From their birth in the manufacturing process, materials inherently contain defects that affect the mechanical behavior across multiple length and time-scales, including vacancies, dislocations, voids and cracks. Understanding, modeling, and real-time simulation of the underlying stochastic micro-structure defect evolution is therefore vital towards multi-scale coupling and propagating numerous sources of uncertainty from atomistic to eventually aging continuum mechanics. We develop a graph-based surrogate model of dislocation glide for computation of dislocation mobility. We model an edge dislocation as a random walker, jumping between neighboring nodes of a graph following a Poisson stochastic process. The network representation functions as a coarse-graining of a molecular dynamics simulation that provides dislocation trajectories for an empirical computation of jump rates. With this construction, we recover the original atomistic mobility estimates, with remarkable computational speed-up and accuracy. Furthermore, the underlying stochastic process provides the statistics of dislocation mobility associated to the original molecular dynamics simulation, allowing an efficient propagation of material parameters and uncertainties across the scales.
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…
The nature of mechanically induced dislocations in SrTiO3 at low temperatures has been a disputed matter for a long time. Here we provide a systematic overview of the existing knowledge on dislocations in stoichiometric SrTiO3 complemented by computational models of several of the proposed dislocation types. Based on atomistic simulations we reveal their structure and mobility and put our focus on the splitting into partial dislocations, because this mechanism is held responsible for the good dislocation mobility in strontium titanate. Our results reveal that dislocations with a {1-10} glide p…
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…
Revisiting quantum effects on dislocation glide in bcc metals from DFT calculations and machine-learning potentials
ASNR/PSN-RES/SEMIA/LSMA Centre d’études de Cadarache（法国原子能和替代能源委员会卡达拉舍研究中心）；Université Paris-Saclay, CEA, Service de recherche en Corrosion et Comportement des Matériaux, SRMP（巴黎萨克雷大学，法国原子能和替代能源委员会材料腐蚀与行为研究服务处）；Univ. Lyon, UCBL, Institut Lumière Matière, UMR CNRS 5306（里昂大学，里昂第一大学，光物质研究所）
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 $a/2<111>$…
The fundamental dislocation processes of glide, climb, and annihilation are studied on diffusive time scales within the framework of a continuum field theory, the Phase Field Crystals (PFC) model. Glide and climb are examined for single edge dislocations subjected to shear and compressive strain, respectively, in a two dimensional hexagonal lattice. It is shown that the natural features of these processes are reproduced without any explicit consideration of elasticity theory or ad hoc construction of microscopic Peierls potentials. Particular attention is paid to the Peierls barrier for disloc…
It was recently shown that to predict reliable Peierls stresses from atomistic simulations, one has to correct the Peierls barrier by the zero-point energy difference between the initial and activated states of the dislocation. The corresponding quantum Peierls stresses are studied here in α-Fe modeled with two embedded atom method potentials. First, we show that the quantum correction arises from modes localized near the dislocation core, such that partial Hessian matrices built on small cylinders centered on the dislocation core can be used to compute the zero-point energy difference. Second…
The nonequilibrium dynamics of diffusion-mediated plasticity and creep in materials subjected to constant load at high homologous temperatures is studied atomistically using Phase Field Crystal (PFC) methods. Creep stress and grain size exponents obtained for nanopolycrystalline systems, $m \simeq 1.02$ and $p \simeq 1.98$, respectively, closely match those expected for idealized diffusional Nabarro-Herring creep. These exponents are observed in the presence of significant stress-assisted diffusive grain boundary migration, indicating that Nabarro-Herring creep and stress-assisted boundary mig…
We present a combined study by Scanning Tunneling Microscopy and atomistic simulations of the emission of dissociated dislocation loops by nanoindentation on a (001) fcc surface. The latter consist of two stacking-fault ribbons bounded by Shockley partials and a stair-rod dislocation. These dissociated loops, which intersect the surface, are shown to originate from loops of interstitial character emitted along the <110> directions and are usually located at hundreds of angstroms away from the indentation point. Simulations reproduce the nucleation and glide of these dislocation loops.
