Activation Of Dislocation Sources Research Articles

Optimizing misfit dislocation glide kinetics for enhanced threading dislocation density reduction in Si1−xGex/Si(001) layers through dynamic growth rate control

Relaxed Si1−xGex layers on Si(001) serve as virtual substrates for strained Si or Ge layers. However, plastically relaxed layers inevitably contain misfit and threading dislocations, negatively affecting devices. Deposition of a SiGe layer on the backside of the substrate introduces a dislocation reservoir at the wafer edge that can reduce the threading dislocation density (TDD) of Si0.98Ge0.02/Si layers, as these preexisting dislocations start gliding toward the wafer center upon reaching the critical thickness. Here, we show that this low-strain system can be used effectively to study dislocation glide kinetics. In agreement with the literature, dislocation glide is a thermally activated process with an activation energy of 2.12–2.16 eV. Near the critical thickness, relaxation is sluggish and inefficient due to the linear dependence of the glide velocity on excess stress. At lower growth rates, dislocations from the edge reservoir are activated in a lower density due to the increase in the critical thickness through partial strain relaxation by already activated dislocations. Contrary to common models, here, the lowest possible growth rate is not essential for minimizing the TDD. Instead, a careful balance between low and high growth rates is beneficial. Overcoming the initial sluggish and inefficient relaxation phase is critical while also avoiding accumulation of strain energy, and, therefore, the activation of dislocation sources. Only in a later stage of buffer growth, the growth rate should be reduced to a minimum. With this method, the TDD of strain relaxed Si0.84Ge0.16 layers is reduced to 7 × 104 cm−2.

Calculating the grain size effect during strain hardening through a probabilistic analysis of the mean slip distance in polycrystals

Grain refinement is an important mechanism to produce stronger alloys. Strain hardening is an essential phenomenon in metal forming processes. The interaction between grain size and strain hardening is evident: a decrease in grain size (dg)causes an increase in ultimate tensile strength but a decrease in uniform elongation. The Kocks-Mecking (KM) model for strain hardening is based on the relationship between shear strain and the path length for dislocation slip. It provides good general estimates for stress-strain curves, and empirical modifications have been made to include dg. Here, the empirical approach is substituted by theoretical probability calculations, accounting for the fact that the grain size imposes a bound on the mean slip distance, while strain compatibility defines a relationship between grain boundary-dislocation interaction and bulk storage and annihilation. The resulting differential only uses the two parameters inherent to KM. Fitting to published tensile curves for Al, Cu, and Ni produces excellent results. The fitting parameters allow to predict the tensile strength as a function of dgto good approximation, for dg>1μm. Below this limit, fundamental changes in dislocation statistics impose the activation of grain boundary dislocation sources and may induce dislocation density gradients, which seem to determine the flow stress in the sub-μm range.

High friction stress and weak grain-refinement strengthening effect induced by severe lattice distortion in ZrTiNb medium entropy alloys

In this work, we have studied the grain-refinement strengthening effect of body-centered cubic Zr50Ti35Nb15 medium entropy alloy. The results suggest that the yield strength increases as grain size decreases from 530 μm to 0.51 μm, reaching the maximum value of 651 MPa, and still having decent ductility. Moreover, it is found that the alloys exhibit a high Hall–Petch intercept of 564 MPa and a low Hall–Petch slope, which means strong lattice friction stress and weak grain-refinement strengthening. The high lattice friction stress originates from the obstruction of dislocation motion caused by atomic size and modulus misfit. Dislocation interaction and multiplication in grain interior is difficult due to the high dislocation slip resistance, leading to a weak dislocation pile-up capability at grain boundary. Instead, dislocations nucleation and emission become the dominant deformation process since low shear modulus promotes dislocation source activation.

On the slip burst amplitude cutoff in dislocation-rich microcrystals

The plastic deformation of small-scale face-centered cubic metals exhibits intermittent slip burst events that appear on stress-strain curves as sudden strain jumps and/or load drops. These events are generally attributed to the avalanche-like cooperative motion of several dislocations, or to the repeated activation of single-arm dislocation sources. We explore the influence of the load train compliance on the amplitude of such slip bursts by testing in tension microcast monocrystalline silver specimens 3.4 µm in diameter under two different load-train compliance conditions. Resulting data show that the statistics of slip burst amplitudes in the higher-amplitude, cutoff, regime depend on the compliance of the total testing load train, whereas the stress drop distributions do not. We propose a mechanism and derive an expression for the slip burst cutoff by assuming that higher-intensity slip bursts are driven by the stochastic activation of dislocation sources induced by forest dislocation motion. The resulting expression accounts for the influence of the load train compliance on the statistics of larger-amplitude slip bursts, resembles the expression for the slip amplitude cutoff that was proposed by Zaiser and Nikitas, and agrees with observed cutoff amplitude data from this and earlier studies on microcast FCC single crystals tested in tension.

