Edge Dislocation In Bcc Iron Research Articles

Kinetics of segregation formation in elastic field of edge dislocation in bcc iron

We study the kinetics of the redistribution of impurity atoms in the elastic fields of dislocations. Study is based on taking into account the influence of elastic fields on diffusion fluxes of interstitial impurity atoms. The study is performed by computer simulation methods and consists of several stages. The first is the simulation of a dislocation core structure with a Burgers vector along [100] direction by using the modified molecular static method. The second is obtaining the coefficients that determine the influence of the components of the strain tensor on the diagonal elements of the matrix of diffusion coefficients and in the equations for fluxes of carbon atoms in bcc iron. The third stage is associated with modeling the diffusion characteristics of carbon atoms by the method of molecular dynamics in a crystal without defects. The fourth and final stage uses the data about atomic structure that we obtained at first stage, as well as the characteristics calculated in the second and third, is a simulation of the formation of segregations of interstitial atoms, which is based on solving diffusion equations that take into account the elastic deformations created by the dislocation. The complex of developed models is used to analyze the kinetics of segregation formation. 3D graphs illustrate the distribution of interstitial atoms in the vicinity of a dislocation for different times at certain temperatures.

Influence of helium-decoration on the interaction between 1/2 dislocation loop and edge dislocation in BCC iron

For ferritic steels served as structural materials for future nuclear reactors, a large number of helium atoms are expected to be introduced through transmutation reaction. Current experimental results prove that these helium atoms tend to segregate at different crystal defects and deteriorate the mechanical properties of materials severely. In this work, the helium segregation on 1/2[11‾1] dislocation loops (DLs) in body-centered cubic iron and the concomitant hardening effects were investigated by a combination of Monte Carlo and molecular dynamics methods. The Monte Carlo results reveal that the helium atoms are inclined to segregate as helium bubbles at six energetic favorable sites which divide the DLs periphery uniformly, irrespective of the shapes of DLs. The Molecular dynamics simulations were then performed to study the interaction between a moving edge dislocation and the helium-decorated DLs. In order to investigate the helium-decoration effects systematically, influence factors including the DLs size, helium content, and the relative geometric position between edge dislocations and DLs were considered. It is shown that the decoration of helium bubbles suppresses the absorption of DLs by the moving edge dislocation through hindering the movement of dislocation segments during the interaction. Four types of residual products induced by the edge dislocation-DLs interaction are observed, while three of them, including a pure <100> DL and two kinds of bi-DLs, had never been reported before. It is also found that helium-segregation overall increases the critical shear stress for the edge dislocation bypassing DLs. These results may be helpful for a deeper atomic-scale comprehension of the helium-induced hardening and embrittlement in ferritic steels.

Atomistic Study of the Role of Defects on α → ϵ Phase Transformations in Iron under Hydrostatic Compression

It has long been known that iron undergoes a phase transformation from body-centered cubic/ α structure to the metastable hexagonal close-packed/ ε phase under high pressure. However, the interplay of line and planar defects in the parent material with the transformation process is still not fully understood. We investigated the role of twins, dislocations, and Cottrell atmospheres in changing the crystalline iron structure during this phase transformation by using Monte Carlo methods and classical molecular dynamics simulations. Our results confirm that embryos of ε -Fe nucleate at twins under hydrostatic compression. The nucleation of the hcp phase is observed for single crystals containing an edge dislocation. We observe that the buckling of the dislocation can help to nucleate the dense phase. The crystal orientations between the initial structure α -Fe and ε -Fe in these simulations are 110 b c c | | 0001 h c p . The presence of Cottrell atmospheres surrounding an edge dislocation in bcc iron retards the development of the hcp phase.

Multiscale modeling of dislocation-precipitate interactions in Fe: From molecular dynamics to discrete dislocations.

