Core Structure Of Screw Dislocations Research Articles

Moment tensor potential for static and dynamic investigations of screw dislocations in bcc Nb

A new machine-learning interatomic potential, specifically a moment tensor potential (MTP), is developed for the study of screw-dislocation properties in body-centered-cubic (bcc) Nb in the thermally- and stress-assisted temperature regime. Importantly, configurations with straight screw dislocations and with kink pairs are included in the training set. The resulting MTP reproduces with near density-functional theory (DFT) accuracy a broad range of physical properties of bcc Nb, in particular, the Peierls barrier and the compact screw-dislocation core structure. Moreover, it accurately reproduces the energy of the easy core and the twinning-anti-twinning asymmetry of the critical resolved shear stress (CRSS). Thereby, the developed MTP enables large-scale molecular dynamics simulations with near DFT accuracy of properties such as for example the Peierls stress, the critical waiting time for the onset of screw dislocation movement, atomic trajectories of screw dislocation migration, as well as the temperature dependence of the CRSS. A critical assessment of previous results obtained with classical embedded atom method potentials thus becomes possible.

Finite-temperature screw dislocation core structures and dynamics in α-titanium

A multiscale approach based on molecular dynamics (MD) and kinetic Monte Carlo (kMC) methods is developed to simulate the dynamics of an 〈a〉 screw dislocation in α-Ti. The free energy barriers for the core dissociation transitions and Peierls barriers for dislocation glide as a function of temperature are extracted from the MD simulations (based on machine learning interatomic potentials and optimization); these form the input to kMC simulations. Dislocation random walk trajectories from kMC agree well with those predicted by MD. On some planes, dislocations move via a locking-unlocking mechanism. Surprisingly, some dislocations glide in directions that are not parallel with the core dissociation direction. The MD/kMC multiscale method proposed is applicable to dislocation motion in simple and complex materials (not only screw dislocations in Ti) as a function of temperature and stress state.

Phase-field modeling of dislocation–interstitial interactions

The mechanical behavior of body-centered cubic (BCC) materials can be dramatically affected by the presence of interstitial solute atoms. We present a new phase-field dislocation dynamics formulation to include the diffusion of interstitials. Short-range interactions are accounted for by a concentration-dependent lattice energy, and long-range interactions are accounted for by modifications to the elastic energy. The interstitial diffusion law introduces gradients that require methods for minimizing Gibbs oscillations, which is done via a modified Green’s function. The formulation is general to any solute-solvent system and is applied here to Nb-O as a model system, whose interstitial parameters are obtained from ab initio calculations. The effect of O on the core structures of Nb edge and screw dislocations is calculated. The diffusion of O to form interstitial atmospheres around dislocation cores is simulated, as well as the critical stresses required for dislocations to break away or cross slip from these atmospheres. Future applications of the method to simulate complex interstitial embrittlement mechanisms are discussed.

Structure and mobility of -type screw dislocation in presence of H in α-Ti from first-principles

Hydrogen has both negative and positive effects on the mechanical properties of titanium and titanium alloys. It has been reported that the plastic deformation of titanium is controlled by the <a>-type screw dislocation and the principal slip plane is the prismatic plane. Herein, we employ first-principles calculations to investigate the modification of the <a>-type screw dislocation core structures caused by addition of H and the interactions between them. It reveals that H is attracted to the pyramidal dislocation partial and tends to segregate to the dislocation region. Then, the slip paths of the <a> screw dislocations along different slip planes in the H inserted Ti system are studied. Furthermore, the mechanism on how H affects the strength and plasticity of Ti under different H concentrations through the change of dislocation mobility is discussed.

