Edge Dislocation Lines Research Articles

Melted grain boundaries in smectic A under imposed bend: role of the anisotropy

ABSTRACT The well-known de Gennes analogy between smectics and superconductors predicts two types of smectic A behaviour under imposed bend. In Type I smectics, the smectic order melts, expelling all of the bend in a bulk nematic region (3D ‘defect’). In Type II smectics, the order melts on 1D defects, edge dislocation lines, which form an Abrikosov-like lattice. Here, I discuss how the strong anisotropy of the smectic coherence lengths influence the smectic A behaviour under imposed bend distortion. I show analytically and numerically that, as proposed previously, a third type of behaviour is possible close to a second-order nematic–smectic A transition, with smectic order melting on the plane of the grain boundary (2D defects). This third kind of behaviour, Melted Grain Boundary (MGB), which has been previously reported experimentally in the smectic A material 9CB, is intermediate between the Type I and Type II behaviours and can be considered as Type ‘one-and-a-half’ smectic A. I define the domain of material parameters in which the planar MGB defect is energetically and topologically stable. I discuss also if similar planar defects may exist, or not, in other anisotropic materials, e.g. superconductors, chiral smectic A, cholesterics and twist-bend nematics.

Observation and quantitative analysis of dislocations in steel using electron channeling contrast imaging method with precise control of electron beam incident direction.

Electron channeling contrast imaging (ECCI) was applied by precisely controlling the primary electron beam incident direction of the crystal plane in scanning electron microscope (SEM), and the dislocation contrast in steel materials was investigated in detail via SEM/ECCI. The dislocation contrast was observed near a channeling condition, where the incident electron beam direction of the crystal plane varied, and the backscattered electron intensity reached a local minimum. Comparing the dislocation contrasts in the visualized electron channeling contrast (ECC) images and transmission electron microscope (TEM) images, the positions of all dislocation lines were coincident. During the SEM/ECCI observation, the dislocation contrast varied depending on the incident electron beam direction of the crystal plane and accelerating voltages, and optimal conditions existed. When the diffraction condition g and the Burgers vector b of dislocation satisfied the condition g⸱b = 0, the screw dislocation contrast in the ECC image disappeared. An edge dislocation line was wider than a screw dislocation line. Thus, the SEM/ECCI method can be used for dislocation characterization and the strain field evaluation around dislocation, like the TEM method. The depth information of SEM/ECCI, where the channeling condition is strictly satisfied, can be obtained from dislocation contrast deeper than 5ξg, typically used for depth of SEM/ECCI.

The channeling effect of symmetrical tilt grain boundaries on helium bubbles in tungsten

Helium atoms can migrate easily and aggregate at various crystal defects, such as grain boundaries, which promote the nucleation and growth of helium bubbles, ultimately causing severe radiation damage to nuclear materials. Structure characteristics of grain boundaries with low-angle symmetrical tilt of the [100] axle and their channeling effects on helium bubbles in tungsten were investigated by molecular dynamics simulations. The triaxial variation curves of the helium bubble size in each grain boundary model and the relationship of the helium diffusion coefficient of each grain boundary to their intrinsic crystal structures are analyzed. The results indicate that the helium bubbles grow into one-dimensional nanochannels at the selected grain boundaries, and there is a significant difference in the maximum number of helium bubbles these grain boundaries can accommodate before forming one-dimensional nanochannels. Furthermore, the existence of helium nanochannels along the 〈100〉 edge dislocation line in the low-angle symmetrical tilt grain boundaries is well verified by molecular dynamics simulation of the helium bubble growth and helium diffusion equations at the 〈100〉 edge dislocation line. This suggests that releasing helium outside of the tungsten matrix through the nanochannel structures of low-angle symmetrical tilt grain boundaries may be a potential strategy to address the root causes of bubble nucleation and swelling of tungsten material.

The strong hardening effect of Re segregation on edge dislocation lines in W

We investigate the radiation hardening induced by the segregation of solute Re atoms along edge dislocation lines in W. Given the Re content and the irradiation temperature (which are chosen to represent both ITER and DEMO conditions), reference atomic configurations are first obtained with Metropolis Monte Carlo, where the equilibrium Re content at the dislocation core is evaluated. Next, the critical unpinning shear stress is evaluated with a molecular dynamics tool and the classical method of Barnett et al. The study reveals that the effect of Re segregation is strong, its magnitude could be compared with the pinning effect of other radiation defects such as nanovoids, dislocation loops and Re-rich precipitates formed in bulk. This form of hardening is therefore important and should be taken into account in higher scale models.

