The elastic potential energy of a thin foil deformed by an in-plane 60° dislocation

An explicit expression of the elastic potential energy, W ^p, stored in a thin foil by a dissociated dislocation running parallel to the free surfaces is obtained in isotropic elasticity. It is used to discuss the metastable elastic equilibrium of a 60° dislocation in an ultrathin silicon foil when the fault plane is slightly inclined with respect to the free surfaces. The energy W ^p depends in particular on the positions of the two partials in the foil and on the thickness h, a situation not fully considered previously. For such ultrathin foils, propitious to the observation of partial dislocations cores at near atomic resolution, the theory predicts rapid changes with h of the separation distance S. This result is in accordance with previous experimental observations of S realized with the so-called “forbidden-reflection lattice imaging” technique.     

Interaction of Lomer–Cottrell locks with screw dislocations

In fcc crystals, dislocations are dissociated into partial dislocations and, therefore, restricted to move on {111} glide planes. By junction reactions with dislocations on two intersecting {111} planes, Lomer–Cottrell dislocations along ?110? directions can be formed which are barriers for approaching screw dislocations. Treating the interaction between a dissociated screw dislocation and a LC lock conventionally, using classical continuum theory and assuming the partials to be Volterra dislocations, leads to erroneous conclusions. A realistic result can only be obtained in the framework of the Peierls model, treating the partials as Peierls dislocations and explicitly taking account of the change in atomic misfit energy in the glide plane. At even moderate stresses (at less than 3 × 10^?3 µ in Cu), the screw will combine with the LC lock to form a Hirth lock. As a result, the nature of the repulsive force will change drastically.     

Dislocation configurations around a nanoindentation in the surface of a fcc metal

We report a scanning tunnelling microscopy investigation of the emission of dislocations around nanoindentations in the form of dislocation arrangements previously called hillocks , consisting of two pairs of Shockley partial dislocations, each encompassing a stacking fault. The spatial arrangement and size distribution of hillocks around the nanoindentation traces are studied. We show that standard dislocation theory for an isotropic continuum can be used to describe the stability of the hillocks, their size and spatial distribution and the broadening of the corresponding extended dislocations near the surface. A model is proposed in which hillocks originate from the split into dislocations partials of primary perfect dislocation loops punched into the crystal by the scanning tunnelling microscope tip. This model implies the operation of a novel dislocation mechanism involving long-range transport of matter across the surface.     

Transmission electron microscopy observation of a deformation twin in TWIP steel by an ex situ tensile test

The formation of deformation twins in twinning-induced plasticity steels was observed in transmission electron microscope by an ex situ tensile test. The twinning process initially includes formation of extended dislocations at primary slip plane, then cross-slip to a conjugate slip plane with dissociation of the leading partial into a stair-rod dislocation and an emitted partial, and finally un-faulting of the original faults and formation of Frank partials. Repetition of the operation of the process on successive conjugate planes results in the formation of deformation twins. The formation mechanism of deformation twins can thus be explained by improving the stair-rod cross-slip model.     

The angular dislocation parallel to a free surface. Application to a (1 1 1)Si low-angle twist boundary

The elastic displacement field of a sharply angular dislocation with its two legs parallel to a planar free surface is given in a practical analytical form. Its expression gives access, in transmission electron microscopy (TEM), to computed images of numerous interacting dislocations all located at a distance h close to the free surface. As an application, this field is used repeatedly to study, in dark-field TEM and a g(3g) diffraction mode with g{2?2?0}, the contrast of dissociated triple nodes of a low-angle twist boundary in silicon extended over a (1?1?1) plane. It is shown that free surface elastic effects can influence the contrasts of some 30° partials if h is at the nanometer scale.     

Full-scale atomistic simulations of dislocations in Ni crystal by embedded-atom method

Full-scale atomistic simulations by the nudged elastic band method are performed to determine the energetics and core structures of dislocations in a Ni lattice using an embedded-atom method potential. We find that for an edge dislocation, the potential yields very weak coupling between the partials which move almost individually. For a screw dislocation, the coupling between the partials is somewhat stronger and the partials move with some dependence. As expected, the results indicate that stacking fault energy has a controlling influence on the coupling behaviour of the partials. The effective Peierls energies and stresses are 1.30?×?10^?6?eV/Å and 2.79?×?10^?6?μ for the edge dislocation, and 1.62?×?10^?4?eV/Å and 2.02?×?10^?4?μ for the screw dislocation.     

