Dislocation Core Energy Research Articles

Relaxation of Misfit Dislocations at Nodes

Experimental studies proved that structures and properties of misfit dislocations and their intersections (nodes) in semi-coherent interfaces strongly affect thermal and mechanical stability of interface. Employing atomistic simulations, we reveal that misfit dislocation lines can exhibit a spiral pattern (SP) or remain straight in association with dislocation character at nodes. By analyzing nodes formation processes in terms of kinetics and energetics, we found that the variation is ascribed to the competition between core energy of misfit dislocation and interface stacking fault energy with respect to coherent interface.

Predicting structure and energy of dislocations and grain boundaries

A microscopic phase field (MPF) model is formulated to describe quantitatively the core structure and energy of dislocations using ab initio data as input. Based on phase field microelasticity theory implemented in the slip plane using Green’s function to describe the long-range elastic interaction, the MPF model is a three-dimensional generalization of the Peierls model. Using the same generalized stacking fault energy as input, the core structure and energy predicted for straight dislocations by the MPF model show complete agreement with those predicted by the Peierls model. The ability of the MPF model to treat dislocations of arbitrary configurations is demonstrated by calculating the structure and energy of a twist grain boundary in aluminum. After discrete lattice sampling a la Nabarro, the grain boundary energy manifests Read–Shockley behavior for low-angle boundaries as well as deep cusps for high-angle special boundaries, indicating a “Peierls torque friction” effect for grain boundaries that has the same physical origin as the Peierls lattice friction for dislocation cores.

Interaction mechanisms of screw dislocations with and twin boundaries in Mg

Molecular dynamics simulations were carried out to investigate the interactions between screw partials and the and twin boundaries in Mg. In the twin, the interaction was attractive and the partials were absorbed readily in the boundary. In the twin, however, they passed through the twin boundary because of a repulsive interaction when a large applied strain was applied. The total energy including the dislocation core energy and the twin boundary energy was found to be similar before and after the absorption of the partials in the twin boundary, while it increased upon the absorption of the partial in the twin boundary. The origins of the total energy variations are discussed from a crystallographic viewpoint.

〈110〉{111} dislocation core properties in L12 Al3 Sc and Al3 Mg based on the Peierls-Nabarro model

The generalized stacking fault (GSF) energy curves along the 〈110〉 direction on {111} slip plane for L12 Al3Sc and Al3Mg are calculated within the framework of density functional theory (DFT), and anti-phase boundary (APB) energies are obtained. Then the structures and properties of collinear dissociated 〈110〉{111} dislocations in Al3Sc and Al3Mg are studied using Peierls–Nabarro (PN) model combined with GSF energies, the obtained dislocation dissociation width of the 〈110〉{111} edge dislocation in Al3Sc is in agreement with the available experimental value. In comparison with Al3Mg, the dislocation dissociation widths of both screw and edge in Al3Sc are narrower and the Peierls energies and stresses are lower, while the core energies are much higher. Furthermore, for both Al3Sc and Al3Mg, the core energy of screw dislocation is smaller than that of edge dislocation, while the Peierls energy and stress of screw dislocation is slightly larger.

Dislocation core field.II. Screw dislocation in iron

The dislocation core field, which comes in addition to the Volterra elastic field, is studied for the <111> screw dislocation in alpha-iron. This core field, evidenced and characterized using ab initio calculations, corresponds to a biaxial dilatation, which we modeled within the anisotropic linear elasticity. We show that this core field needs to be considered when extracting quantitative information from atomistic simulations, such as dislocation core energies. Finally, we look at how dislocation properties are modified by this core field, by studying the interaction between two dislocations composing a dipole, as well as the interaction of a screw dislocation with a carbon atom.