Coupled effect of Cr and Al on interactions between a prismatic interstitial dislocation loop and an edge dislocation line in Fe-Cr-Al alloy

Segregation of alloying elements to a prismatic dislocation loop under irradiation is an important phenomenon in understanding the role of loops in radiation effects in alloys. In this work, various segregation sequences of Cr and Al atoms to a 〈100〉 and a 1/2〈111〉prismatic dislocation loop in a Fe-Cr-Al alloy are explored using molecular dynamics method and ab initio energy calculation. The results reveal that Cr can readily segregate to the loops while Al atoms cannot by themselves, but the segregated Cr atoms are able to promote Al segregation at the loops, defined as a coupled segregation of Cr and Al. After interacting with Cr and Al, a previously mobile 1/2〈111〉 loop becomes sessile. Al segregation through the coupled segregation process can further affect the pinning behavior of a dislocation loop to an edge dislocation motion. By varying the Al fraction in the segregated solutes, a nonlinear dependence of the pinning effect on dislocation motion is determined. At lower fractions, the pinning strength increases with the increasing Al fraction until Al fraction reaches a critical value of about 19%, above which the pinning strength decreases with further increase of Al fraction. All these results suggest that, in addition to the effect of Al on the surface resistance to oxidation, Al effect on the dislocation loop behavior is important to optimize the composition of Fe-Cr-Al alloys for their applications in accident tolerant fuel concepts.

Vacancy Energetics and Diffusivities in the Equiatomic Multielement Nb-Mo-Ta-W Alloy.

In this work, we study vacancy energetics in the equiatomic Nb-Mo-Ta-W alloy, especially vacancy formation and migration energies, using molecular statics calculations based on a spectral neighbor analysis potential specifically developed for Nb-Mo-Ta-W. We consider vacancy properties in bulk environments as well as near edge dislocation cores, including the effect of short-range order (SRO) by preparing supercells through Metropolis Monte-Carlo relaxations and temperature on the calculation. The nudged elastic band (NEB) method is applied to study vacancy migration energies. Our results show that both vacancy formation energies and vacancy migration energies are statistically distributed with a wide spread, on the order of 1.0 eV in some cases, and display a noticeable dependence on SRO. We find that, in some cases, vacancies can form with very low energies at edge dislocation cores, from which we hypothesize the formation of stable ‘superjogs’ on edge dislocation lines. Moreover, the large spread in vacancy formation energies results in an asymmetric thermal sampling of the formation energy distribution towards lower values. This gives rise to effective vacancy formation energies that are noticeably lower than the distribution averages. We study the effect that this phenomenon has on the vacancy diffusivity in the alloy and discuss the implications of our findings on the structural features of Nb-Mo-Ta-W.

The combined effect of carbon and chromium enrichment on 〈1 0 0〉 loop absorption in iron

In this work we study the effects of C and Cr enrichment of 〈100〉 dislocation loops (DL) on their absorption and obstacle strength when interacting with an edge dislocation. To do so, we have i) developed a C-Cr cross potential based on density functional theory data as part of a ternary FeCrC interatomic potential; ii) performed exchange Monte Carlo simulations employing the developed interatomic potential to obtain the distribution of the solutes enriching the DL in the energetically optimum configurations; iii) performed large scale molecular dynamics simulations employing the interatomic potential to characterize the interaction between an edge dislocation line and the decorated DL. We found that the obstacle stress scales to the same obstacle strength regardless the DL density. On the other hand, we found that C, the level of Cr enrichment, loop size and interaction temperature have a significant impact on the obstacle strength and level of absorption of the loops. The presented results can be used to help parameterize and validate discrete dislocation dynamics codes and therein integrated constitutive laws to enable accounting for irradiation-induced chemical segregation effects.

Observation of Hidden Parts of Dislocation Loops in Thin Pb Films by Means of Scanning Tunneling Spectroscopy

Local electronic properties of quasi-two-dimensional Pb(111) islands with screw dislocations of different types on their surfaces were experimentally studied by means of low-temperature scanning tunneling microscopy and spectroscopy in the regime of constant current. A comparison of the topography map, the maps of tunneling current variation and the differential tunneling conductance acquired simultaneously allows one to visualize the hidden parts of the dislocation loops under the sample surface. We demonstrate that two closely-positioned screw dislocations with the opposite Burgers vectors can either (i) connect to each other by the sub-surface dislocation loop or (ii) generate independent hidden edge dislocation lines which run towards the perimeter of the Pb island. In addition, we found a screw dislocation, which does not produce outcoming sub-surface dislocation loops. Screw dislocations and the hidden dislocations lines are the source of the non-quantized variation of the local thickness of the Pb terraces, affecting the local electronic properties.

