Kink Nucleation Research Articles

Unravelling the jerky glide of dislocations in body-centred cubic crystals.

In situ straining tests in high purity α-Fe thin foils at low temperatures1 have demonstrated that crystal line defects, called dislocations, have a jerky type of motion made of intermittent long jumps of several nanometres. This observation conflicts with the standard Peierls mechanism for plastic deformation in body-centred cubic crystals, where the screw dislocation jumps are limited by inter-reticular distances, that is, distances of a few angstroms. Employing atomic-scale simulations, we show that although the short jumps are initially more favourable, their realization requires the propagation of a kinked profile along the dislocation line, which yields coherent atomic vibrations acting as travelling thermal spikes. Such local heat bursts favour the thermally assisted nucleation of new kinks in the wake of primary ones. The accumulation of new kinks leads to long dislocation jumps like those observed experimentally. Our study constitutes an important step towards predictive atomic-scale theory for materials deformation.

Charge-transfer interatomic potential to reproduce 30° partial dislocation movements for 4H-SiC in the surface vicinity and its application to BPD-TED conversion

4H-SiC has recently attracted attention as a new power semiconductor material to replace silicon. One of the challenges impeding its practical use is the elimination of killer defects in its epitaxial layer, such as dislocations and stacking faults. The conversion of basal plane dislocations (BPDs) into threading edge dislocations (TEDs) is crucial for reducing harmful mobile dislocations. However, the atomistic mechanism underlying the process remains elusive. To clarify the BPD–TED conversion mechanism, we developed a charge-transfer interatomic potential to reproduce 30° partial dislocation dynamics in the surface vicinity of 4H-SiC. The proposed potential significantly improved the accuracy of estimating the stacking fault energy and dislocation mobility in the regions where the dislocation core and surface overlap. Using the developed potential, we investigated the mechanism underlying the contraction of a pair of 30° partial dislocations in the vicinity of the surface. From the energy landscape, the equilibrium distance between the two partials decreased as the depth from the surface decreased because of the strong image force near the surface. The equilibrium distance decreased to zero when the depth reached 0.25 nm. This result is qualitatively consistent with the dislocation theory and the known effect of image force. From the viewpoint of the activation energies of kink nucleation and migrations, the activation energy for C-core and Si-core partial contractions decreased below a depth of 1 nm from the C-face and S-face surfaces, respectively, and became almost equal to that of C-core and Si-core expansions, respectively, when the depth reached 0.25 nm. Therefore, the partial BPDs can contract easily in the corresponding structures, particularly when the depth from the surface is less than 1 nm.

Long-range Tersoff potential for silicon to reproduce 30° partial dislocation migration

Dislocation in silicon has been studied from atomistic viewpoints for many years. It is widely acknowledged that the bond-order Tersoff potential does not reproduce the dislocation dynamics. Addressing the abovementioned shortcoming remains challenging for over three decades. We have developed a new long-range Tersoff potential to reproduce the 30° dislocation dynamics in silicon. We also clarified that the first-neighbor cutoff distance of the original Tersoff potential inhibited the smooth breaking and formation of bonds within the dislocation cores, resulting in non-smooth reaction pathways during kink formation and migration. Consequently, we incorporated a long cutoff distance of 4.5 Å, corresponding to the third-neighbor distance. We also modified the distance-difference term of the Tersoff potential to eliminate an artificial energy increase attributed to the long-range cutoff. The developed potential accurately reproduced the stacking fault energy and the activation energies of kink nucleation and migration, leading to a smoother reaction pathway than the original Tersoff potential. The stacking fault energies of our potential and the original Tersoff potential were 74 and 0 mJ/m2, respectively. The activation energies of kink formation, left kink migration, and right kink migration were 1.09, 0.97, and 0.68 eV, which are closer to the experimental values than those of the original Tersoff. We also confirmed the smooth movement of partial 30° dislocations using molecular dynamics simulation. Our developed potential could contribute the microscopic studies of dislocation in silicon.

