Kink-pair Nucleation Research Articles

Effect of Cr content on thermally activated deformation in single-crystal micropillars of Fe–Cr binary alloys

This study identifies the role of solute Cr in the thermal activation process in the plastic deformation of α-(Fe, Cr) ferrite (BCC solid solutions) using micropillar compression tests for micron-sized single-crystals fabricated on various Fe–Cr binary alloys that were solution-treated at 1573 K. Fe–18%Cr single-crystal micropillars with a mean diameter d of ∼2 μm exhibited a relatively higher strain rate sensitivity (m) of 0.12 for the stress required for slip initiation. Larger Fe–18%Cr micropillars (d = 5 μm) exhibited a lower m value of 0.04. The corresponding activation volume of 50 b3 was equivalent to the millimeter-sized pure Fe and Fe–18%Cr alloy specimens (60–70 b3), indicating the prevalence of a general mechanism involving dislocation motion (kink-pair nucleation of screw dislocations). This mechanism controls the thermal activation process of plastic deformation in the Fe–18%Cr alloy, which has sufficient sources for dislocation multiplication. In the Fe–25%Cr and Fe–40%Cr single crystal micropillars, a less pronounced size-dependent m value (0.01–0.03) was determined, almost independent of specimen size. The corresponding activation volumes of large micropillars (74–77 b3) were similar to those of millimeter-sized specimens, which indicates a mild effect of solute Cr atoms on the thermal activation process of dislocation motion in Fe–Cr binary alloys at ambient temperature. Initial dislocations, rather than Cr content in Fe–Cr binary alloys, led to the low changes in size-dependent activation volume of Fe–Cr alloys with higher Cr content. Planar faults (Cr-enriched regions) were observed in Fe–40%Cr alloys, which may become sufficient sources for dislocation nucleation. However, the influence of Cr-enriched regions on dislocation motion remains unclear.

Multiscale modeling of dislocation-mediated plasticity of refractory high entropy alloys

Refractory high entropy alloys (RHEAs) have drawn growing attention due to their remarkable strength retention at high temperatures. Understanding dislocation mobility is vital for optimizing high-temperature properties and ambient temperature ductility of RHEAs. Nevertheless, fundamental questions persist regarding the variability of dislocation motion in the rugged energy landscape and the effective activation barrier for specific mechanisms, such as kink-pair nucleation and kink migration. Here we perform systematic atomistic simulations and conduct statistical analysis to obtain the effective activation barriers for the mechanisms underlying various types of dislocation motion in a typical RHEA, NbMoTaW. Moreover, a stochastic line tension model is developed to calculate the activation barrier with substantially reduced computational costs. By incorporating the effective activation barriers into the crystal plasticity model, a multiscale simulation framework for predicting the mechanical properties of RHEAs is established. The ambient temperature yield strength of NbMoTaW is well-predicted by the kink-pair nucleation mechanism of screw dislocations, while the strengthening originating from screw dislocations does not predominate at high temperatures. Our work provides a robust foundation for atomistic studies of effective dislocation behaviors in random solution solids, elucidating the intricate relationship between microscopic mechanisms and macroscopic properties.

The behavior of 12⟨111⟩ screw dislocations in W–Mo alloys analyzed through atomistic simulations

Analyzing plastic flow in refractory alloys is relevant to many different commercial and technological applications. In this study, screw dislocation statics and dynamics were studied for various compositions of the body-centered cubic binary alloy tungsten–molybdenum (W–Mo). The core structure did not appear to change for different alloy compositions, consistent with the literature. The pure tungsten and pure molybdenum samples had the lowest plastic flow, while the highest dislocation velocities were observed for equiatomic, W0.5Mo0.5 alloys. In general, dislocation velocities were found to largely align with a well-established dislocation mobility phenomenological model supporting two discrete dislocation mobility regimes, defined by kink-pair nucleation and migration and phonon drag, respectively. Velocities were observed to increase with temperature and applied shear stress and with decreasing kink-pair formation energies. The 50 at. % W alloy was found to possess the lowest kink-pair formation energy, consistent with its higher dislocation velocity. Furthermore, molybdenum segregation to the dislocation line was found to be thermodynamically favorable specifically at low temperatures and was observed to significantly delay the onset of dislocation glide and then generally enhance dislocation velocities thereafter. This behavior was explained by examining the energy landscape of dislocation glide. Furthermore, a segregation/de-segregation phase transition was observed to occur around 2500 K beyond which no preferential segregation to the dislocation was found. Overall, our findings suggest strong dependencies of plastic flow in W–Mo alloys on composition and elemental segregation, in agreement with the available literature, and may provide useful information to guide the design of next generation structural materials.

