Behavior Of Screw Dislocations Research Articles

Phase field dislocation dynamics (PFDD) modeling of non-Schmid behavior in BCC metals informed by atomistic simulations

Body-Centered Cubic (BCC) metals exhibit anomalous mechanical properties such as twinning/anti-twinning and tension/compression asymmetry, which are attributed to asymmetric behavior of screw dislocations. Unlike Face-Centered Cubic (FCC) metals, the Critical Resolved Shear Stress (CRSS) of BCC metals deviates from the Schmid law. We use a mesoscale modeling approach called Phase Field Dislocation Dynamics (PFDD) to understand the critical factors that control this non-Schmid behavior and reproduce atomistic predictions of the CRSS (Peierls stress). All inputs to the PFDD model are obtained from Molecular Statics (MS) simulations. Multiple pathways for modeling the non-Schmid behavior are investigated by incorporating the representative dislocation properties into different energy terms in the PFDD model. One way to understand non-Schmid behavior is to incorporate stress components projected on inclined planes into the external energy term within PFDD. Alternatively, we propose that non-Schmid behavior can also be accounted for by considering the variation of the {110} unstable stacking fault energy and the dislocation core width as a function of the applied tensorial stress field. The CRSS predicted using PFDD modeling is in excellent agreement with MS predictions.

Effect of applied strain on the interaction between hydrogen atoms and [formula omitted] screw dislocations in α-iron

We address the role of hydrogen in modifying the behaviour of screw dislocations in α-iron under the influence of the tensile and compressive stresses that are expected to arise in the vicinity of a crack tip. The quantum mechanical tight binding approximation is employed to calculate the variation of the hydrogen/screw dislocation interaction with strain. The locations and binding energies of hydrogen trap-sites surrounding the unstrained core are shown to be of similar accuracy to previous ab-initio results. Bi-axial tension and compression is applied normal to the dislocation line; the binding energies are found to vary linearly with strain. Estimations of the effect of hydrogen in strained regions are made based on the proposition that hydrogen may both enhance the nucleation of kink-pairs by lowering the formation energy, and slow the movement of kinks by a solute drag effect. Our results suggest that these effects will be enhanced in tensile regions. The chance of hardening by the collision of crossed kinks, to form a jog, is estimated by comparing the nucleation and annihilation rate of kinks on a straight screw dislocation for a range of hydrogen concentrations and temperatures, suggesting a greatly increased incidence with tension that is accentuated at lower temperatures.

The role of slow screw dislocations in controlling fast strain avalanche dynamics in body-centered cubic metals

Plasticity in body centered cubic (BCC) crystals is shown to be controlled by slow screw dislocation motion, owing to the thermally-activated process of kink pair nucleation and migration. Through three dimensional discrete dislocation dynamics simulations, this work unravels the mystery of how such slow screw dislocation behavior contributes to extremely rapid strain bursts in submicron BCC tungsten (W) pillars, which is typical of BCC metals. It is found that strain bursts are dominated by the motion of non-screw dislocations at low strain rate, but are more influenced by screw dislocations at high strain rate. The total, and partial strain burst magnitude due to screw dislocations alone, are found to exhibit rate dependence following a power law statistics with exponent of 0.65. Similar power law statistics are also obeyed for the standard deviation of the corresponding plastic strain rate. The role of screw dislocations is attributed to the changing nature of dislocation source operation at different strain rates. The corresponding spatial distribution of plastic deformation is also discussed based on the uniqueness of the simulation method in reproducing the distribution of slipped area and plastic strain with very high spatial resolution.

