Temperature dependence of screw dislocation mobility on shuffle-set of silicon

Large-scale atomistic simulations are performed in order to observe local behaviors of screw dislocations located on the shuffle set of (111) in single crystal silicon, focusing on the propagation process of the screw dislocations. A quadrupolar arrangement of screw dislocations is utilized to impose the periodic boundary conditions along each of the three spatial directions. With the aid of molecular dynamics simulations, the dislocation mobility is investigated in terms of the critical resolved shear stress. Based on the results from the simulations, we discuss effects of the model size and temperature on the critical resolved shear stress. After choosing the proper model size to reduce undesirable interference between the dislocations, we further estimate the Peierls stress by fitting from a set of the critical resolved shear stresses at various temperatures. Meanwhile, we observe a double kink mechanism in the dislocation propagation which is the most energetically favorable dislocation movement in silicon. We investigate the formation and migration of kink pairs on an undissociated screw dislocation in silicon.     

Interactions between non-screw lattice dislocations and coherent twin boundaries in face-centered cubic metals

In a first report [Jin ZH, Gumbsch P, Ma E, Albe K, Lu K, Hahn H, et al. Scripta Mater 2006;54:1163], interactions between screw dislocation and coherent twin boundary (CTB) were studied via molecular dynamics simulations for three face-centered cubic (fcc) metals, Cu, Ni and Al. To complement those preliminary results, purely stress-driven interactions between 60° non-screw lattice dislocation and CTB are considered in this paper. Depending on the material and the applied strain, slip has been observed to interact with the boundary in different ways. If a 60° dislocation is forced by an external stress into a CTB, it dissociates into different partial dislocations gliding into the twin as well as along the twin boundary. A sessile dislocation lock may be generated at the CTB if the transited slip is incomplete. The details of the interaction are controlled by the material-dependent energy barriers for the formation of Shockley partial dislocations from the site where the lattice dislocation impinges upon the boundary.     

A half-space Peierls–Nabarro model and the mobility of screw dislocations in a thin film

In this paper, a half-space Peierls–Nabarro (HSPN) model is proposed to re-examine the mobility of a screw dislocation along a thin film/substrate (half-space) interface. In this configuration, the screw dislocation is subjected to an image force due to the free surface, and we are concerned with the interaction between the dislocation and the free surface. Unlike the original Peierls–Nabarro (P–N) model, the HSPN model takes into account the effect of the image force, which leads to modifications on analytical expression of the Peierls barrier stress. The modified Peierls stress is a function of the thin film thickness, which allows us to accurately predict the mobility of a dislocation in the interface between the thin film and the substrate. Based on the proposed HSPN model, we have found that the Peierls stress of a surface screw dislocation may be about 5–15% less than that in bulk materials.     

Atomistic aspects of the deformation of NiAl

Properties of dislocations in B2-NiAl have been studied atomistically using an embedded atom potential. The response of dislocation cores to applied homogeneous shear stresses is investigated and the Peierls stresses of straight dislocations are determined. The results are in many details in excellent agreement with experimental observations. Specifically, the behaviour of the 〈1 1 1〉 dislocations, their slip planes, cross-slip behaviour and the limiting role of the screw dislocation can be explained. Similarly, the appearance of the {2 1 0} plane as a secondary slip plane for the 〈1 0 0〉 dislocations can be rationalised. Furthermore, the interaction of the dislocations with structural point defects is studied. Comparison with the flow stress of off-stoichiometric NiAl from the literature shows that the individual point defects cannot be made responsible for the strong increase of the flow stress, suggesting that more complex defect structures may play an important role.     

Multiscale modeling of plastic deformation of molybdenum and tungsten. III. Effects of temperature and plastic strain rate

In this paper, we develop a link between the atomic-level modeling of the glide of 1/2〈1 1 1〉 screw dislocations at 0 K and the thermally activated motion of these dislocations via nucleation of pairs of kinks. For this purpose, we introduce the concept of a hypothetical Peierls barrier, which reproduces all the aspects of the dislocation glide at 0 K resulting from the complex response to non-glide stresses expressed in a compact form by the yield criteria advanced in Part II. To achieve this, the barrier is dependent not only on the crystal symmetry and interatomic bonding but also on the applied stress tensor. Standard models are then employed to evaluate the activation enthalpy of kink-pair formation, which is now also a function of the full applied stress tensor. The transition state theory then links this mechanism with the temperature and strain rate dependence of the yield stress.     

