Interaction of two edge dislocations in free-space propagation

This paper studies in detail the interaction of two edge dislocations nested in a Gaussian beam propagating in free space. It shows that in free-space propagation the edge dislocations are unstable and vanish, and two noncanonical vortices with opposite topological charge take place when off-axis distances cl and c2 of two edge dislocations are nonzero, and the condition k2w08＋ 32c1c2（w02- 2C1C2）Z2 〉 0 is fulfilled （k-wave number, w0-waist width）. A noncanonical vortex appears when one off-axis distance is zero. However, one edge dislocation is stable when two edge dislocations are perpendicular and one off-axis distance is zero. Two perpendicular edge dislocations both with zero off-axis distance are also stable. The analytical results are illustrated by numerical examples.

Atomic simulation for influence of helium atom on movement of edge dislocation in nickel

The molecular dynamics （MD） simulation and the modified analytical embedded-atom method （MAEAM） were used to study the influence of a He atom on the movement of the（a/2）？110？{111} edge dislocation in Ni. First, the calculated Burgers vector distribution shows that the equilibrium dissociation distance （Ded） and the stacking fault energy （Esf） between two partial edge dislocations are about 25.95 ？ and 108 mJ/m2, respectively. Then, the obtained formation energies （Ef） of a He atom at some different sites demonstrate that the He atom is attracted and repelled in the tension and compression regions, respectively. And the He？dislocation interaction reveals that an interstitial He atom plays a more significant role in the dislocation movement than a substitutional He atom. Finally, it is found that the movement of an interstitial He atom is apparent as the first partial dislocation bypasses and the edge dislocation offers fast-diffusion path for the migration of a He atom.

Investigation of dislocations in 8° off-axis 4H-SiC epilayer

This paper reports that the etching morphology of dislocations in 8° off-axis 4H-SiC epilayer is observed by using a scanning electronic microscope. It is found that different types of dislocations correspond with different densities and basal plane dislcation （BPD） array and threading edge dislocation （TED） pileup group lie along some certain crystal directions in the epilayer. It is concluded that the elastic energy of threading screw dislocations （TSDs） is highest and TEDs is lowest among these dislocations, so the density of TSDs is lower than TEDs. The BPDs can convert to TEDs but TSDs can only propagate into the epilyer in spite of the higher elastic energy than TEDs. The reason of the form of BPDs array in epilayer is that the big step along the basal plane caused by face defects blocked the upstream atoms, and TEDs pileup group is that the dislocations slide is blocked by dislocation groups in epilayer.

Molecular dynamics study of interactions between edge dislocation and irradiation-induced defects in Fe–10Ni–20Cr alloy

Irradiation-induced defects frequently impede the slip of dislocations, resulting in a sharp decline in the performance of nuclear reactor structural materials, particularly core structural materials. In the present work, molecular dynamics method is used to investigate the interactions between edge dislocations and three typical irradiation-induced defects(void,Frank loop, and stacking fault tetrahedron) with the sizes of 3 nm, 5 nm, and 7 nm at different temperatures in Fe–10Ni–20Cr alloy. The critical resolved shear stresses(CRSSs) are compared among different defect types after interacting with edge dislocations. The results show that the CRSS decreases with temperature increasing and defect size decreasing for each defect type during the interaction with edge dislocations, except for the case of 3-nm Frank loops at 900 K. According to a comparison, the CRSS in Frank loop is significantly higher than that of others of the same size, which is due to the occurrence of unfaulting and formation of superjog or stacking-fault complex during the interaction. The atomic evolution of irradiation-induced defects after interacting with dislocations can provide a novel insight into the design of new structural materials.

Elastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack

The interaction between an edge dislocation and a crack emanating from a senti-elliptic hole is dealt with. Utilizing the complex variable method, closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the edge dislocation are also calculated. The influence of the morphology of the blunt crack and the position of the edge dislocation on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases acutely when the dislocation approaches the tip of the crack. The effect of the morphology of the blunt crack on the stress intensity factor of the crack and the image force is very significant.

Propagation of partially coherent beams carrying an edge dislocation through atmospheric turbulence along a slant path

This paper derives the explicit expressions for the average intensity, beam width and angular spread of Gaussian Schell-model （GSM） beams with edge dislocation propagating through atmospheric turbulence along a slant path. The propagation of GSM beams with edge dislocation through horizontal atmospheric turbulence can be treated as a special case through a slant one. The propagation properties of GSM beams with edge dislocation through slant atmospheric turbulence are studied, where the influence of edge dislocation parameters including the slope p and off-axis distance d on the spreading of GSM beams with edge dislocation in atmospheric turbulence is stressed. It shows that the spreading of the intensity profile of GSM beams with edge dislocation along a slant path is smaller than that along a horizontal path in the long-distance atmospheric propagation. The larger the slope ｜p｜ and the smaller the off-axis distance ｜d｜ are, the less the beam-width spreading and angular spread of GSM beams with edge dislocation are affected by turbulence. The CSM beams with edge dislocation is less affected by turbulence than that of GSM beams without edge dislocation. The results are illustrated numerically and their validity is interpreted physically.

