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DD maps of the ab initio dislocation cores: (a) Ta easy, (b) Ta hard; and (c) Mo easy. Dotted lines indicate axes of C 2 symmetry of the D 3 symmetry group.
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We report the first ab initio density-functional study of 〈111 〉 screw dislocations cores in the bcc transition metals Mo and Ta. Our results suggest a new picture of bcc plasticity with symmetric and compact dislocation cores, contrary to the presently accepted picture based on continuum and interatomic potentials. Core energy scales in this new p...
Citations
... In a final display of our potential's suitability for the present work, Fig. 4 reveals the core structure of a 1 2 < 111> screw dislocation predicted by the employed potential. The three larger arrows in the center, surrounded by six smaller arrows in the clockwise direction reflects a non-degenerate, compact core, consistent with numerous works in the literature [36][37][38][39][40][41] . ...
Utilizing a preliminary interatomic potential, this work represents an initial exploration into the thermomechanical behavior of NbCr solid solutions. Specifically, it examines the effect of different amounts of Cr solute, for which information in the literature is limited. The employed interatomic potential was developed according to the embedded atom model (EAM), and was trained on data derived from density functional theory calculations. While the potential demonstrated reasonable accuracy and predictive power when tested, various results highlight deficiencies and encourage further development and training. Mechanical strength, heat capacities, thermal expansion coefficients, and thermal conductivities were found to decrease with Cr content. Elastic coefficients, too, were observed to be strongly dependent on Cr composition. The Pugh embrittlement criterion was not satisfied for any of the compositions and temperatures explored. Gibbs free energy calculations performed on C14, C15, and C36 NbCr2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2}$$\end{document} allotropes predicted the C36 structure to be the most thermodynamically favorable across all investigated temperatures and it was found that C36 becomes increasingly more stable relative to the other two phases with increased pressure. The inability of this work to accurately capture the stability of the different Laves phases is most likely due to the shortcomings in the developed potential.
... In bcc metals, screw dislocation mobility is generally much lower than edge dislocation mobility. Thus, the yield and flow of bcc metals are dominated by the glide resistance of screw dislocation components, which becomes the limiting factor regarding plastic strength [36,37]. Primary slip systems are <111>{110} and <111>{112}; these are the glide systems typically studied in MD investigations [5,38] and resolved in continuum crystal plasticity models of bcc metals, for example [39]. ...
Since the 1980s, constitutive modeling has steadily migrated from phenomenological descriptions toward approaches that are based on micromechanics considerations. Despite significant efforts, crystal plasticity remains an open field of research. Among the unresolved issues are the anomalous behavior of metals at low temperatures and the stress upturn at extreme dynamics. This work is focused on the low-temperature responses of body-centered-cubic (bcc) metals, among them, molybdenum (Mo). At these conditions, the plastic flow strength is governed by the motion of screw dislocations. The resultant non-planarity of core structures and slip causes the following: the shear stress includes non-glide components, the Schmid law is violated, there is a tension-compression asymmetry, and the yield surface and plastic potential are clearly decoupled. We find that the behavioral complexities can be explained by atomistically resolved friction coefficients in macroscopic yield and flow. The plastic flow mechanisms establish the departure point into the follow-up analysis of yield surfaces. For example, we know that while the von Mises stress is explained based on energy considerations, we will also show that the stress has a clear geometric interpretation. Moreover, the von Mises stress is just one case within a much broader class of equivalent stresses. Possible correlations among non-Schmid effects (as represented macroscopically by friction coefficients), volume change (i.e., residual elastic dilatation) from dislocation lines, and elastic anisotropy are investigated. Extensions to the shock regime are also established.
... First-principles density functional theory (DFT) calculations have thus been employed extensively to provide quantitative information on fundamental defect properties, such as the generalized stacking fault energy, dislocation core structure and Peierls barrier. In particular, DFT calculations have unequivocally determined the non-degenerate (ND) core structure of the 111 /2 screw dislocations (e.g., Ta [16,17], Mo [16][17][18], W [19], and Fe [18,20,21]) and its 2D Peierls potential for all 7 BCC TMs [22]. These DFT calculations played an instrumental role in advancing fundamental plasticity theory of BCC structure materials. ...