Classical and machine learning interatomic potentials for BCC vanadium

BCC transition metals (TMs) exhibit complex temperature and strain-rate dependent plastic deformation behavior controlled by individual crystal lattice defects. Classical empirical and semiempirical interatomic potentials have limited capability in modeling defect properties such as the screw dislocation core structures and Peierls barriers in the BCC structure. Machine learning (ML) potentials, trained on DFT-based datasets, have shown some successes in reproducing dislocation core properties. However, in group VB TMs, the most widely used DFT functionals produce erroneous shear moduli ${C}_{44}$ which are undesirably transferred to machine-learning interatomic potentials, leaving current ML approaches unsuitable for this important class of metals and alloys. Here, we develop two interatomic potentials for BCC vanadium (V) based on (i) an extension of the partial electron density and screening parameter in the classical semiempirical modified embedded-atom method (XMEAM-V) and (ii) a recent hybrid descriptor in the ML Deep Potential framework (DP-HYB-V). We describe distinct features in these two disparate approaches, including their dataset generation, training procedure, weakness and strength in modeling lattice and defect properties in BCC V. Both XMEAM-V and DP-HYB-V reproduce a broad range of defect properties (vacancy, self-interstitials, surface, dislocation) relevant to plastic deformation and fracture. In particular, XMEAM-V reproduces nearly all mechanical and thermodynamic properties at DFT accuracies and with ${C}_{44}$ near the experimental value. XMEAM-V also naturally exhibits the anomalous slip at 77 K widely observed in group VB and VIB TMs and outperforms all existing, publically available interatomic potentials for V. The XMEAM thus provides a practical path to developing accurate and efficient interatomic potentials for nonmagnetic BCC TMs and possibly multiprincipal element TM alloys.

Twinning dynamics in nanoscale body-centered cubic tungsten

The non-planar core structure of screw dislocations in body-centered cubic (BCC) metals strongly influences its twinning dynamics, resulting in a minimum embryo size of six-layers {112} planes and discrete three-layers thickening behavior. By considering the energetically-stable three-layers “zonal dislocation” as a unit of twinning front, we rationalize such discrete twinning behavior to the two units for twin embryo and one unit for growth, in consistent with the description of classical twinning theory.

The core structure of screw dislocations with [001] Burgers vector in Mg 2 SiO 4 olivine

In this study, we report atomistic calculations of the core structure of screw dislocations with [001] Burgers vector in Mg2SiO4 olivine. Computations based on the THB1 empirical potential set for olivine show that the stable core configurations of the screw dislocations correspond to a dissociation in {110} planes involving collinear partial dislocations. As a consequence, glide appears to be favorable in {110} planes at low temperature. This study also highlights the difference between dislocation glide mechanism in {110} versus (010) or (100) for which glide is expected to occur through a locking–unlocking mechanism.

Screw dislocation core structure in the paramagnetic state of bcc iron from first-principles calculations

Iron-based alloys are widely used as structural components in engineering applications. This calls for a fundamental understanding of their mechanical properties, including those of pure iron. Under operational temperatures the mechanical and magnetic properties will differ from those of ferromagnetic body-centered-cubic iron at 0 K. In this theoretical work we study the effect of disordered magnetism on the screw dislocation core structure and compare with results for the ordered ferromagnetic case. Dislocation cores control some local properties such as the choice of glide plane and the associated dislocation mobility. Changes in the magnetic state can lead to modifications in the structure of the core and affect dislocation mobility. In particular, we focus on the core properties of the $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ screw dislocation in the paramagnetic state. Using the noncollinear disordered local moment approximation to address paramagnetism, we perform structural relaxations within density functional theory. We obtain the dislocation core structure for the easy and hard cores in the paramagnetic state, and compare them with their ferromagnetic counterparts. By averaging the energy of several disordered magnetic configurations, we obtain an energy difference between the easy- and hard-core configurations, with a lower, but statistically close, value than the one reported for the ferromagnetic case. The magnetic moment and atomic volume at the dislocation core differ between paramagnetic and ferromagnetic states, with possible consequences on the temperature dependence of defect-dislocation interactions.

Configurational thermodynamics of a 1/2〈111〉 screw dislocation core in Mo–W solid solutions using cluster expansion

In this work, we have developed a methodology to obtain an ab initio cluster expansion of a system containing a dislocation and studied the effect of configurational disorder on the 1/2〈111〉 screw dislocation core structure in disordered Mo1−xWx alloys. Dislocation cores control the selection of glide planes, cross slip, and dislocation nucleation. Configurational disorders in alloys can impact the dislocation core structure and affect dislocation mobility. For our calculations, we have used a quadrupolar periodic array of screw dislocation dipoles and obtained the relaxed structures and energies using density functional theory. We have obtained the dislocation core structure as a function of composition and the interaction energies of solutes with the dislocation as a function of position with respect to the core. With these energies, we performed mean-field calculations to assess segregation toward the core. Finally, with the calculated energies of 1848 alloy configurations with different compositions, we performed a first principle cluster expansion of the configurational energetics of Mo1−xWx solid solutions containing dislocations.

