Peierls Barrier Research Articles

Ab initio investigation of the Peierls potential of screw dislocations in bcc Fe and W

The easy, hard and split core configurations of the 〈111〉 screw dislocation and the energy pathways between them are studied in body-centered cubic (bcc) Fe and W using different density functional theory (DFT) approaches. All approaches indicate that in Fe, the hard core has a low relative energy, close to or even below that of the saddle configuration for a straight path between two easy cores. This surprising result is not a direct consequence of magnetism in bcc Fe. Moreover, the path followed by the dislocation core in the (111) plane between easy cores, identified here using two different methods to locate the dislocation position, is almost straight, while the energy landscape between the hard core position and the saddle configuration for a straight path is found to be very flat. These results in Fe are in contrast with predictions from empirical potentials as well as DFT calculations in W, where the hard core has an energy about twice that of the maximum energy along the Peierls barrier, and where the dislocation trajectory between easy cores is curved. Also, the split core configuration is found to be unstable in DFT and of high energy in both Fe and W, in contrast with predictions from most empirical potentials.

Energetic Analysis of Deformation Twins and Twinning Dislocations in Magnesium

Twin boundaries and twinning dislocations for (10\bar{1}2) and (10\bar{1}1) twins in Mg are investigated, using the generalized-embedded-atom-method interatomic potential. The twin boundary energy for the (10\bar{1}2) twin is found to be larger than that for the (10\bar{1}1) twin. On the other hand, both the dislocation energy and the Peierls barrier of the twinning dislocation are low for the (10\bar{1}2) twin. This implies that the (10\bar{1}2) twin is capable of having a winding morphology and can grow easily.

The kinetic relation for twin wall motion in NiMnGa—part 2

A combined theoretical and experimental investigation of twin wall motion in ferromagnetic shape memory alloy (FSMA) NiMnGa is presented. A general analysis of twinning dynamics in ferroelastic and ferroelectric crystals reveals that different kinetic relations for sidewise twin wall motion appear under different ranges of the driving force. All these relations are shown to be governed by several nano-scale properties of the twin wall. For high values of the driving force with respect to a crystal's Peierls barrier, uniform viscous motion is obtained. Recently (Faran and Shilo, 2011), we reported on a pioneering experimental demonstration of this important kinetic relation through magnetically induced twin wall motion in NiMnGa. In the lower driving force range, twin wall propagates through thermally activated nucleation and growth of twin wall steps. Here, we present a model for step nucleation that leads to an exponential-type kinetic relation that is governed by the values of the step's physical properties. Comparison of experimental results for type I and type II twin walls with model predictions allow for the extraction of all the fundamental material properties that govern twinning dynamics in NiMnGa. In addition, the effect of demagnetization energy on twin wall motion and local variations in viscosity values are presented and discussed.

The influence of transition metal solutes on the dislocation core structure and values of the Peierls stress and barrier in tungsten

Several transition metals were examined to evaluate their potential for improving the ductility of tungsten. The dislocation core structure and Peierls stress and barrier of 1/2〈111〉 screw dislocations in binary tungsten–transition metal alloys (W1−xTMx) were investigated using density functional theory calculations. The periodic quadrupole approach was applied to model the structure of the 1/2〈111〉 dislocation. Alloying with transition metals was modeled using the virtual crystal approximation and the applicability of this approach was assessed by calculating the equilibrium lattice parameter and elastic constants of the tungsten alloys. Reasonable agreement was obtained with experimental data and with results obtained from the conventional supercell approach. Increasing the concentration of a transition metal from the VIIIA group, i.e. the elements in columns headed by Fe, Co and Ni, leads to reduction of the C′ elastic constant and increase of the elastic anisotropy A = C44/C′. Alloying W with a group VIIIA transition metal changes the structure of the dislocation core from symmetric to asymmetric, similarly to results obtained for W1−xRex alloys in the earlier work of Romaner et al (2010 Phys. Rev. Lett. 104 195503). In addition to a change in the core symmetry, the values of the Peierls stress and barrier are reduced. The latter effect could lead to increased ductility in a tungsten-based alloy. Our results demonstrate that alloying with any of the transition metals from the VIIIA group should have a similar effect to alloying with Re.

