Screw Dislocation In Ta Research Articles

A fully discrete Peierls model for the screw dislocation in Ta

ABSTRACT The discrete Peierls model is generalised to be able to study the nonplanar dislocations as well as the planar dislocations. In the discrete model, the six-fold screw dislocation that is widely studied in numerical simulation and analytical theory splits into two different cores: the six-fold B core and the six-fold O core. The six-fold B core has the lowest energy and is the most stable while the six-fold O core has about 38 meV more energy in a period length. Because local dislocation hopping can only occur along the folds and hopping to sites out of the folds is not allowed, the dislocation movement is realised by transforming itself into a planar one in the model. The Peierls stress associated with this transition tunnel is , which is much higher than that obtained in simulations. Limitations of the model can be removed by using the two-dimensional energy landscape that is a natural consequence of the concept of the nonplanar dislocation. In the leading terms approximation of the two dimensional energy landscape, the non-Schmid behaviour of the screw dislocation in Ta is quantitatively predicted based on the model.

Nonplanar core structure of the screw dislocations in tantalum from the improved Peierls–Nabarro theory

The extended structure of screw dislocation in Ta has been studied theoretically using the improved Peierls–Nabarro model combined with the first principles calculation. An instructive way to derive the fundamental equation for dislocations with the nonplanar structure is presented. The full -surface of plane in tantalum is evaluated from the first principles. In order to compare the energy of the screw dislocation with different structures, the structure parameter is introduced to describe the core configuration. Each kind of screw dislocation is described by an overall-shape component and a core component. Far from the dislocation centre, the asymptotic behaviour of dislocation is uniquely controlled by the overall-shape component. Near the dislocation centre, the structure detail is described by the core component. The dislocation energy is explicitly plotted as a function of the core parameter for the nonplanar dislocation as well as for the planar dislocation. It is found that in the physical regime of the core parameter, the sixfold nonplanar structure always has the lowest energy. Our result clearly confirms that the sixfold nonplanar structure is the most stable. Furthermore, the pressure effect on the dislocation structure is explored up to 100 GPa. The stability of the sixfold nonplanar structure is not changed by the applied pressure. The equilibrium structure and the related stress field are calculated, and a possible mechanism of the dislocation movement is discussed briefly based on the structure deformation caused by the external stress.

Structure of screw dislocation core in Ta at high pressure

The core structure and Peierls stress of the 12⟨111⟩{110} screw dislocation in Ta have been investigated theoretically using the modified Peierls–Nabarro theory that takes into account the discreteness effect of crystal. The lattice constants, the elastic properties, and the generalized-stacking-fault energy(γ-surface) under the different pressures have been calculated from the electron density functional theory. The core structure of dislocation is determined by the modified Peierls equation, and the Peierls stress is evaluated from the dislocation energy that varies periodically as dislocation moves. The results show the core width and Peierls stress in Ta are weakly dependent of the pressure up to 100 GPa when the length and stress are measured separately by the Burgers vector b and shear modulus μ. This indicates that core structure is approximately scaling invariant for the screw dislocation in Ta. The scaled plasticity of Ta changes little in high pressure environment.

Modeling of Dislocation Interaction with Solutes, Nano-Precipitates and Interfaces: A Multiscale Challenge