Neural network atomic potential to investigate the dislocation dynamics in bcc iron

To design the mechanical strength of body-centered-cubic (bcc) iron, clarifying the dislocation dynamics is very important. Using systematically constructed reference data based on density functional theory (DFT) calculations, we construct an atomic artificial neural network (ANN) potential to investigate the dislocation dynamics in bcc iron with the accuracy of DFT calculations. The bulk properties and defect formation energies predicted by the constructed ANN potential are in good agreement with the reference DFT calculations. The ${a}_{0}/2\ensuremath{\langle}111\ensuremath{\rangle}{110}$ screw dislocation core structure predicted by the ANN potential is compact and nondegenerate. The Peierls barrier predicted by the ANN potential is 35.3 meV per length of the Burgers vector. These results are consistent with the DFT results. Furthermore, not only the Peierls barrier, but also the two-dimensional energy profile of the screw dislocation core position predicted by the ANN potential are in excellent agreement with the DFT results. These results clearly demonstrate the reproducibility and transferability of the constructed ANN potential for investigating dislocation dynamics with the accuracy of the DFT. Combined with advanced atomistic techniques, the ANN potential will be highly useful for investigating the dislocation dynamics in bcc iron at finite temperatures.

An iterative scheme for the generalized Peierls–Nabarro model based on the inverse Hilbert transform

A new and efficient semi-analytical iterative scheme is proposed in this work for solving the generalized Peierls–Nabarro model. The numerical method developed here exploits certain basic properties of the Hilbert transform to achieve a reduction of the nonlocal and nonlinear equations characterizing the generalized Peierls–Nabarro model to a local model which is then solved using a fixed point iteration scheme. This is in sharp contrast to existing schemes for solving the generalized Peierls–Nabarro model like the semi-discrete variational Peierls–Nabarro model, or methods involving the fitting of the slip distribution to a linear combination of predefined elementary slip distributions, all of which involve the solution of nonlinear and nonlocal equations using gradient-based optimization tools. The key idea behind the proposed technique is to transform the nonlocal Peierls–Nabarro model into an equivalent local model, called the inverse Peierls–Nabarro model. From a computational viewpoint, the resulting local model is attractive since it can be solved without recourse to any gradient based algorithms; combined with appropriate acceleration schemes, the proposed algorithm provides a computationally expedient alternative to solving the generalized Peierls–Nabarro model. Further, the fixed point iterative scheme developed here easily lends itself to parallelization, unlike iterative methods for the fully nonlocal and nonlinear models currently in use. The proposed numerical scheme is validated both with simple examples involving the 1D Peierls–Nabarro model corresponding to a sinusoidal stacking fault energy, and with realistic examples involving calculations of the core structure of both edge and screw dislocations on the close-packed [Formula: see text] planes in Aluminum. An approximate technique to incorporate external stresses within the framework of the proposed iterative scheme is also discussed with applications to the equilibration of a dislocation dipole. Finally, the advantages, limitations and avenues for future extension of the proposed method are discussed.

Modeling solution hardening in BCC refractory complex concentrated alloys: NbTiZr, Nb1.5TiZr0.5 and Nb0.5TiZr1.5