Mechanism of thermally-activated prismatic slip in Mg

Prismatic slip of the screw <a> dislocation in magnesium at temperatures ≳ 150 K is understood to be governed by double-cross-slip of the stable basal screw through the unstable prism screw and back to the basal screw, with the activation energy controlled by the formation energy of two basal-basal kinks. However, atomistic studies of the double-kink process predict activation energies roughly twice those derived experimentally. Here, a new mechanism of prism glide is proposed, analyzed theoretically, and demonstrated qualitatively and quantitatively via direct molecular dynamics (MD) simulations. The new mechanism is intrinsically 3d, and involves the nucleation of a single kink at the junction where a 3d prismatic dislocation loop transitions from the basal screw segment to non-screw prismatic character. The relevant kink energies are calculated using recently-developed Neural-Network Potentials (NNPs) for Mg that show good agreement versus DFT for basal and prism <a> dislocations, enabling a parameter-free analytic model for the activation barrier. Direct MD simulations show both operation of the precise proposed mechanism and a stress-dependent activation barrier that agrees reasonably with the analytic model. Predictions of dislocation velocity compare very well with in-situ TEM data, and macroscopic strength versus temperature can also be understood. Overall, the new intrinsically 3d mechanism for dislocation glide due to single kink nucleation rather than double-kink nucleation explains key features of the prismatic slip in Mg and may have broader applicability in other metals where kink nucleation processes control thermally-activated flow.

Microscopic Characteristics of Kinking Phenomenon in Vertically Free-Standing Nanowires

Vertically free-standing nanowires, synthesized through vapor-based growth, can undergo changes in their growth directions known as kinking. These alterations can significantly influence the physical and chemical properties of nanowires, thereby expanding their potential applications. The occurrence of kinks is commonly associated with variations in vapor, temperature, seed, and/or their combinations. However, the interplay among different growth factors complicates the identification of the dominating factor and, consequently, limits precise control over nanowire morphology. Theoretical models, incorporating factors like supersaturation, wetting angle, nanowire size, and surface/interface energies tied to growth conditions, have been developed to describe and predict kinking during nanowire growth. While a few pivotal parameters, such as surface/interface energies and wetting angles, can be subtly adjusted through minor alterations in growth conditions, accurately predicting the occurrence of kinks remains a practical challenge. Conversely, in the present review, we attempted to elucidate connections between microscopic aspects, such as changes in composition and the formation of defects, and the nucleation and progression of kinks. This effort aims to construct a predictive framework that enhances our understanding of the tendencies in nanowire growth.

Numerical study on the ductility improvement mechanism of dilute Mg-Ca alloys

In recent years, magnesium (Mg) alloys have attracted extensive attention because of their potential use as alternatives to dense metals and Al alloys. Therefore, the low ductility of Mg alloys should be improved. Previous studies indicated that the addition of low concentrations of Ca improves the ductility of Mg alloys; however, the associated mechanisms are not well understood. The present numerical study demonstrates that the ratio of the critical resolved shear stresses associated with prismatic and basal < a > slip systems is significantly reduced (to a value of approximately 1) in a Mg-0.1 at.% Ca alloy. The incorporation of Ca was also found to harden the basal slip system while softening the prismatic slip system. The addition of Ca to Mg evidently provides a thermal-like effect that promotes the nucleation of kinks and enhances the dislocation motion. This effect is significantly more pronounced in the case of a prismatic slip system. The difference in importance of the thermal effect between the basal and prismatic slip systems and the Ca-promoted nucleation of kinks are the two main factors responsible for softening the prismatic slip system and improving the ductility of dilute Mg-Ca alloys.

Correlating dislocation mobility with local lattice distortion in refractory multi-principal element alloys

Multi-principal element alloys (MPEAs) exhibit different degrees of intrinsic lattice distortion, which varies with constituent species. Using atomistic simulations, here we found the mobilities of both edge and screw dislocations are dependent on lattice distortion in body-centered-cubic (BCC) MPEAs. Lattice distortion influences not only the activation of kink nucleation and propagation governing screw dislocation motion, but also the strength of local pinning for edge dislocations. As a consequence, the disparity between the velocities of screw and edge dislocations decreases with increasing lattice distortion. We further demonstrate that lattice distortion can be taken as an indicator to correlate with the reported brittleness of BCC MPEAs. This implies that maximizing lattice distortion could be a plausible strategy to improve the ductility for brittle BCC MPEAs.

Glide Mobility of a-Type Edge Dislocations in Aluminum Nitride by Molecular Dynamics Simulation.