The peierls energy and kink energy in fcc metals

In fcc crystals, dislocations are dissociated on the {111} glide plane into pairs of partial dislocations. Since each partial interacts individually with the Peierls potential and is coupled to its neighbour by a stacking fault, periodic variations in the separation distance d of the partials occur when dislocations running along closed packed lattice directions are displaced. This can drastically reduce the effective Peierls stress. By using the Peierls model the structure of 0°, 30°, 60° and 90° dislocations in a typical fcc metal with the elastic properties of Cu and a stacking-fault energy γ₀ in the interval 0.04?≤?γ₀?≤?0.05?J/m² was studied, and the magnitude of the Peierls energy ΔE _P and the resulting kink energies E _K were determined. Since the energies involved are of the order of 10^?3?eV/b or less, their magnitude cannot be asserted with high confidence, considering the simplifying assumptions in the model. The difference in the changes of the core configuration during displacement of dislocations of different orientations should, however, be of physical significance. It is found that a dissociated 60° dislocation generally has a higher effective Peierls energy than a screw dislocation, but the reverse is true for the kink energy, at least in Cu.     

Non-singular descriptions of dislocation cores: a hybrid ab initio continuum approach

The core structure of straight and curved dislocations is studied by developing a hybrid approach that links the parametric dislocation dynamics method with ab initio calculations. The approach is an extension of the Peierls–Nabarro (PN) model, with the following features: (1) all three components of the displacement vector for atoms within the dislocation core are included; (2) the entire generalized stacking fault energy surface (GSFS) obtained from ab initio calculations is utilized; and (3) the method is generalized to treat curved dislocations. We combine the parametric dislocation dynamics (DD) approach for the interaction and motion of dislocations with ab initio calculations of lattice restoring forces. These forces, which are extracted from the GSFS (γ-surface), are calculated from both first-principles density functional theory (DFT) and the embedded-atom method (EAM). Dislocation core structures in aluminium and silver are determined. For straight dislocations, the results from the model are shown to be in excellent agreement with experiments for both Al and Ag. In contrast to undissociated dislocation loops in Al, it is found that the core width and the separations between partials in Ag vary along the angular direction measured with respect to the Burgers vector. It is also shown that the core-cutoff radius, which is usually employed in DD calculations to avoid singularities, must be adjusted as a function of loop size to account for the correct dislocation core energy.     

Study of yield stress anomaly of Fe2MnAl single crystal by in situ TEM straining

L2₁-structured Fe₅₉Mn₁₇Al₂₄ shows a yield stress anomaly with a peak yield stress at 700?K. The aim of the work reported here was to determine the dislocation mechanisms involved in this anomalous behaviour by performing in situ straining on Fe₅₉Mn₁₇Al₂₄ single crystals in a transmission electron microscope at 300–900?K. Cross-slip of ?111? dislocations was frequently found to occur between {110} and {211} planes at all temperatures tested. At 300?K, dislocations were four-fold dissociated and the partials moved together under stress. At 700–800?K, partial dislocations with a Burgers vector of a/2?111? dominated the deformation. These partial dislocations moved independently in the ordered matrix in a jerky manner, with rapid motion between long periods of locking. X-ray diffraction measurements showed that the degree of L2₁-order slightly decreased with increasing temperature in the range 300–700?K, and dropped rapidly above 700?K. At 900?K, the material was B2-ordered. The increased yield stress at elevated temperatures is primarily attributed to the uncoupling of a/2?111? partial dislocations trailing shear-induced anti-phase boundaries.     

On low temperature glide of dissociated 〈1 1 0〉 dislocations in strontium titanate

An elastic interaction model is presented to quantify low temperature plasticity of SrTiO₃ via glide of dissociated 〈1 1 0〉{1 1 0} screw dislocations. Because 〈1 1 0〉 dislocations are dissociated, their glide, controlled by the kink-pair mechanism at T < 1050 K, involves the formation of kink-pairs on partial dislocations, either simultaneously or sequentially. Our model yields results in good quantitative agreement with the observed non-monotonic mechanical behaviour of SrTiO₃. This agreement allows to explain the experimental results in terms of a (progressive) change in 〈1 1 0〉{1 1 0} glide mechanism, from simultaneous nucleation of two kink-pairs along both partials at low stress, towards nucleation of single kink-pairs on individual partials if resolved shear stress exceeds a critical value of 95 MPa. High resolved shear stress allows thus for the activation of extra nucleation mechanisms on dissociated dislocations impossible to occur under the sole action of thermal activation. We suggest that stress condition in conjunction with core dissociation is key to the origin of non-monotonic plastic behaviour of SrTiO₃ at low temperatures.     