Chemo-mechanical study of dislocation mediated ion diffusion in lithium-ion battery materials

A mechanically coupled diffusion model combined with finite element formulation is developed to study the influence of dislocations on ion diffusion in lithium-ion batteries. The dislocation is modeled by the regularized eigenstrain based on a non-singular continuum dislocation theory. The model is validated with the analytical solution of the stress field of edge dislocations and the solution for the stress-dependent equilibrium concentration around the dislocation. Simulation results on LiMn2O4 demonstrate strong ion enrichment and depletion on the tensile and compressive sides of an edge dislocation, respectively. A stronger influence of the edge dislocation on diffusion is found at a lower state-of-charge, which verifies the experimental observation reported in the literature. The diffusion-induced stress compensates partially the stress field of the edge dislocation and is ascertained to have a state-of-charge dependency. The existence of dislocation does not introduce obvious mobility anisotropy in the bulk material but it results in local mobility heterogeneity around the dislocation. A three-dimensional simulation of the diffusion along the edge dislocation line reveals that the pipe diffusion can be initiated or accelerated on the tensile side of the edge dislocation.

Impact of interstitial impurities on the trapping of dislocation loops in tungsten

Ab initio simulations are employed to assess the interaction of typical interstitial impurities with self-interstitial atoms, dislocation loops and edge dislocation lines in tungsten. These impurities are present in commercial tungsten grades and are also created as a result of neutron transmutation or the plasma in-take process. The relevance of the study is determined by the application of tungsten as first wall material in fusion reactors. For the defects with dislocation character, the following ordering of the interaction strength was established: H < N < C < O < He. The magnitude of the interaction energy was rationalized by decomposing it into elastic (related to the lattice strain) and chemical (related to local electron density) contributions. To account for the combined effect of impurity concentration and pinning strength, the impact of the presence of these impurities on the mobility of isolated dislocation loops was studied for DEMO relevant conditions in the non-elastic and dilute limit.

Interdependent Linear Complexion Structure and Dislocation Mechanics in Fe-Ni

Using large-scale atomistic simulations, dislocation mechanics in the presence of linear complexions are investigated in an Fe-Ni alloy, where the complexions appear as nanoparticle arrays along edge dislocation lines. When mechanical shear stress is applied to drive dislocation motion, a strong pinning effect is observed where the defects are restricted by their own linear complexion structures. This pinning effect becomes weaker after the first dislocation break-away event, leading to a stress-strain curve with a profound initial yield point, similar to the static strain aging behavior observed experimentally for Fe-Mn alloys with the same type of linear complexions. The existence of such a response can be explained by local diffusion-less and lattice distortive transformations corresponding to L10-to-B2 phase transitions within the linear complexion nanoparticles. As such, an interdependence between a linear complexion structure and dislocation mechanics is found.

The effect on the mechanical response of Cr and Ni segregation on dislocation lines in bcc Fe

The understanding of irradiation-induced strengthening in ferritic-martensitic high-Cr steels remains an essential issue in the assessment of materials for fusion and next generation fission reactors. Recent advanced experimental studies revealed the importance of solute-rich clusters, containing Cr, Ni, Si, P and Mn, which often are created as a consequence of segregation at dislocation lines. In this work, Metropolis Monte Carlo (MMC) is applied to investigate segregation of Cr and Ni atoms around edge dislocation lines in bcc Fe. The content of Cr is varied between 7% and 10%, with and without 0.25% of Ni. Molecular dynamics has subsequently been applied to the enriched dislocation lines to study the critical resolved shear stress at 300 K and 600 K for different concentrations of solutes in the alloy. It is found that even small amounts of Ni significantly increase the hardening of the material.

