Cross-slip Process Research Articles

Energetics and stability of screw dislocations in magnesium: A first-principles study

Magnesium (Mg), as the lightest structural metal, suffers from poor ductility and formability. Although in literature, the cross-slips in Mg have been identified as the key factors that are decisive for ductility, there are still many controversies and ambiguities in these cross-slip processes, e.g., energy, stability, etc. In this study, we propose a force correction method to eliminate the surface effects, which thus effectively enhances the efficiency/accuracy of the first-principles DFT calculations of screw dislocations. Based on this method, both a and c+a screw dislocations are calculated with convergence carefully examined. Our results show that a dislocation on the Basal plane has a lower energy than on the Prism plane, by 62 meV/b. The Prism core is energetically unstable since no barrier appears in the Prism-Basal cross-slip path. However, the energy landscape around the Prism core is extremely flat, where the tiny configurational forces could be below the convergence criterion, making the Prism core obtainable in the atomistic simulations. Then for the c+a dislocation, the ground state is revealed to dissociate on the Pyramidal II plane. Since multiple metastable c+a core structures are found on the Pyramidal planes, the energy difference during the c+a cross-slip is thus within a range of 8–19 meV/b. All these findings here provide the basis and guidance for understanding and enhancing the ductility in Mg and Mg alloys.

Atomistically informed dislocation dynamics simulations: application to dislocation-loop interactions in zirconium

Neutron irradiation of zirconium alloys leads to the formation of high densities of small dislocation loops. Their interactions with gliding dislocations are responsible for hardening and early necking of the material. Multi-scale numerical simulations of the interactions between dislocations and loops are undertaken to predict the mechanical properties evolution of these materials due to irradiation. Molecular dynamics simulations are first performed to assess the critical ingredients needed for dislocation dynamics simulations. Appropriate models and associated coefficients are then introduced in dislocation dynamics simulations in order to reliably reproduce the dislocation line energy, the cross-slip process from basal to prismatic planes and the mobility of straight and jogged dislocations. Based on this parametrization, interactions between dislocations and loops are finally computed with the two numerical methods. Careful comparisons between the two types of simulations show qualitative and quantitative agreement, opening the path to investigations of irradiation effects at the grain scale through large scale dislocation dynamics simulations.

Screw dislocation core interaction with C or Nb in [formula omitted]-TiAl: A multiscale study

The solute strengthening caused by the interaction between dislocations and solutes in random solid solution alloys has already been investigated widely provided that the solutes outside the dislocation core interact through nominally elastic interactions. However, the topological variation of dislocation core due to the solute segregation can influence the strengthening of system. We investigate the dislocation core reconstruction with solute C and Nb and their effects on dislocation glide in γ-TiAl by multiscale QM/MM scheme due to the long-range elastic field of a dislocation. The solutes doping in dislocation core region can influence the core energy and eventually cause a violation of Frank’s rule. The contribution analysis of lattice distortion and chemical effect between dislocations and solutes is further investigated. The energy barriers of constriction and transition state in pure γ-TiAl and under solutes environment in the process of external stress reveal electronically the effects of alloying elements and heterogeneous mechanisms on cross-slip process. The carbon diffusion along and across dislocation core by the CI-NEB method are also investigated.

Accurate complex-stacking-fault Gibbs energy in Ni3Al at high temperatures

To gain a deeper insight into the anomalous yield behavior of Ni3Al, it is essential to obtain temperature-dependent formation Gibbs energies of the relevant planar defects. Here, the Gibbs energy of the complex stacking fault (CSF) is evaluated using a recently proposed ab initio framework [Acta Materialia, 255 (2023) 118986], accounting for all thermal contributions—including anharmonicity and paramagnetism—up to the melting point. The CSF energy shows a moderate decrease from 300K to about 1200K, followed by a stronger drop. We demonstrate the necessity to carefully consider the individual thermal excitations. We also propose a way to analyze the origin of the significant anharmonic contribution to the CSF energy through atomic pair distributions at the CSF plane. With the newly available high-temperature CSF data, an increasing contribution to the energy barrier for the cross-slip process in Ni3Al with increasing temperature is unveiled, necessitating the refinement of existing analytical models.

