The interaction between carbon and screw dislocations in tungsten is investigated using ab initio calculations. The presence of carbon atoms in the vicinity of the dislocation induces a reconstruction, with the dislocation relaxing to a configuration, the hard core structure, which is unstable in pure tungsten. The reconstruction corresponds to a strong binding of carbon in the prismatic sites created by the dislocation which is perfect for high concentrations of carbon segregated on the dislocation line. However, the reconstruction is only partial for lower atomic fractions, with the dislocation tending to fall back in its easy core ground state. This pinning by carbon atoms of the dislocation in an unstable position is well described by a simple line tension model. A strong carbon-dislocation attraction is also evidenced at larger separation distances, when the solute is in the fourth nearest neighbour octahedral sites of the reconstructed core. The equilibrium concentrations of carbon in these different segregation sites are modelled with an Ising model and using a mean-field approximation. This thermodynamic model evidences that screw dislocations remain fully saturated by carbon atoms and pinned in their hard core configuration up to about 2500 K.
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 picture are in much better agreement with the Peierls energy barriers to dislocation motion suggested by experiments.
Body-centred cubic (BCC) transition metals tend to be brittle at low temperatures, posing significant challenges in processing and major concerns for damage tolerance. The brittleness is largely dictated by the screw dislocation core; the nature and control of which remain a puzzle after nearly a century. Here, we introduce a physics-based material index \{chi}, the energy difference between BCC and face-centred-cubic structures, that guides manipulation of core properties. The lattice friction and nucleation barrier have near-linear scaling with \{chi} and the core transforms from non-degener…
We show here how density functional theory calculations can be used to predict the temperatureand orientation-dependence of the yield stress of body-centered cubic (BCC) metals in the thermallyactivated regime where plasticity is governed by the glide of screw dislocations with a 1/2 <111> Burgers vector. Our numerical model incorporates non-Schmid effects, both the twinning/antitwinning asymmetry and non-glide effects, characterized through ab initio calculations on straight dislocations. The model uses the stress-dependence of the kink-pair nucleation enthalpy predicted by a line tension mod…
The interplay of screw dislocations with carbon atoms is investigated in tungsten at high temperature using in situ straining experiments in a transmission electron microscope (TEM) and through ab initio calculations. When the temperature is high enough to activate carbon diffusion, above 1373 K, carbon segregates in the core of screw dislocations and modifies their mobility, even for a carbon concentration as low as 1 appm. TEM observations reveal the reappearance of a Peierls mechanism at these high temperatures, with screw dislocations gliding viscously through nucleation and propagation of…
We investigate the effect of hydrogen on the mobility of a screw dislocation in body-centered cubic (bcc) iron using first-principles calculations, and show that an increase of screw dislocation velocity is expected for a limited temperature range. The interaction energy between a screw dislocation and hydrogen atoms is calculated for various hydrogen positions and dislocation configurations with careful estimations of the finite size effects, and the strongest binding energy of a hydrogen atom to the stable screw dislocation configuration is estimated to be $256\pm32$ meV. These results are i…
By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2<111> screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation, as proposed by Koester A, Ma A, Hartmaier A. Acta Mater 2012;60:3894 but, instead, on their combination that causes an equibiaxi…
The fully two-dimensional Peierls barrier map of screw dislocations in BCC iron has been calculated using the first principles method to identify the migration path of a dislocation core. An efficient method to correct the effect of the finite size cell used in the first principles method on the energy of a lattice defect was devised to determine the accurate barrier profile. We find that the migration path is close to a straight line which is confined in a $\{110\}$ plane and the Peierls barrier profile is single-humped. This result clarifies a reason that the existing empirical potentials of…
Owing to their non-planar cores 1/2<111> screw dislocations govern the plastic deformation of BCC metals. Atomistic studies of the glide of these dislocations at 0 K have been performed using Bond Order Potentials for molybdenum and tungsten that account for the mixed metallic and covalent bonding in transition metals. When applying pure shear stress in the slip direction it displays significant twinning-antitwinning asymmetry for molybdenum but not for tungsten. However, for tensile/compressive loading the Schmid law breaks down in both metals, principally due to the effect of shear stresses …
