Burgers Vector Research Articles

Investigation of reflection anisotropy induced by micropipe defects on the surface of a 4H-SiC single crystal using scanning anisotropy microscopy

Optical reflection anisotropy microscopy mappings of micropipe defects on the surface of a 4H-SiC single crystal are studied by the scanning anisotropy microscopy (SAM) system. The reflection anisotropy (RA) image with a ‘butterfly pattern’ is obtained around the micropipes by SAM. The RA image of the edge dislocations is theoretically simulated based on dislocation theory and the photoelastic principle. By comparing with the Raman spectrum, it is verified that the micropipes consist of edge dislocations. The different patterns of the RA images are due to the different orientations of the Burgers vectors. Besides, the strain distribution of the micropipes is also deduced. One can identify the dislocation type, the direction of the Burgers vector and the optical anisotropy from the RA image by using SAM. Therefore, SAM is an ideal tool to measure the optical anisotropy induced by the strain field around a defect.

Modulated martensite in NiTi shape memory alloy exposed to high stress at high temperatures

NiTi shape memory wire was deformed in martensite state at low temperature −125 °C up to 750 MPa stress and subsequently heated far above the Af temperature while the stress 750 MPa was held constant. Under such conditions, the heated B19’ martensite in the wire was driven towards its thermomechanical stability limits and eventually transformed into plastically deformed austenite. In order to evaluate the mechanism by which such highly constrained reverse martensitic transformation proceeds, martensite variant microstructures and lattice defects evolving in the heated wire were analyzed by TEM and HRTEM.It is found that, the oriented B19’ monoclinic martensite deformed plastically via kwinking deformation involving coordinated dislocation slip and twinning and simultaneously adopted a long period modulated crystal structure, before it transformed to austenite upon heating under applied stress. It is proposed that the modulated martensite structure forms from the B19’ structure via coordinated slip of partial dislocations with Burgers vector b = a/2 [100] on (001) crystal planes. Coordinated slip was enforced by the kwinking deformation and partial dislocations started to glide because the martensite was exposed to elevated temperatures. Plastic deformation of oriented B19’ martensite enabling the reverse martensitic transformation upon the constrained heating is discussed in view of its impact on NiTi functionality in engineering applications.

Dissociation of edge and screw pyramidal I and II dislocations in magnesium

Pyramidal dislocations in magnesium (Mg) and other hexagonal close-packed metals play an important role in accommodating plastic strains along the c-axis. Bulk single crystal Mg only presents very limited plasticity in c-axis compression, and this behavior was attributed to out-of-plane dissociation of pyramidal dislocations onto the basal plane and resulted in an immobile dislocation configuration. In contrast, other simulations and experiments reported in-plane dissociation of pyramidal dislocations on their slip planes. Thus, the core structure and mode of dissociation of pyramidal dislocations are still not well understood. To better understand the dissociation behavior of pyramidal dislocations in Mg at room temperature, in this work, atomistic simulations were conducted to investigate four types of pyramidal dislocations at 300 K: edge and screw Py-I on {101¯1}, edge and screw Py-II on {112¯2} by using a modified embedded atom method (MEAM) potential for Mg and anisotropic elasticity dislocation model. The results show that when energy minimization was performed before relaxation, in-plane dissociation of edge dislocations on respective pyramidal plane could be obtained at room temperature for all four types of dislocation. Without energy minimization, the edge dislocations dissociated out-of-plane onto the basal plane. Calculations of potential energy and hydrostatic stress of individual atoms at the edge dislocation core show that the extraordinarily high energy and atomic stresses in the as-constructed dislocation structures caused the out-of-plane dissociation onto the basal plane. The core structures of all four types of pyramidal dislocation after in-plane dissociation were analyzed by computing the distribution of the Burgers vector.