Large scale, atomistic simulations of the core structure and mobility of ½[111] screw, edge and mixed dislocations in ternary multicomponent alloys (e.g. High Entropy alloys), NbTiZr, Nb1.5TiZr0.5 and Nb0.5TiZr1.5, are presented. The core structure of ½[111] screw dislocations continuously varies from compact to 3-fold with decreasing Nb content. The screw dislocation core structures in NbTiZr and Nb1.5TiZr0.5 are calculated using Embedded Atom Potentials (Johnson-Zhou) and compared with first-principles calculations of the screw dislocation in a quasi-random structure. In both simulations the dislocation core spreads on different (110) glide planes as the composition varies along the dislocation line in stoichiometric NbTiZr. The Nb-rich composition Nb1.5TiZr0.5 shows a compact core with very little core structure variation along the dislocation line in both First Principles and atomistic simulations. The screw dislocation deposits interstitial and vacancy dipole debris as it moves under stress. Average solute-dislocation core interaction energies in NbTiZr, Nb1.5TiZr0.5 and Nb0.5TiZr1.5 are derived from the average interatomic potential derived for each of the three systems. The interaction energies are used to determine the critical stress for the motion of ½[111] screw dislocations in the three systems as a function of temperature using the Suzuki model of kink migration controlled mobility developed for concentrated BCC random alloys. This analysis shows that the relatively high barrier for kink migration caused by fluctuations in solute concentration along the screw dislocation line and the dipole dragging stress associated with the screw dislocation motion results in a shallow fall-off of critical stress with temperature in these alloys as compared to simple BCC metals. Finally, the screw dislocation to edge and mixed dislocation critical stress ratio in NbTiZr are shown to be low, ∼2 at 5 K, in contrast to simple BCC metals, where it could be as high as 100–1000.

Effect of non-Schmid stresses on 〈a〉-type screw dislocation core structure and mobility in titanium

Density functional theory calculations of 〈a〉-type screw dislocation core structures in hcp titanium under a series of applied stresses with zero critical resolved shear stress were performed to investigate the origin of non-Schmid law slip behavior in α-titanium alloys. It was found that compression applied on the [11¯00] direction perpendicular to the Burgers vector leads to more compact pyramidally-oriented cores, while tension applied on the same axis causes an extension of these cores along the prismatic plane. Nudged elastic band calculations of the barrier to slip of the dislocations on the prismatic plane show that extension along this plane leads to reduced slip barriers. This suggests that non-Schmid stresses alter the critical resolved shear stress by inducing changes in the equilibrium core structure.

Screw dislocation structure and mobility in body centered cubic Fe predicted by a Gaussian Approximation Potential

The plastic flow behavior of bcc transition metals up to moderate temperatures is dominated by the thermally activated glide of screw dislocations, which in turn is determined by the atomic-scale screw dislocation core structure and the associated kink-pair nucleation mechanism for glide. Modeling complex plasticity phenomena requires the simulation of many atoms and interacting dislocations and defects. These sizes are beyond the scope of first-principles methods and thus require empirical interatomic potentials. Especially for the technological important case of bcc Fe, existing empirical interatomic potentials yield spurious behavior. Here, the structure and motion of the screw dislocations in Fe are studied using a new Gaussian Approximation Potential (GAP) for bcc Fe, which has been shown to reproduce the potential energy surface predicted by density-functional theory (DFT) and many associated properties. The Fe GAP predicts a compact, non-degenerate core structure, a single-hump Peierls potential, and glide on {110}, consistent with DFT results. The thermally activated motion at finite temperatures occurs by the expected kink-pair nucleation and propagation mechanism. The stress-dependent enthalpy barrier for screw motion, computed using the nudged-elastic-band method, follows closely a form predicted by standard theories with a zero-stress barrier of ~1 eV, close to the experimental value of 0.84 eV, and a Peierls stress of ~2 GPa consistent with DFT predictions of the Peierls potential.

First-principles calculations of interaction between solutes and dislocations in tungsten

Changes in mechanical properties due to transmutation products (Re and Os) in W alloys is a central issue for plasma-facing materials in fusion reactors. We conducted density functional theory calculations to investigate the effect of Re, Os, and other 5d solutes on core structure and motion of screw dislocations associated with plastic deformation. Ir, Pt, Au, and Hg solutes show strong attractive interactions with screw dislocations, causing solution strengthening by the pinning mechanism. On the other hand, Hf, Ta, and Re cause softening by facilitating dislocation motion around solutes. This prediction corresponds well with the experimental observation of softening behavior in W-Re alloys.