单晶铜纳米线屈服机理的原子模拟研究

采用分子静力学方法模拟了〈100〉单晶铜纳米线的拉伸变形过程,研究了纳米线屈服的机理. 结果表明：1） 纳米线初始屈服通过部分位错随机激活的{111}〈112〉孪生实现,后继屈服通过{111}〈112〉部分位错滑移实现;2） 纳米线变形初期不同滑移面上的部分位错在两面交线处相遇形成压杆位错,变形后期部分位错在刚性边界处塞积,两者都阻碍位错滑移,引起一定的强化作用. 关键词： 纳米线 屈服 位错 分子静力学     

Electrical activities of stacking faults and partial dislocations in 4H-SiC homoepitaxial films

The electrical activities of stacking faults (SFs) and partial dislocations in 4H-SiC homoepitaxial films were investigated by using the electron-beam-induced current (EBIC) technique. The basal plane dislocation was dissociated into Si_(g) 30^° and C_(g) 30^° partials under electron-beam irradiation, with a SF formed in between. The SF shows bright contrast at RT and dark contrast at 50 K in EBIC images. The reasons were discussed according to the quantum-well state of SF. C_(g) 30^° partial is always more electrically active than Si_(g) 30^° partial at each specific accelerating voltage. The EBIC contrasts of those two partials were discussed with the number of recombination centers.     

The Peierls stress for coupled dislocation partials near a free surface

The effect of a free surface on the Peierls stress of a perfect dislocation, as well as on one of two dislocation partials under a free surface, has been accounted for by considering the Lubarda–Markenscoff variable-core dislocation model (VCM). The VCM dislocation smears the Burgers vector, while producing on the slip plane the Peierls–Nabarro sinusoidal relation between the stress and the slip discontinuity with a variable width. Here the core radius is allowed to depend on the distance to the free surface and the other partial. The Peierls stress is computed as a configurational force by accounting for all the energies and the image stresses to satisfy the traction-free boundary conditions. The results are applied to aluminum and copper and comparisons are made with atomistic calculations in the literature that show that the partials merge as they approach the free surface.     

Size dependent deformation behaviour and dislocation mechanisms in 〈1 0 0〉 Cu nanowires

Abstract

Molecular dynamics simulations have been performed to understand the size-dependent tensile deformation behaviour of 〈1 0 0〉 Cu nanowires at 10 K. The influence of nanowire size has been examined by varying square cross-section width (d) from 0.723 to 43.38 nm using constant length of 21.69 nm. The results indicated that the yielding in all the nanowires occurs through nucleation of partial dislocations. Following yielding, the plastic deformation in small size nanowires occurs mainly by slip of partial dislocations at all strains, while in large size nanowires, slip of extended dislocations has been observed at high strains in addition to slip of partial dislocations. Further, the variations in dislocation density indicated that the nanowires with d > 3.615 nm exhibit dislocation exhaustion at small strains followed by dislocation starvation at high strains. On the other hand, small size nanowires with d < 3.615 nm displayed mainly dislocation starvation at all strains. The average length of dislocations has been found to be same and nearly constant in all the nanowires. Both the Young’s modulus and yield strength exhibited a rapid decrease at small size nanowires followed by gradual decrease to saturation at larger size. The observed linear increase in ductility with size has been correlated with the pre- and post-necking deformation. Finally, dislocation–dislocation interactions leading to the formation of various dislocation locks, the dislocation–stacking fault interactions resulting in the annihilation of stacking faults and the size dependence of dislocation–surface interactions have been discussed.     

Interaction of dislocation pile-up with a low-angle tilt boundary: a discrete dislocation dynamics study

Abstract

The pile-up of dislocations between two low-angle tilt boundaries (LATB) in an fcc crystal was simulated using three-dimensional discrete dislocation dynamics. The LATB was constructed using glissile edge dislocations stacked on each other. The dislocations in the pile-up were chosen such that their reactions with the dislocations in the LATB resulted in glissile junctions. Parallel pairs of dislocations were inserted to a maximum allowable value estimated from theoretical expressions. A resolved shear stress was applied and increased in steps so as to move the dislocations in the pile-up towards the boundaries. The shear stress required to break the lead dislocation from the wall was determined for varying spacings between the two boundaries. The shear stress and boundary spacing followed the Hall–Petch type relation. Dislocation pile-ups without a LATB were also simulated. The spacing of the dislocations in the pile-up with LATB was found to be closer (ie higher dislocation density) than that without LATB. It was shown through analytical expressions that LATB exerts an attractive force on the dislocations in the pile-up thereby creating a denser pile-up.     