Coupled size and temperature effects on intermittent plasticity of BCC micro-crystals

The intermittent plasticity of pure Mo microcrystals with diameters from 500 to 3500 nm was studied using micro-pillar compression methodology at temperatures ranging from 25 °C to 200 °C, in order to explore its dependence on external size and temperature. The technological background is the potential value of BCC metals in the manufacture of high-temperature components in modern fields requiring miniaturization, such as microelectronics. We analyzed plastic fluctuations in terms of wildness, avalanche size distribution, and burst peak velocity. This reveals coupled size and temperature effects on a mild-to-wild transition: the transition temperature decreases with decreasing sample diameter, while the transition diameter increases with rising temperature. In addition, strain-rate sensitivity tests were conducted, implying that mild plasticity is associated to screw dislocation motions controlled by thermally activated nucleation of kink-pairs, whereas wild plasticity is nearly athermal. This experimental observation is interpreted by a damping effect of the thermally activated motion of screw dislocations on the propagation of avalanches. From this, we propose a controlling parameter based on a simple dislocation source model, which unifies the coupled sample size and temperature effects on the mild-to-wild transition, and which could be of practical significance for microscale applications.

Thermally activated nature of synchro-Shockley dislocations in Laves phases

Synchro-Shockley dislocations, as zonal dislocation, are the major carrier of plasticity in Laves phases at high temperatures. The motion of synchro-Shockley dislocations is composed of localized transition events, such as kink-pair nucleation and propagation, which possess small activation volumes, presumably leading to sensitive temperature and strain rate dependence on the Peierls stress. However, the thermally activated nature of synchro-Shockley dislocation motion is not fully understood so far. In this study, the transition mechanisms of the motion of synchro-Shockley dislocations at different shear and normal strain levels are studied. The transition processes of dislocation motion can be divided into shear-sensitive and -insensitive events. The external shear strain lowers the energy barriers of shear-sensitive events. Thermal assistance is indispensable in activating shear-insensitive events, implying that the motion of synchro-Shockley dislocations is prohibited at low temperatures.

Temperature dependence of the yield stress in TiZrNbHfTa body-centred cubic high-entropy alloy

Body-centred cubic (bcc) high-entropy alloys exhibit high strength. However, their yield behaviour and controlling mechanisms are still ambiguous. In this study, the temperature dependence of the yield stress, effective stress, activation volume, and activation enthalpy in a polycrystalline bcc refractory high-entropy alloy of TiZrNbHfTa were measured by tensile tests at 77–750 K. At temperatures above 650 K, the temperature dependence of the yield stress disappeared, and serration appeared in stress–strain curves. By extrapolating the effective shear stress to 0 K, the Peierls stress was estimated to be 580 MPa. The value was compared with different crystals using the relationship τpμ and hb, where τp is the Peierls stress, μ is the shear modulus, h is the distance between the slip planes, and b is the Burgers vector. The τpμ value in this study was slightly higher than that of other bcc crystals. The activation enthalpy below 260 K corresponds to that of other bcc crystals with high Peierls potentials, suggesting kink-pair nucleation is the controlling mechanism of the dislocation glide in this temperature range. Meanwhile, the activation enthalpy above 260 K deviated from the trendline, indicating the changes in the dislocation glide from the kink-pair nucleation to other one.