Based on the atomistic studies presented in Part I we develop analytical yield criteria for single crystals that capture the effect of shear stresses other than the Schmid stress (non-glide stresses) on the shear stress needed for dislocation glide (Peierls stress). These yield criteria characterize a non-associated plastic flow that originates owing to the complex response of 1/2<111> screw dislocations to an applied stress tensor. Employing these criteria we identify the operative slip systems for tensile/compressive loading along various axes within the standard stereographic triangle and d…
We use atomistic simulations to investigate grain boundary (GB) phase transitions in el- emental body-centered cubic (bcc) metal tungsten. Motivated by recent modeling study of grain boundary phase transitions in [100] symmetric tilt boundaries in face-centered cu- bic (fcc) copper, we perform a systematic investigation of [100] and [110] symmetric tilt high-angle and low-angle boundaries in bcc tungsten. The structures of these boundaries have been investigated previously by atomistic simulations in several different bcc metals including tungsten using the the γ-surface method, which has limi…
Hydrogen segregation around a straight screw dislocation in bcc iron
Laboratoire des Sciences de l’Ingénieur pour l’Environnement (LaSIE) - UMR CNRS 7356（环境工程科学实验室）；Laboratoire des Sciences des Procédés et des Matériaux (LSPM) - UPR 3407（工艺与材料科学实验室）
The validity of the structure-property relationships governing the deformation behavior of bcc metals was brought into question with recent {\it ab initio} density functional studies of isolated screw dislocations in Mo and Ta. These existing relationships were semiclassical in nature, having grown from atomistic investigations of the deformation properties of the groups V and VI transition metals. We find that the correct form for these structure-property relationships is fully quantum mechanical, involving the coupling of electronic states with the strain field at the core of long $a/2<111>$…
In traditional body-centered cubic (bcc) metals, the core properties of screw dislocations play a critical role in plastic deformation at low temperatures. Recently, much attention has been focused on refractory high-entropy alloys (RHEAs), which also possess bcc crystal structures. However, unlike face-centered cubic high-entropy alloys (HEAs), there have been far fewer investigations on bcc HEAs, specifically on the possible effects of chemical short-range order (SRO) in these multiple principal element alloys on dislocation mobility. Here, using density functional theory, we investigate the…
Unlike the tensile mode, compressive deformation of a bcc metallic nanostructure is mediated by the glide of screw dislocation. Although the bcc screw dislocations are well known to possess unusual attributes, it is still unclear how these unique effects manifest in a nanoscale solid. In the present study, atomistic simulations render a close look at the dislocation activities underlying the compressive deformation of bcc iron nanopillars. It is found that instead of performing simple glide motion, the line defects exhibit a host of complex features. In this regard, the temperature is observed…
We report a computational discovery of novel grain boundary structures and multiple grain boundary phases in elemental bcc tungsten. While grain boundary structures created by the γ-surface method as a union of two perfect half crystals have been studied extensively, it is known that the method has limitations and does not always predict the correct ground states. Here, we use a newly developed computational tool, based on evolutionary algorithms, to perform a grand-canonical search of a high-angle symmetric tilt boundary in tungsten, and we find new ground states and multiple phases that cann…
In body-centred-cubic (bcc) metals migrating 1/2<111> screw dislocations experience a periodic energy landscape with a triangular symmetry. Atomistic simulations, such as those performed using the nudged-elastic-band (NEB) method, generally predict a transition-pathway energy-barrier with a double-hump; contradicting Ab Initio findings. Examining the trajectories predicted by NEB for a particle in a Peierls energy landscape representative of that obtained for a screw dislocation, reveals an unphysical anomaly caused by the occurrence of monkey saddles in the landscape. The implications for mot…
Interactions among dislocations and solute atoms are the basis of several important processes in metals plasticity. In body-centered cubic (bcc) metals and alloys, low-temperature plastic flow is controlled by screw dislocation glide, which is known to take place by the nucleation and sideward relaxation of kink pairs across two consecutive \emph{Peierls} valleys. In alloys, dislocations and solutes affect each other's kinetics via long-range stress field coupling and short-range inelastic interactions. It is known that in certain substitutional bcc alloys a transition from solute softening to…
This paper presents the thermodynamic dislocation theory containing several modifications over its first version which was originally proposed by Langer, Bouchbinder, and Lookman (2010). Employing a small set of physics-based material parameters identified by the large scale least squares analysis, we show that the theory can fit the stress-strain curves of bcc crystals niobium, tantalum, tungsten, and vanadium over a wide range of temperatures and strain rates.