Thickness-dependent creep rate caused by climbing control of a superdislocation in a Ni-based single crystal superalloy

Creep tests are carried out on Ni-based single crystal superalloy sheet samples with different thicknesses at 1100 °C/130 MPa. The results indicate that the secondary creep rate at constant stress exhibits a strong thickness dependence and increases with the decrease in sample thickness. Under load in [001] direction, two types of a<100> family superdislocations with Burgers vectors a[100] and a[010] enter γ′ rafts in thin samples, whereas only the type of a[100] superdislocation enter γ′ rafts in thicker samples. The density of a<100> superdislocations is higher in thin sheets than in thick ones. It is proved that the movement mode of a<100> superdislocations in γ′ rafts is pure climb according to non-compact dislocation core structure. In addition, the climb velocity of the a<100> superdislocations in thin samples is determined to be greater than that in thick ones caused by the fact that the a<100> superdislocations in thin samples experience a higher driving force. On these bases, it is revealed that more types of Burgers vectors, higher density and greater climb velocity of a<100> superdislocations in γ′ rafts contributes to higher secondary creep rate in thinner samples.

Influence of Dislocation Substructure on Size-Dependent Strength of High-Purity Aluminum Single-Crystal Micropillars

In order to understand the influence of dislocation substructures on the size-dependent strength (smaller is stronger) of micron-sized metals, we have fabricated single-crystal cylindrical micropillars with various diameters approximately ranging from 1 to 10 μm, which were prepared on the surface of the fully annealed sample and the subsequently cold-rolled samples of high-purity aluminum (Al). The annealed micropillars exhibited a size dependence of the resolved shear stress required for slip. The shear stress (τi) normalized by shear modulus (G) and the specimen diameter (d) normalized by Burgers vector (b) followed the correlation of τi/G=0.33(d/b)−0.63. The size-dependent strength was reduced by cold-rolling, resulting in lower power-law exponents (0.26~0.31) for the correlation in the cold-rolled specimens. The fine dislocation substructures introduced by the cold-rolling could be associated with the reduced size-dependent strength, which can be rationalized using the stochastic model of the dislocation source length in an assumption of homogenously distributed dislocations existing in the experimental micropillars. The inhomogeneous dislocation substructure with various dislocation cell sizes would contribute to a variation in the measured strength depending on the location, likely due to the probability of exiting the dislocation cell walls (local variation in dislocation density) in the micropillars fabricated on the cold-rolled Al samples.

Microstructure Evolution and Dislocation Mechanism of a Third-Generation Single-Crystal Ni-Based Superalloy during Creep at 1170 °C.

The present study investigates the creep behavior and deformation mechanism of a third-generation single-crystal Ni-based superalloy at 1170 °C under a range of stress levels. Scanning electron microscopes (SEM) and transmission electron microscopes (TEM) were employed to observe the formation of a rafted γ' phase, which exhibits a topologically close-packed (TCP) structure. The orientation relationship and elemental composition of the TCP phase and matrix were analyzed to discern their impact on the creep properties of the alloy. The primary deformation mechanism of the examined alloy was identified as dislocation slipping within the γ matrix, accompanied by the climbing of dislocations over the rafted γ' phase during the initial stage of creep. In the later stages of creep, super-dislocations with Burgers vectors of a<010> and a/2<110> were observed to shear into the γ' phase, originating from interfacial dislocation networks. Up to the fracture, the sequential activation of dislocation shearing in the primary and secondary slipping systems of the γ' phase occurs. As a consequence of this alternating dislocation shearing, a twist deformation of the rafted γ' phase ensued, ultimately contributing to the fracture mechanism observed in the alloy during creep.

On the migration of {10[formula omitted]1} and {10[formula omitted]3} coherent twin boundaries in magnesium

In this work, migrations of (101¯1) and (101¯3) coherent twin boundaries (CTB) in pure magnesium are studied by first-principles methods. The migration process is divided into nucleation and gliding of twinning disconnection (TD), with the TD nucleation being approximated by a rigid-shifting of the CTB. Full energetic maps obtained from this analysis reveal the necessity of applying shear strains simultaneously along the twinning direction η1 and along k1, which is normal to η1, to activate the 2-layer CTB migration in these two different twinning modes. The energetic map identifies the most efficient external shear strain direction for activating CTB migration. This direction lies between the Burgers vectors bTD-2 of the 2-layer-height TD and η1. The shear strain required to initiate TD gliding is smaller than that needed for TD nucleation, implying that the migrations of (101¯1) and (101¯3) CTBs are primarily governed by the TD nucleation.