Analysis of strained nitride quantum dots as threading dislocation filters

A finite element model is proposed to quantitatively predict the critical condition for a nitride quantum dot to bend threading dislocation to interfacial misfit dislocation. The energy balance approach adopted is based on the elastic residual strain energy and non-elastic dislocation core energy. We find that the critical misfit, beyond which the inclination of threading dislocation is energetically favorable, depends strongly on the shape, size and aspect ratio. The results provide guidelines for the design of quantum dot dislocation filter.

Effect of core energy on mobility in a continuum dislocation model

We present a first-principles-based, multiscale single-crystal plasticity model for fcc metals and apply it to nickel. The model consists of a phase field approach to dislocation dynamics (PFDD) with all its input parameters obtained from equilibrium and nonequilibrium molecular-dynamics (MD) simulations. The atomistic information used to inform the phase field model includes elastic constants, dislocation core energy, crystal disregistry energy (gamma surface), and dislocation mobility. We show that the PFDD model can be simplified to the Frenkel-Kontorowa equations for straight dislocations, and under these conditions an analytical time-dependent solution enables a direct connection to nonequilibrium MD simulations. This time-dependent analytical solution provides a relationship between dislocation mobility (ratio between dislocation velocity and applied stress) and fundamental atomic-scale materials properties that arise from the atomistics: unstable stacking fault energy and dislocation core energy and width. We find that the dislocation mobility increases linearly with the ratio between the core energy and unstable stacking fault energy in the PFDD theory.

A phase-field model for deformation twinning

We propose a phase-field model for modeling microstructure evolution during deformation twinning. The order parameters are proportional to the shear strains defined in terms of twin plane orientations and twinning directions. Using a face-centered cubic Al as an example, the deformation energy as a function of shear strain is obtained using first-principle calculations. The gradient energy coefficients are fitted to the twin boundary energies along the twinning planes and to the dislocation core energies along the directions that are perpendicular to the twinning planes. The elastic strain energy of a twinned structure is included using the Khachaturyan's elastic theory. We simulated the twinning process and microstructure evolution under a number of fixed deformations and predicted the twinning plane orientations and microstructures.

Melting in two-dimensional Yukawa systems: A Brownian dynamics simulation

We studied the melting behavior of two-dimensional colloidal crystals with a Yukawa pair potential by Brownian dynamics simulations. The melting follows the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario with two continuous phase transitions and a middle hexatic phase. The two phase-transition points were accurately identified from the divergence of the translational and orientational susceptibilities. Configurational temperatures were employed to monitor the equilibrium of the overdamped system and the strongest temperature fluctuation was observed in the hexatic phase. The inherent structure obtained by rapid quenching exhibits three different behaviors in the solid, hexatic, and liquid phases. The measured core energy of the free dislocations, E(c) = 7.81 ± 0.91 k(B)T, is larger than the critical value of 2.84 k(B)T, which consistently supports the KTHNY melting scenario.

Simulations of stress-induced twinning and de-twinning: A phase field model

Twinning in certain metals or under certain conditions is a major plastic deformation mode. Here we present a phase field model to describe twin formation and evolution in a polycrystalline fcc metal under loading and unloading. The model assumes that twin nucleation, growth and de-twinning is a process of partial dislocation nucleation and slip on successive habit planes. Stacking fault energies, energy pathways (γ surfaces), critical shear stresses for the formation of stacking faults and dislocation core energies are used to construct the thermodynamic model. The simulation results demonstrate that the model is able to predict the nucleation of twins and partial dislocations, as well as the morphology of the twin nuclei, and to reasonably describe twin growth and interaction. The twin microstructures at grain boundaries are in agreement with experimental observation. It was found that de-twinning occurs during unloading in the simulations, however, a strong dependence of twin structure evolution on loading history was observed.

Equilibrium critical size of coherent InSb/GaSb quantum dot

We present a finite element method to simulate the strain field in InSb/GaSb quantum dots in the framework of anisotropic elasticity, before and after the onset of plastic relaxation. Taking the interaction between dislocation and free surface into consideration, the model directly calculates the residual strain in the dislocated system. Based on the energy balance between the two isolated states, the equilibrium critical size is determined. In the criterion, only the non-elastic dislocation core energy should be considered separately. The results are in satisfactory agreement with experimental data.