This paper evaluates qualitatively as well as quantitatively the accuracy of a recently proposed Peierls--Nabarro Finite Element (PN-FE) model for dislocations by a direct comparison with an equivalent molecular statics simulation. To this end, a two-dimensional microstructural specimen subjected to simple shear is considered, consisting of a central soft phase flanked by two hard-phase regions. A hexagonal atomic structure with equal lattice spacing is adopted, the interactions of which are described by the Lennard--Jones potential with phase specific depths of its energy well. During loading…
Atomistic studies are carried out to investigate the formation and evolution of defects during nanoindentation of a gold crystal. The results in this theoretical study complement the experimental investigations [J. D. Kiely and J. E. Houston, Phys. Rev. B, v57, 12588 (1998)] extremely well. The defects are produced by a three step mechanism involving nucleation, glide and reaction of Shockley partials on the {111} slip planes noncoplanar with the indented surface. We have observed that slip is in the directions along which the resolved shear stress has reached the critical value of approximate…
Atomistic simulations, based either on an empirical interatomic potential or on ab initio calculations, are used to study the pyramidal glide of a 1/3 <1-210> screw dislocation in hexagonal close-packed zirconium. Generalized stacking fault calculations reveal a metastable stacking fault in the first order pyramidal {10-11} plane, which corresponds to an elementary pyramidal twin. This fault is at the origin of a metastable configuration of the screw dislocation in zirconium, which spontaneously appears when the dislocation glides in the pyramidal plane.
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…
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…
The interaction between edge dislocations and Guinier-Preston zones in an Al-Cu alloy was analyzed by means of atomistic simulations. The different thermodynamic functions that determine the features of these obstacles for the dislocation glide were computed using molecular statics, molecular dynamics and the nudged elastic band method. It was found that Guinier-Preston zones are sheared by dislocations and the rate at which dislocations overcome the precipitate is controlled by the activation energy, $ΔU$, in agreement with the postulates of the harmonic transition state theory. Moreover, the…
This paper presents PANIC, a 3D discrete mesoscale dislocation dynamics model which includes a fully quantitative treatment of both dislocation climb and dislocation glide, including climb driven by both osmotic and mechanical stresses and climb enabled by both bulk and pipe diffusion, including full elastic anisotropy for materials with hexagonal symmetry. Efficient calculations can be performed for epitaxial thin films, multilayers and device structures with free surfaces, including those with irregular geometries (e.g. islands). The model also includes the capability to simulate dislocation…
A long-standing discrepancy exists between experiments and atomistic models concerning the critical strain needed for surface nucleation of dislocations in silicon-germanium systems. While dislocation nucleation is readily observed in hetero-epitaxial thin films with misfit strains less than 4%, existing atomistic models predict that a critical strain over 7.8% is needed to overcome the kinetic barrier for dislocation nucleation. Using zero-temperature energy barrier calculations and finite-temperature Molecular Dynamics simulations, we show that 3-dimensional surface features such as a sharpl…
Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results that demonstrate the ability of phase field crystal (PFC) models to describe complex defect evolution phenomena on atomistic length scales and over long, diffusive time scales. Primary emphasis is given to the unification of conservative and non- conservative dislocation creation mechanisms in three-dimensional FCC and BCC materials. These include Frank-Read-ty…
Solids with spatial variations in the crystalline axes naturally evolve into cells or grains separated by sharp walls. Such variations are mathematically described using the Nye dislocation density tensor. At high temperatures, polycrystalline grains form from the melt and coarsen with time: the dislocations can both climb and glide. At low temperatures under shear the dislocations (which allow only glide) form into cell structures. While both the microscopic laws of dislocation motion and the macroscopic laws of coarsening and plastic deformation are well studied, we hitherto have had no simp…