We review here several multiscale methods that we have developed to determine dislocation properties and interactions in metals. The review includes: (1) dislocation core properties in fcc and bcc metals; (2) the effect of solutes or nanoprecipitates on the mobility of a screw dislocation in bcc metals; (3) the interaction between dislocations and precipitates in intermetallic compounds; and (4) the transmission of dislocations through coherent and incoherent interfaces. In the concurrent quantum mechanical (QM) and molecular mechanical (MM) coupling approach, the quantum mechanical treatment is spatially confined to a small region, surrounded by a larger classical atomistic region. This approach is particularly useful for systems where quantum mechanical interactions in a small region, such as lattice defects or chemical impurities, can affect the macroscopic properties of a material. We discuss how the coupling across the different scales can be accomplished efficiently and accurately. We have applied this method to study the core structure and mobility of an edge dislocation in Al and of a screw dislocation in Ta, which are prototypical fcc and bcc metals. We find that the local environment of W solutes in Ta has a dramatic effect both on the dislocation mobility and slip paths. Isolated W solutes enhance the dislocation mobility, W nanoclusters of triangular shape pin the dislocation, while those of hexagonal shape result in spontaneous dislocation glide. The first sequential multiscale approach is a hybrid ab initio-based approach of Suzuki’s atomic-row (AR) model, which allows the study of the dislocation core of a screw dislocation in bcc metals. The second hybrid approach, based on an extension of the Peierls-Nabarro model to study the dislocation-interface and the dislocation-precipitate interactions, integrates the atomistic nature from ab initio calculations of the generalized stacking fault energy surface (GSFS) into the parametric dislocation dynamics method. The ab initio-based calculations reveal that Cu nano-clusters in -Fe dramatically alter the core structure of a screw dislocation from non-polarized in pure Fe to polarized, in agreement with experiments. In contrast, Cr clusters do not change the core polarization and increase the Peierls stress, thus hardening Fe. The hybrid method with four different interaction models was applied to study the interaction of a superdislocation with a spherical -precipitate embedded in the � -matrix of a nickel-based superalloy. The dislocation core structure was found to play an important role in determining the critical resolved shear stress. Based on these simulations, analytical equations for the precipitate strengthening are derived. For the Cu/Ni interface, the dislocation is found to dissociate into partials in both Cu and Ni, and the dislocation core is squeezed near the interface facilitating the spreading process, and leaving an interfacial ledge. It is shown that the strength of the bimaterial can be greatly enhanced by the spreading of the glide dislocation, and also increased by the pre-existence of misfit dislocations.

The Peierls stress of the moving screw dislocation in Ta**This work was supported by the National Natural Science Foundation of China (10774196),the Science Foundation Project of CQ CSTC (2006BB4156) and Chongqing UniversityPostgraduates’ Science and Innovation Fund (200707A1A0030240).

The Peierls stress of the moving screw dislocation with a planar and non-dissociated core structure in Ta has beencalculated. The elastic strain energy which is associated with the discrete effect of thelattice and ignored in classical Peierls–Nabarro (P–N) theory has been taken into accountin calculating the Peierls stress, and it can make the Peierls stress become smaller. ThePeierls stress we obtain is very close to the experimental data. As shown in the numericalcalculations and atomistic simulations, the core structure of the screw dislocationundergoes significant changes under the explicit stress before the screw dislocation moves.Moreover, the mechanism of the screw dislocation is revealed by our results and theexperimental data that the screw dislocation retracts its extension in three {110}planes and transforms its dissociated core structure into a planar configuration.Therefore, the core structure of the moving screw dislocation in Ta is proposed to be planar.

Kinks in the a/2 screw dislocation in Ta

We study the structure and formation energy of kinks in the 1/2a〈111〉 screw dislocations in metallic Tantalum (Ta) using molecular dynamics with a first principles based many-body interatomic potential. In our study, four a/3〈112〉 kinks are constructed in a quadrupole arrangement in the simulation cell. To the simulation cell, we impose periodic boundary conditions in the directions perpendicular to the [111] direction and fix boundary condition in the [111] direction. We find that two, energetically equivalent, core configurations for the 1/2a〈111〈 dislocation lead to 8 distinguishable single kinks and 16 kinds of kink pairs. The different mismatches of the core configurations along [111] direction attributed to the differences in the formation energy for various types of kinks. Formation energies for all possible kinds of isolated single kinks and kink pairs have been determined. It was found that 0.730 eV was the lowest energy cost to form a kink pair in the a/2〈111〉: screw dislocation in Ta.

Multiscale Modeling of Dislocation Processes in Bcc Tantalum: Bridging Atomistic and Mesoscale Simulations

AbstractPlastic deformation in bcc metals at low temperatures and high-strain rates is controlled by the motion of a/2<111> screw dislocations, and understanding the fundamental atomistic processes of this motion is essential to develop predictive multiscale models of crystal plasticity. The multiscale modeling approach presented here for bcc Ta is based on information passing, where results of simulations at the atomic scale are used in simulations of plastic deformation at mesoscopic length scales via dislocation dynamics (DD). The relevant core properties of a/2<111> screw dislocations in Ta have been obtained using quantum-based interatomic potentials derived from model generalized pseudopotential theory and an ab-initio data base together with an accurate Green's-function simulation method that implements flexible boundary conditions. In particular, the stress-dependent activation enthalpy for the lowest-energy kink-pair mechanism has been calculated and fitted to a revealing analytic form. This is the critical quantity determining dislocation mobility in the DD simulations, and the present activation enthalpy is found to be in good agreement with the previous empirical form used to explain the temperature dependence of the yield stress.