Irradiation hardening behavior of high entropy alloys using random field theory informed discrete dislocation dynamics simulation

High entropy alloys (HEAs) exhibit outstanding radiation resistance over traditional alloys owing to severe lattice distortion, and therefore, would be regarded as candidate materials for advanced reactors. However, the complex evolution of dislocation configurations in the irradiated HEAs subjected to the external loads has not been uncovered at the micron scale. To elucidate this key mechanism, we develop the random field theory informed discrete dislocation dynamics simulations based on high-resolution transmission electron microscopy, to systematically clarify the role of heterogeneous lattice strain on the complex interactions between the dislocation loop and dislocation in three-dimensional (3D) space. The results show that the lattice-strain-induced irradiation hardening decreases, in agreement with the excellent irradiation hardening resistance of the HEAs from the recent experiment. Based on the analysis of the micrometer-scale dislocation multiplication process, a new cross-slip mechanism through the collinear reaction between dislocations and rhombus perfect loops is revealed. The peaks and valleys of the heterogeneous lattice strains induced by severe lattice distortion are randomly distributed in a 3D space, reducing an aggregation of lattice point and dislocation density at the local region. The cross-slip process occurs by the joint action of the lattice distortion and rhombus-perfect-loop dislocation reaction, leading to the strong irradiation resistance attributed to a large number of narrow defect-free channel under a relatively random strain localization. The present study gives an insight into the fundamental irradiation damage behavior at the mesoscopic scale, thereby guiding the development of advanced HEA materials through the regulation of heterogeneous lattice strain for nuclear energy applications.

A low-temperature prismatic slip instability in Mg understood using machine learning potentials

Prismatic slip in magnesium at temperatures T≲150 K occurs at ∼ 100 MPa independent of temperature, and jerky flow due to large prismatic dislocation glide distances is observed; this athermal regime is not understood. In contrast, the behavior at T≳150 K is understood to be governed by a thermally-activated double-cross-slip of the stable basal screw dislocation through an unstable or weakly metastable prism screw configuration and back to the basal screw. Here, a range of neural network potentials (NNPs) that are very similar for many properties of Mg including the basal-prism-basal cross-slip path and process, are shown to have an instability in prism slip at a potential-dependent critical stress. One NNP, NNP-77, has a critical instability stress in good agreement with experiments and also has basal-prism-basal transition path energies in very good agreement with DFT results, making it an excellent potential for understanding Mg prism slip. Full 3d simulations of the expansion of a prismatic loop using NNP-77 then also show a transition from cross-slip onto the basal plane at low stresses to prismatic loop expansion with no cross-slip at higher stresses, consistent with in-situ TEM observations. These results reveal (i) the origin and prediction of the observed unstable low-T prismatic slip in Mg and (ii) the critical use of machine-learning potentials to guide discovery and understanding of new important metallurgical behavior.

Orientation dependent plastic localization in the refractory high entropy alloy HfNbTaTiZr at room temperature

A statistical and quantitative perspective on the incipient slip localization behavior of the HfNbTaTiZr refractory high entropy alloy is presented, after monotonic tensile testing at room temperature. High-resolution digital image correlation (HR-DIC) data collected in the scanning electron microscope (SEM) is coupled with electron back-scattered diffraction (EBSD) over millimeter-scale fields of view containing over a hundred crystal orientations. Two populations of grains are identified with respect to their slip localization: a vast majority of the grains exhibit a high density of apparently straight slip bands of low intensity, while the remaining grains show few but very intense and wavy slip bands at the mesoscopic scale. The slip localization behavior is strongly correlated to the crystal orientation with respect to the loading direction. This behavior is discussed with regard to dislocation glide and cross-slip processes.