Modified analytic embedded atom method potential for chromium

In the present paper, we have developed a modified analytic embedded atom method potential for chromium. To solve the problem of a negative Cauchy relation for body-centered cubic metal at zero Kelvin temperature, a modification term is added to the total energy. Compared with available interatomic potentials, the present one is easier to be extended because of its analytic form. The fitted or input parameters are all well reproduced, and the properties beyond the fitting range (such as Cauchy relation, melting point and self-interstitial atom formation energies) are also well predicted. We have also studied the relation between the stacking faults energy and screw dislocation core structure with different potentials. Especially, only our potential predicts a compact core structure, which agrees with the results obtained by density functional theory calculations.

Dislocation core structures of tungsten with dilute solute hydrogen

In this paper, a combination of quantum mechanical and interatomic potential-based atomistic calculations are used to predict the core structures of screw and edge dislocations in tungsten in the presence of a particular concentration of hydrogen atoms. These configurations of the core structures are the results of two competing energies: the interaction between the partial dislocations and the corresponding generalized stacking fault energy in between the two partial dislocations, which are presented in this work. With this, we can precisely predict the configurations of the hydrogen-doped dislocation core structures.

Ab initio based empirical potential applied to tungsten at high pressure

Density-functional theory forces, stresses and energies comprise a database from which the optimal parameters of a spline-based empirical potential combining Stillinger-Weber and modified embedded-atom forms are determined. Accuracy of the potential is demonstrated by predictions of ideal shear, stacking fault, vacancy migration, elastic constants and phonons all between 0 and 100 GPa. Consistency with existing models and experiments is demonstrated by application to screw dislocation core structure and deformation twinning in a tungsten nanorod. Lastly, the potential is used to study the high-pressure bcc to fcc phase transition.

Interatomic potential to study plastic deformation in tungsten-rhenium alloys

In this work, an interatomic potential for the W-Re system is fitted and benchmarked against experimental and density functional theory (DFT) data, of which part are generated in this work. Having in mind studies related to the plasticity of W-Re alloys under irradiation, emphasis is put on fitting point-defect properties, elastic constants, and dislocation properties. The developed potential can reproduce the mechanisms responsible for the experimentally observed softening, i.e., decreasing shear moduli, decreasing Peierls barrier, and asymmetric screw dislocation core structure with increasing Re content in W-Re solid solutions. In addition, the potential predicts elastic constants in reasonable agreement with DFT data for the phases forming non-coherent precipitates (σ- and χ-phases) in W-Re alloys. In addition, the mechanical stability of the different experimentally observed phases is verified in the temperature range of interest (700–1500 K). As a conclusion, the presented potential provides an excellent tool to study plasticity in W-Re alloys at the atomic level.

Mobility of dissociated mixed dislocations under an Escaig stress

In FCC metals, the structure of a mixed dislocation core consists of two Shockley Partials which have different screw and edge character. The interactions between the partial dislocations can influence the stacking fault width (SFW). The SFW can also be manipulated by controlling the non-glide component of the total shear stress within the glide plane, commonly referred to as the ‘Escaig stress’, or τe. Molecular dynamics simulations were used to reproduce the dynamic behaviour of the atomistic core and stacking fault of a moving mixed 30° dislocation in copper and with several magnitudes of τe stress. Results showed that the must be relatively large to cause a significant effect on the SFW and that once the SFW is changed it also has a corresponding effect on the drag coefficient for a dislocation moving at steady-state. The reduction of the SFW, to the extent that the partial dislocations come within close proximity (i.e., partially merge into an imperfect full dislocation), changed the linear curve-fit of the stress–velocity curve and could be associated with a ‘quasi-Peierls barrier’ effect. The SFW was also shown to change under a pure glide stress without the addition of a τe stress when the velocity approached the supersonic limit, and caused an increase of the SFW in one direction and a reduction of the SFW in the other direction. This result demonstrates a unique characteristic of mixed dislocations which cannot be observed in the traditionally representative core structures of pure screw and pure edge dislocations because of their perfect symmetry. Surprisingly, the effects of the glide stress on the SFW were similar in magnitude to the effects of , and also were found to have a corresponding effect on the drag coefficient. The unique characteristics observed are summarised in terms of a unified equation for the force equilibrium at steady-state, which considers the drag coefficient of the two partials as independent functions of the velocities. This relationship is rationalised in terms of a drag force imbalance between the two partials of a mixed 30° dislocation, caused by a slightly higher drag force in the ‘mildly non planar’ 0° partial than in the 60° partial.