Classical molecular dynamics simulations are performed to investigate the motion of a-type edge dislocations in wurtzite aluminum nitride (AlN). The nucleation and propagation of kinks are observed via the dislocation extraction algorithm. Our simulation results show that the nucleation energy of the kink pair in AlN is 1.2 eV and that the migration energy is 2.8 eV. The Peierls stress of the 1/3⟨112̅0⟩{101̅0} edge dislocation at 0 K is 15.9 GPa. The viscous motion of dislocations occurs when τ > τp, and the dislocation velocity is inversely proportional to the temperature and directly proportional to the applied stress. Below room temperature, the value of the critical resolved shear stress (CRSS) on the prismatic plane is the lowest, which suggests that the dislocation mobility on the prismatic plane is the easiest. The CRSS on the pyramidal plane is always the highest at all temperatures, which suggests that pyramidal slip is the hardest among these three slip systems.

Cooperative roles of stacking fault energies on dislocation nucleation at bimetal interface through tunable potentials

By tuning consistent potentials for bimetal system, the cooperative roles of stacking fault energies (SFEs) such as intrinsic SFE (ISFE) and unstable SFE (USFE) on the dislocation nucleation are comprehensively explored. It reveals that the dislocation nucleation at semi-coherent interface is determined by the misfit dislocations, but the critical yield stress depends strongly on the values of ISFE and USFE that are function of external loadings. To account for such relationship, a modified analytical model is proposed based on the nucleation and propagation of double kinks at the interface, showing good agreement with the simulation results. These results not only resolve the previous inconsistency in the role of stacking faults on plastic deformation but shed light on evaluating the atomistic mechanism according to the synergistic effect between stacking faults and loading schemes.

Effect of Si content on the uniaxial tensile behavior of Mo-Si solid solution alloys

Recrystallized binary Mo-0.2 wt.% Si (Mo-0.68 at.% Si) and Mo-0.3 wt.% Si (Mo-1.0 at.% Si) alloys and a ternary Mo-0.75 wt.% Si-0.14 wt.% B (Mo-2.5 at.% Si-1.2 at.% B) alloy were tested in uniaxial tension as a function of temperature in vacuum and the results are compared to previous results on recrystallized commercial purity (CP) Mo and a binary Mo-0.1 wt.% Si (Mo-0.34 at.% Si) solid solution alloy. Yield strength increases with increasing Si content at all temperatures examined except at room temperature where the 0.1 wt.% Si alloy demonstrates softening; atomistic simulation confirms this behavior to be associated with Si segregation to the core and the associated ease of kink nucleation. Tensile ductility at room temperature rapidly deteriorates with increasing Si content in solid solution but in the Mo-0.3 wt.% Si solid solution alloy, tensile ductility of ~10% was measured at 300°C and thereafter, it increases rapidly at higher temperatures. Serrated flow occurs in the temperature range 600°C~800°C with the serration amplitude increasing with increasing Si content; atomistic simulation illustrates O trapping by Si in solid solution and subsequent de-trapping/release at higher temperatures that can account for the onset temperature delay of serrated flow in these Mo-Si solid solution alloys relative to commercial purity Mo. The serrated flow phenomenon is accompanied by significant work hardening; the presence of dislocation tangles, dipoles and prismatic loops in specimens fractured above ≥ 700°C accounts for the observed work hardening.

Solid solution softening in dislocation-starved Mg–Al alloys

Here, we report molecular dynamics (MD) calculations of spall strength in pure magnesium and magnesium alloys with 1–8 at.% aluminum in solid solution. The Mg–Al solid solution alloys are found to have a weaker spall strength than pure magnesium, e.g. the spall strength of Mg-8 at.% Al is found to be 12% lower than pure magnesium. Moreover, we find that the spall strength of Mg–Al alloys monotonically decreases with increasing concentration of Al content. We term this phenomena solid solution softening (SSS) of spall strength, which is contrary to the conventional solid solution strengthening observed in most alloys (including Mg–Al alloys) deformed at quasi-static loading rates. We argue that this transition from solid solution strengthening at quasi-static rates to SSS at extreme loading rates is due to a transition from dislocation glide dominated failure at low rates to dislocation nucleation dominated failure at extreme rates. The distortion of the host lattice by solute atoms is found to retard dislocation glide, but aids dislocation nucleation. We thus conclude that SSS may manifest in any dislocation-starved system, regardless of loading rate. To this end, we propose a theoretical model for spall strength in dislocation-starved bulk and nanoporous alloys that exhibits remarkable agreement with our molecular dynamics calculations. Our theory bares some resemblance to the double kink nucleation enhancement theory for low-temperature SSS in some body centered cubic metals, e.g. refractory metals alloyed with group IV-VIII elements.