Germanium is the base element in many phase-change materials, i.e. systems that can undergo reversible transformations between their crystalline and amorphous phases. They are widely used in current digital electronics and hold great promise for the next generation of non-volatile memory devices. However, the ultra fast phase transformations required for these applications can be exceedingly complex even for single component systems, and a full physical understanding of these phenomena is still lacking. In this paper we study nucleation and growth of crystalline Ge from amorphous thin films at…
The influence of the stress state on the cross-slip rate in Al was analyzed by means of molecular dynamics simulations and transition state theory. The activation energy barrier in the absence of thermal energy was determined through the nudged elastic band method while the cross-slip rates were determined using molecular dynamics simulations for different magnitudes of the Schmid stress on the cross-slip plane, and of the Escaig stresses on the cross-slip and glide planes. The enthalpy barrier and the effective attempt frequency were determined from the average rates of cross-slip obtained fr…
Dislocations in single-phase concentrated random alloys, including high- entropy alloys (HEAs), repeatedly encounter pinning during glide, resulting in jerky dislocation motion. While solute-dislocation interaction is well understood in conventional alloys, the origin of individual pinning points in concentrated random alloys is a matter of debate. In this work, we investigate the origin of dislocation pinning in the CoCrFeMnNi HEA. In- situ transmission electron microscopy studies reveal wavy dislocation lines and a jagged glide motion under external loading, even though no segregation or clu…
We present a methodology for the investigation of dislocation energetics in segregated alloys based on Monte Carlo simulations which equilibrate the topology and composition of the dislocation core and its surroundings. An environment-dependent partitioning of the system total energy into atomic contributions allows us to link the atomistic picture to continuum elasticity theory. The method is applied to extract core energies and radii of 60 degrees glide dislocations in segregated SiGe alloys which are inaccessible by other methods.
In this research, atomistic molecular dynamics simulations are combined with mesoscopic phase-field computational methods in order to investigate phase-transformation in polycrystalline Aluminum microstructure. In fact, microstructural computational modeling of engineering materials could help to optimize their mechanical properties for industrial applications (e.g. directional solidification for turbine blades). As a result, a multiscale modeling approach is developed to find a relation between manufacturing variables (e.g. temperature) and microstructural properties of crystalline materials …
Plastic deformations in body-centered-cubic (BCC) crystals have been of critical importance in diverse engineering and manufacturing contexts across length scales. Numerous experiments and atomistic simulations on BCC crystals reveal that classical crystal plasticity models with the Schmid law are not adequate to account for abnormal plastic deformations often found in these crystals. In this paper, we address a continuum mechanical treatment of anomalous plasticity in BCC crystals exhibiting non-Schmid effects, inspired from atomistic simulations recently reported. Specifically, anomalous fea…
Misfit-dislocation hierarchy governs sliding of asymmetric non-CSL grain boundaries
Woodruff School of Mechanical Engineering, Georgia Institute of Technology（佐治亚理工学院机械工程学院）；School of Mechanics and Engineering Science, Peking University（北京大学力学与工程科学学院）；Institute of Microstructure and Property of Advanced Materials, Beijing Key Lab of Microstructure and Property of Advanced Materials, Beijing University of Technology（北京工业大学先进材料微结构及性能研究所）
The design of next-generation alloys through the Integrated Computational Materials Engineering (ICME) approach relies on multi-scale computer simulations to provide thermodynamic properties when experiments are difficult to conduct. Atomistic methods such as Density Functional Theory (DFT) and Molecular Dynamics (MD) have been successful in predicting properties of never before studied compounds or phases. However, uncertainty quantification (UQ) of DFT and MD results is rarely reported due to computational and UQ methodology challenges. Over the past decade, studies have emerged that mitigat…