Atomistic simulations of dislocation activity in Si nanofibers in Al-Si eutectics

Atomistic simulations were used to elucidate the mechanisms of localized plasticity and fracture in Si nanofibers embedded in Al matrix, with uniaxial tensile straining along the fiber axis. The Si nanofibers within the Al matrix exhibited large non-linear elastic strains followed by localized plasticity with the latter accounting for approximately 5 % permanent length increase in the fibers. On the other hand, simulations with aligned Si nanofibers in vacuum (no Al matrix) exhibited elastic deformation only followed by cleavage fracture. Localized plasticity in Si nanofibers is accomplished by gliding of “zonal” partial dislocations with Burgers vector b=aSi3〈112〉, which leads to synchronous shear of two shuffle-sets. Local stress concentration in Si nanofibers due to non-screw segments of dislocation loops around fibers triggers yielding in the nanofibers through the activation of dislocation sources at or near the interfaces but only below some critical fiber diameter, highlighting the role of nanoscale refinement in activating plasticity in embedded Si nanofibers in Al matrix. In addition, the kinetic barriers associated with the glide of edge/screw zonal dislocation in the perfect crystal and twinned crystal are computed using climbing-image nudge elastic band method. A higher mobility of the zonal dislocation in the twinned crystal suggests that twin boundaries can assist in dislocation glide parallel to the boundary. On the other hand, a nano-crack is nucleated at the interaction position of a glide partial dislocation with an intersecting growth twin boundary suggesting that intersecting twins serve to block glide and provide sites for crack nucleation.

Confluent effects of initial dislocation microstructures on yield behavior in single-crystal tungsten at high temperature

Though it is well known that initial dislocation microstructures play an important role in the deformation behavior of materials, how dislocation microstructures affect the macroscopic properties is still subjected to intensive research due to their complexity. In this work, we use discrete dislocation dynamics (DDD) to understand the effect of initial dislocation microstructures on the dynamic yield behavior of single-crystal tungsten above the critical temperature (800 K). DDD results suggest that the dislocation source length and the dislocation density are responsible for the initial yield stress and the flow stress of tungsten under dynamic loading, respectively. As and increase, the plastic yield mechanism transforms from dislocation-source activation into dislocation-dislocation interactions, resulting in the initial yield stress decreasing and the flow stress increasing. The confluent effects of and on the steady-state flow stress can be unified by a linear relationship between and Our results could be a valuable piece that connects dynamic yield behavior to the initial dislocation microstructures.

Additional dislocation slip determined excess yield stress in titanium

The excess yield stress induced slip system variations at the early stage of plastic deformation in Ti was in-depth studied. As a common sense, both the normal grain refinement according to the Hall-Petch relationship and the suppressed dislocation source activation in refined-grain can extensively increase the yield stress. In this study, combined calculations of Schmid factor and critical resolved shear stress suggest that small-grain samples with much higher yield stress could incorporate both <a>-prismatic slip and <c+a>-pyramidal slip, while only <a>-prismatic slip can be activated in the large-grain counterparts. This slip system transition can explain the abnormal fine-grain strengthening effect, which the experimental yield stress of small-grain sample deviates from the value that predicted by using Hall-Petch relationship, as well as the stress drop right after yielding in Ti. These findings could also provide a new strategy for designing high-strength metallic materials.