Elastic behaviour and radiation tolerance in Nb-based 211 MAX phases

MAX phase carbides are a set of materials that have attracted the research and industrial interest due to their unique combination of metallic and ceramic properties. In recent experimental studies it was determined that Nb-based MAX phases have good mechanical and thermal properties. In the present systematic density functional theory study we examine the elastic behaviour and radiation tolerance of a range of Nb2AC (A = Al, Ga, Ge, In, Sn, As, P, and S) MAX phases. It is found that the Nb-based 211 MAX phases studied here are mechanically stable and elastically anisotropic. Elastically, Nb2GeC possesses the highest level of anisotropy and Nb2InC, the lowest. The cross-slip pinning process is enhanced in Nb2GeC that is considerably reduced in Nb2InC. Nb2GeC, Nb2SnC, and Nb2SC are ductile, whereas the other Nb-based MAX phases considered here are brittle in nature. In particular, Nb2GeC is highly ductile and Nb2AlC is more brittle. Nb2PC and Nb2SnC are respectively, more stiff and flexible under tension or compression. Nb2SnC has the best thermal shock resistance among the Nb-based MAX phase carbides studied here. Regarding the radiation tolerance of these MAX phases it is anticipated that Nb2SnC will be the most resistant to radiation.

First-Principles Calculations of Oxygen-Dislocation Interaction in Magnesium.

The interaction between interstitial oxygen atoms and <a>-type screw dislocations was investigated via first-principles calculations to elucidate the effect of oxygen solutes on the deformation behaviors of Mg. The results show that repulsive interactions exist between basal screw dislocation cores and oxygen atoms, which would enable the full basal dislocation to bypass the oxygen atoms in the dislocation glide plane through the cross-slip process. This repulsion also increases the resistance to the motion of dissociated basal dislocations. Moreover, the energy of prismatic <a>-type screw dislocation cores is reduced by the presence of oxygen, which would stabilize the screw dislocation core on the prismatic plane, accordingly facilitating the prismatic slip. This information can complement the fundamental knowledge of alloying Mg using interstitial solutes.

Analysis of double cross-slip of pyramidal I [formula omitted] screw dislocations and implications for ductility in Mg alloys

Solute accelerated cross-slip of pyramidal 〈c+a〉 screw dislocations has recently been recognized as a crucial mechanism in enhancing the ductility of solid-solution Mg alloys. In pure Mg, cross-slip is ineffective owing to the energy difference between the high energy pyramidal I and low energy pyramidal II 〈c+a〉 screw dislocations. A small addition of solutes, especially rare earth (RE) elements, can reduce this energy difference and accelerate cross-slip, thus enabling enhanced ductility. With increasing solute concentrations, the pyramidal I dislocation can become energetically favorable, which switches the primary 〈c+a〉 slip plane and alters the cross-slip process. Here, the transition path and energetics for double cross-slip of pyramidal I 〈c+a〉 dislocations are analysed in the regime where the pyramidal I dislocation is energetically more favorable than the pyramidal II. This is achieved using nudged elastic band simulations on a proxy MEAM potential for Mg designed to favor the pyramidal I over pyramidal II. The minimum energy transition path for pyramidal I double cross-slip is found to initiate with cross-slip onto a pyramidal II plane followed by cross-slip onto a pyramidal I plane parallel to the original pyramidal I plane. A previous mechanistic model for ductility is then extended to higher solute concentrations where pyramidal I is favorable. The model predicts an upper limit of solute concentrations beyond which ductility again becomes poor in Mg alloys. The model predictions are consistent with limited experiments of Mg-RE alloys at high concentrations and motivate further experimental studies in the high concentration regime.

First-Principles Calculations of Structural, Mechanical, and Electronic Properties of the B2-Phase NiTi Shape-Memory Alloy Under High Pressure

A first-principles calculation program is used for investigating the structural, mechanical, and electronic properties of the cubic NiTi shape-memory alloy (SMA) with the B2 phase under high pressure. Physical parameters including dimensionless ratio, elastic constants, Young’s modulus, bulk modulus, shear modulus, ductile-brittle transition, elastic anisotropy, and Poisson’s ratio are computed under different pressures. Results indicate that high pressure enhances the ability to resist volume deformation along with the ductility and metallic bonds, but the biggest resistances to elastic and shear deformation occur at P = 35 GPa for the B2-phase NiTi SMA. Meanwhile, the strong anisotropy produced by the high pressure will motivate the cross-slip process of screw dislocations, thereby improving the plasticity of the B2-phase NiTi SMA. Additionally, the results of the density of states (DOS) reveal that the B2-phase NiTi SMA is essentially characterized by the metallicity, and it is hard to induce the structural phase transition for the B2-phase NiTi SMA under high pressure, which provides valuable guidance for designing and applying the NiTi SMA under high pressure.