Effects of temperature on surface-controlled dislocation multiplication in body-centered-cubic metal nanowires

Recent computational studies revealed that screw dislocations in body-centered-cubic (bcc) metal nanowires can self-multiply through cross-slip near the free surface. This unique process was termed surface-controlled dislocation multiplication (SCDM). In bcc metals, screw dislocation motion and its cross-slip behavior are often related to thermally activated processes; due to this relation, SCDM is expected to be highly temperature-sensitive. In this study, therefore, we investigated how temperature influences the SCDM in bcc molybdenum and niobium nanowires using atomistic simulations. Regardless of the difference in lattice resistance at a given temperature, both systems show similar trends of critical shear stress of SCDM with respect to temperature. The temperature dependence was found to be divided into three different regimes; (1) lattice-resistance-dominant; (2) segmentation-dominant; (3) steady-state segmentation. The presence of these three regimes will be discussed in terms of the temperature-dependence of the lattice resistance and the dynamics of dislocation segmentation in the nano-scale volume. Our results provide a fundamental understanding of screw dislocation behavior in bcc metals at the nanometer scale and varying temperatures.

Mesoscale plastic texture in body-centered cubic metals under uniaxial load

We develop a minimal continuum dislocation dynamics model for slip in bcc metals that accounts explicitly for non-Schmid behavior of screw dislocations in these materials. The dislocation substructure is represented by a continuum distribution of $1/2[111]$ screw dislocations moving on three possible ${110}$ planes according to the flow rule that describes the response of isolated screw dislocations to external loads. The cross-slip of dislocations is assessed using the master equation which takes into account different energy barriers for dislocations moving on the three slip planes. To demonstrate the performance of the model, we study the buildup of plastic strain at 77 K in both tension and compression for a number of loading directions covering the entire area of the standard stereographic triangle. The non-Schmid behavior of screw dislocations is shown to persist to the continuum level, whereby interactions between dislocations merely affect the rate of plastic flow.

Screw dislocation equations in a thin film and surface effects

The fundamental equations of screw dislocations in a thin film are derived for arbitrary boundary conditions: free surface, fixed surface and gradient loading imposed on the surface. The new equations make it possible to study the modification in dislocation structure and other surface effects. According to the modification of interaction between dislocations, boundary conditions can be essentially classified into two types: the stressed boundary (fixed stress on the surface) and the strained boundary (fixed strain on the surface). The interaction between dislocations decreases near stressed boundary and increases near strained boundary. The external stress (strain) field is separated as an independent superimposition with the modification of dislocation interaction. Surface effects on a single extended screw dislocation behavior in a thin film are investigated quantitatively. We show that the dislocation becomes narrower near a free surface, and wider near a fixed surface, where the reduction and increase of dislocation width scales proportionally to the reciprocal of distance between dislocation and surface. Correspondingly, the Peierls stress increases and decreases respectively. The image force on dislocation is attractive for the free surface and repulsive for the fixed surface. The amplitude of image force is smaller than that given in elastic theory, and the reduction is reversely proportional to the square of distance to the surface. Furthermore, the dislocation in a free standing thin film is considered and the distance between the dislocation and surface affect the amplitude of surface effect mostly.

Twin Boundaries merely as Intrinsically Kinematic Barriers for Screw Dislocation Motion in FCC Metals.

Metals with nanoscale twins have shown ultrahigh strength and excellent ductility, attributed to the role of twin boundaries (TBs) as strong barriers for the motion of lattice dislocations. Though observed in both experiments and simulations, the barrier effect of TBs is rarely studied quantitatively. Here, with atomistic simulations and continuum based anisotropic bicrystal models, we find that the long-range interaction force between coherent TBs and screw dislocations is negligible. Further simulations of the pileup behavior of screw dislocations in front of TBs suggest that screw dislocations can be blocked kinematically by TBs due to the change of slip plane, leading to the pileup of subsequent dislocations with the elastic repulsion actually from the pinned dislocation in front of the TB. Our results well explain the experimental observations that the variation of yield strength with twin thickness for ultrafine-grained copper follows the Hall-Petch relationship.