Role of c-screw dislocations on indium segregation in InGaN and InAlN alloys

Indium segregation induced by c-screw dislocations in wurtzite InGaN and InAlN alloys is investigated with molecular dynamics based on Stillinger–Weber potentials [Stillinger and Weber, Phys. Rev. B 31, 5262 (1985)]. Beginning with the analysis of atomic structures and energetic stability of c-screw dislocations in AlN, GaN, and InN compounds, their interaction with In atoms in GaN and AlN is explored. The results show that In atoms reduce the core energy of c-screw dislocation when they are located at the center of the core region. The distance dependence of the interaction energy indicates that In atoms will tend to gather around the dislocation line and form an In-rich region. These results agree with experimental observations in InGaN and should predict a similar behavior in InAlN.

Plasticity in carbon nanotubes: Cooperative conservative dislocation motion

Monte Carlo simulations are used to study dislocation glide mediated plasticity in carbon nanostructures. A detailed analysis of the simulations leads to identification of a type of defect, a dislocation screened by multiple dislocation dipoles, as the mediator of plastic deformation. The defects appear under high stress conditions. The appearance of these defects is rationalized in terms of the competition between dislocation core energy and the buckling inherent to dislocation motion within an essentially two-dimensional membrane. These defects thus represent a deformation mechanism that is uniquely found in nominally two-dimensional nanostructures. The influence of these defects on the predicted mechanical properties of carbon nanostructures is discussed.

Discrete dislocations in graphene

In this work, we present an application of the theory of discrete dislocations of Ariza and Ortiz (2005) to the analysis of dislocations in graphene. Specifically, we discuss the specialization of the theory to graphene and its further specialization to the force-constant model of Aizawa et al. (1990). The ability of the discrete-dislocation theory to predict dislocation core structures and energies is critically assessed for periodic arrangements of dislocation dipoles and quadrupoles. We show that, with the aid of the discrete Fourier transform, those problems are amenable to exact solution within the discrete-dislocation theory, which confers the theory a distinct advantage over conventional atomistic models. The discrete dislocations exhibit 5–7 ring core structures that are consistent with observation and result in dislocation energies that fall within the range of prediction of other models. The asymptotic behavior of dilute distributions of dislocations is characterized analytically in terms of a discrete prelogarithmic energy tensor. Explicit expressions for this discrete prelogarithmic energy tensor are provided up to quadratures.

Investigation of the Effect of Deformation on γ‐α Phase Transformation Kinetics in Hot‐Rolled Dual Phase Steel by Phase Field Approach

Dual phase steels, consisting of hard martensite particles in a ductile ferritic matrix, offer high strength and deformability at the same time. Additionally, they are cost effective by a dilute alloying concept. In industrial production, two manufacturing concepts have been implemented: intercritical annealing of cold rolled sheet, or hot rolling. The current work has investigated the effect of deformation on the γ-α phase transformation kinetics in the dual phase steel production using the hot rolling scheme. The pancaked austenite grains containing denser nucleation sites have a strong influence on the ferrite transformation kinetics. In addition, the multiplication of dislocations which results in the increase in elastic strain energy and dislocation core energy contributes to some acceleration in ferrite growth kinetics. A modelling approach for the γ-α phase transformation kinetics in dual phase steels has been developed employing the phase field theory. The nucleation behaviour, i.e. the number and size of nuclei developed after an elapsed time as well as their nucleation sites which were evaluated from microstructure analysis, and the increase in the driving force of grain growth were integrated into this model.

Dislocation Core Energies and Core Fields from First Principles

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.