Statistics and Mechanisms of Intermittent Plasticity in FCC and BCC Microcrystals

Plastic deformation in crystalline materials consists of an ensemble of collective dislocation glide processes, which lead to strain burst emissions in micro-scale samples. To unravel the combined role of crystalline structure, sample size and temperature on these processes, we performed a comprehensive set of strict displacement-controlled micropillar compression experiments in conjunction with large-scale molecular dynamics and physics-based discrete dislocation dynamics simulations. The results indicate that plastic strain bursts consist of numerous individual dislocation glide events, which span over minuscule time intervals. The size distributions of these events follow a power-law function which bifurcates from an incipient slip regime of uncorrelated glide (spanning ≈ 2.5 decades of slip sizes) to a large avalanche domain of collective glide (spanning ≈ 4 decades of emission probability) at a critical slip magnitude sc. This critical slip size characterizes the transition between bulk-like and localized plasticity. In face-centered cubic (FCC) metals, sc is essentially governed by the interplay between dislocation annihilation, cross-slip and junction formation processes developing as a function of microcrystal size and stacking fault width in Al, Ni and Cu. Dislocation starvation then rules the avalanche statistics in smaller microcrystals. In body-centered cubic (BCC) metals, sc evaluates the combined role of temperature and the applied stress level upon the glide of the sluggish screw dislocations via cross-kinking mechanisms. Different sc values result in BCC Ta and W due to the distinctive thermal and stress-dependent activation of cross-kinking. These FCC and BCC dislocation glide mechanisms determine the evolution from self-organized to stress-tuned avalanching processes.

Cross-slip in face centred cubic metals: a general full stress-field dependent activation energy line-tension model

ABSTRACT Cross-slip is a thermally activated process by which a screw dislocation changes its slip plane. Understanding and modelling the activation barrier of the cross-slip process as a free-energy barrier that depends on the stress conditions at the vicinity of the dislocation is crucial. In this work, we employ the line-tension model for the cross-slip of screw dislocations in face-centred cubic (FCC) metals in order to calculate the energy barrier when both Escaig stresses are applied on the primary and cross-slip planes and Schmid stress is applied on the cross-slip plane. We propose a closed-form expression for the activation energy for cross-slip in a large range of stresses, without any fitting parameters. The results of the proposed model are in good agreement with previous numerical results and atomistic simulations. We also show that, when Schmid stress is applied on the cross-slip plane, the energy barrier is decreased, and in particular, cross-slip can occur even when the Escaig stress in the primary plane is smaller than that on the cross-slip plane. The proposed closed-form expression for the activation energy can be easily implemented in dislocation dynamics simulations, owing to its simplicity and universality. This will allow cross-slip to be more accurately related to macroscopic plasticity.

Atomistic modeling of dislocation cross-slip in nickel using free-end nudged elastic band method

Cross-slip of screw dislocations plays an important role in the plastic deformation of face-centered cubic (FCC) metals and alloys. Here we use the free-end nudged elastic band (FENEB) method to determine the atomistic reaction pathways and energy barriers of cross-slip in an FCC single crystal of Ni. We focus on the cross-slip process mediated by an array of pinning vacancy clusters in the form of stacking fault tetrahedra. We also study a competing process of screw glide by direct cutting of those pinning obstacles on the original slip plane. The activation energies of both cross-slip and obstacle-cutting are determined for different stresses, obstacle spacings and sizes. Using FENEB-calculated energy barriers, we construct dislocation mechanism maps to reveal the effects of resolved shear stress, obstacle spacing and size on the rate-controlling dislocation process for plastic deformation. We further evaluate the activation volumes of cross-slip and obstacle-cutting. The latter result emphasizes the notion of finite strength of the atomically sized pinning obstacles to dislocation motion and also validates the Nabarro scaling law of the linear dependence of activation volume on obstacle spacing.