Viscous stability of quasi-periodic tori

AbstractThis paper is devoted to the study of$P$-regularity of viscosity solutions$u(x,P)$,$P\in {\Bbb R}^n$, of a smooth Tonelli Lagrangian$L:T {\Bbb T}^n \rightarrow {\Bbb R}$characterized by the cell equation$H(x,P+D_xu(x,P))=\overline {H}(P)$, where$H: T^* {\Bbb T}^n\rightarrow {\Bbb R}$denotes the Hamiltonian associated with$L$and$\overline {H}$is the effective Hamiltonian. We show that if$P_0$corresponds to a quasi-periodic invariant torus with a non-resonant frequency, then$D_xu(x,P)$is uniformly Hölder continuous in$P$at$P_0$with Hölder exponent arbitrarily close to$1$, and if both$H$and the torus are real analytic and the frequency vector of the torus is Diophantine, then$D_xu(x,P)$is uniformly Lipschitz continuous in$P$at$P_0$, i.e., there is a constant$C\gt 0$such that$\|D_xu(\cdot ,P)-D_xu(\cdot ,P_0)\|_{\infty }\le C\|P-P_0\|$for$\|P-P_0\|\ll 1$. Similar P-regularity of the Peierls barriers associated with$L(x,v)- \langle P,v \rangle $is also obtained.

Screw dislocation in zirconium: Anab initiostudy

Plasticity in zirconium is controlled by $1/3\ensuremath{\langle}1\overline{2}10\ensuremath{\rangle}$ screw dislocations gliding in the prism planes of the hexagonal close-packed structure. This prismatic and not basal glide is observed for a given set of transition metals like zirconium and is known to be related to the number of valence electrons in the d band. We use ab initio calculations based on the density functional theory to study the core structure of screw dislocations in zirconium. Dislocations are found to dissociate in the prism plane in two partial dislocations, each with a pure screw character. Ab initio calculations also show that the dissociation in the basal plane is unstable. We calculate then the Peierls barrier for a screw dislocation gliding in the prism plane and obtain a small barrier. The Peierls stress deduced from this barrier is lower than 21 MPa, which is in agreement with experimental data. The ability of an empirical potential relying on the embedded atom method (EAM) to model dislocations in zirconium is also tested against these ab initio calculations.

The effect of light doping on the creep of β-Sn single crystals induced by superconducting transition

Yield strength and characteristics of the transient creep in β-Sn single crystals doped with substitutional impurities In, Cd, Zn at the concentration of 0.01 at. % were measured at T = 1.6 K. The transient creep in samples with (100) 〈010〉 plastic slip orientation was observed after their normal–superconducting transition. As was earlier shown by the authors, plastic flow in such a slip system in pure β-Sn at low temperatures is determined by the dislocations overcoming Peierls barriers through the mechanism of nucleation and expansion of paired kinks (fluctuation creep stage) or over-barrier dislocation motion (dynamic creep stage). Comparison of the creep behavior in the pure and doped specimens allowed obtaining the information on the influence of impurity atoms on kinetics and dynamics of the motion of dislocation string in Peierls energy landscape. It was found that In and Cd impurities form weak obstacles for dislocations and cause a minor increase in yield strength while stimulating the dynamic creep stage. On the contrary, Zn atoms produce high barriers for dislocation motion, significantly increase the yield point and strongly reduce the contribution of dynamic effects.

Width-to-thickness ratio dependence on photoplastic effect of ZnS nanobelt

Photoplastic effect (PPE) of individual ZnS nanobelt with different width-to-thickness (w/t) ratios was investigated by using a nanoindenter in conjunction with an incident ultraviolet light source system. The results show that the positive and negative PPEs are observed for the w/t ratios 4.9–9.6 and 3.2–4.1. At the peak indentation loads 20–50 μN, the positive and negative PPEs occur for the w/t ratios 4.9 and 3.2, however, they disappear at 60 μN. PPE is determined by w/t ratio not peak indentation load, and it is interpreted by the competing mechanisms of increase of Peierls barrier and radiation enhanced dislocation glide.

Surface effect on the screw dislocation mobility over the Peierls barrier

The effect of the image force on the Peierls stress (τ p ) of a screw dislocation below a free surface is studied via a self-consistent semidiscrete variational Peierls–Nabarro model. The consequence of reduction in elastic energy and increase in stacking fault energy by the presence of the free surface is found to additively increase the Peierls stress (τ p ). This model gives a physical interpretation of the same tend observed in a recent molecular dynamic study, while previous continuum analysis predicted the opposite.

