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 Carlo model applied on the obtained energy landscape are indistinguishable, independently of the stress. Moreover, an object kinetic Monte Carlo (OKMC) model including the effect of the dislocation strain field to first order shows indeed a slight anisotropic component in the diffusion in more complex dislocation configurations. However, the OKMC results highlight the fact that the thermodynamic component is the dominant driving force. We conclude that in $α$-Fe under thermal conditions, the main source of bias is given by the difference in vacancy chemical potentials, which is small enough to hinder the process for dynamic atomistic simulations.
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…
The classical modeling of dislocation climb based on a continuous description of vacancy diffusion is compared to recent atomistic simulations of dislocation climb in body-centered cubic iron under vacancy supersaturation [Phys. Rev. Lett. 105 095501 (2010)]. A quantitative agreement is obtained, showing the ability of the classical approach to describe dislocation climb. The analytical model is then used to extrapolate dislocation climb velocities to lower dislocation densities, in the range corresponding to experiments. This allows testing of the validity of the pure climb creep model propos…
We employ the methods of atomistic simulation to investigate the climb of edge dislocation at nanovoids by analyzing the energetics of the underlying mechanism. A novel simulation strategy has been demonstrated to estimate the release of surface energy of the nanovoid during the void induced climb. The curvature of the pinned dislocation segment is found to play a key role in mediating this unique mechanism of dislocation climb. Our study reveals that the kinetics of void-induced climb process is fundamentally distinct from the conventional diffusion-mediated climb.
Dislocation climb mobilities, assuming vacancy bulk diffusion, are derived and implemented in dislocation dynamics simulations to study the coarsening of vacancy prismatic loops in fcc metals. When loops cannot glide, the comparison of the simulations with a coarsening model based on the line tension approximation shows a good agreement. Dislocation dynamics simulations with both glide and climb are then performed. Allowing for glide of the loops along their prismatic cylinders leads to faster coarsening kinetics, as direct coalescence of the loops is now possible.
In this paper, we present a phase field model for the self-climb motion of prismatic dislocation loops via vacancy pipe diffusion driven by elastic interactions. This conserved dynamics model is developed under the framework of the Cahn-Hilliard equation with incorporation of the climb force on dislocations, and is based on the dislocation self-climb velocity formulation established in Ref.[1]. The phase field model has the advantage of being able to handle the topological and geometrical changes automatically during the simulations. Asymptotic analysis shows that the proposed phase field mode…
It has been shown in experiments that self-climb of prismatic dislocation loops by pipe diffusion plays important roles in their dynamical behaviors, e.g., coarsening of prismatic loops upon annealing, as well as the physical and mechanical properties of materials with irradiation. In this paper, we show that this dislocation dynamics self-climb formulation that we derived in Ref. [1] is able to quantitatively describe the properties of self-climb of prismatic loops that were observed in experiments and atomistic simulations. This dislocation dynamics formulation applies to self-climb by pipe …
The effects of dislocation climb on plastic deformation during loading and unloading are studied using a two-dimensional discrete dislocation dynamics model. Simulations are performed for polycrystalline thin films passivated on both surfaces. Dislocation climb lowers the overall level of the stress inside thin films and reduces the work hardening rate. Climb decreases the density of dislocations in pile-ups and reduces back stresses. These factors result in a smaller Bauschinger effect on unloading compared to simulations without climb. As dislocations continue to climb at the onset of unload…
Active room temperature diffusion-less climb of the <a> edge dislocations in model Mg-Al alloys was observed using molecular dynamics simulations. Dislocations on prismatic and pyramidal I planes climb through the basal plane to overcome solute obstacles. This out-of-plane dislocation motion softens the high resistance pyramidal I glide and significantly reduces the anisotropy of dislocation mobility, and could help improve the ductility of Mg. The flow stress scales linearly with solute concentration, cAl. Dislocations climb predominantly in the negative direction, with climb angle on the ord…
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 continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain boundaries is driven by grain boundary dislocations climb. The model is stated in terms of general balance laws and completed by the choice of constitutive equations consistent with classical non-equilibrium thermodynamics. The kinetics of diffusional creep is derived from physically-based mechanisms of climb of dislocations at grain boundaries, thus introducin…
Many systems where a liquid metal is in contact with a polycrystalline solid exhibit deep liquid grooves where the grain boundary meets the solid-liquid interface. For example, liquid Ga quickly penetrates deep into grain boundaries in Al, leading to intergranular fracture under very small stresses. We report on a series of molecular dynamics simulations of liquid Ga in contact with an Al bicrystal. We identify the mechanism for liquid metal embrittlement, develop a new model for it, and show that is in excellent agreement with both simulation and experimental data.