Dislocation and stacking fault core fields in fcc metals

Atomistic models were used to determine the properties of dislocation core fields and stacking fault fields in Al and Cu using embedded atom method (EAM) potentials. Long-range, linear elastic displacement fields due to nonlinear behaviour within dislocation cores, the core field, for relevant combinations of Shockley partial dislocations for edge, screw, and mixed (60° and 30°) geometries were obtained. Displacement fields of stacking faults were obtained separately and used to partition the core field of dissociated dislocations into core fields of partial dislocations and a stacking fault expansion field. Core field stresses were derived from which the total force, including the Volterra field plus core field, between dislocations for several dislocation configurations was determined. The Volterra field dominates when the distance between dislocations exceeds about 50b but forces due to core fields are important for smaller separation distances and were found to affect the equilibrium angle of edge dislocation dipoles and to contribute to the force between otherwise non-interacting edge and screw dislocations. Interactions among the components of a dissociated dislocation modify the equilibrium separation for Shockley partials suggesting that methods that determine stacking fault energies using measurements of separation distances should include core fields.     

Dislocation transmission across the Cu/Ni interface: a hybrid atomistic–continuum study

The strengthening mechanisms in bimetallic Cu/Ni thin layers are investigated using a hybrid approach that links the parametric dislocation dynamics method with ab initio calculations. The hybrid approach is an extension of the Peierls–Nabarro (PN) model to bimaterials, where the dislocation spreading over the interface is explicitly accounted for. The model takes into account all three components of atomic displacements of the dislocation and utilizes the entire generalized stacking fault energy surface (GSFS) to capture the essential features of dislocation core structure. Both coherent and incoherent interfaces are considered and the lattice resistance of dislocation motion is estimated through the ab initio-determined GSFS. The effects of the mismatch in the elastic properties, GSFS and lattice parameters on the spreading of the dislocation onto the interface and the transmission across the interface are studied in detail. The hybrid model shows that the dislocation dissociates into partials in both Cu and Ni, and the dislocation core is squeezed near the interface facilitating the spreading process, and leaving an interfacial ledge. The competition of dislocation spreading and transmission depends on the characteristics of the GSFS of the interface. The strength of the bimaterial can be greatly enhanced by the spreading of the glide dislocation, and also increased by the pre-existence of misfit dislocations. In contrast to other available PN models, dislocation core spreading in the two dissimilar materials and on their common interface must be simultaneously considered because of the significant effects on the transmission stress.     

Dislocations hétéro-interfaciales vis perçant une plaquette mince

A specimen observed in high-resolution transmission electron microscopy is electron transparent and its thickness is often less than about 10 nm. When it contains a linear defect like a screw dislocation, the obtained image can exhibit more or less important perturbations due to elastic relaxation nearby both free surfaces. Therefore, the theoretical interpretation of an image should include this relaxation in the calculation model. In the present work, it is evaluated for screw misfit dislocations piercing normally an elastically heterogeneous bicristalline plate (thickness 2h) from the following assumptions: there is no applied force on the thin plate and any surface stress related to a possible nanometric structure along the two free surfaces is neglected. The solution is found from an appropriate combination of known elastic fields in an infinite medium, which enables total stresses applying on two planes distant of 2h to be cancelled. This solution generalizes for the first time that of Eshelby and Stroh (1951), who consider an isolated screw dislocation normal to a homogeneous plate.     

On the shearing mechanism of γ′ precipitates by a single ( a /6)⟨112⟩ Shockley partial in Ni-based superalloys

The weak-beam technique of transmission electron microscopy has been used to analyse a new shearing configuration of γ′ precipitates after creep at 700°C of a Ni-based superalloy for gas turbine discs. The shearing configurations are made up of superlattice extrinsic stacking faults, matrix stacking faults and individual (a/6)?112? Shockley dislocations. This mechanism is initiated by the decorrelated movement of the two Shockley partials of a single (a/2)?110? matrix dislocation. The propagation of the leading partial creates this shearing process. This phenomenon that occurs in small γ channels owing to the flexibility of dislocations can be used to evaluate microstructural evolutions during ageing in the alloy.