Atomistic aspects of screw dislocation behavior in α-iron and the derivation of microscopic yield criterion

The plastic deformation of body-centered cubic iron at low temperatures is governed by slip behavior of screw dislocations. Their non-planar core structure gives rise to a strong temperature dependence of the yield stress and overall plastic behavior that does not follow the Schmid law common to most close-packed metals. In this work,we carry out a systematic study of the screw dislocation behavior in α-Fe by means of atomistic simulations using a state-of-the-art magnetic bond-order potential. Based on the atomistic simulations of the screw dislocations under various external loadings, we formulate an analytical yield criterion that correctly captures the non-Schmid plastic response of iron single crystals under general loading conditions. The theoretical predictions of operative slip systems for uniaxial loadings agree well with available experimental observations, and demonstrate the robustness and reliability of such atomistically based yield criterion. In addition, this bottom-up approach can be directly utilized to formulate dislocation mobility rules in mesoscopic discrete dislocation dynamics simulations.

Assessment of interatomic potentials for atomistic analysis of static and dynamic properties of screw dislocations in W

Screw dislocations in bcc metals display non-planar cores at zero temperature which result in high lattice friction and thermally-activated strain rate behavior. In bcc W, electronic structure molecular statics calculations reveal a compact, non-degenerate core with an associated Peierls stress between 1.7 and 2.8 GPa. However, a full picture of the dynamic behavior of dislocations can only be gained by using more efficient atomistic simulations based on semiempirical interatomic potentials. In this paper we assess the suitability of five different potentials in terms of static properties relevant to screw dislocations in pure W. Moreover, we perform molecular dynamics simulations of stress-assisted glide using all five potentials to study the dynamic behavior of screw dislocations under shear stress. Dislocations are seen to display thermally-activated motion in most of the applied stress range, with a gradual transition to a viscous damping regime at high stresses. We find that one potential predicts a core transformation from compact to dissociated at finite temperature that affects the energetics of kink-pair production and impacts the mechanism of motion. We conclude that a modified embedded-atom potential achieves the best compromise in terms of static and dynamic screw dislocation properties, although at an expense of about ten-fold compared to central potentials.

Orbital-free density functional theory simulations of dislocations in magnesium

Metal plasticity is controlled by nucleation and motion of dislocations. Key metrics determining the ease of these two events are stacking fault energies (SFEs) and dislocation structures. Here we study screw and edge dislocation structures on the basal, prismatic and pyramidal planes in hexagonal-close-packed magnesium (Mg) using orbital-free density functional theory (OFDFT) in order to gain insight into plastic deformation mechanisms in Mg. The accuracy of the method is first benchmarked against the more accurate Kohn–Sham DFT (KSDFT) with emphasis on testing OFDFT's main approximations, i.e. the kinetic energy density functional and the bulk-derived local pseudopotential by comparing predicted equilibrium bulk energies, elastic constants and various SFEs. Then we compare generalized SFEs for the basal, prismatic and pyramidal slip systems calculated by OFDFT versus two mainstream counterparts, KSDFT and the classical potential embedded atom method (EAM). The latter produces spurious minima along the generalized SFE surface on the prismatic plane whereas OFDFT agrees with qualitative experimental observations. Thereafter, we optimize isolated dislocation structures within periodic cells containing a few thousand atoms. We predict that on the basal plane, the screw and edge dislocations separate into partial dislocations with widths of ∼12 and ∼24 Å, respectively. Screw dislocations on the prismatic and pyramidal planes preferentially cross-slip and dissociate on the basal plane although a local minimum exists for a dissociated prismatic screw dislocation with widths of ⩾∼5 Å. By contrast, the edge dislocations on prismatic and pyramidal planes are predicted to remain undissociated. Such cross-slip behavior of screw dislocations is not reproduced by EAM simulations. We propose that the propensity for screw dislocations to remain on or cross-slip to Mg's basal plane, along with the compact nature of edge dislocations on non-basal planes, is likely to be responsible for its limited ductility.