Plastic deformation of wadsleyite: IV Dislocation core modelling based on the Peierls–Nabarro–Galerkin model

In this paper, we determine dislocation core structures and Peierls stresses of wadsleyite, a high-pressure mineral present in the Earth mantle. We use a Peierls–Nabarro model combined with a finite-element method in which we introduce two-dimensional generalized stacking fault energies. Several potential slip planes of wadsleyite are considered. The results show that dislocations in this mineral can exhibit complex dislocation cores with linear or non-collinear dissociation and even three-dimensional dislocation cores. The calculation of the Peierls stresses gives information on the potential activity of slip systems governing the plasticity of wadsleyite. Our study confirms experimental observations that ½〈1 1 1〉{1 0 1} is the easiest slip system in this structure at high-pressure and that [1 0 0](0 1 0) is the second easiest. Both these easily slip systems have dislocations that dissociate into collinear partial dislocations. In contrast [0 1 0] dislocations with very large Burgers vector (11.2 Å) are stabilized by complex dissociations involving four partial dislocations.     

α-Al2O3 sapphire and rubies deformed by dual basal slip at intermediate temperatures (900–1300 °C): II. Dissociation and stacking faults

Sapphire and rubies (undoped and Cr-doped α-Al₂O₃ single crystals) have been deformed in compression at temperatures lower than those previously used in studies of dislocations in the basal slip plane. Above 1400 °C, several features associating stacking faults out of the basal planes and partial dislocations (dissociation and faulted dipoles) have been observed in previous transmission electron microscopy investigations. The formation of these features involves climb controlled by atomic diffusion. Properties of climb-dissociated dislocations are discussed in relation to dislocation dynamics. Transmission electron microscopy examination of dislocation structures at lower deformation temperatures (1000–1100 °C) shows that similar features are formed but that they often imply cross-slip. A new mechanism for the formation of faulted dipole by glide is presented and an explanation for the 30° Peierls valley orientation is proposed. The presence of chromium has a small influence on stacking fault energies on planes perpendicular to the basal plane.     

12Ni3CrMoVA钢热激活塑性形变特征的研究

本文研究了12Ni3CrMoVA合金钢流变应力随温度及应变速率的变化规律,以及组织因素的影响,测算了该材料激活能及激活体积等热激活参数。根据P-N机制由螺型位错芯结构分析了bcc金属的塑性形变规津,该规律同试验结果吻合,说明有效应力与温度关系曲线中的拐点是由于Peierls势能呈双驼峰分布所致,相应的位错线激活态形状呈双扭折对分布。显微组织仅影响位错的长程障碍阻力,而对位错热激活运动没有影响。     

Creep behaviour of Ti-6Al-2Sn-4Zr-2Mo: II. Mechanisms of deformation

Constant load creep tests are performed in Ti-6242(Si) alloy with a lath microstructure, at temperatures of 538 and 565 °C. A change in the stress exponent values from ˜1 at low stresses to between 5 and 7 at high stresses, is indicative of a change in creep mechanism. TEM analysis indicates that the deformation is dominated by a-type dislocations in the phase, with little evidence of dislocation activity in the β laths. At higher stress (310 MPa), the a-type dislocations are pinned frequently along their screw direction by tall jogs. A creep model is proposed based on the premise that movement of these jogged screw dislocations may control the creep rate. In contrast, at low stress (172 MPa), the a-type dislocations have long straight screw segments with no apparent pinning points. The near-edge segments are in climb configurations. The creep rates here are close to those predicted, based on Harper–Dorn creep, although the dislocation density is larger than that normally associated with this regime.     

Core structure and mobility of an edge dislocation in aluminum

The core structure of an edge dislocation in aluminum is studied by molecular dynamics simulation with the glue potential. The dislocation splits into two partials. The separation distance between the two partials is about 9 Å. The half width of the two partial dislocations is deduced to be 6.5 Å by fitting the Burgers vector density to an arctangent function, giving a half width of the whole dislocation of 12 Å. Dislocation mobility is studied by applying a shear stress on the crystal and observing the corresponding shift of the Burgers vector density. By considering the minor force acting on the dislocation, a Peierls stress in the order of 10⁻⁴ μ for the motion of the whole dislocation in aluminum is obtained.     

Application of the Peierls-Nabarro Model to Symmetric Tilt Low-Angle Grain Boundary with Full <a> Dislocation in Pure Magnesium

Three types of symmetric (11\(\bar{2}\)0) tilt low-angle grain boundaries (LAGBs) with array of basal, prismatic, and pyramidal edge full dislocations in pure Mg have been studied by using the improved Peierls-Nabarro model in combination with the generalized stacking fault energy curve. The results show that with decreasing distance between the dislocations in all the three types of tilt LAGBs, the stress and strain fields are gradually suppressed. The reduction extent of the stress and strain fields decreases from the prismatic to basal to pyramidal dislocations. The variation of dislocation line energy (DLE) for all tilt LAGBs is divided into three stages: DLE changes slightly and linearly when the distance is larger than 300 Å, ~10%; DLE declines exponentially and quickly when the distance goes from 300 to 100 Å, ~70%; and finally, the descent speed lowers when the distance is smaller than 100 Å and the dislocation core energy is nearly half of the DLE. The grain boundary energy (GBE) decreases when the tilt angle of LAGB increases from 1° to 2° for all cases. The tilt LAGB consists of pyramidal dislocations always has the largest GBE, while that with array of prismatic dislocations has the smallest one in the whole range. The Peierls stress of dislocation in tilt LAGB is nearly unchanged, the same as that of single dislocation. This work is useful for further study of dissociated dislocation, solute segregation, precipitate nucleation in tilt LAGB and its interaction with single dislocations.     