We study the sharp interface limit and well-posedness of a phase field model for self-climb of prismatic dislocation loops in periodic settings. The model is set up in a Cahn-Hilliard/Allen-Cahn framework featured with degenerate phase-dependent diffusion mobility with an additional stablizing function. Moreover, a nonlocal climb force is added to the chemical potential. We introduce a notion of weak solutions for the nonlinear model. The existence result is obtained by approximations of the proposed model with nondegenerate mobilities. Lastly, the numerical simulations are performed to valida…
Dislocations can climb out of their glide plane by absorbing (or emitting) point defects (vacancies and self-interstitial atoms (SIAs)). In contrast with conservative glide motion, climb relies on the point defects' thermal diffusion and hence operates on much longer timescales, leading to some forms of creep. Whilst equilibrium point defect concentrations allow dislocations to climb to relieve non-glide stresses, point defect supersaturations also lead to osmotic forces, driving dislocation motion even in the absence of external stresses. Self-interstitial atoms typically have significantly h…
Recently, a dislocation free deformation mechanism was proposed by Kiritani et al., based on a series of experiments where thin foils of fcc metals were deformed at very high strain rates. In the experimental study, they observed a large density of stacking fault tetrahedra, but very low dislocation densities in the foils after deformation. This was interpreted as evidence for a new dislocation-free deformation mechanism, resulting in a very high vacancy production rate. In this paper we investigate this proposition using large-scale computer simulations of bulk and thin films of copper. To fa…
In the present work, we conduct large-scale orbital-free DFT calculations to study the energetics of vacancy clustering in aluminum from electronic structure calculations. The simulation domains considered in this study are as large as those containing a million atoms to accurately account for both the electronic structure and long-ranged elastic fields. Our results indicate that vacancy clustering is an energetically favorable mechanisms with positive binding energies for a range of vacancy clusters considered in the present study. In particular, the $19$ vacancy hexagonal cluster lying in $\…
We use three-dimensional discrete dislocation dynamics simulations (DDD) to study the evolution of interfacial dislocation network (IDN) in particle-strengthened alloy systems subjected to constant stress at high temperatures. We have modified the dislocation mobility laws to incorporate the recovery of the dislocation network by the climb. The microstructure consists of uniformly distributed cuboidal inclusions embedded in the simulation box. Based on the systematic simulations of IDN formation as a function of applied stress for prescribed inter-particle spacing and glide-to-climb mobility r…
The interaction of vacancy with dislocations in Al is studied using the Semidiscrete Variational Peierls-Nabarro model with ab initio determined gamma surface. For the first time, we confirm theoretically the so-called vacancy lubrication effect on dislocation motion in Al, a discovery that can settle a long-standing controversy in dislocation theory for fcc metals. We provide insights on the lubrication effect by exploring the connection between dislocation mobility and its core width. We predict an increased dislocation splitting in the presence of vacancy. We find that on average there is a…
Dislocations are a central concept in materials science, which dictate the plastic deformation and damage evolution in materials. Layered materials such as graphite admit two general types of interlayer dislocations: basal and prismatic dislocations, of which prismatic dislocations have been relatively less studied. Using density functional theory (DFT) calculations, we have examined different prismatic core structures in graphite and evaluated their structure, energetics and mobility. We find close energetic interplay between bonded and "free-standing" core structures in both zigzag and armch…
Production rates in long-term predictive radiation damage accumulation models are generally considered independent of the material's microstructure for reactor components. In this study, the effect of pre-existing microstructural elements on primary damage production in alpha-Zr -- and vice-versa -- is assessed by molecular dynamics (MD) simulations. a-type dislocation loops, c-component dislocation loops and a tilt grain boundary (GB) were considered. Primary damage production is reduced in the presence of all these microstructural elements, and clustering behavior is dependent on the microst…
The interaction between vacancies and edge dislocations in face centered cubic metals (Al, Au, Cu, Ni) is studied at different length scales. Using empirical potentials and static relaxation, atomic simulations give us a precise description of this interaction, mostly in the case when the separation distance between both defects is small. At larger distances, elasticity theory can be used to predict this interaction. From the comparison between both approaches we obtain the minimal separation distance where elasticity applies and we estimate the degree of refinement required in the calculation…