Dimensionality effects in crystal plasticity, from 3D silicon to 2D silicene

To characterize the effects of free surfaces on dislocation mobility, the edge dislocation glide process in thin silicon films is modeled using an interatomic potential and first principles calculations. The influence of film thickness is determined, starting with the simulation of a silicene monolayer and then increasing the number of layers. The energy barrier for dislocation glide in silicene was calculated to be 1.5 eV, indicating a relatively high mobility of dislocation defects. In thin Si films a glide mechanism via consecutive bond rotations was identified, with kink nucleation being observed at the free surfaces of the film with subsequent migration. The influence of the free edge in finite size films is shown to be negligible in relation to glide for dislocations at distances from the free edge larger than three Burgers vectors. Molecular dynamics simulations reveal the possibility of more complex but lower energy barrier atomic reconstructions triggered at the free surfaces of the film near the dislocation core that may increase dislocation mobility at higher temperatures.

Unusual activated processes controlling dislocation motion in body-centered-cubic high-entropy alloys.

Atomistic simulations of dislocation mobility reveal that body-centered cubic (BCC) high-entropy alloys (HEAs) are distinctly different from traditional BCC metals. HEAs are concentrated solutions in which composition fluctuation is almost inevitable. The resultant inhomogeneities, while locally promoting kink nucleation on screw dislocations, trap them against propagation with an appreciable energy barrier, replacing kink nucleation as the rate-limiting mechanism. Edge dislocations encounter a similar activated process of nanoscale segment detrapping, with comparable activation barrier. As a result, the mobility of edge dislocations, and hence their contribution to strength, becomes comparable to screw dislocations.

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.

Statistical analysis of emission, interaction and annihilation of phonons by kink motion in ferroelastic materials

Our early work showed that the evolution of the twin boundary pattern exhibits an avalanche behavior upon external loading of ferroelastic materials [Salje et al., Phys. Rev. B 83, 104109 (2011)]. The distribution of “jerks” (singularities of potential energy change) was found to follow a power law distribution below a Vogel–Fulcher temperature, mainly related to the movement of kinks in domain boundaries. We use molecular dynamics simulations to study the nucleation, scattering, and annihilation of phonons that are generated by the nucleation and propagation of such kinks. The interaction and scattering of phonons are correlated over a short time period and gradually become uncorrelated before annihilation at large temperature intervals. The movement and interaction of phonons show avalanche behavior. The probability of finding energy jerks follows a power law with exponents around 2.5–3. The distribution of waiting times between jerks also follows a power law. At temperatures above the Vogel–Fulcher temperature, scattering with thermal phonons becomes predominant and no phononic avalanches were observed.

Revealing the Grain Boundary Formation Mechanism and Kinetics during Polycrystalline MoS2 Growth.

Controllable synthesis of MoS2 with desired grain morphology via chemical vapor deposition (CVD) or physical vapor deposition (PVD) remains a challenge. Hence, it is important to understand polycrystalline growth of MoS2 and further provide guidelines for its CVD/PVD growth. Here, we formulate a kinetic Monte Carlo (kMC) model aiming at predicting the grain boundary (GB) formation in the CVD/PVD growth of polycrystalline MoS2. In the kMC model, the grain growth is via kink nucleation and propagation, whose energetic parameters and initial nucleus details are either from first-principles calculations or from experiments. Using the kMC model, we perform extensive simulations to predict the GB formation by using two, three, four, and five initial nuclei and compare the simulation results with previous experimental results. The obtained GB morphologies are in an excellent agreement with those experimental results. These agreements suggest that the proposed kMC model can correctly capture the mechanism and kinetics of GB formation. In particular, we reveal that the formation of smooth/rough GB is dictated by the two growth vectors for the kink propagation at the two associated grain edges, which is validated by our high-resolution scanning transmission electron microscopy images for PVD growth of MoS2 grains. Besides, we have made predictions beyond reproducing experimental observations, including the growth with artificially designed nuclei, the morphology transformation by tuning the Mo and S sources, and the formation of high-quality single-crystalline monolayer MoS2 by using single-crystalline substrates with vicinal steps. Our kMC model may serve as a powerful predictive tool for the CVD/PVD growth of monolayer MoS2 with desired GB configurations.