Stress dependence of the Peierls barrier of 1/2〈1 1 1〉 screw dislocations in bcc metals

The recently formulated constrained nudged elastic band method with atomic relaxations (NEB + r) (Gröger R, Vitek V. Model Simul Mater Sci Eng 2012;20:035019) is used to investigate the dependence of the Peierls barrier of 1/2〈1 1 1〉 screw dislocations in body-centered cubic metals on non-glide stresses. These are the shear stresses parallel to the slip direction acting in the planes of the 〈1 1 1〉 zone different from the slip plane, and the shear stresses perpendicular to the slip direction. Both these shear stresses modify the structure of the dislocation core and thus alter both the Peierls barrier and the related Peierls stress. Understanding of this effect of loading is crucial for the development of mesoscopic models of thermally activated dislocation motion via formation and propagation of pairs of kinks. The Peierls stresses and related choices of the glide planes determined from the Peierls barriers agree with the results of molecular statics calculations (Gröger R, Bailey AG, Vitek V. Acta Mater 2008;56:5401), which demonstrates that the NEB + r method is a reliable tool for determining the variation in the Peierls barrier with the applied stress. However, such calculations are very time consuming, and it is shown here that an approximate approach of determining the stress dependence of the Peierls barrier (proposed in Gröger R, Vitek V. Acta Mater 2008;56:5426) can be used, combined with test calculations employing the NEB + r method.     

Comparing Modeling Predictions of Aluminum Edge Dislocations: Semidiscrete Variational Peierls–Nabarro Versus Atomistics

Multiple computational methods for modeling dislocations are implemented within a high-throughput calculation framework allowing for rigorous investigations comparing the methodologies. Focusing on aluminum edge dislocations, 21 classical aluminum interatomic potentials are used to directly model dislocation core structures using molecular dynamics and to provide input data for solving the semidiscrete variational Peierls–Nabarro dislocation model. The predicted dislocation core spreading obtained from both computational methods shows similar trends across the potentials. Additionally, tests are done to rigorously determine if a recent correction to the Peierls–Nabarro model results in better agreement with the atomistic calculations.     

Void growth by dislocation emission

Laser shock experiments conducted at an energy density of 61 MJ/m² revealed void initiation and growth at stress application times of approximately 10 ns. It is shown that void growth cannot be accomplished by vacancy diffusion under these conditions, even taking into account shock heating. An alternative, dislocation-emission-based mechanism, is proposed for void growth. The shear stresses are highest at 45° to the void surface and decay with increasing distance from the surface. Two mechanisms accounting for the generation of geometrically necessary dislocations required for void growth are proposed: prismatic and shear loops. A criterion for the emission of a dislocation from the surface of a void under remote tension is formulated, analogous to Rice and Thomson’s criterion for crack blunting by dislocation emission from the crack tip. The critical stress is calculated for the emission of a single dislocation and a dislocation pair for any size of initial void. It is shown that the critical stress for dislocation emission decreases with increasing void size. Dislocations with a wider core are more easily emitted than dislocations with a narrow core.     

First-principles study on the mobility of screw dislocations in bcc iron

The fully two-dimensional Peierls barrier map of screw dislocations in body-centered cubic (bcc) iron has been calculated using the first-principles method to identify the migration path of a dislocation core. An efficient method to correct the effect of the finite size cell used in the first-principles method on the energy of a lattice defect was devised to determine the accurate barrier profile. We find that the migration path is close to a straight line that is confined in a {1 1 0} plane and the Peierls barrier profile is single humped. This result clarifies why the existing empirical potentials of bcc iron fail to predict the correct mobility path. A line tension model incorporating these first-principles calculation results is used to predict the kink activation energy to be 0.73 eV in agreement with experiment.     