Dislocation exhaustion and ultra-hardening of nanograined metals by phase transformation at grain boundaries

The development of high-strength metals has driven the endeavor of pushing the limit of grain size (d) reduction according to the Hall-Petch law. But the continuous grain refinement is particularly challenging, raising also the problem of inverse Hall-Petch effect. Here, we show that the nanograined metals (NMs) with d of tens of nanometers could be strengthened to the level comparable to or even beyond that of the extremely-fine NMs (d ~ 5 nm) attributing to the dislocation exhaustion. We design the Fe-Ni NM with intergranular Ni enrichment. The results show triggering of structural transformation at grain boundaries (GBs) at low temperature, which consumes lattice dislocations significantly. Therefore, the plasticity in the dislocation-exhausted NMs is suggested to be dominated by the activation of GB dislocation sources, leading to the ultra-hardening effect. This approach demonstrates a new pathway to explore NMs with desired properties by tailoring phase transformations via GB physico-chemical engineering.

Plasticity of zirconium hydrides: a coupled edge and screw discrete dislocation model

Understanding the plastic behaviour of thin zirconium hydrides is important for its implications on crack nucleation in the Zirconium alloy cladding used in fission reactors. Microvoids originate at fractured hydrides, and their coalescence may lead to the failure of the component. In this work, an innovative discrete dislocation framework is presented together with the preliminary results. The aim is to develop a model that is significantly faster than existing 3D formulations, to make it possible to run a statistical analysis on a simulated microstructure. This comes with limitations, which are discussed together with the planned developments. The model combines two planar and orthogonal simulations. In one only edge, in the other only screw dislocations are allowed, thereby describing all sides of a dislocation loop approximated as a rectangle. The two families of dislocations interact via their elastic stress, and this coupling proved to be important and significantly enhanced the dislocation density. The proposed model enables us to implement a 3D stress analysis of the hydrides. The simulations show that the most critical scenario is when neighbouring slip planes become populated with opposite-signed dislocations. This was observed both in the edge and in the screw case, and was reflected in the principal stress calculated by combining the two. It was also observed that the degree of permeability of the interface to dislocation crossing is inversely correlated to the stress inside the hydride and to the dislocation source activation.

Dislocation-grain boundary interaction in metallic materials: Competition between dislocation transmission and dislocation source activation

Dislocation transmission across grain boundary (GB) and activation of dislocation source in adjacent grains are considered common features of dislocation-GB interactions in regulating mechanical properties and behaviors of metallic materials and structures. However, it is currently unclear which of dislocation transmission and dislocation source activation plays the dominant role in regulating dislocation-GB interaction. To study the competition between dislocation transmission and dislocation source activation, a theoretical framework is established based on a dislocation pile-up model. It is found that both dislocation transmission and dislocation source activation exhibit strong dependence on the GB misorientation angle. The critical transmission stress derived based on an energy method also depends on the grain size in a scaling form similar to the Hall-Petch relation. The outgoing slip systems during dislocation transmission are successfully predicted and agree with experimental observations. Regarding the dislocation source activation, the critical activation stress is investigated by examining the local stress fields generated by single and multiple slip dislocation pile-ups. It is found that compared with single slip dislocation pile-up, the result of multiple slip dislocation pile-ups displays lower critical activation stresses and exhibits feature of sensitivity to loading direction, interpreting the reported results of dislocation source activation in polycrystals. Further comparison between dislocation transmission and dislocation source activation for ⟨100⟩ tilt GBs indicates that the dislocation transmission prevails at low angle GB, while dislocation source activation is prone to occur at high angle GB. Our theoretical studies quantify the dislocation-GB interaction induced by dislocation pile-ups, shed light on the competition between dislocation transmission and dislocation source activation, and might provide essential guidance for high-performance metallic material design.

In-situ study of initiation and extension of nano-thick defect-free channels in irradiated nickel

Radiation defects-induced plastic flow localization is the origin of loss of ductility in irradiated metals. Defect-free channels (DFCs) are a typical form of strain localization that lead to crack initiation and premature failure. A comprehensive understanding of the DFC dynamics is key to managing radiation boosted property degradation. Despite great research efforts, a clear mechanism of DFC remains unknown. Here, our in-situ tests on irradiated Ni pillars provide a real-time observation of the dynamics of DFCs, including DFC initiation, extension and thickening. The merging and spreading of dislocation loops serve as an alternative mechanism of dislocation sources that emit massive dislocations and initiate nano-thick DFCs inside the grain. Nano-thick DFCs were formed through chopping up or sweeping away of loops by mobile dislocations. Annihilation of opposite loops and interactions between loops and vacancies accelerate DFC extension. Activation of multiple dislocation sources and dislocation cross-slips are the mechanisms for DFC thickening.