The stress-driven motion of dislocations in crystalline solids, and thus the ensuing plastic deformation process, is greatly influenced by the presence or absence of various pointlike defects such as precipitates or solute atoms. These defects act as obstacles for dislocation motion and hence affect the mechanical properties of the material. Here we combine molecular dynamics studies with three-dimensional discrete dislocation dynamics simulations in order to model the interaction between different kinds of precipitates and a 1/2〈111〉{110} edge dislocation in BCC iron. We have implemented immobile spherical precipitates into the ParaDis discrete dislocation dynamics code, with the dislocations interacting with the precipitates via a Gaussian potential, generating a normal force acting on the dislocation segments. The parameters used in the discrete dislocation dynamics simulations for the precipitate potential, the dislocation mobility, shear modulus, and dislocation core energy are obtained from molecular dynamics simulations. We compare the critical stresses needed to unpin the dislocation from the precipitate in molecular dynamics and discrete dislocation dynamics simulations in order to fit the two methods together and discuss the variety of the relevant pinning and depinning mechanisms.

Density Functional Theory Study of Kink with P in BCC Iron

The optimal geometries and mechanical properties of a kink with P are studied by applying density functional theory to the ½[111](1¯10) edge dislocation in bcc iron. The calculated impurity segregation energy shows that the P atom can be potentially trapped by the kink, and the doping P preferably segregates to the core region of the ½[111](1¯10) edge dislocation rather than to the &lt;100&gt;(010) edge dislocation. The analysis of the electronic structure indicates that the sideward motion of the kink is impeded owing to strong a interaction between P and neighboring Fe atoms. That is, the P induces a pinning effect on the ½[111](1¯10) edge dislocation. The hybridizations between P and Fe come from P 3p and Fe 3d4s4p. The p and d states have an obvious orientation, which may not be favorable to the toughness of iron. The localized effect of the P-kink complex distinctly affects the electronic structure as well as the energy of the system.

Electronic States and Doping Effect of Carbon in the Kink of BCC Iron

By the use of the first-principles method, based upon density functional theory, we investigated the effect of C upon the electronic structure of a kink on the ½[111](1¯10) edge dislocation in bcc iron. The results show that C has a tendency to segregate towards the kink. The structural energies of some atoms of interest in the kink with C are lower than those of corresponding atoms in the clean kink. Furthermore, the interactions between C and the neighboring Fe atoms are very strong due to the hybridization between the C 2p state and the Fe 3d4s4p states. We find that there exists some charge accumulations between C and the neighboring Fe atoms. The analysis of the electronic structure indicates that the introduction of C can stabilize the kink system and impede the sideways motion of the kink. The C induces a strong pinning effect on the ½[111](1¯10) edge dislocation and may result in solid solute hardening.

Elastic energy of a straight dislocation and contribution from core tractions

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach–Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than those gliding in {112} planes.

Structure and mobility of the [formula omitted] edge dislocation in BCC iron studied by molecular dynamics

In this paper, we carried out atomistic calculations to investigate in detail the core structure and motion mechanism of the 1 2 < 1 1 1 ¯ > { 1 1 2 } edge dislocation in α-iron. First, molecular statics simulations are used to characterise the dislocation-core structure in the framework of the Peierls–Nabarro model. It is shown that the accommodation of the distortion due to the insertion of the extra half-planes is not equivalent in the planes above and below the dislocation slip plane and that the relative atomic-displacement profile in the dislocation-core region is asymmetrical. Then, molecular dynamics simulations are used to study the mechanism of the dislocation motion at different temperatures. At low temperature, the dislocation is found to move by nucleation and propagation of kink-pairs along its line. Independently of temperature, when loading is performed in the twinning direction, the critical stress is found to be lower than the one corresponding to the antitwinning loading direction.

First-Principles Investigation of the Alloying Effect of Mn and Cr in the Kink on the Edge Dislocation in BCC Iron

Using the first-principles self-consistent discrete variational method based on density functional theory, we investigated the energetics and the electronic structure of 3d impurity Mn and Cr in the kink on the [100](010) edge dislocation in bcc iron. The calculations of binding energies show that both Mn and Cr can stabilize the system containing kink. We also calculate the structural energy, the interatomic energy, the local density of states and the charge density difference. The results indicate that both Mn and Cr in the kink can enhance the interatomic interaction between the impurity atom and the neighboring Fe atoms due to the hybridization of impurity d-Fe d orbitals. The introduction of the Mn and Cr impurity leads to a strong pinning effect on the dislocation motion in bcc iron, which may explain the solid solute hardening of Mn and Cr.