Atomistic simulations of the experimental W L$_3$-edge extended X-ray absorption fine structure (EXAFS) of bcc tungsten at T = 300 K were performed using classical molecular dynamics (MD) and reverse Monte Carlo (RMC) methods. The MD-EXAFS method based on the results of MD simulations allowed us to access the structural information, encoded in EXAFS, beyond the first coordination shell and to validate the accuracy of two interaction potential models - the embedded atom model potential and the second nearest-neighbor modified embedded atom method potential. The RMC-EXAFS method was used for mor…
An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile…
We study the influence of the atomic structure in the vicinity of voids on their growth rate anisotropy. In the first part, we model the atomic structure in the vicinity of nanovoids in Fe and W using the advanced Molecular Statics method. In the second part, we use the earlier obtained equations that taking the influence of elastic fields into account to calculate the shifting rate of the void surface elements, and to evaluate the components of the strain tensor we use the atomic structure modeling results from the first part. The calculations are performed for voids of several sizes at certa…
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…
We introduce interatomic potentials for tungsten in the bcc crystal phase and its defects within the Gaussian Approximation Potential (GAP) framework, fitted to a database of first principles density functional theory (DFT) calculations. We investigate the performance of a sequence of models based on databases of increasing coverage in configuration space and showcase our strategy of choosing representative small unit cells to train models that predict properties only observable using thousands of atoms. The most comprehensive model is then used to calculate properties of the screw dislocation…
Twin boundaries (TBs) are assumed to be obstacles to dislocation motion and increase the strength of metals. Here, we report the abnormal phenomenon that TBs reduce the strength of body-centered cubic (BCC) tungsten (W). [1-11]-oriented W nanowires with (121) twin planes and free of dislocations were fabricated by chemical vapor deposition. In situ tensile tests within the transmission electron microscope were performed on single-crystal and twinned W nanowires. The fracture strength of the twinned W nanowire was 13.7 GPa, 16% lower than that of the single-crystal W nanowire (16.3 GPa). The we…
We propose a mesoscopic model that explains the factor of two to three discrepancy between experimentally measured yield stresses of BCC metals at low temperatures and typical Peierls stresses determined by atomistic simulations of isolated screw dislocations. The model involves a Frank-Read type source emitting dislocations that become pure screws at a certain distance from the source and, owing to their high Peierls stress, control its operation. However, due to the mutual interaction between emitted dislocations the group consisting of both non-screw and screw dislocations can move at an ap…
Unraveling the temperature dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal plasticity calculations
University of California Los Angeles（加州大学洛杉矶分校）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Universidad Politécnica de Madrid（马德里理工大学）；Max-Planck-Institut für Eisenforschung（马克斯·普朗克铁研究所）
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 rele…
Two-dimensional (2D) layered tungsten diselenides (WSe2) material has recently drawn a lot of attention due to its unique optoelectronic properties and ambipolar transport behavior. However, direct chemical vapor deposition (CVD) synthesis of 2D WSe2 is not as straightforward as other 2D materials due to the low reactivity between reactants in WSe2 synthesis. In addition, the growth mechanism of WSe2 in such CVD process remains unclear. Here we report the observation of a screw-dislocation-driven (SDD) spiral growth of 2D WSe2 flakes and pyramid-like structures using a sulfur-assisted CVD meth…
Dislocation motion in body centered cubic (bcc) metals displays a number of specific features that result in a strong temperature dependence of the flow stress, and in shear deformation asymmetries relative to the loading direction as well as crystal orientation. Here we develop a generalized dislocation mobility law in bcc metals, and demonstrate its use in discrete Dislocation Dynamics (DD) simulations of plastic flow in tungsten (W) micro pillars. We present the theoretical background for dislocation mobility as a motivating basis for the developed law. Analytical theory, molecular dynamics…
Although the effects of the electronic excitations during high-energy radiation damage processes are not currently understood, it is shown that their role in the interaction of radiation with matter is important. We perform molecular dynamics simulations of high-energy collision cascades in bcc-tungsten using the coupled two-temperature molecular dynamics (2T-MD) model that incorporates both the effects of electronic stopping and electron-phonon interaction. We compare the combination of these effects on the induced damage with only the effect of electronic stopping, and conclude in several no…