Unified Model for Size-Dependent to Size-Independent Transition in Yield Strength of Crystalline Metallic Materials.

Size-dependent yield strength is a common feature observed in miniaturized crystalline metallic samples, and plenty of studies have been conducted in experiments and numerical simulations to explore the underlying mechanism. However, the transition in yield strength from bulklike to size-affected behavior has received less attention. Here a unified theoretical model is proposed to probe the yield strength of crystalline metallic materials with sample size from nanoscale to macroscale. We show that the transition in yield strength versus size can be fully explained by the competition between the stresses required for dislocation source activation and dislocation motion, which is regulated by dislocation density, irradiation defect, grain boundary, and so on. Based on various grain boundary densities, the extended Hall-Petch relation, incorporated into the unified model, captures the reverse size effect for polycrystalline samples. The proposed model predictions agree well with reported experimental measurements of various specimens, including the prestrained nickel, irradiated copper, ultrafine grain tungsten, and so on.

TEM Observation of Loops Decorating Dislocations and Resulting Source Hardening of Neutron-Irradiated Fe-Cr Alloys

Several open issues remain concerning the quantitative understanding of irradiation hardening in high-Cr steels. One of these issues is addressed here by correlating yield points that are observed in stress-strain curves with dislocation decoration observed by TEM for neutron-irradiated Fe-Cr alloys. It is found that both higher neutron exposure and higher Cr content promote irradiation-induced loops to arrange preferentially along dislocation lines. Consequently, the activation of dislocation sources requires unlocking from the decorating loops, thus resulting in a yield drop. This process is considered within the source hardening model as opposed to the dispersed barrier hardening model, the latter aimed to describe dislocation slip through a random array of obstacles. Microstructure-informed estimates of the unlocking stress are compared with measured values of the upper yield stress. As functions of neutron exposure, a cross-over from the dominance of dispersed-barrier hardening accompanied by smooth elastic-plastic transitions to the dominance of source hardening accompanied by yield drops is observed for Fe-9% Cr and Fe-12% Cr.

Does the stacking fault energy affect dislocation multiplication?

This paper investigates the interdependence of the stacking fault energy (SFE) and the stress required for dislocation multiplication. For this purpose copper-aluminum (Cu-Al) alloys with varying Al content are investigated by spherical nanoindentation. The load-displacement curve shows a characteristic pop-in, which is interpreted as elastic-plastic transition and correlated to the dislocation source nucleation and/or activation stress. The statistical analysis of the pop-in behaviour documents a strong dependence of the maximum shear stress beneath the indenter on the Al content, which cannot be explained by a variation in shear modulus. Instead, the pop-in stress clearly increases with increasing stacking fault energy.

Spherical nanoindentation on tungsten single crystal: The transition from source-controlled plasticity to bulk plasticity

Spherical nanoindentation was performed on tungsten single crystal to investigate the effects of tip radius on the pop-in stress. The results show that the pop-in stress decreases as the tip radius increases. A statistical model with randomly distributed dislocation sources captures experimentally observed source-controlled indentation size effect. The discrepancy between model and experimental data especially for a large tip was corrected by considering the collective activation of multiple dislocation sources. Our results provide a quantitative insight into the understanding of the transition from source-controlled plasticity to bulk plasticity under spherical nanoindentation.

Ductility enhancement of tungsten after plastic deformation

An unusual room temperature mechanical behavior of pure tungsten is investigated by focusing on three specimens prepared with different microstructures: as-received (hot-rolled), recrystallized, and cold-rolled specimens. Contrary to ordinary expectations in metallic materials, only the cold-rolled specimen exhibits significant plastic deformation during tensile testing, with improved strength and ductility, while the recrystallized and the as-received specimens fail in the elastic region. We further provide an explanation of such characteristics by systematically utilizing experimental and theoretical analysis at a small scale: nano-indentation tests clarify the inherent mechanical response inside grains and provide a statistical distribution of the maximum shear stress during pop-in events, corresponding to onset of plastic yielding; atomistic simulations provide information on the overall fracture strength of various grain boundaries. By comparing the maximum shear stress and the grain boundary fracture stress, we could explain that the distinctive plasticity in the cold-rolled specimen is caused by the movement of pre-existing dislocations before grain boundary fracture. This contrasts the recrystallized and as-received specimens, where grain boundary fracture occurs prior to the nucleation of dislocations or activation of dislocation sources.