Thermally activated plastic deformation of Si single crystals at temperatures above 1173 K

The effect of high-temperature heat treatment during production on the mechanical property of Si wafer, namely yield stress, was studied through tensile tests of Si single crystals at 1123–1373 K, where stress–strain curves were obtained along the and directions. The critical resolved shear stress showed a remarkable temperature dependence, and it decreased with increasing test temperature. Below 1348 K, the activation enthalpy determined through strain rate jump tests showed no significant difference between crystals made by the Chokralski and the floating zone methods. This indicated that the solute oxygen does not influence the thermally activated dislocation glides. The activation enthalpy of 4.9 eV for a dislocation glide was much higher than that reported by previous studies (2.2 eV at temperatures below 1100 K), indicating that the thermal activation of dislocation glide is different from kink-pair nucleation. It was found that self-diffusion can assist the dislocation glide at temperatures above 1130 K.

Mobility of carbon-decorated screw dislocations in bcc iron

We investigate the mobility of screw dislocations decorated by carbon solutes in body-centred cubic iron based on density functional theory (DFT) calculations and transmission electron microscopy (TEM) observations of in-situ straining experiments. We focus on the high-temperature domain, between 500 and 800 K, where plasticity is controlled by the slow glide of decorated screw dislocations with a mobility similar to the Peierls mechanism existing below 300 K, at variance with the athermal regime observed at intermediate temperatures. We propose that due to the strong pinning of reconstructed dislocation lines by carbon solutes, dislocation glide occurs by the formation and migration of kinks, both controlled by the jumps of carbon atoms. We calculate the associated kink-pair nucleation and formation energies as well as the migration energies of isolated kinks and use these DFT values to predict the dislocation velocity as a function of temperature, applied stress and dislocation length. The validity of the mobility law is assessed by the comparison with dislocation velocities measured in TEM observations at different temperatures and local shear stresses. The quantitative agreement between the experimental measurements and the analytical model supports the proposed glide mechanism and the DFT values obtained for kink energies.

Fundamental insights on ductile to brittle transition phenomenon in ferritic steel

Ductile to brittle transition (DBT) is a well-known phenomenon responsible for deteriorating the low temperature fracture toughness of ferritic steels. It is unambiguous to state that the transition phenomenon is a direct consequence of the strong temperature and strain rate sensitivity of flow stress, which in turn is regulated by the thermally activated motion of screw dislocation at the atomic scale. Due to very high Peierls stress, screw dislocation motion is accompanied by the nucleation and propagation of kink-pairs along the dislocation line. Thus, the activation energy required for kink-pair nucleation is an essential ingredient for correctly predicting the flow stress sensitivity and hence the ductile to brittle transition temperature (DBTT) of ferritic steel. However, experimental determination of kink-pair activation energy is rather tedious and there exists a strong discrepancy between atomistic simulation results (using Density Functional Theory and empirical potentials). Therefore, the present review is aimed at understanding the mechanism of screw dislocation motion in BCC Fe lattice and comparing the results obtained for kink-pair activation energy through experiments and simulations. The effect of different alloying elements on the overall flow stress sensitivity of Fe is also discussed with reference to the interaction of screw dislocation with solute atoms or clusters. Finally, the importance of screw dislocation on predicting the DBTT is explored to identify the present knowledge gaps and the future research directions.