Dislocation dynamics in aluminum containing θ’ phase: Atomistic simulation and continuum modeling

We investigate the interaction of edge dislocation with θ′ phase in aluminum matrix using atomistic simulations. The thickness of θ′ phase is chosen to be constant of 2.2 nm and the diameter is varied in range from 3 to 10 nm. It is shown that first interactions of dislocation with θ′ phase occur according to the mechanism of Orowan loop formation around the obstacle. In this case, the cross-slip processes, the formation of dislocation jogs in adjacent slip plane and the emission of vacancies upon the return of a segment to the initial slip plane are possible. During these interactions, the material of θ′ phase is subjected to high shear stresses up to 3 GPa in a layer of 2 nm thickness. Such a high stress leads to a θ′ phase cutting on the third or fourth overcoming of the obstacle by dislocation. A study is carried out of the dependence of the average stress in the system on the size of inclusion and the distance between inclusions. It is shown that an increase in the diameter of inclusion causes an increase in the average stresses in the system in proportion close to the square root of the diameter of the inclusion. Increasing the distance between inclusions causes the inversely proportional reduction of the average stress. The conducted investigation of the strain rate sensitivity showed that in the case of high shear rates, the average stresses in the system continuously increase that does not allow applying the time averaging procedure to them. The described effect is also registered in the case of pure aluminum. The existence of two regions on the temperature dependence of the average stresses in the system on the strain rate in the case of θ′ phase, previously described by Yanilkin et al. (2014) for the Guinier-Prestone zones, is confirmed. In the case of high strain rates, heating of the system leads to a decrease in the dislocation velocity, while at low strain rates the dislocation velocity increases with increasing temperature at a fixed shear rate. An interesting result obtained with long-term molecular-dynamics simulations when the tracing time is up to 2 ns, there is a tendency to reduce the average stress in the system through time. This result can be explained by destruction of the structure and form of θ’ phase.The law of motion of a dislocation in the approximation of the constancy of θ′ phase properties is proposed to describe the response of the system to shear deformation. The model contains a dislocation mass, phonon friction, and takes into account the effect of the inclusion of θ’ phase through an increase in the elastic energy of a dislocation during the formation of the Orowan loop around an obstacle.

Large-scale dislocation dynamics simulations of strain hardening of Ni microcrystals under tensile loading

The strain hardening in FCC Ni was studied along low index directions using 3-dimensional discrete dislocation dynamics. Large (20 × 20 × 50 μm) Ni microcrystals were simulated using rectangular parallelepiped-cells loaded in tension along four low-index directions ([111], [001], [110] and [112]) to shear strains of ∼0.01–0.02. Loading was at a constant strain rate of 10/sec, and all surfaces of the cell are treated as free surfaces. The FCC dislocation mobility routines were modified to include thermally activated cross-slip processes, as a function of three different stress components, using the results of previous atomistic simulations. These include bulk cross slip (cross-slip at atomic jogs), intersection cross slip (attractive and repulsive) as well as surface cross slip. One of these, repulsive intersection cross-slip, has zero activation energy and is present at all simulated deformation temperatures. The simulations were performed for three different temperatures, 5, 150 and 300 K. The strain-hardening rate is independent of temperature and of the order of μ/200 – μ/400, in agreement with experimental data for the <111> and <001> orientations of deformation. For the [001] orientation, at 5 and 150 K, the strain hardening rate decreases considerably when repulsive intersection cross-slip is removed from the simulations. The [110] and [112] orientations exhibit single-slip glide and a very low strain-hardening rate (∼μ/3000). Heterogeneity of dislocation microstructure develops spontaneously at the higher temperatures as a result of increased cross slip. Even though the strain-hardening rate is independent of temperature, the increase in dislocation density with shear strain is larger at higher temperatures. It is proposed that higher temperatures deformation produces larger dislocation-microstructure heterogeneities, providing for higher average dislocation densities and regions of low density where deformation can proceed. Also, the strain hardening rate at 300 K is controlled by the rate of increase of forest dislocation density in these lean regions.