Interactions between displacement cascade and dislocation and their influences on Peierls stress in Fe-20Cr-25Ni alloys

The interactions between dislocations and displacement cascades are investigated using molecular dynamics simulations. The primary knock-on atoms (PKAs) are placed at different distances to edge and screw dislocation lines. Specifically, an fcc Fe-20Cr-25Ni system is studied; the alloy is the based alloy for Alloy 709. The number of defects is calculated using Wigner-Seitz analysis in order to illustrate the effect of dislocations on cascades. The displacement cascades in systems containing dislocations tend to generate more total defects compared with bulk systems, but eventually lead to less surviving defects in the materials matrix due to interactions with dislocations. The changes in atomic structures of the dislocations after interacting with cascades are analyzed to understand how the primary damage affects dislocations. The displacement cascade potentially causes dislocation climb in edge dislocations and cross-slip in screw dislocations, which could serve as additional mechanisms contributing to the radiation-induced hardening (RIH) compared with conventional RIH models. To reveal this, Peierls stresses are calculated before and after cascades using molecular static simulations. This study provides critical information of how defect production and dislocations are correlated, especially when total dose is high, which needs to be taken into account in upper scale models, such as mean-field rate theory.

Atomistic study of hydrogen behavior around dislocations in α iron

Atomic-level studies have been performed to investigate the hydrogen behavior near a 1/2<111>{110} edge dislocation and a 1/2<111> screw dislocation in α iron. Molecular statics analysis has been carried out to determine the stress distributions and hydrogen binding energy around the dislocation cores. The results reveal that the hydrogen binding is more sensitive to the hydrostatics stress than the shear stress around the edge dislocation, while the shear stress plays a leading role on the hydrogen binding around the screw dislocation. In addition, nudged elastic band (NEB) calculations have been applied to explore different migration paths and the corresponding migration energy barriers of a single hydrogen atom at the dislocation cores. It is of interest to note that both edge and screw dislocations are not able to offer fast pipe diffusion of hydrogen atoms along the dislocation line, as normally considered. Instead, hydrogen atoms prefer to diffuse slowly along oblique paths crossing the edge dislocation line on the slip plane and spiral paths surrounding the screw dislocation line. Furthermore, molecular dynamics simulations have been performed to study the diffusion behavior of hydrogen at the dislocation cores, which verifies the results of NEB calculations.

Line tension of a dislocation moving through an anisotropic crystal

ABSTRACTPlastic deformation, at all strain rates, is accommodated by the collective motion of crystalline defects known as dislocations. Here, we extend an analysis for the energetic stability of a straight dislocation, the so-called line tension (Γ), to steady-state moving dislocations within elastically anisotropic media. Upon simplification to isotropy, our model reduces to an explicit analytical form yielding insight into the behaviour of Γ with increasing velocity. We find that at the first shear wave speed within an isotropic solid, the screw dislocation line tension diverges positively indicating infinite stability. The edge dislocation line tension, on the other hand, changes sign at approximately of the first shear wave speed, and subsequently diverges negatively indicating that the straight configuration is energetically unstable. In anisotropic crystals, the dependence of Γ on the dislocation velocity is significantly more complex; at velocities approaching the first shear wave speed within the plane of the crystal defined by the dislocation line, Γ tends to diverge, with the sign of the divergence strongly dependent on both the elastic properties of the crystal and the orientation of the dislocation line. We interpret our analyses within the context of recent molecular dynamics simulations of the motion of dislocations near the first shear wave speed. Both the simulations and our analyses are indicative of instabilities of nominally edge dislocations within fcc crystals approaching the first shear wave speed. We apply our analyses towards predicting the behaviour of dislocations within bcc crystals in the vicinity of the first shear wave speed.

Modeling of polarization distribution around vibrating edge dislocation in ferroelectric crystal

On the assumption that the dislocation oscillates according to the harmonic law, the authors was found a general expression for the polarization components around the dislocation. The case of small dislocation oscillations is considered. It was assumed that the active ferroelectric axis coincides with an equilibrium position of the edge dislocation line. The amplitude of the polarization around the vibrating edge dislocation at the distance from the dislocation line in the two cases, corresponding local oscillations, is found. The laws of decreasing the modulus of the polarization amplitude at the distance from the dislocation line are determined.

Superfluid field response to edge dislocation motion

We study the dynamic response of a superfluid field to a moving edge dislocation line to which the field is minimally coupled. We use a dissipative Gross-Pitaevskii equation, and determine the initial conditions by solving the equilibrium version of the model. We consider the subsequent time evolution of the field for both glide and climb dislocation motion and analyze the results for a range of values of the constant speed $V_D$ of the moving dislocation. We find that the type of motion of the dislocation line is very important in determining the time evolution of the superfluid field distribution associated with it. Climb motion of the dislocation line induces increasing asymmetry, as function of time, in the field profile, with part of the probability being, as it were, left behind. On the other hand, glide motion has no effect on the symmetry properties of the superfluid field distribution. Damping of the superfluid field due to excitations associated with the moving dislocation line occurs in both cases.

