess RC-broadenings.

Different structural origins for different sized surface pits observed on a-plane GaN film

A correlation study between the observed surface morphology using high-resolution scanning electron microscopy (HRSEM) and the observed structural imperfections using transmission electron microscopy (TEM) has been conducted for a-plane GaN. There are three different sized asymmetric surface pits: large pit of 500 nm–2 µm in side length, medium pit of 50 nm in side length, and small pit with side lengths of less than 5 nm, which originate from incomplete island coalescence, screw dislocation, and partial dislocation (PD), respectively. Both screw dislocation and PD can produce pits on the free surface because they have a perpendicular line tension to the surface, which must remain in balance with the surface tension. The two types of dislocation lead to distinctive pit sizes because the PD has a smaller Burgers vector component along the dislocation line than the pure screw dislocation. A pit that is produced in the island-coalescing process is much larger than those caused by dislocations because island coalescence is a kinetic process that involves large-scale mass transportation, whereas the dislocation mediates the surface in the local area. These three types of surface pits sometimes interact with one another in space. The coalescence of the island determines the surface morphology at large scales, whereas the defects affect the details.

LONG RANGE STRESSES IN EPITAXIAL FILMS GENERATED WITH MISFIT DISLOCATIONS

The equation connecting the misfit parameter f, the number of misfit dislocation (MD) families and the distances between MDs of the same family with the edge Burgers vector components taken for different dislocation families is obtained for the first time. It is valid for various interface boundaries ( hkl ). To get the equation, the long range normal and shear stresses associated with MD distribution have been considered. The optimum and non−optimum stress releasing processes are discussed. The problem of threading dislocation density diminution with generation of intersecting MDs with the same Burgers vector (L−shape MDs) is also considered for (001) and (111) interfaces. It is shown that such type MDs grow the level of the long range shear stresses and can be effectively generated only at an early stage of relaxation.

Solid-solution hardening of a high-Entropy AlTiVCrNbMo alloy

The nature of solid-solution hardening of high-entropy alloys is discussed using an equiatomic bcc AlTiVCrNbMo alloy as an example. The hardening of the alloy is found to be characterized by an increase in the temperature dependence of the component of the critical shear strength and by anomalously high athermic hardening due to the perpendicular slip plane of the Burgers vector component. A relatively simple expression is proposed to estimate the detected hardening ΔH(Δσ).

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.

Dislocation Conversion in 4H-SiC Crystals Grown by Metastable Solvent Epitaxy

Dislocation conversion in 4H-SiC single crystals grown by metastable solvent epitaxy (MSE) was investigated using synchrotron X-ray topography, repeated polishing and molten KOH etching, and transmission electron microscopy (TEM). The conversion of basal plane dislocations to threading edge dislocations occurred not only near the interface between the MSE layer and the substrate, but also throughout the MSE layer. At the initial stage of MSE growth, all threading screw dislocations (TSDs) were converted into Frank-type basal plane stacking faults (Frank SFs). High resolution TEM observation revealed that the four extra SiC planes generated by this conversion were inserted among adjacent basal planes. These results suggest that the driving force for the conversion of TSDs is significantly larger for MSE growth than for growth by conventional chemical vapor deposition. A g·b analysis of the Frank partial dislocations (PDs) associated with the Frank SFs revealed that the total sum of the Burgers vectors of the four Frank PDs had two different values of b = c and b = c + a, and that approximately 50% of TSDs in the substrate had a Burgers vector component parallel to the a-axis.

Complex Behavior of Threading Dislocations Observed in PVT-Grown 4H-SiC Single Crystals

Structures and propagating behaviors of threading dislocations (TDs) in PVT-grown 4H-SiC single crystals were both investigated using Synchrotron monochromatic X-ray topography. Comparative studies by examining images obtained for the crystals with different diffraction geometries of (0004) and (11-20) of 4H-SiC revealed that a large amount of TDs are likely to be mixed in character, i.e., dislocations with Burgers vector components of both &lt;0004&gt; and &lt;11-20&gt;. Closer observations of topography images has revealed that, although TDs lie largely along the c-axis direction, some of the TDs show quite a complex propagating behavior: not extending in a straight line but meandering along the growth direction.