Dislocation slip transmission through a coherent Σ3{111} copper twin boundary: Strain rate sensitivity, activation volume and strength distribution function

We present the first measurement of the strain rate sensitivity of the ideal dislocation slip transmission through a coherent Σ3{111} copper twin boundary. For this purpose we have deformed 129 geometrically identical samples at different strain rates. The micron-sized samples are either single crystalline (87 pillars) or contain one vertical Σ3{111} twin boundary (42 pillars). The strain rate sensitivity of the ideal slip transmission event is 0.015 ± 0.009. This value is considerably lower than the strain rate sensitivity observed for nano-twinned bulk materials, which is addressed to multiple simultaneously activated deformation processes present in the latter case. The activation volume of the ideal slip transmission points towards a cross-slip like transmission process of dislocations through the twin boundary. Furthermore, the high number of geometrically identical samples is used to discuss the ability to identify the strength distribution function of micropillars.

Competition between two Fleischer modes of cross slip in silver

Two Fleischer cross slip modes of a dissociated screw dislocation 〈1 1 0〉/2 are quantitatively investigated in silver by molecular dynamics simulations. It is shown that contrary to previous studies where the acute angle mode is always preferred, the obtuse angle mode is also obtained. Our theoretical analysis demonstrates that the transition of the preferred mode in simulations arises from the dissociation width between the conjugate partials on the primary plane. This implies that all the interactions of dislocations have to be considered to describe the process of cross slip.

Screw dislocation mediated solution strengthening of substitutional α-Ti alloys - First principles investigation

The mechanical properties of hexagonal Ti alloys depend substantially on the glide of <a> type screw dislocations. The configurations and stabilities of these line defects are, however, known only in pure Ti and Ti + O solutions, where the locking-unlocking mechanism and a strong pinning effect control their activity. In this study, we investigated the unclear, screw dislocation mediated solution strengthening of substitutional α-Ti alloys. To this end, a first principle computational scheme was used to determine the structures and energies of the considered line defects during planar and cross-slip processes in the vicinity of the solute element. Two phenomena were determined that are crucial in terms of plastic deformation: (i) enhanced polymorphism of the dislocation cores leading to multiple new core configurations, and (ii) relatively large positive and negative interaction energies between the solutes and the line defects. Both these effects are strongly affected by the valence configuration of the alloying elements. Due to their pronounced structure and energy variations, dislocation planar and cross slip processes can occur under different scenarios, through diverse non-planar core geometries. Accordingly, an improvement in material strength is related to the overall energy amplitude of the dislocation states that can occur in the neighbourhood of the alloying element, which agrees well with experimental data. The calculations performed also indicate In as a potential alloy element for improving both the strength and ductility of Ti by stabilizing a special, compact core geometry able to spread on an arbitrary glide plane with a low energy barrier. All of the above effects are discussed in terms of the physical factors (solute size misfit, stacking fault energy and electronic structure) that affect the energy and geometry of dislocation cores.

Kinetics of dislocation cross-slip: A molecular dynamics study

The kinetics of cross-slip and annihilation of a screw dislocation dipole in face-centered cubic (FCC) copper crystals were studied by multiple molecular-dynamics simulations of long (200b) dislocations at selected stresses and temperatures with the aim to account for the thermally activated nature of the cross-slip process. A novel cross-slip mechanism was identified; this mechanism required the formation of a finite length constriction before cross-slip could be initiated. It was shown that point constrictions are not the transition state of cross-slip. A study of the kinetics confirmed that cross-slip is a first-order process. By fitting the rate constant to an Arrhenius form, the activation energy was found to be 1.05eV±15%. The activation volume for the Escaig stress in the glide plane was in the range of 5–40b3, and the prefactor for the rate constant was evaluated to be 1THz/b.