Solid solution softening and hardening in binary BCC alloys

Solute-dislocation interaction energies are calculated using Density Functional Theory and the 2-D lattice Greens function approach for Al, Ti, Cr, Fe, Zr, Nb, Mo, Ru, Hf, Ta, W, Re solutes in BCC Nb, Ta, Mo, and W. The predictions are then used in an extension of the Rao-Suzuki model to analyze the experimentally observed solid solution strengthening and softening in Nb-X, Fe-X, Ta-X, Mo-X and W-X crystals, X= Mo, W, Ta, Si or Re. DFT predictions for the solute dislocation interaction energies for Fe-Si, taken from the literature are also analyzed. The original Rao-Suzuki model considers kink migration controlled mobility of screw dislocations in body-centered cubic (BCC) structures and is valid for high solute concentrations (>5 at%) as well as above a critical temperature. Here, we extend the Rao-Suzuki model to include kink-pair nucleation statistics in the presence of solutes which is expected to be the rate limiting process at low temperatures (<0.2Tmelt). Such an extension should be valid up to low concentration of solutes as well as fairly low temperatures. The key parameters required for the model are solute – ½[111] screw dislocation interaction energies in pure Nb, Ta, Mo or W. These parameters were derived in this paper using first principles calculations. Using the calculated interaction energies, the model satisfactorily reproduces experimentally observed solution strengthening data in Nb-Mo, Nb-W, Nb-Re crystals at temperatures from 77 to 600K, for solute concentrations in the range 8.5 to 19 at% for Mo, 6 to 15 at.% for W and 5 to 9 at.% for Re. Similar agreement is found for strengthening/softening data for Ta-W, Ta-Re, Ta-Nb, Fe-Si, Mo-Re and W-Re crystals in the temperature range 77 – 600K. We also explore sensitivity of these predictions to the variation in the solute-dislocation energies. In Ta-W, a 10% variation (±0.015 eV) produces a modest change in solution hardening, which is within experimental error. The refined Rao-Suzuki model can be used in designing high strength, multi-component BCC alloys for high temperature applications.

Temperature-dependent nanoindentation and activation volume in high-purity body-centered cubic chromium

The thermally activated dislocation plasticity of body-centered cubic (BCC) metals is controlled by the nucleation of dislocation kink pairs at low temperatures. We probed this deformation mechanism with high-temperature nanoindentation in chromium using very fine temperature increments. The established kink pair nucleation models are modified for the high-temperature nanoindentation method and applied to characterize the deformation behavior of high-purity BCC chromium from room temperature to 698 K. The measured hardness, strain rate sensitivity, and apparent activation volume are compared with a modified kink-pair nucleation model based on Seeger’s work. A change in the apparent slip plane from {110} to {112} with increasing temperature is inferred from self-consistent predictions and experimental measurements of the hardness-dependent activation volume from temperature-dependent hardness measurements using the line tension model for kink-pair nucleation.

The hierarchical energy landscape of screw dislocation motion in refractory high-entropy alloys

High-entropy alloys (HEAs) with concentrated solid solutions are conceived to possess a rugged atomic and energy landscape in which dislocation motion necessarily proceeds to accommodate mechanical deformation. Fundamental questions remain as to how rough the energy landscape is and to what extent it can be influenced by the local ordering of their constituent elements. Here, we construct and report the potential energy landscape (PEL) governing screw dislocation motion in refractory HEAs that reveals a hierarchical and multilevel structure with a collection of small basins nested in large metabasin. This striking feature pertaining to HEAs exerts a trapping force and back stress on saddle point activations, retarding dislocation movement. By introducing chemical short-range order, the energy landscape is smoothed but skewed to different degrees that shifts the rate-liming process from kink-glide to kink-pair nucleation. The chemical disorder-roughened PEL in HEAs, analogous to structural disorder induced in metallic glasses, signifies the role of various barrier-hopping processes underlying the extraordinary mechanical behaviors of the two distinct groups of materials.

Temperature and Stress Dependence of Screw Dislocation Mobility in Nb-V-Ta Alloys Using Kinetic Monte Carlo Simulations

In this work we present simulations of thermally-activated screw dislocation motion in Nb-Ta-V alloys for two distinct scenarios, one where kink propagation is solely driven by chemical energy changes, i.e., thermodynamic energy differences, and another one where a migration barrier of 1.0 eV is added to such changes. The simulations have been performed using a kinetic Monte Carlo model for screw dislocation kinetics modified for complex lattice-level chemical environments. At low stresses, we find that dislocation motion in the case with no barrier is controlled by long waiting times due to slow nucleation rates and extremely fast kink propagation. Conversely, at high stress, the distribution of sampled time steps for both kink-pair nucleation and kink propagation events are comparable, resulting in continuous motion and faster velocities. In the case of the 1.0-eV kink propagation energy barrier, at low stresses kink motion becomes the rate-limiting step, leading to slow dynamics and large kink lateral pileups, while at high stresses both kink pair nucleation and kink propagation coexist on similar time scales. In the end, dislocation velocities differ by more than four orders of magnitude between both scenarios, emphasizing the need to have accurate calculations of kink energy barriers in the complex chemical environments inherent to these alloys.