Dislocation equilibrium in a misfitted composite structure with partially coherent interfaces

The effect of misfit strain on the equilibrium positions of two edge dislocations of the same Burgers vector that are symmetrically displayed in a matrix with respect to its two interfaces with a thin film has been theoretically investigated from a Peach–Koehler force-based analysis. Assuming the film/matrix interfaces are partially coherent, the stable and unstable equilibrium positions of the dislocations have been determined as well as the resulting stability diagram versus the misfit strain, the interface inconsistency length and the layer thickness.

Non-destructive identification of edge-component burgers vector of threading dislocations in SiC wafers by birefringence imaging

Non-destructive characterization of crystalline defects in SiC wafers is important for manufacturing high-performance SiC power devices with high productivity. The present study shows that the edge component of the Burgers vector can be identified by birefringence imaging under conditions deviating slightly from the crossed-Nicols condition and by calculation of the in-plane shear stress distribution. It is also found that the combination of birefringence observation and X-ray topography allows the discrimination of the family of threading screw dislocations. The present results will further the understanding of the relationship between defect structure and the properties of SiC power devices.

Dislocation-mediated brittle-ductile transition of diamond under high pressure

Recent confirmation of room temperature dislocation plasticity in single-crystal diamond and the activation of {001}<110> slip system in experiments has opened up a new era to understand the deformation mechanism of brittle covalent crystals. However, few theoretical research and simulation has been conducted on the dislocation gliding in {001}<110> slip system. In this work, a new potential function is derived from the original Tersoff potential to the Tersoff High Pressure potential with a novel bond order term with the nearest neighbors. This model has been validated with series of molecular dynamic simulations of both {001}<110> and {111}<110> dislocation slip systems in diamond, successfully describing the dislocation mediated brittle-ductile transition under high hydrostatic pressure. The gliding mechanism of dislocation on {001} plane presents a jumping character with a large burgers vector under high hydrostatic pressure. Whereas, the diamond exhibits a zipper-like Griffith cleavage upon shearing under zero hydrostatic pressure. Similar deformation processes are also found in polycrystalline diamond. The current model is expected to prove useful in related simulations focusing on the strengthening mechanism in diamond and related research.

In situ Growth Transition Towards Helical Crystals of Achiral Molecules

The synthesis of chiral crystals such as helical crystals is important due to their chirality‐dependent applications in various fields. Since chiral crystals of achiral molecules are getting more attention, it is important to establish synthetic strategies for helical crystals of achiral molecules. Quite surprisingly, there are numerous examples of helical crystals of achiral molecules, although they are mostly obtained without specific synthetic strategies. Herein, it is proposed that Eshelby twist can be applied to noncovalent molecular crystals by introducing screw dislocations and demonstrates a successful synthesis of helical tube crystals of achiral titanyl phthalocyanine by vapor‐phase crystal growth. The dislocations form where interfaces are created via growth transition from wire growth to tube growth upon growth temperature change. The screw dislocation is confirmed by Burgers vector analysis using transmission electron microscopy. The screw dislocation induces crystal twisting along the growth direction to dissipate the strain applied around the dislocation. The diffraction peak broadening of the (200) and (002) planes confirms the nonuniform strain, i.e., twisting force. This work offers a new approach for the synthesis of helical crystals from achiral molecules.

Bridging microstructure and crystallography with the crack propagation behavior in Ti-6Al-4V alloy fabricated via dual laser beam bilateral synchronous welding

The microstructure evolution and crack propagation behavior were systematically and thoroughly investigated in α/β Ti-6Al-4V alloy obtained under the inhomogeneous heating effect of a coupled dual laser beam via a combination of postmortem electron backscattering diffraction analyses and numerical simulations. The effect of microstructural attributes (grain size, grain boundary, dislocation) on the fracture property and crack propagation behavior was investigated based on thermodynamic and crystallographic analyses, as well as the examinations of dislocation density and the Burgers vector. By quantifying the degree of variant selection using the degree of variant selection (DVS) equation, it was found that the higher the energy input, the weaker the variant selection, as the secondary α phase suppresses further dislocation-induced variant selection via autocatalytic nucleation and growth. The proportion of high angle grain boundaries (HAGBs) concentrated around 60° gradually increases with improving cooling rate, mainly due to the change in the tendency of martensite transformation to be induced. The grain refinement was the primary mechanism for the enhancement of Ti-6Al-4V alloy T-joints, while the suppression of crack propagation by HAGBs also played a crucial role in improving strength and ductility. The crack propagation direction frequently changes when the order is approximately parallel to the short axis of α′ martensite grains, forming a zigzag propagation path. The above findings should shed light on optimizing dual laser beam bilateral synchronous welding (DLBSW) technology to tailor the microstructure and improve the mechanical properties of Ti-6Al-4V alloy T-joints.