Theoretical study of pressure effect on the dislocation core properties in semiconductors

The effect of an applied pressure on the core of screw dislocations in semiconductors such as Si, $\ensuremath{\beta}\text{-SiC}$, and diamond has been investigated by carrying out tight-binding and first-principles calculations of the variations in dislocation core energies and in energy barriers for dislocation translation. Pressure is found to have a sizable effect and can lead to either decreases or increases in the latter quantities. It is also shown that it is advisable to take into account all pressure-dependent parameters for accurately determining this effect. Nevertheless, we found that for the investigated materials, the effect of pressure was not strong enough to induce structural transformations of the dislocation core. The mobility of the cores was also found to be dependent on pressure, which tends to increase or decrease the energy barriers according to the direction of the dislocation displacement.

Equilibrium critical thickness for misfit dislocations in III-nitrides

The critical thickness gives the transition point between fully strained and relaxed heteroepitaxial films and determines the onset of defect generation, including misfit dislocations, cracks, and V-pits. An important variable in critical thickness calculations concerning misfit dislocations is the dislocation energy. It consists of two contributions: the elastic energy of the bulk material around a dislocation and the energy of the dislocation core. The latter part is often neglected. Recent atomistic calculations have estimated this quantity together with the radius of dislocation cores in wurtzite III-nitrides. The effect of the dislocation core energy on equilibrium critical thickness values for III-nitrides is investigated theoretically and is shown to be significant. The calculated values of the critical thickness are compared with experimentally determined values of the critical thickness for misfit dislocations in the InGaN/GaN system using transmission electron microscopy and x-ray diffraction techniques. A comparison of the present model with experimental observations, together with a wide range of data from the literature for both AlGaN/GaN and InGaN/GaN systems, shows reasonable agreement. Finally, we speculate on a possible reason for differences between theory and experiment.

Plastic strain field caused by dislocations

Although dislocations have been investigated for almost a 100 years, plastic strains caused by them are not known. Because of that the dislocation energy and the strain field around a dislocation are described using a very simple model e.g. Volterra approach. On the other hand methods of atomistic calculations like ab initio and molecular dynamics allow for relatively precise mechanical description of highly distorted region of dislocation core. Their disadvantages are that the boundary conditions have to be applied periodically. Until now, the discrepancy between results of atomistic calculation and continuum mechanics simulations in a dislocation core region was ascribed to a strong nonlocal interaction. The present article shows a method that allows for a proper energetic description of dislocation cores using the continuum mechanics. A very good correspondence between the dislocation core's energy obtained here and those resulting from atomistic simulations reveals that the proposed methodology may establish new possibilities for the continuum description. The approach is validated by considering a screw dislocation in silicon. Full anisotropy is taken into account. The most important information originated from this paper is that a reliable energetic description of dislocations using continuum methods at the nanoscale is possible.

Non-singular descriptions of dislocation cores: a hybrid ab initio continuum approach

The core structure of straight and curved dislocations is studied by developing a hybrid approach that links the parametric dislocation dynamics method with ab initio calculations. The approach is an extension of the Peierls–Nabarro (PN) model, with the following features: (1) all three components of the displacement vector for atoms within the dislocation core are included; (2) the entire generalized stacking fault energy surface (GSFS) obtained from ab initio calculations is utilized; and (3) the method is generalized to treat curved dislocations. We combine the parametric dislocation dynamics (DD) approach for the interaction and motion of dislocations with ab initio calculations of lattice restoring forces. These forces, which are extracted from the GSFS (γ-surface), are calculated from both first-principles density functional theory (DFT) and the embedded-atom method (EAM). Dislocation core structures in aluminium and silver are determined. For straight dislocations, the results from the model are shown to be in excellent agreement with experiments for both Al and Ag. In contrast to undissociated dislocation loops in Al, it is found that the core width and the separations between partials in Ag vary along the angular direction measured with respect to the Burgers vector. It is also shown that the core-cutoff radius, which is usually employed in DD calculations to avoid singularities, must be adjusted as a function of loop size to account for the correct dislocation core energy.