... First-principles density functional theory (DFT) calculations have thus been employed extensively to provide quantitative information on fundamental defect properties, such as the generalized stacking fault energy, dislocation core structure and Peierls barrier. In particular, DFT calculations have unequivocally determined the non-degenerate (ND) core structure of the 111 /2 screw dislocations (e.g., Ta [16,17], Mo [16][17][18], W [19], and Fe [18,20,21]) and its 2D Peierls potential for all 7 BCC TMs [22]. These DFT calculations played an instrumental role in advancing fundamental plasticity theory of BCC structure materials. ...
... For DP-HYB-V, we use the general Deep Potential Generator (DP-GEN) scheme with the new hybrid descriptor [44] and a "specialization" strategy [81] to generate the training datasets. The new hybrid descriptor includes two-and three-body functions modelled by embedding neural networks of sizes (20,40,80) and (4,8,16), respectively. The fitting neural network size is (240, 240, 240). ...
BCC transition metals (TMs) exhibit complex temperature and strain-rate dependent plastic deformation behaviour controlled by individual crystal lattice defects. Classical empirical and semi-empirical interatomic potentials have limited capability in modelling 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 C44 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 semi-empirical 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 modelling lattice and defect properties in BCC V. Both XMEAM-V and DP-HYB-V reproduce a broad range of defect properties relevant to plastic deformation and fracture. In particular, XMEAM-V reproduces nearly all mechanical and thermodynamic properties at DFT accuracies and with C44 near 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 multi-principal element TM alloys.
... [1][2][3] It has been recognized a long time ago that molecular simulations complete adequately the elastic approach in studies of plasticity mechanisms involving prevalently dislocation cores. [4][5][6][7][8][9][10][11] In such simulations, boundary conditions that remedy their size limitations should also account for the long-range displacement and stress fields of dislocations for their results are representative of dislocated crystals at the macroscopic scale. Several kinds of boundary conditions have been used in the literature, all imposing lattice periodicity along the dislocation line. ...
... Such periodic arrays were used in simulations of the screw [111] dislocation in body centered cubic (bcc) metals. 8,9,[12][13][14] Edge dislocations in aluminum and copper have been studied with free-surface terminations along the Burgers vector and semi-rigid boundaries along the direction normal to the glide planes 4,5 or a combination of periodic boundaries along the dislocation line and rigid otherwise. 6,7 Flexible boundary conditions have permitted studying isolated dislocations in bcc Mo and Ta. 10 These consisted in embedding the dislocation cores within a region where lattice Green functions reproduce a stress field consistent with the response function of the studied metal. ...
... Moreover, the findings of the present work on the relative stability of dislocation cores with different polarizations in W are compared with results from the literature for this and other bcc metals. 8,9,12,13 Finally, the perspectives opened by the present work are briefly discussed. ...
A new set of boundary conditions is proposed for molecular simulations of isolated elastic defects such as dislocations and cracks. The case study of the <111> screw dislocation in body centered cubic (bcc) tungsten, modeled via a phenomenological, n-body cohesion functional, serves validating the new boundary conditions by computing structural properties of this defect and comparing these with results from the literature. Lowest energy configurations of the dislocated crystal have been obtained by Molecular Statics incorporating the new boundary conditions. The associated displacement and energy landscapes reveal conformal to the predictions of the elastic theory for a screw dislocation
embedded in an infinitely extended crystal. In particular, no energy gradients and positional mismatch of atoms are found at the terminations of the computational box, validating thereby the new boundary conditions. Furthermore, it is shown that the structure, the spatial extension and the excess energy of the two possible core polarizations of this
dislocation compare consistently with existing findings for this and other bcc metals. Close to the dislocation line, energy minimization triggers the emergence of anelastic edge displacements extending over distances unexpectedly much larger than the dislocation core radius. Therefore the conclusion is reached that in molecular simulations, the
transverse to the dislocation line dimensions of the atomistic model should be taken considerably larger than it is accustomed. Perspectives opened by the present work are briefly discussed.
... Whereas it is possible to explain {110} slip in metals and alloys exhibiting compact cores by the formation of kink-pairs on {110} planes [47] , the presence of slip in {112} seems to require kink-pair nucleation on {112} and specific three-fold degenerate cores as reported by simulations using empirical potentials some decades ago [48][49][50] . However, such asymmetrical character of screw dislocation core has never been found in recent ab-initio calculations which predict the existence of non-degenerate cores and glide on {110} planes only [51] . Relative once again to the S1 slip system studied in Fig. 8 , the second reason stems from the SFs for both (011) and (101) are significant (0.49 and 0.24, respectively); thus, it is possible to consider that slip in (101) is also activated and that we could expect to observe (112) as a result of elementary slip taking place in these two elementary {110} planes ( Fig. 10 ) indicates that kink-pairs should form in twinning or anti-twinning directions to explain {112} traces. ...