Grain Boundary Structure Dependence of Extrinsic Grain Boundary Dislocation Emission Phenomena: A Molecular Dynamics Study

Recently, it has been reported that extrinsic grain boundary dislocations (EGBDs) are often present in the grain boundaries of ultrafine-grained (UFG) metals produced by severe plastic deformation; therefore, the emission of EGBDs from the grain boundaries could afect the mechanical characteristics of UFG metals. In this paper, we use molecular dynamics to simulate the emission of EGBDs from grain boundaries, and we examine the grain boundary structure dependence of the emissions. Then we apply J-integral analysis to evaluate the Peach–Koehler force required for the grain boundaries to emit the EGBD. It can be confirmed that the Peach–Koehler force required to emit the EGBD is highly dependent on the relationship between the Burgers vector components of the EGBD and intrinsic grain boundary dislocations (IGBDs), which form the equilibrium grain boundaries. Comparing analyses of the linear elastic theory with atomic simulations, we confirm that nonlinear structural changes in the dislocation cores of the EGBD and IGBDs, which can only be expressed by atomic scale resolution, are responsible for such strong grain boundary structural dependence. We also verify that normal stress components perpendicular to the slip plane of EGBDs have a significant effect on the emission of EGBDs.

Crystal bending, subgrain boundary development, and recrystallization in orthopyroxene during granulite-facies deformation

A prominent feature of a granulite-facies shear zone from the Hidaka Main Zone (Japan) is the folding of orthopyroxene (opx) porphyroclasts. Dislocation density estimated by transmission electron microscope (TEM) and chemical etching in homogeneously folded domains is too low to account for the amplitude of crystallographic bending, leading us to propose a model similar to ''flexural slip'' folding, where folded layers are micrometer-wide opx layers between thin planar clinopyroxene (cpx) exsolu- tions. Extension (compression) in the extrados (intrados) of the folded layer is accommodated by dislocations at the cpx-opx interfaces. Alternatively to distributed deforma- tion, crystal bending also localizes in grain boundaries (GBs), mostly oriented close to the (001) plane and with various misorientation angles but misorientation axes consistently close to the b-axis. For misorientation up to a few degrees, GBs were imaged as tilt walls composed of regularly spaced (100)(001) dislocations. For misorienta- tion angles of 7� , individual dislocations are no longer visible, but high-resolution TEM (HRTEM) observation showed the partial continuity of opx tetrahedral chains through the boundary. For 21� misorientation, the two adjacent crystals are completely separated by an incoherent boundary. In spite of these atomic-scale variations, all GBs share orientation and rotation axis, suggesting a continuous process of misorientation by symmetric incorporation of (100)(001) dislocations. In addition to the dominant GBs perpendicular to the (100) plane, boundaries at low angle with (100) planes are also present, incorporating disloca- tions with a component of Burgers vector along the a-axis. The two kinds of boundaries combine to delimit subgrains, which progressively rotate with respect to host grains around the b-axis, eventually leading to recrystallization of large porphyroclasts.

A Comparative Study of the Morphologies of Etch Pits in Semi-Insulating Silicon Carbide Single Crystals

Contactless resistivity mapping, scanning electron microscope (SEM) and confocal laser microscope have been used to study the relationship of the resistivity and the etching behavior of the semi-insulating 6H-SiC wafer. Evidence is presented that the morphologies of the etch pits vary significantly with the impurity concentrations. The V impurity strongly affects the etch rates of edge, screw and mixed dislocations. For the dislocation containing the Burgers vector component of &lt;0001&gt;, its vertical etch rate is enhanced distinctly. In contrast, the horizontal etch rate becomes larger for the dislocation containing the Burgers vector component of &lt; &gt;. The shape of the etch pits reflects the Fermi level of the semi-insulating wafer and the net shallow impurity concentration.