Spatio-temporal plastic instabilities at the nano/micro scale

Recent experimental observations revealed the inherent nature of strong intermittent and heterogeneous plastic deformation at the nano- to micrometer scale. We present here a review of quantitative measures of temporal and spatial material instabilities associated with small-scale plastic flow. Spatial correlation characterization methods are developed and used to obtain information on the width of shear bands resulting from spatial instabilities. The effects of atomic-scale barriers to dislocation motion and the influence of sample size on temporal and spatial plastic instabilities are discussed. A simplified branching model of dislocation source activation is extended to predict dislocation barrier effects on strain burst statistics, and the transition from power law scaling to an exponential-like distribution. The connection between temporal and spatial plastic instabilities is discussed, and the efforts of considering these effects in crystal plasticity theory are also highlighted.

The effect of layer thickness ratio on the plastic deformation mechanisms of nanoindented Ti/TiN nanolayered composite

Molecular dynamics simulations were performed to identify the underlying deformation mechanisms controlling the plastic behavior of nanoindented nanoscale multilayered Ti/TiN. MD simulations were conducted on pure Ti and pure TiN as well as on four different layer-thickness ratios of Ti/TiN multilayers, Ti:TiN = 1, 2.5, 4, and 7.5. The Ti layer thickness varied from 2 nm to 15 nm while the TiN layer thickness is kept constant of 2 nm. The plastic deformation of nanoindented pure Ti was dominated by the formation of dislocation loops resulting from basal partial dislocations, while very few perfect dislocations that tie dislocation loops together were observed. The plastic deformation of nanoindented pure TiN was controlled by the activation of perfect dislocation propagation along the (111) plane that dissociates into two partials. Depending on the thickness ratio, either dislocation pile-up or single dislocation crossing through the interface was the controlling plastic deformation mechanism of nanoindented Ti/TiN multilayers. For metal layer thicknesses above 5 nm, significant dislocation pile-ups were observed at the interface of the multi-layered samples. The Ti/TiN multilayer with a thickness ratio of 1:1 with individual layer thickness of 2 nm exhibited the highest strain-hardening rate. At this length scale, the activation of dislocation sources requires very high stresses, and the single dislocation crossing process is the most dominant deformation mechanism. The initiation of plasticity in the TiN layer occurs at a high level of stress since there is no dislocation pile-up at the interface.

Size-Tuned Plastic Flow Localization in Irradiated Materials at the Submicron Scale.

Three-dimensional discrete dislocation dynamics (3D-DDD) simulations reveal that, with reduction of sample size in the submicron regime, the mechanism of plastic flow localization in irradiated materials transitions from irradiation-controlled to an intrinsic dislocation source controlled. Furthermore, the spatial correlation of plastic deformation decreases due to weaker dislocation interactions and less frequent cross slip as the system size decreases, thus manifesting itself in thinner dislocation channels. A simple model of discrete dislocation source activation coupled with cross slip channel widening is developed to reproduce and physically explain this transition. In order to quantify the phenomenon of plastic flow localization, we introduce a "deformation localization index," with implications to the design of radiation-resistant materials.

Using spherical indentation to measure the strength of copper-chromium-zirconium

Precipitation hardened CuCrZr will be used in heat-sink components in the ITER tokomak and is a primary candidate for EU DEMO. The measurement of mechanical properties of irradiated CuCrZr using conventional, standardised techniques is difficult due to the challenges involved in working with radioactive material and the relatively large specimen size required. Spherical nano-indentation offers a technique to measure stress-strain properties from far smaller volumes than conventional tests. In this work, CuCrZr has been heat-treated at different temperatures to vary the Cr precipitate size and spacing. Spherical nano-indentation using multiple tip radii was then used to produce stress-strain curves for all samples, from which values of initial flow stress were calculated. It was found that there was a strong indentation size effect (ISE) in the stress required to initiate plasticity, however at higher indentation strains the flow stress became constant for tip radii, R, ≥8 μm. This suggests that at the initiation of plastic deformation the ISE is dominated by dislocation source activation but in later stages the interaction with microstructural material length-scales dominate the measured mechanical strength. The mechanical response of these small-scale tests is governed by multiple mechanisms, which convolute interpretation of data and must be considered when measuring the effects of irradiation on the mechanical properties.