Unusual F3 stacking fault in magnesium

An unusual F3 basal stacking fault resulting from twin-dislocation interaction in magnesium is observed in molecular dynamics simulation. The F3 fault is produced in the twin lattice from the interaction between a migrating (101¯2) twin boundary and a partial dislocation of either a prismatic 〈c〉 edge, or a prismatic 〈c+a〉 mixed dislocation in the matrix. The condition is that the partial dislocation needs to have a negative sign and lie on a plane intersecting a compression site of the twin boundary. The F3 fault can also be generated when a positive basal 〈a〉 mixed dislocation in the twin lattice, with slip plane intersecting a compression site of the twin boundary, interacts with a basal-prismatic twinning disconnection. The F3 fault comprises two I1 faults that have the same character but are separated by two basal layers. It has one end connected to the twin boundary, and the other end bounded by a lattice defect with a Burgers vector identical to that of a 30° Shockley partial dislocation. The formation frequency of the F3 fault is higher at a lower shear stress (below ∼400 MPa) and/or a lower temperature (100 K and 200 K). The F3 fault can decompose into a glissile 30° Shockley and a T2 fault at a temperature above ∼400 K. The relationships between the F3 fault and other types of basal stacking faults such as I2, T2 or paired I1 faults that are separated by multiple basal layers are discussed.

Automated extraction of interfacial dislocations and disconnections from atomistic data

We introduce Interfacial Line Defect Analysis (ILDA), a method for identifying and extracting interfacial dislocations and disconnections with little-to-no input from the user on the nature of the interface. By simply providing the orientations and coherency strains for the crystals in a coherent reference state of the interface, ILDA provides exact Burgers vectors. Alternatively, these orientations and strains can be estimated using local atomic deformation gradients, making ILDA fully automated and providing estimated Burgers vectors. ILDA also determines the step height associated with each defect line segment, in case the associated defect is a disconnection. The heart of the method is the identification of atoms residing at co-incidence sites between the two crystals and the construction of a surface mesh connecting these sites that is used to compose Burgers circuits and insert defect line segments. We demonstrate the performance of ILDA in two test cases: a twist grain boundary and a phase boundary.

Delayed plasticity during spherical nanoindentation of an iron-chromium-aluminum alloy: Effect of ferric ion irradiation

Spherical nanoindentation of an iron-chromium-aluminum alloy was conducted to study the effect of ferric-ion (Fe3+) irradiation on the time-dependent plasticity behavior in the surface layers of this alloy. It was observed that the initiation of plasticity by the appearance of displacement burst or “pop-in” event occurred after a period of waiting time in the apparent elastic regime and that Fe3+ irradiation at 360 °C and up to ∼0.5 displacements per atom could make it happen under the lower applied loads but with a reduced magnitude. Through the experimental data, an activation volume and activation energy were extracted for the delayed plasticity. The results show that Fe3+-irradiation significantly reduced its activation volume from ∼3.05b3 to ∼1.75b3 (where b = Burgers vector), but slightly increased its activation energy from ∼0.65 to ∼0.71 eV. On the other hand, high-resolution scanning transmission electron microscopy observations reveal that the irradiation at the elevated temperature created interstitial atom pair onto the (100) habit plane that can serve as the nucleation site of a 〈100〉 dislocation loop while eliminating the pre-existing dislocations. Consequently, it is indicated that heterogeneous nucleation of the dislocation loop was predominant in the delayed plasticity initiation of this alloy and that the nucleation of the interstitial-type dislocation loop was involved due to Fe3+-irradiation.