Screw dislocations in BCC transition metals: from ab initio modeling to yield criterion

We show here how density functional theory calculations can be used to predict the temperatureand orientation-dependence of the yield stress of body-centered cubic (BCC) metals in the thermallyactivated regime where plasticity is governed by the glide of screw dislocations with a 1/2 Burgers vector. Our numerical model incorporates non-Schmid effects, both the twinning/antitwinning asymmetry and non-glide effects, characterized through ab initio calculations on straight dislocations. The model uses the stress-dependence of the kink-pair nucleation enthalpy predicted by a line tension model also fully parameterized on ab initio calculations. The methodology is illustrated here on BCC tungsten but is applicable to all BCC metals. Comparison with experimental data allows to highlight both the successes and remaining limitations of our modeling approach.

Thermally-activated dislocation mobility in bcc metals: An accelerated molecular dynamics study

Plastic deformation in metals is controlled by dislocation density and mobility. In bcc metals the mobility of screw dislocations, which takes place by temperature- and stress-driven nucleation of critical kink-pairs, is most essential for deformation. However, the critical resolved shear stresses at low temperatures, as determined from molecular dynamics (MD) simulations performed at constant strain rate, are typically 2–3 times larger than the yield stresses measured experimentally. Here, an accelerated MD procedure is developed and employed to investigate the onset of dislocation mobility in the prototypical system bcc Nb. The method combines constant strain and temperature MD with hyperdynamics, using a bond-boost potential. We demonstrate, with a careful statistical analysis, that the method enables nucleation of critical kink-pairs and the determination of the Gibbs energy of kink-pair formation from accelerated MD simulations at experimentally-measured shear stresses.

Theory of kink migration in dilute BCC alloys

Plastic deformation in elemental BCC metals and dilute alloys is controlled by the slower of the kink pair nucleation and kink migration processes along screw dislocations. In alloys nucleation is facilitated and migration inhibited, leading to a concentration- and temperature-dependent transition from nucleation dominance to migration dominance. Here, an analytical statistical model for the stress-dependent kink migration barrier in dilute BCC alloys is developed and validated. The barrier depends only on a clearly-defined solute/screw dislocation interaction parameter, the kink width, and dislocation length between jogs. The analytic model is extensively validated via fully atomistic nudged-elastic band calculations and stochastic simulations in a model Fe-Si alloy. Combined with a recent validated double-kink nucleation theory, a fully-analytic model for the temperature- and concentration-dependent flow stress is obtained that includes the transition from nucleation to migration control. The overall model is applied to Fe-Si and W-Re using independently-determined material properties and good agreement is obtained with experiments over a range of concentrations and temperatures. Overall, the two theories represent a unified, fully-statistical, parameter-free understanding of screw dislocation strength in dilute BCC alloys.

Effect of applied strain on the interaction between hydrogen atoms and [formula omitted] screw dislocations in α-iron

We address the role of hydrogen in modifying the behaviour of screw dislocations in α-iron under the influence of the tensile and compressive stresses that are expected to arise in the vicinity of a crack tip. The quantum mechanical tight binding approximation is employed to calculate the variation of the hydrogen/screw dislocation interaction with strain. The locations and binding energies of hydrogen trap-sites surrounding the unstrained core are shown to be of similar accuracy to previous ab-initio results. Bi-axial tension and compression is applied normal to the dislocation line; the binding energies are found to vary linearly with strain. Estimations of the effect of hydrogen in strained regions are made based on the proposition that hydrogen may both enhance the nucleation of kink-pairs by lowering the formation energy, and slow the movement of kinks by a solute drag effect. Our results suggest that these effects will be enhanced in tensile regions. The chance of hardening by the collision of crossed kinks, to form a jog, is estimated by comparing the nucleation and annihilation rate of kinks on a straight screw dislocation for a range of hydrogen concentrations and temperatures, suggesting a greatly increased incidence with tension that is accentuated at lower temperatures.