Isolated kinks on thermally fluctuating (1/2)<111> screw, <100> edge and (1/2)<111> edge dislocations in bcc iron are simulated under zero stress conditions using molecular dynamics (MD). Kinks are seen to perform stochastic motion in a potential landscape that depends on the dislocation character and geometry, and their motion provides fresh insight into the coupling of dislocations to a heat bath. The kink formation energy, migration barrier and friction parameter are deduced from the simulations. A discrete Frenkel-Kontorova-Langevin (FKL) model is able to reproduce the coarse grained data …
Properties of point defects resulting from the incorporation of inert-gas atoms in bcc tungsten are investigated systematically using first-principles density functional theory (DFT) calculations. The most stable configuration for the interstitial neon, argon, krypton and xenon atoms is the tetrahedral site, similarly to what was found earlier for helium in W. The calculated formation energies for single inert-gas atoms at interstitial sites as well as at substitutional sites are much larger for Ne, Ar, Kr and Xe than for He. While the variation of the energy of insertion of inert-gas defects …
Thermally-activated $\small{\nicefrac{1}{2}}<111>$ screw dislocation motion is the controlling plastic mechanism at low temperatures in body-centered cubic (bcc) crystals. Motion proceeds by the nucleation and propagation of atomic-sized kink pairs susceptible of being studied using molecular dynamics (MD). However, MD's natural inability to properly sample thermally-activated processes as well as to capture $\{110\}$ screw dislocation glide calls for the development of other methods capable of overcoming these limitations. Here we develop a kinetic Monte Carlo (kMC) approach to study single s…
The thermodynamic description of dislocation glide in crystals depends crucially on the shape of the Peierls barrier that the dislocation has to overcome when moving in the lattice. While the height of this barrier can be obtained unequivocally using saddle-point search algorithms such as the Nudged Elastic Band (NEB) method, its exact shape depends on the chosen approximation of the transition pathway of the system. The purpose of this paper is to formulate a procedure that allows to identify the position of the dislocation directly from the displacements of atoms in its core. We investigate …
Temperature-activated dislocation avalanches signaling brittle-to-ductile transition in BCC micropillars
School of Mechanics & Engineering Science, Shanghai University（上海大学力学与工程科学学院）；Department of Mechanical & Aerospace Engineering, University of Miami（迈阿密大学机械与航空航天工程系）；School of Physics, Sun Yat-sen University（中山大学物理学院）；Department of Mechanical & Aerospace Engineering, University of California Los Angeles（加州大学洛杉矶分校机械与航空航天工程系）
Several transition metals were examined to evaluate their potential for improving the ductility of tungsten. The dislocation core structure and Peierls stress and barrier of $1/2<111>$ screw dislocations in binary tungsten-transition metal alloys (W$_{1-x}$TM$_{x}$) were investigated using first principles electronic structure calculations. The periodic quadrupole approach was applied to model the structure of $1/2<111>$ dislocation. Alloying with transition metals was modeled using the virtual crystal approximation and the applicability of this approach was assessed by calculating the equilib…
The body centered cubic (BCC) high entropy alloys MoNbTaW and MoNbTaVW show exceptional strength retention up to 1900K. The mechanistic origin of the retained strength is unknown yet is crucial for finding the best alloys across the immense space of BCC HEA compositions. Experiments on Nb-Mo, Fe-Si and Ti-Zr-Nb alloys report decreased mobility of edge dislocations, motivating a theory of strengthening of edge dislocations in BCC alloys. Unlike pure BCC metals and dilute alloys that are controlled by screw dislocation motion at low temperatures, the strength of BCC HEAs can be controlled by edg…
Equation of state (EOS) for bcc tungsten at 300 K (or 3000 K) up to 1000 GPa (or 300 GPa) was predicted for the first time by solving the partition function via a direct integral approach (DIA) with ab initio calculations of the atoms' interactions. Compared with available experiments under static compressions up to 150 GPa (or 35 GPa) for room temperature (or 1673 K), all the calculated results are within the experimental uncertainty achieved very recently. Furthermore, the same procedure was performed to investigate the shock wave experiments on the EOS up to 400 GPa and 10000 K, and the cal…
In this paper we develop a link between the atomic-level modeling of the glide of 1/2<111> screw dislocations at 0 K and the thermally activated motion of these dislocations via nucleation of pairs of kinks. For this purpose, we introduce the concept of a hypothetical Peierls barrier, which reproduces all the aspects of the dislocation glide at 0 K resulting from the complex response to non-glide stresses and is expressed in a compact form by the yield criteria advanced in Part II. To achieve this the barrier is dependent not only on the crystal symmetry and interatomic bonding but also on the…
The Peierls stress for a [111]-screw dislocation in bcc Tantalum is calculated using an embedded atom potential. More importantly, a method is presented which allows accurate calculations of the Peierls stress in the smallest periodic cells. This method can be easily applied to ab initio calculations, where only the smallest unit cells capable of containing a dislocation can be conviently used. The calculation specifically focuses on the case where the maximum resolved shear stress is along a {110}-plane.