The current study reports the analysis of the deformation mechanisms at 600°C in a two-phase, BCC+B2, refractory complex concentrated alloy (RCCA) Al0.5NbTa0.8Ti1.5V0.2Zr. At this temperature, the alloy microstructure is unstable and dynamic coarsening of B2 precipitates is evidenced during the mechanical testing. After true plastic strain of 0.030 at strain rate of 10−4 s−1, the deformation becomes highly localized in wavy bands reflecting the profusion of cross-slip. Scanning transmission electron microscopy (STEM) observations highlight the presence of paired a/2<111> dislocations that shear the B2 precipitates in a cooperative process. In addition, some chemical segregation effect is observed along the narrow dislocation bands likely induced to decrease the antiphase boundary (APB) energy of the system.
... Actually, this method has been proven to rapidly converge the dislocation core energy [34,35] and has been widely employed in recent DFT calculations of bcc metals [24,33,36]. Accordingly, a symmetrical and non-degenerate core structure was obtained, which is in agreement with previous studies [37,38]. The unit cell vector of dislocation in pure Mo is was two times as large as the Burger vector, resulting from a 270-atom (2 → b ) supercell. ...
... Actually, this method has been proven to rapidly converge the dislocation core energy [34,35] and has been widely employed in recent DFT calculations of bcc metals [24,33,36]. Accordingly, a symmetrical and non-degenerate core structure was obtained, which is in agreement with previous studies [37,38] Mo atoms (only 1 ⃗ along the dislocation line). To simulate the behaviors of C/O in the dislocation and reduce the periodic solute-solute interaction, the simulation box in the dislocation line was two times as large as the Burger vector, resulting from a 270-atom (2 ⃗ ) supercell. ...
The plasticity and hardness of metals are largely dependent on how dislocation interacts with solute atoms. Here, taking bcc molybdenum (Mo) as the example, the interaction of interstitial solutes carbon (C) and oxygen (O) with screw dislocation, and their influences on the dislocation motion, have been determined using first-principles calculations and thermodynamic models. Due to the incompact atomic structure and variation of electronic states in the dislocation core, C and O will segregate from the bulk system to the dislocation region. Notably, the presence of C/O at the dislocation induces the reconstruction of the core structure, from an easy-core to hard-core configuration. This originates from the fact that the hard-core structure provides a larger available volume at the interstitial site than the easy-core structure and, thus, facilitates the dissolution of C and O. More importantly, the addition of C/O in the dislocation significantly increases the Peierls stresses and double-kink formation enthalpies of screw dislocation in Mo, from 1.91 GPa and 1.18 eV for C/O-free dislocation to 5.63/4.69 GPa and 1.77/1.58 eV for C/O-saturated dislocation. Therefore, these interstitial solutes have a pinning effect on the dislocation motion, and this effect becomes stronger with higher segregating levels. This work reveals the profound effect of interstitial solutes on the properties of the dislocation core and provides a fundamental factor to account for the interstitial solutes-related phenomena in bcc metals.
... Such characteristics of deformation of BCC metals under external loading are the function of both the crystallography of BCC lattice and the high lattice friction (Peierls barrier) arising from the non-planar core of the screw dislocations [4,5]. Starting from the pioneering work of Hirsch et al. [6], the core structure of the screw dislocation in BCC metals has been studied extensively using semiempirical potentials [7][8][9][10][11] and first-principle methods [12][13][14][15]. The screw dislocation core is observed to be spread equally onto three {1 1 0} planes in the ⟨1 1 1⟩ zone. ...
... From Fig. 10a, we can observe variations in critical strain ( 23 ) occurring because of the application of the non-glide strains. 23 values for positive 12 are lower compared to the situation where 12 of the same magnitude is applied in the opposite direction. It should also be noted that the glide plane of the dislocation switches from (1 0 1) plane to (1 1 2) plane when the direction of 12 reverses. ...