Size-dependent plasticity and activation parameters of lithographically-produced silicon micropillars

Silicon is brittle at ambient temperature and pressure, but using micro-scale samples fabricated by focused ion beam (FIB) plasticity has been observed. However, typical drawbacks of this methodology are FIB-damage and surface amorphization. In this study, lithographic etching was employed to fabricate a large number of 〈100〉-oriented Si pillars with various diameters in the micro-scale. This allowed quantitative study of plasticity and the size effect of FIB-free Si in the brittle temperature range (25–500 °C) by conducting monotonic and transient microcompression in situ in the scanning electron microscope (SEM). Lithographic pillars achieved the ideal strength in temperature range of 25–100 °C and displayed significantly higher strengths (30–60%) than FIB-machined pillars because of the undamaged surface and the oxide layer confinement. The activation energy of deformation revealed a transition in dislocation mechanisms as a function of temperature. Strain rate sensitivity and activation volume measured from strain rate jump and stress relaxation tests indicated the surface nucleation of kink-pairs associated with the constricted dislocation motion in Si during deformation at temperatures below the brittle-ductile transition. A modified analytical model is proposed to accurately evaluate the size-dependent strength of covalent crystalline Si. The weak size effect observed in Si is attributed to the surface nucleation of dislocations and high lattice friction during their motion.

Anomalous solution softening by unique energy balance mediated by kink mechanism in tungsten-rhenium alloys

Nucleation of transmutation products such as rhenium (Re) and osmium (Os) is a central issue contributing to changes in mechanical properties under neutron irradiation in fusion reactors. In particular, Re solutes in tungsten (W) not only affect hardening via radiation-induced precipitation but also have a notable softening effect. We explored the softening/strengthening behaviors of various solutes in a W matrix by density functional theory (DFT) calculations combined with a solid solution model. Our DFT calculations of the solutes show a clear trend in the interaction energy between different solutes and screw dislocations, which also influences the solid solution behavior. These predictions, based on a solid solution model and DFT calculations, reasonably reproduce the complex softening/strengthening behavior as a function of temperature and solute concentration. Notably, solutes such as Re have relatively weak attractive interactions and do not markedly influence the pinning effect; however, such solutes can reduce the energy barrier for kink pair nucleation. We conclude that this specific balance is the origin of macroscopic solid solution softening in dilute body-centered cubic alloys.

Theory of screw dislocation strengthening in random BCC alloys from dilute to “High-Entropy” alloys

Random body-centered-cubic (BCC) “High Entropy” alloys are a new class of alloys, some having high strength and good ductility at room temperature and some having exceptional high-temperature strength. There are no theories of strengthening of screw dislocations in BCC metals that span naturally from the dilute limit to the multi-component, non-dilute concentrations typical of the high-entropy domain. Here, such a theory is developed and validated. Unlike low-temperature elemental BCC metals and very dilute BCC alloys, strength is not controlled by the kink-pair nucleation mechanism. Rather, screw dislocations naturally adopt a kinked structure as the minimum total energy configuration in the field of random alloying atoms. The characteristic length and energy scales for the low-energy kinked screw dislocation are derived for random alloys, leading to a characteristic spacing of both kinks and cross-kinks that depends on the kink formation energy and a characteristic collective solute/screw dislocation interaction energy parameter. Glide motion of this initially-kinked screw dislocation occurs via Peierls-type motion, lateral kink glide, and failure of cross-kinks. All these features are observed in molecular dynamics simulations. The resulting strength versus temperature, strain rate, and composition is analytic. The theory is validated by comparison to experiments on non-dilute Fe-Si, Nb-Mo, Nb-W, and Ti-Nb-Zr-based high entropy alloys versus composition and temperature. The theory provides a framework for tailored design of new high-performance BCC alloys.