Dislocation mechanisms of low-temperature acoustic relaxation in iron

An integrated approach to the study of the mechanisms of low-temperature dislocation relaxation during low-temperature cyclic deformations of crystalline materials has been developed and tested. The approach is based on the combined use of experimental methods of mechanical spectroscopy in wide frequency-temperature ranges and theoretical methods of statistical and thermoactivation analysis of experimental results. The efficiency of this approach was demonstrated by studying low-temperature relaxation resonances in iron crystals whose dislocation structure was varied by preliminary plastic deformation. In this study, the previous mechanical spectroscopy results for iron in the temperature range of 4 K &amp;lt; T &amp;lt; 150 K at vibrational frequencies of about 1 Hz and 105 Hz were supplemented by a detailed study of the temperature spectra of internal friction and the Young’s modulus of a single-crystal iron plate at intermediate frequencies of about 103 Hz. A two-mode dislocation relaxator model was suggested for interpreting the entire set of experimental results. Its first component is a linear segment of a dislocation line in a first-kind Peierls relief whose relaxation properties are determined by thermal activation of kink pairs. The second component is a chain of geometric kinks capable of thermally activated diffusion movement in a second-kind Peierls relief. Empirical estimates of the energy, force, inertial, and geometric characteristics of both components of such a relaxator have been obtained. This study complements the earlier analysis of the processes of mechanical relaxation in crystals caused by nucleation and movements of kinks on dislocation lines [a review: A. Seeger and C. Wüthrich, Nuovo Cimento B 33, 38 (1976)].

Origin of ultrafast growth of monolayer WSe2 via chemical vapor deposition

The ultrafast growth of large-area, high-quality WSe2 domains with a compact triangular morphology has recently been achieved on a gold substrate via chemical vapor deposition. However, the underlying mechanism responsible for ultrafast growth remains elusive. Here, we first analyze growth processes and identify two possible pathways that might achieve ultrafast growth: Path 1, fast edge attachment and ultrafast edge diffusion; Path 2, fast kink nucleation and ultrafast kink propagation. We perform kinetic Monte Carlo simulations and first-principles calculations to assess the viability of these two paths, finding that Path 1 is not viable due to the high edge diffusion barrier calculated from first-principles calculations. Remarkably, Path 2 reproduces all the experimental growth features (domain morphology, domain orientation, and growth rate), and the associated energetic data are consistent with first-principles calculations. The present work unveils the underlying mechanism for the ultrafast growth of WSe2, and may provide a new route for the ultrafast growth of other two-dimensional materials.

A new reconstruction core of the 30° partial dislocation in silicon

ABSTRACTThe partial dislocation in silicon is investigated theoretically in the framework of the fully discrete Peierls–Nabarro model and first-principles calculations. A new reconstructed core composed of a periodic arrangement of one tetragon and two heptagons (477-core) is proposed. Similar to the partial dislocation, we find that there are actually two types of reconstructed cores for the partial dislocation, namely, a well-known 558-core and a new 477-core. The energy of the 477-core is 0.137 eV/Å higher than that of the 558-core. However, from the molecular dynamics simulation, we found that the 477-core may have a macroscopic lifetime for temperature below 30 K. The full kinks and the partial kinks due to the appearance of the 477-core are also studied. Remarkably, it is found that formation and migration of the global kinks deeply involve with the partial kinks, and the creation and motion of partial kinks can be attributed to the rotation of a single bond. Our results are helpful in understanding the mechanism of kink nucleation and the plasticity of silicon.

A crystal plasticity model for body-centered cubic molybdenum: Experiments and simulations

A physics-based finite strain crystal plasticity constitutive model for body-centered-cubic (BCC) single crystals is developed to capture the strong temperature, rate, and orientation dependence of mechanical behavior. The key features of the model include twinning-anti-twinning asymmetry of shearing resistance, a yield criterion that incorporates atomistics-informed non-Schmid effects, and a flow rule formulated based on the theory of thermally activated motion of screw dislocations via nucleation of double kinks. The implementation of the constitutive model in a finite-element program is briefly discussed. The material constants in the model are determined by calibrating the model against literature-based experimental data on single-crystal Molybdenum subjected to uniaxial compression and uniaxial tension. Experiments of uniaxial compression on a single crystal specimen with a hole were performed for validation of the calibrated model for BCC Molybdenum. Measurements of deformations in the vicinity of the hole were used to assess the ability of the model in predicting localized deformation patterns around the hole. The model is able to effectively describe the anisotropic and temperature-dependent stress-strain response of a molybdenum crystal up to a homologous temperature of 0.3.