Stress and temperature dependence of screw dislocation mobility inα-Fe by molecular dynamics

The low-temperature plastic yield of $\ensuremath{\alpha}$-Fe single crystals is known to display a strong temperature dependence and to be controlled by the thermally activated motion of screw dislocations. In this paper, we present molecular dynamics simulations of $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$${112}$ screw dislocation motion as a function of temperature and stress in order to extract mobility relations that describe the general dynamic behavior of screw dislocations in pure $\ensuremath{\alpha}$-Fe. We find two dynamic regimes in the stress-velocity space governed by different mechanisms of motion. Consistent with experimental evidence, at low stresses and temperatures, the dislocations move by thermally activated nucleation and propagation of kink pairs. Then, at a critical stress, a temperature-dependent transition to a viscous linear regime is observed. Critical output from the simulations, such as threshold stresses and the stress dependence of the kink activation energy, are compared to experimental data and other atomistic works with generally very good agreement. Contrary to some experimental interpretations, we find that glide on ${112}$ planes is only apparent, as slip always occurs by elementary kink-pair nucleation/propagation events on ${110}$ planes. Additionally, a dislocation core transformation from compact to dissociated has been identified above room temperature, although its impact on the general mobility is seen to be limited. This and other observations expose the limitations of inferring or presuming dynamic behavior on the basis of only static calculations. We discuss the relevance and applicability of our results and provide a closed-form functional mobility law suitable for mesoscale computational techniques.

Variational equivalence between Ginzburg-Landau, XY spin systems and screw dislocations energies

We introduce and discuss discrete two-dimensional models for XY spin systems and screw dislocations in crystals. We prove that, as the lattice spacing e tends to zero, the relevant energies in these models behave like a free energy in the complex Ginzburg-Landau theory of superconductivity, justifying in a rigorous mathematical language the analogies between screw dislocations in crystals and vortices in superconductors. To this purpose, we introduce a notion of asymptotic variational equivalence between families of functionals in the framework of Γ-convergence. We then prove that, in several scaling regimes, the complex Ginzburg-Landau, the XY spin system and the screw dislocation energy functionals are variationally equivalent. Exploiting such an equivalence between dislocations and vortices, we can show new results concerning the asymptotic behavior of screw dislocations in the | log e| energetic regime.

Elastic behavior of screw dislocations in porous solids

Dislocation behavior in porous solids with different 2D arrangements of closed cylindrical voids is discussed. It is suggested that in many cases important for practice, the approximation of two closest voids may be quite effective. The stress field and strain energy of a screw dislocation in an elastically isotropic solid containing two cylindrical voids are rigorously derived by the technique of infinite ensembles of image dislocations and analyzed in detail. The image force exerted by the voids on such a dislocation is also calculated and studied. As a limiting case of the solution obtained, we derive the stress field of a screw dislocation in a half-space containing a cylindrical void.

Nonplanar core and dynamical behavior of screw dislocations in copper at high velocities

Nonplanar core and dynamical behavior of screw dislocations in copper at high velocities

Synthesis and analysis of linear and nonlinear acoustical vortices

Acoustical screw dislocations are synthesized in various configurations with a versatile experimental setup. The experimental setup is based on the inverse filter technique and allows one to synthesize one or more acoustical vortices with a chosen width, position, and topological charge. An interesting feature of this experimental facility to study screw dislocation behavior is the direct measurement in amplitude and phase. This characteristic is used to develop an original method of decomposition of an acoustical vortex field in order to analyze the acoustical vortices. Moreover, the behaviors of two acoustical vortices of the same or opposite charge have been studied experimentally and compared to theoretical laws.