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 {110} 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 0.73eV in agreement with experiment.

Constrained nudged elastic band calculation of the Peierls barrier with atomic relaxations

We demonstrate that the straightforward application of the nudged elastic band (NEB) method does not determine the correct Peierls barrier of 1/2〈1 1 1〉 screw dislocations in bcc metals. Although this method guarantees that the states (images) of the system are distributed uniformly along the minimum energy path, it does not imply that the dislocation positions are distributed uniformly along this path. In fact, clustering of dislocation positions near potential minima occurs which leads to an overestimate of both the slope of the Peierls barrier and the Peierls stress. We propose a modification in which the NEB method is applied only to a small number of degrees of freedom that determine the position of the dislocation, while all other coordinates of atoms are relaxed by molecular statics as in any atomistic study. This modified NEB method with relaxations gives the Peierls barrier that increases smoothly with the dislocation position and the corresponding Peierls stress agrees well with that evaluated by the direct application of stress in the atomistic modeling of the dislocation glide.

Properties of Shockley partials in InP: core width, Peierls barrier and stress

The core width and Peierls barrier and stress for Shockley partials in InP have been investigated using the improved P-N theory. The core width of 90° partial is about 1.6 times wider than that of 30° partial, and both of them are very narrow: core width ξ < 0.5b. In calculating the Peierls barrier and stress, the contribution from stain energy ignored by classical P-N theory has been considered. The calculated results show that when the dislocation moves, both the misfit and strain energies change periodically. They cancel each other due to the same order but opposite phases. Accordingly, the Peierls barrier and stress calculated from improved P-N theory are much lower than those calculated from the classical P-N theory. The Peierls barrier for 90° and 30° partials obtained by us is respectively about ~0.047 eV/A and 0.044–0.075 eV/A, the Peierls stress is respectively about 3.7–5.0 GPa and 4.2–6.9 GPa.

THE DISLOCATION ENERGY, PEIERLS BARRIER AND STRESS FOR ZIGZAG SINGLE-WALLED CARBON NANOTUBES

The dislocation energy, Peierls barrier and Peierls stress of pentagon–heptagon (p–h) pair dislocation in zigzag single-walled carbon nanotube (SWCNT) are studied by the improved Peierls–Nabarro (P–N) theory. The contribution of the strain energy is considered in evaluating the dislocation energy and Peierls barrier and stress. Using the γ-surface obtained from the first-principle calculations, it is found that the misfit energies of p–h pair dislocations are weakly dependent on the perimeters of the SWCNTs, while the strain and total energies have logarithmic behaviors with the perimeters of larger SWCNTs (N&gt;10). For the smaller SWCNTs (N⩽10), the strain and total energies have a little deviation from the logarithmic behaviors due to the curvature and size effects. The calculated Peierls barrier and Peierls stress are about 4.2–4.8 eV and 0.3μ, respectively. For the (12,0)–(11,0) carbon nanotube with different modification factors, the dislocation energy remains almost invariant (about 18 eV). The Peierls barrier and Peierls stress increase linearly with the increasing of the modification factor. When modification factor changes from 0.10 to 0.45, the Peierls barrier changes from 3.6 eV to 7.4 eV, and the Peierls stress changes from 0.2μ to 0.5μ.

Calculation of shuffle 60° dislocation width and Peierls barrier and stress for semiconductors silicon and germanium

The dislocation width for shuffle 60° dislocation in semiconductors Si and Ge have been calculated by the improved P-N theory in which the discrete effect has been taken into account. Peierls barrier and stress have been evaluated with considering the contribution of strain energy. The discrete effect make dislocation width wider, and Peierls barrier and stress lower. The dislocation width of 60° dislocation in Si and Ge is respectively about 3.84 A and 4.00 A (∼1b, b is the Burgers vector). In the case of 60° dislocation, after considering the contribution of strain energy, Peierls barrier and stress are increased. The Peierls barrier for 60° dislocation in Si and Ge is respectively about 15 meV/A and 12–14 meV/A, Peierls stress is about 3.8 meV/A3 (0.6 GPa) and 2.7–3.3 meV/A3 (0.4–0.5 GPa). The Peierls stress for Si agrees well with the numerical results and the critical stress at 0 K extrapolated from experimental data. Ge behaves similarly to Si.