In the present work, we report on the effect of introducing carbon atom in the core of the screw dislocations in body centered iron (Fe) using classical interatomic potentials available in open literature. Reconstruction of dislocation core from easy to hard core configuration is observed irrespective of the initial position of the carbon atom, which eventually settles in the dislocation core occupying the prismatic sites formed by the rows of Fe atoms in hard core. Loading is carried out parallel and perpendicular to the Burgers vector to understand the effect of carbon on the non-Schmid characteristics of the slip. Twinning-antitwinning (T/AT) asymmetry of CRSS is observed when the dislocation core symmetry of the easy core configuration is retained after the core reconstruction occurs. The CRSS of dislocation in both easy and hard core configuration is sensitive to the loading conditions. The asymmetry in CRSS and choice of glide planes are correlated with the dislocation core spreading onto the {1 1 0} planes in the 〈1 1 1〉 zone under the influence of the applied loads.
... Instead, to avoid external boundary issues, a method allowing the use of a tri-periodic cell was developed (Bigger et al., 1992;Ismail-Beigi and Arias, 2000). To have fully periodic conditions, a dislocation dipole of opposed Burgers vectors is inserted to obtain a null total Burgers vector. ...
Ferritic steels, made of a body-centered cubic (bcc) iron matrix with interstitial carbon solutes, are widely-used structural materials. However, the atomic-scale mechanisms which control their plasticity are still only partially understood. At low temperature, the plastic deformation of bcc metals is controlled by the mobility of the screw dislocations, which is hindered by both a strong resistance of the lattice itself, and the presence of other crystal defects, among which are solute atoms. Atomic-scale models of dislocation mobility based on the Transition State Theory (TST) constitute a useful framework to model plastic flow in pure metals and in alloys. However, the approximations often used (harmonic approximation, constant activation entropy) yield poor predictions in iron. We used the recent projected average force integrator method to compute the activation free enthalpy for kink pair nucleation, including anharmonic effects. The data show that the harmonic regime is limited to very low temperatures, below 20 K. Non-linearities remain small below 100 K, allowing to compute an effective activation entropy, which increases when the activation enthalpy decreases, corresponding to an inverse Meyer-Neldel behavior. Integrating these effects in dislocation mobility models greatly improves the agreement with direct molecular dynamics (MD) simulations. Extensions to Fe-C alloys are limited by the realism of the interatomic potentials available for this system. To address this issue, we combined two existing empirical potentials for Fe and Fe-C to reproduce both the Peierls mechanism and the carbon-induced screw dislocation core reconstruction found in ab initio calculations. Using this hybrid potential, MD simulations of the glide of screw dislocations in random solid solutions confirm a strong solute strengthening, caused by complex short-ranged interaction processes. We also considered an idealized geometry where a screw dislocation interacts with a row of carbon atoms. Combining MD simulations and saddle-point search methods, we unveil a very strong pinning when the solute separation is below about 100 Burgers vectors. This effect is due to the necessity to nucleate two consecutive kink pairs on the screw dislocation, with the second kink pair having a markedly increased activation enthalpy. We developed a harmonic TST model of this process that also integrates the entropic effects observed in pure iron, which yields a good agreement with MD simulations conducted up to 300 K. This work provides elementary processes and parameters that will be useful for larger-scale models and in particular kinetic Monte Carlo simulations.
... In the present study, we trained a Behler-Parinello type ANN potential 36 . As the low-temperature plasticity of bcc materials is controlled by the properties of the 1/2 111 screw dislocations, the core properties of this defect have been addressed by DFT and interatomic potential calculations [37][38][39] . Dezerald et al. employed DFT calculations and reported that the core structure of the 1/2 111 screw dislocation is non-degenerate and the easy core structure is the lowest energy configuration 40 . ...
A high dimensional artificial neural network interatomic potential for Mo is developed. To train and validate the potential density functional theory calculations on structures and properties that correlate to fracture, such as elastic constants, surface energies, generalized stacking fault energies, and surface decohesion energies, have been employed. The potential provides total energies with a root mean square error less than 5 meV per atom both in the training and validation data sets. The potential was applied to investigate screw dislocation core properties as well as to conduct large scale fracture simulations. These calculations revealed that the 1/2 111 screw dislocation core is non-degenerate and symmetric and mode I fracture is brittle. It is anticipated that the thus constructed potential is well suited to be applied in large scale atomistic calculations of plasticity and fracture.
... 121 Owing to the applications of this metal in engineering, there are several important properties, ranging from the elastic constants and the formation energy of isolated vacancy defects to the delicate core structure of its screw dislocations. 244,245 While properties such as the elastic constants can be derived from computations in small unit cells, and are therefore routinely obtained from DFT, other structural problems require thousands of atoms (and more) in the simulation cell. The GAP model introduced in ref 121 correctly describes the aforementioned core structure and can be used to study extended defects and their interaction using many thousands of atoms. ...
We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.