Multiscale Modeling of Dislocation Processes in Bcc Tantalum: Bridging Atomistic and Mesoscale Simulations

Plastic deformation in bcc metals at low temperatures and high-strain rates is controlled by the motion of a/2 screw dislocations, and understanding the fundamental atomistic processes of this motion is essential to develop predictive multiscale models of crystal plasticity. The multiscale modeling approach presented here for bcc Ta is based on information passing, where results of simulations at the atomic scale are used in simulations of plastic deformation at mesoscopic length scales via dislocation dynamics (DD). The relevant core properties of a/2 screw dislocations in Ta have been obtained using quantum-based interatomic potentials derived from model generalized pseudopotential theory and an ab-initio data base together with an accurate Green's-function simulation method that implements flexible boundary conditions. In particular, the stress-dependent activation enthalpy for the lowest-energy kink-pair mechanism has been calculated and fitted to a revealing analytic form. This is the critical quantity determining dislocation mobility in the DD simulations, and the present activation enthalpy is found to be in good agreement with the previous empirical form used to explain the temperature dependence of the yield stress.

Atomistic Simulations for Multiscale Modeling in bcc Metals

Quantum-based atomistic simulations are being used to study fundamental deformation and defect properties relevant to the multiscale modeling of plasticity in bcc metals at both ambient and extreme conditions. Ab initio electronic-structure calculations on the elastic and ideal-strength properties of Ta and Mo help constrain and validate many-body interatomic potentials used to study grain boundaries and dislocations. The predicted Σ5 (310) [100] grain boundary structure for Mo has recently been confirmed in HREM measurements. The core structure, γ surfaces, Peierls stress, and kink-pair formation energies associated with the motion of a/2〈111〉 screw dislocations in Ta and Mo have also been calculated. Dislocation mobility and dislocation junction formation and breaking are currently under investigation.

Anelastic study of screw-dislocation motion in high-purity tantalum

The kink pair formation (KPF) process on screw dislocations in Ta was investigated by means of the anelastic creep (AEC) measurements near room temperature. The effect of σ eff on H KPF and that on ν 0 were investigated for σ eff below 16 MPa, where σ eff denotes the effective stress applied to screw dislocations responsible for the AEC through KPF, H KPF the activation enthalpy of the KPF process, and ν 0 the pre-exponential factor of the inverse of the relaxation time of the KPF process. The extrapolation of the observed σ eff dependence gives 2 H k = 0.97 ± 0.03 eV and In[ ν 0,0(s −1)] = 29.6 ± 1, where H k denotes the enthalpy of an isolated single kink and ν 0.0 is ν 0 at σ eff = 0. Both H KPF and ν 0 show a strong decrease with increasing σ eff. These features for H KPF and ν 0 are very similar to those reported for Nb and Fe after the AEC measurements. We surmise that a change in the core structure of screw dislocation plays an important role for the rate of KPF on screw dislocations in the b.c.c. metals. The AEC results are discussed together with the strong decrease in H KPF with increasing σ eff reported for Fe, Nb and Ta after the flow stress measurements.

Mechanisms of inelastic deformation in metallic glasses

The kink pair formation (KPF) process on screw dislocations in Ta was investigated by means of the anelastic creep (AEC) measurements near room temperature. The effect of σeff on HKPF and that on ν0 were investigated for σeff below 16 MPa, where σeff denotes the effective stress applied to screw dislocations responsible for the AEC through KPF, HKPF the activation enthalpy of the KPF process, and ν0 the pre-exponential factor of the inverse of the relaxation time of the KPF process. The extrapolation of the observed σeff dependence gives 2Hk = 0.97 ± 0.03 eV and In[ν0,0(s−1)] = 29.6 ± 1, where Hk denotes the enthalpy of an isolated single kink and ν0.0 is ν0 at σeff = 0. Both HKPF and ν0 show a strong decrease with increasing σeff. These features for HKPF and ν0 are very similar to those reported for Nb and Fe after the AEC measurements. We surmise that a change in the core structure of screw dislocation plays an important role for the rate of KPF on screw dislocations in the b.c.c. metals. The AEC results are discussed together with the strong decrease in HKPF with increasing σeff reported for Fe, Nb and Ta after the flow stress measurements.