Objective molecular dynamics study of cross slip under high-rate deformation

In this paper, we investigate high-strain-rate deformations in crystalline materials using a novel implementation of Objective Molecular Dynamics (OMD). The OMD method is exact and has a rigorous foundation based on the fundamental invariance of the underlying potential energy surface: all atoms out to infinity satisfy the equations of molecular dynamics to high accuracy. Using this OMD method, we compute how dislocations filling all of the space in a crystalline material undergo time-dependent, three-dimensional motions during deformation. We apply this method to investigate the dynamics of screw dislocations in FCC nickel. Our key finding is that the macroscopic motion (i.e., loading conditions) and initial conditions greatly affect the atomic scale deformation mechanisms—such as the formation, motion, multiplication, annihilation, and abrupt changes of the slip plane and Burgers vector of dislocations. Small changes in the macroscopic loading conditions generate a rich variety of atomic deformation pathways. In certain macroscopic motions, we observe the growth of a stacking fault into a mechanical twin, which subsequently thickens by a process of step motion. In other macroscopic motions, we observe the initiation and subsequent development of cross-slip by the Friedel–Escaig (FE) or Fleischer mechanisms (FL). Under mixed loading conditions, a novel mechanism, with a combination of both FE and FL mechanisms was also observed. Our findings on the effect of external strain rate and temperature on the critical stress for homogeneous cross-slip quantitatively agree with a version of transition state theory with a stress-dependent activation barrier. Beyond dislocation motion, we demonstrate the modeling of sliding surfaces using the OMD framework. These examples highlight potential applications of the OMD framework to the mechanisms underlying plastic deformation and friction in material systems.

The etching behaviour of dislocations in N-doped 4H-SiC substrate

The substrate-induced dislocations in the homo-epitaxial film could affect the quality of the epitaxial layer and lead to degradation of the device performance and stability. Effective evaluation of dislocations in 4H-SiC substrate is crucial for the quality control of the material. This work reported the etching behaviours of threading screw dislocation (TSD), threading edge dislocation (TED), and basal plane dislocation (BPD) in 4H-SiC substrate. Potassium hydroxide (KOH) and sodium peroxide (Na2O2) with different mass ratios were used as etchants. It was found that the average size of etching pits for each kind of dislocation increased linearly with the increase in the mass ratios of Na2O2. Interestingly, the slope of the linear increase for TSD was significantly larger than that of TED or BPD, which implies that the etching behaviour of TSD is more sensitive to the oxidant content in etchants, compared to TED and BPD. This outcome is related to the larger Burgers vector in TSD. In addition, the slope of TED was nearly equal to that of BPD due to the same Burgers vectors in them. The results in the work are helpful for understanding the etching mechanism and improving the etching technology for 4H-SiC substrate and epitaxial film.

Formation mechanism of dislocation network of cell structure in cyclically deformed near-[formula omitted] copper single crystals

As the initiation and propagation of fatigue crack is strongly correlated to the dislocations in cell structures of metals, investigating the formation of dislocation cell structures is essential for understanding the fatigue process. Although the cell boundary evolves from the dislocation network, the formation process of the dislocation network of fatigued copper single crystal is not completely realized. In this study, the dislocation structures in near-[1‾11] copper single crystals cyclically deformed at 293 K were investigated to analyze the formation mechanism of the dislocation network. The dislocation networks were characterized using a high-voltage scanning transmission electron microscope, where the virtual-scanning transmission electron microscope technique (virtual-STEM) was employed to conduct the Burgers vector analysis of the dislocations. The low-dislocation-density network was consistent with the three perfect screw dislocations (b = a/2 [1‾01], a/2 [1‾10], and a/2 [011‾]) in the (111) primary slip plane. For the high-dislocation-density region, the perfect and partial dislocations coexisted in the network. As the dislocation density increased, the perfect dislocations dissociated into Shockley partial dislocations (b = a/6 [1‾21‾], a/6 [112‾], and a/6 [2‾11]). This study provides a reference for future applications of the virtual-STEM technique in the field of dislocation analysis.

Bound states at disclinations: an additive rule of real and reciprocal space topology

Focusing on the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model, we propose an additive rule between the real-space topological invariant s of disclinations (related to the Burgers vector B) and the reciprocal-space topological invariant p of bulk wave functions (the vectored Zak phase). The disclination-induced bound states in the 2D SSH model appear only if (s + p/2π) is nonzero modulo the lattice constant. These disclination-bound states are robust against perturbations respecting C4 point group symmetry and other perturbations within an amplitude determined by p. Besides the disclination-bound states, the proposed additive rule also suggests that a half-bound state extends over only half of a sample and a hybrid-bound state, which always have a nonvanishing component of s + p/2π.

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.