We develop a mesoscopic dislocation dynamics model for vacancy-assisted dislocation climb by upscalings from a stochastic model on the atomistic scale. Our models incorporate microscopic mechanisms of (i) bulk diffusion of vacancies, (ii) vacancy exchange dynamics between bulk and dislocation core, (iii) vacancy pipe diffusion along the dislocation core, and (iv) vacancy attachment-detachment kinetics at jogs leading to the motion of jogs. Our mesoscopic model consists of the vacancy bulk diffusion equation and a dislocation climb velocity formula. The effects of pipe diffusion and the jog str…
Large-scale atomistic calculations, using empirical potentials for modeling semiconductors, have been performed on a stressed system with linear surface defects like steps. Although the elastic limits of systems with surface defects remain close to the theoretical strength, the results show that these defects weaken the atomic structure, initializing plastic deformations, in particular dislocations. The character of the dislocation nucleated can be predicted considering both the resolved shear stress related to the applied stress orientation and the Peierls stress. At low temperature, only gli…
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…
The study of ion transport in electrochemically active materials for energy storage systems requires simulations on quantum- atomistic- and mesoscales. The methods accessing these scales not only have to be effective but also well compatible to provide a full description of the underlying processes. We propose to adapt the Generalized Shadow Hybrid Monte Carlo (GSHMC) method to atomistic simulation of ion intercalation electrode materials for batteries. The method has never been applied to simulations in solid state chemistry but it has been successfully used for simulation of biological macro…
Experimental results on the dislocation dynamics in a two-dimensional plasma crystal are presented. Edge dislocations were created in pairs in lattice locations where the internal shear stress exceeded a threshold and then moved apart in the glide plane at a speed higher than the sound speed of shear waves, $C_T$. The experimental system, a plasma crystal, allowed observation of this process at an atomistic (kinetic) level. The early stage of this process is identified as a stacking fault. At a later stage, supersonically moving dislocations generated shear-wave Mach cones.
A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of i…
It is well known that grain boundaries (GBs) have a strong influence on mechanical properties of polycrystalline materials. Not as well-known is how different GBs interact with dislocations to influence dislocation movement. This work presents a molecular dynamics study of 33 different FCC Ni bicrystals, each subjected to four different strain states to induce incident dislocation-GB interactions for 132 unique configurations. The resulting simulations are analyzed to determine properties of the interaction that affect the likelihood of transmission of the dislocation through the GB in an effo…
Trillion-atom molecular dynamics simulations with ab initio accuracy
Beijing Lonxun Quantum Co., Ltd.（北京龙迅量子有限公司）；Suzhou Laboratory（苏州实验室）；National High Performance Computer Engineering Technology Research Center（国家高性能计算机工程技术研究中心）；Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences（中国科学院宁波材料技术与工程研究所）；State Key Laboratory of Optoelectronic Materials and Devices, Institute of Semiconductors, Chinese Academy of Science（中国科学院半导体研究所光电材料与器件国家重点实验室）；College of Physical Science and Technology, Bohai University（渤海大学物理科学与技术学院）；School of Physics and Electronic Science, East China Normal University（华东师范大学物理与电子科学学院）；Shanghai Institute of Technical Physics, Chinese Academy of Sciences（中国科学院上海技术物理研究所）；Beijing Advanced Innovation Center for Materials Genome Engineering, University of Science and Technology Beijing（北京科技大学材料基因组工程高精尖创新中心）
The mechanical behaviour of Mg-Al alloys can be largely improved by the formation of an intermetallic Laves phase skeleton, in particular the creep strength. Recent nanomechanical studies revealed plasticity by dislocation glide in the (Mg,Al)$_2$Ca Laves phase, even at room temperature. As strengthening skeleton, this phase remains, however, brittle at low temperature. In this work, we present experimental evidence of slip transfer from the Mg matrix to the (Mg,Al)$_2$Ca skeleton at room temperature and explore associated mechanisms by means of atomistic simulations. We identify two possible …
This chapter reviews the different methodological aspects of the ab ini-tio modeling of dislocations. Such simulations are now frequently used to study the dislocation core, i.e. the region in the immediate vicinity of the line defect where the crystal is so strongly distorted that an atomic description is needed. This core region controls some dislocation fundamental properties, like their ability to glide in different crystallographic planes. Ab initio calculations based on the density functional theory offer a predictive way to model this core region. Because dislocations break the periodic…