High angular resolution electron backscatter diffraction (HR-EBSD) was coupled with focused ion beam (FIB) slicing to characterize the shape of the plastic zone in terms of geometrically necessary dislocations (GNDs) in W single crystal in 3 dimensions. Cantilevers of similar size with a notch were fabricated by FIB and were deformed inside a scanning electron microscope at different temperatures (21$^{\circ}$C, 100$^{\circ}$C and 200$^{\circ}$C) just above the micro-scale brittle-to-ductile transition (BDT). J-integral testing was performed to analyse crack growth and determine the fracture t…
Plasticity in body centered cubic (bcc) refractory metals are largely due to the stress tensor induced either by solute or thermal activation. The mechanism of the solute atom(s) residence causes instability in such metals. Earlier research have considered the mechanism of oxygen (O) or carbon (C) in tungsten (W), even though the major component of the environment is nitrogen (N). In this article, the density functional theory (DFT) was employed to investigate the thermodynamic stable site for an interstitial solute (N or O) in the bcc refractory metals (Mo and Nb) by calculating the equilibri…
Ab initio calculations in bcc iron show that a <111> screw dislocation induces a short-range dilatation field in addition to the Volterra elastic field. This core field is modeled in anisotropic elastic theory using force dipoles. The elastic modeling thus better reproduces the atom displacements observed in ab initio calculations. Including this core field in the computation of the elastic energy allows deriving a core energy which converges faster with the cell size, thus leading to a result which does not depend on the geometry of the dislocation array used for the simulation.
Molecular dynamics (MD) simulation of dislocation migration requires semi-empirical potentials of the interatomic interaction. While there are many reliable semi-empirical potentials for the bcc Fe, the number of the available potentials for the fcc is very limited. In the present study we tested three EAM potentials for the fcc Fe (ABCH97 [Phil. Mag. A, 75, 713-732 (1997)], BCT13 [MSMSE 21, 085004 (2013)] and ZFS18 [J. Comp. Chem. 39, 2420-2431 (2018)]) from literature. It was found that the ABCH97 potential does not provide that the fcc phase is the most stable at any temperature. On the oth…
Computational modeling is usually applied to aid experimental exploration of advanced materials to better understand the fundamental plasticity mechanisms during mechanical testing. In this work, we perform Molecular dynamics (MD) simulations to emulate experimental room temperature spherical-nanoindentation of crystalline W matrices by different interatomic potentials: EAM, modified EAM, and a recently developed machine learned based tabulated Gaussian approximation potential (tabGAP) for describing the interaction of W-W. Results show similarities between load displacements and stress-strain…
Ab initio simulations of dislocations are essential to build quantitative models of material strength, but the required system sizes are often at or beyond the limit of existing methods. Many important structures are thus missing in the training or validation of interatomic potentials, whilst studies of dislocation-defect interactions must mitigate the effect of strong periodic image interactions along the line direction. We show how these restrictions can be lifted through the use of linear machine learning potentials in hybrid simulations, where only a subset of atoms are governed by ab init…