Orientational action of edge dislocations on the director field in antiferroelectric smectic-C_{A}^{*} films.

We report imaging of the director field near edge dislocations in thermotropic antiferroelecric smectic-C_{A}^{*} (SmC_{A}^{*}) liquid crystal. Measurements were made in freestanding films with thickness from two to ten smectic layers. We find two different orientations of the molecular tilt plane with respect to the edge dislocation line. The orientation is determined by the value of the Burgers vector of the dislocation. Elementary edge dislocation and dislocations with a Burgers vector equal to an odd number of layers orient the tilt plane perpendicular on the two sides of the dislocation. Dislocations with a Burgers vector equal to an even number of layers orient the molecular tilt plane parallel to the dislocation line. Difference in the orientation for an odd Burgers vector can be attributed to breaking of antiferroelectric symmetry by the edge dislocation.

Determination of dislocation density of a class of n-GaN based on the variable temperature Hall-effect method

An analytical model for electron mobility in a class of wurtzite n-GaN, whose carrier concentration is over 1018 cm-3 (Mott's critical limit), is developed. With the dislocation density and two donor levels serving as the important parameters, the proposed model can accurately predict the electron mobility as a function of temperature. The edge and screw dislocation densities in two samples, which are respectively grown on sapphire (001) by metal organic chemical vapor deposition and hydride vapor phase epitaxy, are determined by using this model which is discussed in detail. It is shown that the data-fitting of H-T characteristic curve is a highly suitable technique for accurately determining the edge and screw dislocation densities in n-GaN films. Quantitative analyses of donor concentration and donor activation energy indicate that the impurity band occurs when the carrier concentration is under 1017 cm-3, much lower than the critical carrier concentration of Mott transition (1018 cm-3). Such a behavior can also be confirmed by the results from solving the Boltzmann transport equation by using the Rode iterative method. Another anomaly is that the dislocation density in Mott transition material perhaps is lower than that of material with carrier concentration under 1018 cm-3. This fact indicates that the cause of Mott transition should not be the shallow donor impurities around dislocation lines, but perhaps the deeper donor impurities or other defects. In the theoretical model calculation, two transition characteristics together with the donor distribution and its energy equilibrium are taken into account. Based both on the Mott transition and the H-like electron state model, the relaxation energies for the shallow-donor defects along the screw and edge dislocation lines are calculated by using an electrical ensemble average method. Besides, an assumption that should be made is that there are 6 shallow-donor defect lines around one dislocation line. The research results show that the Hall mobility should be taken as the live degree of the ionizing energy for the shallow-donor defects along the dislocation line. The experimental results indicate that our calculation function can be best fit by the experimental curve, with the values of dislocation density being between our model and others determined by X-ray diffraction or by chemical etching method, which are all in good agreement with each other. The method reported can be applied to the wurtzite n-GaN films grown by various preparation technologies under any condition, with the peak-mobility temperature about or over 300 K, whose Hall mobility near 0 K perhaps is over 10 cm2/(Vs) and even 100 cm2/(Vs).

Confined chemical and structural states at dislocations in Fe-9wt%Mn steels: A correlative TEM-atom probe study combined with multiscale modelling

We investigated a high-purity cold-rolled martensitic Fe-9wt%Mn alloy. Tensile tests performed at room temperature after tempering for 6 h at 450 °C showed discontinuous yielding. Such static strain ageing phenomena in Fe are usually associated with the segregation of interstitial elements such as C or N to dislocations. Here we show by correlative transmission electron microscopy (TEM)/atom probe tomography (APT) experiments that in this case Mn segregation to edge dislocations associated with the formation of confined austenitic states causes similar effects. The local chemical composition at the dislocation cores was investigated for different tempering temperatures by APT relative to the adjacent bcc matrix. In all cases the Mn partitioning to the dislocation core regions matches to the one between ferrite and austenite in thermodynamic equilibrium at the corresponding tempering temperature. Although a stable structural and chemical confined austenitic state has formed at the dislocation cores these regions do not grow further even upon prolonged tempering. Simulation reveals that the high Mn enrichment along the edge dislocation lines (25 at.%Mn at 450 °C) cannot be described merely as a Cottrell atmosphere formed by segregation driven by size interaction. Thermodynamic calculations based on a multiscale model indicate that these austenite states at the dislocation cores are subcritical and defect-stabilized by the compression stress field of the edge dislocations. Phenomenologically, these states are the 1D equivalent to the so-called complexions which have been extensively reported to be present at 2D defects, hence have been named linear complexions.