Atomistic simulation of kink structure on edge dislocation in bcc iron

Based on the general theory of dislocation and kink, we have constructed the three kink models corresponding to the 1/2 （111）{011} and 1/2 （111）{112} edge dislocations （EDs） in bcc Fe using the molecular dynamics method. We found that the geometric structure of a kink depends on the type of ED and the structural energies of the atom sites in the dislocation core region, as well as the geometric symmetry of the dislocation core and the characteristic of the stacking sequence of atomic plane along the dislocation line. The formation energies and widths of the kinks on the 1/2 （111）{011} and 1/2 （111）{112} EDs are calculated, the formation energies are 0.05eV and 0.04eV, and widths are 6.02b and 6.51b, respectively （b is the magnitude of the Burgers vector）. The small formation energies indicate that the formation of kink in the edge dislocation is very easy in bcc Fe.

Relaxed energy and structure of edge dislocation in iron

With modified analytical embedded-atom method and molecular dynamics simulation, this paper simulates the strain energy and the equilibrium core structure of a（100） edge dislocation in BCC metal iron on atomistic scale. In addition, the trapping effect of dislocation on vacancy is investigated as well. The results show that the equilibrium dislocation core is quite narrow and has a C2v symmetry structure. Calculated strain energy Es of the dislocation is a linear function of ln（R/2b） while R ≥ 5.16 A（1A = 0.1 nm）, in excellent agreement with the elasticity theory prediction. Determined core radius and energy are 5.16 A and 0.62 eV/A, respectively. The closer the vacancy to the dislocation line is, the lower the vacancy formation energy is, this fact implies that the dislocation has a trend to trap the vacancy, especially for a separation distance of the vacancy from dislocation line being less than two lattice constants.

Influence of dislocations in the GaN layer on the electrical properties of an AlGaN/GaN heterostructure

This paper reports on a comparative study of the spatial distributions of the electrical, optical, and structural properties in an AlGaN/GaN heterostructure. Edge dislocation density in the GaN template layer is shown to decrease in the regions of the wafer where the heterostructure sheet resistance increases and the GaN photoluminescence bandedge energy peak shifts to a high wavelength. This phenomenon is found to be attributed to the local compressive strain surrounding edge dislocation, which will generate a local piezoelectric polarization field in the GaN layer in the opposite direction to the piezoelectric polarization field in the AlGaN layer and thus help to increase the two-dimensional electron gas concentration.

On edge dislocation in a multilayered laminate

We investigate the elastic field induced by an edge dislocation in a multilayered laminated composite composed of(N—2)thin bonded elastic layers sandwiched between two semi-infinite elastic media.A simple closed-form solution is obtained when all the phases have equal shear modulus but different Poisson's ratios,and when the dislocation is located in the upper semi-infinite phase.The image force acting on the dislocation due to its interaction with the multilayered structure is also derived. Several specific examples are discussed in detail to illustrate the mobility of the edge dislocation. Some interesting behaviors of the dislocation are observed.Our results indicate that it is possible to find at most(N—2)equilibrium positions for the edge dislocation in an N-phase composite structure.

Stress Field of Straight Edge Dislocation in Magnetic Field

To study the changes in mechanical properties of materials within magnetic fields and the motion of dislocations, stress fields of dislocation in magnetic field need to be calculated. The straight edge dislocation is of basic importance in various defects . The stress field of straight edge dislocation in an external static magnetic field is determined by the theory of elasticity and electrodynamics according to the Volterra dislocation model for continuous media. This reduces to the known stress field when the magnet field is zero. The results can be used for further study on the strain energy of dislocations and the interactions between dislocations in magnetic fields.

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.

Phase-field crystal simulation of evolution of liquid pools in grain boundary pre-melting regions

Pre-melting is a phenomenon that below the melting point the liquid-like structure appears at the grainboundary while the grain interior remains a crystal structure. The phase-field crystal method was employed to investigate the early evolution of the liquid pools in pre-melting regions, mainly involving four structural transformations: solid-solid state → small droplet → large liquid pool → homogeneous liquid melting. The microscopic morphology and free energy variation with different average atomic densities demonstrate that the average atomic density is sensitive to the morphological characteristics of liquid pools. Both two-dimensional and three-dimensional simulation results show that the amplitude reduction of order parameters can promote the order-disorder transition of grain boundaries, causing pre-melting in the edge dislocation aggregation. The relationship between the average atomic density and the width of the liquid pools is verified from thermodynamics, which provides a prerequisite for the application of high-temperature strain in the later stage to some extent.