The mechanical properties of Mg-Al alloys are greatly influenced by the complex intermetallic phase Mg$_{17}$Al$_{12}$, which is the most dominant precipitate found in this alloy system. The interaction of basal edge and 30$^\text{o}$ dislocations with Mg$_{17}$Al$_{12}$ precipitates is studied by molecular dynamics and statics simulations, varying the inter-precipitate spacing ($L$), and size ($D$), shape and orientation of the precipitates. The critical resolved shear stress $τ_c$ to pass an array of precipitates follows the usual $\ln((1/D + 1/L)^{-1})$ proportionality. In all cases but the…
Atomic-level modeling performed at large scales enables the investigation of mesoscale materials properties with atom-by-atom resolution. The spatial complexity of such cross-scale simulations renders them unsuitable for simple human visual inspection. Instead, specialized structure characterization techniques are required to aid interpretation. These have historically been challenging to construct, requiring significant intuition and effort. Here we propose an alternative framework for a fundamental structural characterization task: classifying atoms according to the crystal structure to whic…
The velocity of dislocations is derived analytically to incorporate and predict the intriguing effects induced by the preferential solute segregation and Cottrell atmospheres in both two-dimensional and three-dimensional binary systems of various crystalline symmetries. The corresponding mesoscopic description of defect dynamics is constructed through the amplitude formulation of the phase-field crystal model which has been shown to accurately capture elasticity and plasticity in a wide variety of systems. Modifications of the Peach-Koehler force as a result of solute concentration variations …
Intermittent plastic deformation in crystals with power-law behaviors has been reported in previous experimental studies. The power-law behavior is reminiscent of self-organized criticality, and mesoscopic models have been proposed that describe this behavior in crystals. In this letter, we show that intermittent plasticity in metals under tensile deformation can be observed in molecular dynamics models, using embedded atom method potentials for Ni, Cu, and Al. Power-law behaviors of stress drop and waiting time of plastic deformation events are observed. It is shown that power-law behavior is…
Machine learning has emerged as a powerful tool for the analysis of mesoscopic and atomically resolved images and spectroscopy in electron and scanning probe microscopy, with the applications ranging from feature extraction to information compression and elucidation of relevant order parameters to inversion of imaging data to reconstruct structural models. However, the fundamental limitation of machine learning methods is their correlative nature, leading to extreme susceptibility to confounding factors. Here, we implement the workflow for causal analysis of structural scanning transmission el…
Hetero-epitaxial growth on a strain-relief vicinal patterned substrate has revealed unprecedented 2D long range ordered growth of uniform cobalt nanostructures. The morphology of a Co sub-monolayer deposit on a Au(111) reconstructed vicinal surface is analyzed by Variable Temperature Scanning Tunneling Microscopy (VT-STM) experiments. A rectangular array of nano-dots (3.8 nm x 7.2 nm) is found for a particularly large deposit temperature range lying from 60 K to 300 K. Although the nanodot lattice is stable at room temperature, this paper focus on the early stage of ordered nucleation and grow…
An experimentally validated end-to-end framework for operando modeling of intrinsically complex metallosilicates
Institute for Materials Science, University of Stuttgart（斯图加特大学材料科学研究所）；Institute of Physical Chemistry, University of Stuttgart（斯图加特大学物理化学研究所）；Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart（斯图加特大学热力学与热力过程工程研究所）
In this work we examine the driving force for edge dislocations to climb in $α$-Fe from atomistic and mesoscale viewpoints. We study the bias for the climb process depending on the dislocation orientation and the applied stress as coming from both the gradient of the chemical potential and the transport coefficients. Both terms are modified by the applied stress and therefore contribute to climb. Surprisingly, even though the vacancy migration barrier distribution is modified by the external stress as obtained by nudged-elastic band calculations, the mobilities resulting from a kinetic Monte C…