Stability of perfect dislocations in rare-earth intermetallic compounds: YCu, YAg and YZn

In this study, we evaluate the stability of prefect dislocations, interaction energy of kink pairs, cross-slip behavior of screw dislocations and the instability of pinned dislocations in ductile rare-earth intermetallic compounds: YCu, YAg and YZn. The results are compared to those seen for the common B2 type intermetallics, NiAl and Fe–25Al. The results indicate that the elastic anisotropy does not cause any instability of ordinary dislocations in YCu, YAg and YZn in contrast to NiAl and Fe–25Al. The cross-slip characteristics and the external driving force required for the instability of pinned dislocations differ considerably, resulting from their lower energy and the absence of negative line tension, from those seen for NiAl and Fe–25Al. The results also elucidate certain differences observed between the single crystalline deformation behavior of YCu, YAg and YZn.

Nanopipes and their relationship to the growth mode in thick HVPE-GaN layers

In this work, we illustrate and analyse long propagating nanopipes in thick HVPE-GaN layers studied by means of transmission electron microscopy. The nanopipes appear to have the characteristics and behaviour of screw-dislocations. They propagate with a constant diameter along tens of micrometers and a pit of a shape of inverted pyramid forms when the top surface of the layer is reached. The generation of the nanopipes is discussed in terms of their relation to the growth mechanism of HVPE-GaN material and the kinetics of screw dislocations in the early stages of growth of highly strained material. The nanopipes appear to promote the crystal growth when the substrate surface does not provide a sufficient nucleation base for subsequent HVPE growth. In this case they mediate the surface morphology terminating surface steps by hexagonal pits and act as centres of growth spirals. When the substrate surface provides a sufficient amount of nucleation sites the step flow mechanism is prevailing and no growth spirals associated with nanopipes are observed.

Modeling of threading dislocation reduction in growing GaN layers

In this work, a model is developed to treat threading dislocation (TD) reduction in (0 0 0 1) wurtzite epitaxial GaN thin films. The model is based on an approach originally proposed for (0 0 1) FCC thin film growth and uses the concepts of mutual TD motion and reactions. We show that the experimentally observed slow TD reduction in GaN can be explained by low TD reaction probabilities due to TD line directions practically normal to the film surface. The behavior of screw dislocations in III-nitride films is considered and is found to strongly impact TD reduction. Dislocation reduction data in hydride vapor phase epitaxy (HVPE) grown GaN are well described by this model. The model provides an explanation for the non-saturating TD density in thick GaN films.

Behavior of screw dislocations near phase boundaries in the gradient theory of elasticity

The solution of the boundary-value problem on a rectilinear screw dislocation parallel to the interface between phases with different elastic moduli and gradient coefficients is obtained in one of the versions of the gradient theory of elasticity. The stress field of the dislocation and the force of its interaction with the interface (image force) are presented in integral form. Peculiarities of the short-range interaction between the dislocation and the interface are described, which is impossible in the classical linear theory of elasticity. It is shown that neither component of the stress field has singularities on the dislocation line and remains continuous at the interface in contrast to the classical solution, which has a singularity on the dislocation line and permits a discontinuity of one of the stress components at the interface. This results in the removal of the classical singularity of the image force for the dislocation at the interface. An additional elastic image force associated with the difference in the gradient coefficients of contacting phases is also determined. It is found that this force, which has a short range and a maximum value at the interface, expels a screw dislocation into the material with a larger gradient coefficient. At the same time, new gradient solutions for the stress field and the image force coincide with the classical solutions at distances from the dislocation line and the interface, which exceed several atomic spacings.

Modeling of Threading Dislocation Reduction in Growing GaN Layers

In this work, a model is developed to treat threading dislocation (TD) reduction in (0001) wurtzite epitaxial GaN thin films. The model is based on an approach originally proposed for (001) f.c.c. thin film growth and uses the concepts of mutual TD motion and reactions. We show that the experimentally observed slow TD reduction in GaN can be explained by low TD reaction probabilities due to TD line directions practically normal to the film surface. The behavior of screw dislocations in III-nitride films is considered and is found to strongly impact TD reduction. Dislocation reduction data in hydride vapor phase epitaxy (HVPE) grown GaN is well-described by this model. The model provides an explanation for the non-saturating TD density in thick GaN films.