The brittle-to-ductile transition in cold rolled tungsten plates: Impact of crystallographic texture,grain size and dislocation density on the transition temperature

The aim of this paper is to elucidate the mechanisms controlling the brittle-to-ductile transition (BDT) in pre-deformed, textured, polycrystalline body-centred cubic (bcc) metals by the example of cold rolled tungsten (W).For this purpose, five sheets were rolled out from one and the same sintered ingot, by various levels, representing degrees of deformation of 1.8, 2.5, 3.0, 3.4, and 4.1 (this refers to 83.5%, 91.8%, 95.0%, 96.7%, and 98.3% in the technical notation). Toughness tests show that the BDT temperature decreases with increasing degree of deformation from 115 °C ± 15 °C (388 K ± 15 K) down to −65 °C ± 15 °C (208 K ± 15 K). This is an improvement of >600 K compared with a sintered ingot.In this paper we perform an in-depth analysis of the microstructure of the five sheets mentioned above. This analysis includes the assessment of (i) crystallographic texture, (ii) grain size and (iii) dislocation density. A comparison between microstructural features and experimental data confirms our working hypothesis which states that the BDT is controlled by the glide of screw dislocations and that the transition temperature decreases with decreasing spacing, λ, of dislocation sources along the crack front. Sources for dislocations may be the intersection points of grain boundaries with the crack front (BDT-temperature-grain-size-relation) or dislocation multiplication processes such as e.g., the expansion of open and closed loops (impact of dislocation density).     

Al薄膜纳米压痕过程的多尺度模拟

采用多尺度准连续介质法分别模拟无缺陷和具有初始缺陷两种状态下,单晶Al薄膜纳米压痕初始塑性变形过程,得到载荷-位移响应曲线和应变能-位移变化曲线.研究了初始缺陷对纳米压痕过程中位错形核与发射、Peierls应力以及位错发射.临界载荷的影响.结果表明,在整个纳米压痕过程中出现了多次位错形核与发射现象,初始缺陷对第1和第3对位错的形核与发射影响较小,而对第2对位错的形核与发射具有明显的推迟作用,并伴随有裂纹扩展现象;由于初始缺陷引起薄膜材料内部严重的晶格畸变,导致系统应变能和位错运动的Peierls应力增加;裂纹扩展前,发射第2对位错需要的临界载荷增加,裂纹失稳后,位错发射需要的临界载荷下降.模拟获得的纳米硬度和Peierls应力与实验结果吻合.     

Evaluation of the Peierls stress for boundary dislocations

The Peierls stress for 1/6〈111〉 twinning dislocations and 1/2〈111〉 perfect dislocations in a bcc structure has been evaluated. The calculations have been performed using the Peierls-Nabarro formalism. The Peierls stresses have been determined from the migration energy of a twin boundary γ_tbm and the energy of an unstable stacking fault γ_us. The values of γ_tbm and γ_us have been calculated using a set of generalized many-body interatomic potentials. The potentials were defined so as to ensure different stability of the bcc structure relative to other structures. It has been shown that this approach provides realistic values of the Peierls stress. The values of the Peierls stress for 1/6〈111〉 twinning dislocations are very sensitive to the model parameters, unlike those for 1/2〈111〉 perfect dislocations.     

A TEM in situ study of alloying effects in iron. II—Solid solution hardening caused by high concentrations of Si and Cr

The hardening effect of a high concentration of substitutional solute atoms in iron has been investigated by means of in situ straining experiments in FeSi and FeCr alloys, between 100 and 300 K. The results show that both screw and edge dislocations interact with solute atoms. This interaction is, however, strongest on screw dislocations, as a result of the formation of superjogs in the vicinity of solute atoms. Under such conditions, hardening takes place above a transition temperature for which the local pinning at superjogs becomes stronger than the Peierls friction stress.     

Some features of the formation and destruction of dislocation barriers in intermetallic compounds: II. Observation of blocked superidislocations upon heating without stress

Experiments have been performed which reveal that heating in the absence of an external stress after a preliminary both low-temperature and high-temperature deformation of intermetallic compounds leads to a fundamental change in their dislocation structure. For the investigation, [251] single crystals of Ni₃(Al, Nb) have been used. The low-temperature deformation was performed at ?196°C; the high-temperature deformation, at 800°C. It has been found that the initial dislocation structure consisting of curvilinear dislocations was changed upon heating without a load by a set of rectilinear blocked dislocations. It has been shown that upon heating after a preliminary low-temperature deformation the barriers present in the structure belong to the cubic cross-slip plane, whereas upon heating after high-temperature deformation, to primary cubic slip planes. It has been found that the decisive effect on the blocking of superdislocations upon heating without stress comes from one of the dislocations that compose the superdislocation, namely, either a superpartial dislocation in the case of low-temperature deformation or a simple partial dislocation in the case of high-temperature deformation. The concept of the possibility of thermoactivated blocking of superdislocations in the absence of external stresses suggested in part I of this work [Phys. Met. Metallogr. 102, 61–68 (2006)] has been confirmed experimentally.