Edge dislocation-induced strains break the limit of PtNi alloys in boosting Pt mass activity for efficient alkaline hydrogen evolution

Creating lattice defects and alloying to produce strain effect in Pt-based bimetallic alloys are both effective methods to optimize the crystal and electronic structure and improve the electrocatalytic performance.Unfortunately,the principles that govern the alkaline hydrogen evolution reaction(HER)performance remain unclear,which is detrimental to the rational design of efficient Pt-based electrocatalysts.Herein,PtNi alloys with different Pt/Ni ratios and edge dislocations were synthesized,and the effects of Pt/Ni composition and edge dislocations on the alkaline HER electrocatalytic activity of PtNi alloys were systematically studied.Combined experimental and theoretical investigations reveal that tuning Pt/Ni ratio results in only 1.1 times enhancements in Pt mass activity,whereas edge dislocations-induced extra tensile strain on Ni site and compressive strain on Pt site further boost the alkaline HER intrinsic activity at all Pt/Ni ratios.Impressively,the introduction of edge dislocations in PtNi alloys could break the limit of alloying in boosting Pt mass activity and result in up to 13.7-fold enhancement,in the case that Pt and Ni contents are nearly identical and thus edge dislocation density reaches the maximum.Fundamental mechanism studies demonstrate that the edge dislocation strategy could make a breakthrough in facilitating water dissociation kinetics of PtNi alloys.

Mode Ⅰ Plane Crack Interacting with an Interfacial Crack Along a Circular Inhomogeneity

The elastic interaction of the mode Ⅰ plane crack with an interracial crack along a circular inhomogeneity is dealt with. The dislocation density and the stress intensity factors （SIFs） of the mode I plane crack are obtained numerically. A new kind of dislocation equilibrium equation about the plane crack is applied. The influence of some material parameters on the dislocation density and SIFs are analyzed.

A Frank-Read Source Model

The temporal dynamics of the edge dislocation (ED) was studied in this work using the inhomogeneous dissipative sine-Gordon (SG) equation. The consideration was carried out for the force action levels both less and more critical. By SG equation numerical calculations it is shown that at the external force value below a critical one the ED takes a shape close to a semicircle. This shape was used as an initial condition for describing the ED temporal dynamics in the FR source operating mode. A particular solution of the SG equation is proposed that describes the temporal dynamics of half the ED in the FR mode, which rests on a stopper at the origin. It is shown that the proposed particular solution corresponds to the left Archimedes spiral displaced at π/2 counterclockwise relative to the azimuth angle equal to zero. It is noted that the temporal dynamics of the second half of the ED segment rested on the second stopper is described by the proposed particular solution, when it is mirrored relative to the problem symmetry axis and the center of the spiral is displaced to a point with a zero azimuthal angle and a radius equal to the distance between the stoppers. The axis of symmetry is a straight line that is perpendicular and halves the distance between the stoppers. A graphical description of the ED temporal dynamics was plotted in the Cartesian coordinate system based on the proposed particular solution and its mirror and displaced image. It is shown that the particular solution of the SG equation in the RF source operation mode involves two Archimedes spirals symmetrical relative to the problem symmetry axis with equal radii increasing linearly with time, which rotate: one (the spiral center coincides with the stopper at the origin) counterclockwise, the second (the spiral center coincides with the second stopper) clockwise.

SOLUTION CRYSTALLIZATION BEHAVIOR OF LINEAR AND STAR-SHAPED POLY(ETHYLENE GLYCOL)-b-POLY(ε-CAPROLACTONE) BLOCK COPOLYMERS

Lamellar crystals of diblock, triblock and four-arm poly（ethylene glycol）-b-poly（ε-caprolactone） （PEG-b-PCL） crystalline-crystalline copolymers were successfully obtained from their solution. Morphology and structure of lamellar crystals of crystalline-crystalline copotymers were investigated using tapping-mode atomic force microscopy （AFM） and selected area electron diffraction （SAED）. All of these samples showed the truncated-lozenge multilayer basal shapes with central screw dislocation or central stack, which were all obtained simultaneously from the oil bath. The diffraction pattern of PEG block lamellar crystal is attributed to the （120） diffracting planes and the pattern of PCL block lamellar crystal is attributed to the （1 I0） diffracting planes and （200） diffracting planes according to the SAED results. Four （110） crystal growth planes and two （200） crystal growth planes are discovered for the PCL blocks, but the （120） crystal growth planes of PEG blocks are hided in the figure of AFM. The crystalline structure of the four-arm copolymers （FA） is more disorder and confused than that of the diblock （DI） copolymer and the striated fold surface structures of lamellar crystals of four-arm copolymers （FA） are smoother than these of linear analogues, owing to the confused crystallization of blocks caused by the mutual restriction of blocks and the hindrance of the dendritic cores. In addition, the aspect ratio of FA is greater than that of the others. It is hypothesized that there are two reasons for the change of aspect ratios. First, the （200） diffracting planes of PCL crystals grew slowly compared to their （110） diffracting planes because of difference in the energy barrier. Secondly, edge dislocations on the （200） diffracting planes are also responsible for the variation of the aspect ratio. Consequently, the crystalline defects are augmented by the competing blocks crystallized simultaneously and the hindrance of the dendritic cores.