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…
The ripplocation is a crystallographic defect which is unique to layered materials, combining nanoscale delamination with the crystallographic slip of a basal dislocation. Here, we have studied basal dislocations and ripplocations, in single and multiple van der Waals layers, using analytical and computational techniques. Expressions for the energetic and structural scaling factors of surface ripplocations are derived, which are in close correspondence to the physics of a classical carpet ruck. Our simulations demonstrate that the lowest-energy structure of dislocation pile-ups in layered mate…
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…
Oxygen Vacancies at Dislocation Core Modulate Plasticity in Strontium Titanate
Ames National Laboratory（艾姆斯国家实验室）；North Carolina State University（北卡罗来纳州立大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Iowa State University（爱荷华州立大学）；University of Virginia（弗吉尼亚大学）
Topological defects play an important role in physics of elastic media and liquid crystals. Their kinematics is determined by constraints of topological origin. An example is the glide motion of dislocations which has been extensively studied by metallurgists. In a recent theoretical study dealing with quantum dualities associated with the quantum melting of solids it was argued that these kinematic constraints play a central role in defining the quantum field theories of relevance to the description of quantum liquid crystalline states of the nematic type. This forms the motivation to analyze…
The mobility of vacancies in alloys may limit dislocation climb. Using a combined density functional theory and kinetic Monte Carlo approach we investigate vacancy diffusion in Ni-Re, Ni-W, and Ni-Ta binary alloys up to 10 at.% solute concentration. We introduce an interaction model that takes into account the chemical environment close to the diffusing atom to capture the effect of solute-host and solute-solute interactions on the diffusion barriers. In contrast to an ideal solid solution it is not only the diffusion barrier of the solute atom that influences the vacancy mobility, but primari…
Vacancy swelling of quasicrystals under irradiation is considered. In quasicrystals, the evolution of dislocations is accompanied by the formation of phasons which are localized topological defects of the vacancy and interstitial types. At moderate temperatures the diffusivity of phasons is low which leads to the formation of ring-or disk-shaped phason trails inside dislocation loops. To find the capture efficiency of point defects by a dislocation loop with the complementary ring of phasons the steady-state drift-diffusional problem is solved in the toroidal geometry by the successive overrel…
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…
Interactions between an edge dislocation and a void in copper are investigated by means of molecular dynamics simulation. The depinning stresses of the leading partial and of the trailing partial show qualitatively different behaviors. The depinning stress of the trailing partial increases logarithmically with the void radius, while that of the leading partial shows a crossover at 1 nm above which two partials are simultaneously trapped by the void. The pinning angle, which characterizes the obstacle strength, approaches zero when the void radius exceeds 3 nm. No temperature dependence is foun…
We present a numerical study of a continuum plasticity field coupled to a Ginzburg-Landau model for superfluidity. The results suggest that a supersolid fraction may appear as a long-lived transient during the time evolution of the plasticity field at higher temperatures where both dislocation climb and glide are allowed. Supersolidity, however, vanishes with annealing. As the temperature is decreased, dislocation climb is arrested and any residual supersolidity due to incomplete annealing remains frozen. Our results provide a resolution of many perplexing issues concerning a variety of experi…
This work introduces a model for large-strain, geometrically nonlinear elasto-plastic dynamics in single crystals. The key feature of our model is that the plastic dynamics are entirely driven by the movement of dislocations, that is, $1$-dimensional topological defects in the crystal lattice. It is well known that glide motion of dislocations is the dominant microscopic mechanism for plastic deformation in many crystalline materials, most notably in metals. We propose a novel geometric language, built on the concepts of space-time "slip trajectories" and the "crystal scaffold" to describe the…
The dynamic generalization of the Peierls-Nabarro equation for dislocations cores in an isotropic elastic medium is derived for screw, and edge dislocations of the `glide' and `climb' type, by means of Mura's eigenstrains method. These equations are of the integro-differential type and feature a non-local kernel in space and time. The equation for the screw differs by an instantaneous term from a previous attempt by Eshelby. Those for both types of edges involve in addition an unusual convolution with the second spatial derivative of the displacement jump. As a check, it is shown that these eq…