Multiscale modelling of MgO plasticity

We propose a multiscale model of plasticity of pure MgO single crystals. The core structure of the rate controlling ½〈1 1 0〉 screw dislocations has been modelled by the Peierls–Nabarro–Galerkin method. This model relies on γ-surfaces calculated ab initio for the {1 1 0}, {1 0 0} and {1 1 1} planes. The ½ 〈1 1 0〉 screw dislocations spread mostly in the {1 1 0} planes. The Peierls friction values are 150 MPa and 1.6 GPa for glide on the {1 1 0} and {1 0 0} planes, respectively. The kink pair theory is applied to model thermal activation of dislocation glide over the Peierls barrier below the athermal temperature T a and to build a velocity law for this regime. The critical resolved shear stresses are deduced below T a from the Orowan law. Above T a the athermal stress τ μ is obtained from discrete dislocation dynamics simulations to account for dislocation–dislocation interactions. This model is found to satisfactorily reproduce the critical resolved shear stresses observed experimentally, provided the contribution of impurities (unavoidable in experiments) is subtracted.

Anisotropy Behavior of Dislocation Nucleation from a Sharp Corner in Copper

By means of reaction pathway analysis, we have investigated the nucleation of 90° and 30° partial dislocation from a sharp corner in an f.c.c. crystal copper. The anisotropy aspects of dislocation nucleation revealed by the results have shown that the stress-dependent activation energy of 30° partial dislocation is approximately twice over the counterpart of 90° partial dislocation, and that the maximum inelastic displacement for the former is also higher. Moreover, the shape of the saddle-point configuration of 30° partial dislocation is similar to a half-ellipse whereas in the case of 90° partial dislocation it is more like a semi-circle, reflecting the different Peierls barriers influenced by the Burgers vectors. Further study of the surface reconstruction demonstrates that although the nucleation of 30° partial dislocation has been enhanced by surface reduction, it is still more energy-unfavorable than the 90° partial dislocation. These results suggest that the higher Peierls barrier is responsible for the larger activation energy of 30° partial dislocation nucleation.

Photoinduced stiffening and photoplastic effect of ZnS individual nanobelt in nanoindentation

The photoinduced stiffening (PIS) and photoplastic effect (PPE) of ZnS individual nanobelt (NB) were observed by using a nanoindenter in conjunction with an incident ultraviolet (UV) light source system. The results show that the elastic modulus and hardness of ZnS individual NB under UV illumination are at least 32% and 20% larger than those in darkness. The mechanisms of PIS and PPE are interpreted by the increase in electronic strain and Peierls barrier due to the photogeneration of free carriers in ZnS individual NB. The research may offer useful guidelines to the application of optoelectronic devices based on individual nanostructures.

Analysis of Deformation Kinetics in Seven Body-Centered-Cubic Pure Metals Using a Two-Obstacle Model

Published temperature and strain-rate-dependent yield stress data in seven nominally pure bcc metals are analyzed according to a two-obstacle model. A strong intrinsic lattice resistance such as a Peierls barrier and a weaker obstacle representing the collective effects of impurity constituents are combined in a single expression and fit to the individual data sets. Sensitivity of the model fits to selected model parameters is assessed. The activation volume for each obstacle is evaluated and examined to validate the underlying model assumptions. Application of the model demonstrates a consistent Peierls barrier in all seven metals and a reasonable carbon-content dependence in iron of the strength of the impurity obstacle.

Dynamic strain aging in materials with a high Peierls relief: Competition of diffusion and dragging impurities

A model of the dynamic interaction of dislocations with the impurity subsystem of crystals that have high Peierls barriers has been developed. It is justified that the impurity kinetics during atmosphere formation includes two stages. The initial stage leads to a negative strain rate and positive temperature dependence of the yield stress of the material in some range.

Modelling thermal activation of {1 1 0} slip at low temperature in SrTiO3

The core structure of {1 1 0} screw dislocations has been modelled in SrTiO3 with the Peierls–Nabarro–Galerkin method. This model relies on γ-surfaces calculated ab initio for the {1 0 0} and {1 1 0} planes. The {1 1 0} screw dislocation has a planar core and its Peierls friction is 350 MPa. The kink-pair theory is applied to model thermal activation of dislocation glide over the Peierls barrier. This model is found to reproduce satisfactorily the critical resolved shear stresses observed experimentally below 1000 K.