Atomistic simulation of kink structure on edge dislocation in bcc iron

Based on the general theory of dislocation and kink, we have constructed the three kink models corresponding to the 1/2 〈111〉{011} and 1/2 〈111〉{112} edge dislocations (EDs) in bcc Fe using the molecular dynamics method. We found that the geometric structure of a kink depends on the type of ED and the structural energies of the atom sites in the dislocation core region, as well as the geometric symmetry of the dislocation core and the characteristic of the stacking sequence of atomic plane along the dislocation line. The formation energies and widths of the kinks on the 1/2 〈111〉{011} and 1/2 〈111〉{112} EDs are calculated, the formation energies are 0.05eV and 0.04eV, and widths are 6.02b and 6.51b, respectively (b is the magnitude of the Burgers vector). The small formation energies indicate that the formation of kink in the edge dislocation is very easy in bcc Fe.

Electronic effect of boron impurity on the kink in bcc iron

Using the first-principles self-consistent discrete variational method based on the density functional theory, we have investigated the effect of B impurity on the kink in the [1 0 0](0 1 0) edge dislocation in bcc iron. Our energetic calculations show that the B has a strong segregation tendency to enter the kink. The structural energy, the interatomic energy, the partial density of states, and the charge density difference are also calculated in the present paper. All the results indicate that B in the kink can enhance the interatomic interaction between the impurity atom and the neighboring Fe atoms due to the hybridization of B 2p–Fe 3d4s4p orbitals. The introduction of B impurity leads to a strong pinning effect on the dislocation motion in bcc iron.

Electronic effect of kink in the edge dislocation in bcc iron: A first-principles study

Using the self-consistent discrete variational method based on density functional theory, we have investigated the electronic effect of kinks in the ⟨100⟩{010} and 1∕2⟨111⟩{011} edge dislocations (EDs) in bcc iron. Our calculations indicate that the kink formation energy is closely related to the type of ED. The EDs containing kinks are less stable than the corresponding EDs without kinks. Furthermore, we have calculated the structural energy, the interatomic energy, the local density of states, and the charge-density difference for these systems. We find that the bonds between the atoms along the slip direction in the kinked EDs are strengthened compared to those in the corresponding EDs. In addition, the calculations of the structural energy and the local density of states show that the atoms on the kink are more active than those in the corresponding ED. These results lead us to conclude that the kinks provide the structural and energetic preparation for the dislocation motion.

Investigation of structure and energy of edge dislocation in bcc iron

Based on the theory of dislocations, we have constructed the four models of the 〈100〉{010}, 〈100〉{011}, 1/2〈111〉{011} and 1/2〈111〉{112} edge dislocations in bcc Fe using the molecular dynamics method, and the formation energy, core energy and core radius of the dislocations have been calculated respectively. The calculated results indicated that the formation energies of 〈100〉{010} and 〈100〉{011} edge dislocations are higher than those of 1/2〈111〉{011} and 1/2〈111〉{112} edge dislocations. This shows that the formation of 1/2〈111〉 edge dislocation is easier than that of 〈100〉 edge dislocation. However, the core radii of 〈100〉{010} and 〈100〉{011} edge dislocations are smaller than those of 1/2〈111〉{011} and 1/2〈111〉{112} edge dislocations. This shows that the atomic numbers locating at the singular region in the 1/2〈111〉 edge dislocation are greater than those in 〈100〉 edge dislocation. Therefore, the motion of 1/2〈111〉 edge dislocation is easier than that of 〈100〉 edge dislocation.

The Interaction Between Point Defects and Edge Dislocation in BCC Iron

We present results of atomistic simulations of the interaction between self interstitial atoms and vacancies with edge dislocations in BCC iron. The calculations are carried out using molecular dynamics with an energy minimization scheme based on the quasi-Newton approach and use the Finnis-Sinclair interatomic potential for BCC iron developed by Ackland et al. Large anisotropy in the strain field of self interstitials is observed and it causes strong interaction with edge dislocations even when the defect is located on the dislocation glide plane. For vacancies, the relaxation volume is smaller and much more isotropic, which results in a far weaker interaction with the dislocation. A temperature dependent capture radius for vacancies and self interstitials is extracted from the simulations. The difference between the capture radii of vacancies and self interstitials is used to define the sink strength of the dislocation. Large deviations are observed from the predictions of elasticity based on treating point defects as isotropic dilatational centers. Further, the capture radius of edge dislocations in BCC iron is observed to be small and is of the order of 1–3 nm for self interstitials.