A model for gas bubble behavior in irradiated amorphous $U_3Si_2$ is generalized to take into account local influence of sinks for point defects and gas atoms as far as defect clustering resulting in growth of dislocation loops. A universality of bubble size distribution function and scaling law of bubble size growth is revealed. Temperature dependencies of main quantities governing bubble growth are discussed. Local distribution of bubbles and dislocation loops inside grains is studied in details to illustrate bubble size change in the vicinity of grain boundaries and estimate local swelling.…
We use new equations for the interstitial impurity diffusion fluxes under strain to study impurity atom redistribution in the vicinity of dislocations. Two levels of simulation are applied. The first one is evaluation of coefficients that determine the influence of strain tensor components on interstitial diffusion fluxes in FCC structures. For this purpose we have developed a model into the framework of a molecular static method taking into account an atom environment both near the interstitial site and for the saddle-point configuration. The second level is modeling the interstitial segregat…
Although titanium nitride (TiN) is among the most extensively studied and thoroughly characterized thin-film ceramic materials, detailed knowledge of relevant dislocation core structures is lacking. By high-resolution scanning transmission electron microscopy (STEM) of epitaxial single crystal (001)-oriented TiN films, we identify different dislocation types and their core structures. These include, besides the expected primary full a/2{110}<1$\bar{1}$0> dislocation, Shockley partial dislocations a/6{111}<11$\bar{2}$> and sessile Lomer edge dislocations a/2{100}<011>. Density-functional theory…
Neutron irradiation progressively changes the properties of zirconium alloys: they harden and their average c/a lattice parameter ratio decreases with fluence. The bombardment by neutrons produces point defects, which evolve into dislocation loops that contribute to a non-uniform growth phenomenon called irradiation-induced growth (IIG). To gain insights into these dislocation loops in Zr we studied them using atomistic simulation. We constructed and relaxed dislocation loops of various types. We find that the energies of <a>-loops on different habit planes are similar, but our results indicat…
Order strengthening in nickel-based superalloys is associated with the extra stress required for dislocations to bypass the $γ'$ precipitates distributed in the $γ$ matrix. A rich variety of bypass mechanism has been identified, with various shearing and Orowan looping processes giving way to climb bypass as the operating conditions change from the low/intermediate temperatures and high stress regime, to the high temperature and low stress regime. When anti phase boundary (APB) shearing and Orowan looping mechanisms operate, the bypass mechanism changes from shearing to looping with increased …
The annealing kinetics of mobile intrinsic defects is investigated by an ab initio method based on density functional theory. The interstitial-vacancy recombination, the diffusion of vacancies and interstitials to defect sinks (e.g. surfaces or dislocations) as well as the formation of interstitial-clusters are considered. The calculated migration and reaction barriers suggest a hierarchical ordering of competing annealing mechanisms. The higher mobility of carbon and silicon interstitials as compared to the vacancies drives the annealing mechanims at lower temperatures including the vacancy-i…
The mechanism of recrystallization in epitaxial (1000) GaN film, introduced by indentation technique, is probed by lattice dynamic studies using Raman spectroscopy. The recrystallized region is identified by Micro-Raman area mapping. Pop-in bursts in loading lines indicate nucleation of dislocations and climb of dislocations. These processes set in plastic motion of lattice atoms under stress field at the center of indentation for the initiation of recrystallization process. A planar defect migration mechanism is evolved. A pivotal role of vacancy migration is pointed out, for the first time, …
Refractory multi-element alloys (RMEA) with body-centered cubic (bcc) structure have been the object of much research over the last decade due to their high potential as candidate materials for high-temperature applications. Most of these alloys display a remarkable strength at high temperatures, which cannot be explained by the standard model of bcc plasticity dominated by thermally-activated screw dislocation motion. Recent research on Nb-Mo-Ta-W alloys points to a heightened role of edge dislocations on deformation, which is generally attributed to atomic-level chemical fluctuations in the …
Fracture material is seriously problem in daily life, and it has connection with mechanical properties itself. The mechanical properties is belief depend on dislocation movement and crack propagation in the crystal. Information about this is very important to characterize the material. In FCC crystal structure the competition between crack propagation and dislocation wake is very interesting, in a ductile material like copper (Cu) dislocation can be seen in room temperature, but in a brittle material like Si only cracks can be seen observed. Different techniques were applied to material to stu…
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…
