Strain-Rate- and Line-Length-Dependent Screw Dislocation Glide Mechanisms in BCC Refractory Metals and Alloys

TL;DR

This study resolves how strain rate, dislocation line length, and chemical composition govern screw-dislocation glide in BCC Nb, Mo, and NbMo by marrying conventional MD with strain-boost hyperdynamics. The authors show that cross-kinks can form in pure metals as well as in alloys, with depinning pathways ranging from defect-assisted cutting at high rates to lateral cross-kink migration, 3D forward–backward cross-slip, and prismatic loop formation at low rates. They demonstrate pronounced line-tension effects at longer dislocation lines and reveal that concentrated NbMo hosts persistent pinning points that evolve into multi-plane cross-kink structures (super-cross-kinks), dominating the critical resolved shear stress. The results imply that strengthening models must treat cross-kinks as a heterogeneous, rate- and chemistry-dependent population and consider emergent obstacle spacing arising from coupled thermodynamics and kinetics, paving the way for more predictive design of refractory concentrated alloys.

Abstract

Plastic flow in body-centered cubic (BCC) metals and dilute/concentrated alloys is governed by the motion of <111> screw dislocations, whose glide is often impeded by cross-kinks (jogs). While existing strengthening models typically treat depinning as defect-assisted cutting or dislocation bowing, the combined strain-rate and dislocation-line-length dependence of cross-kink stability and effective obstacle spacing remains insufficiently resolved at the atomistic scale. Here, we combine conventional molecular dynamics and strain-boost hyperdynamics to investigate screw-dislocation glide in pure Nb and Mo, dilute Nb-Mo alloys, and equiatomic NbMo at 300 K over strain rates from 10^3 to 10^7 s^-1 and dislocation line lengths from 15 to 50 nm. We first demonstrate that low-strain-rate simulations require sufficiently long dislocation lines to capture consistent cross-kink behavior and strength-determining pinning events. Using the 50~nm configurations, we show that cross-kinks form not only in concentrated alloys but also in pure BCC metals, with their stability governed by the relative rates of kink nucleation and migration on primary and cross-slip planes, which differ between Nb- and Mo-rich systems due to distinct core structures and non-Schmid responses. At high strain rates, depinning proceeds predominantly via vacancy-interstitial cluster formation. In contrast, at low strain rates and long line lengths, alternative pathways emerge, including lateral cross-kink migration, three-dimensional forward--backward cross-slip, and prismatic loop formation. The effective obstacle spacing controlling the critical resolved shear stress therefore emerges from coupled thermodynamic roughening and kinetic evolution. These findings highlight the intrinsically rate-, length-, and chemistry-dependent nature of screw-dislocation strengthening in BCC alloys.

Figures (15)

• Figure 1: Schematic illustration of cross-kink formation and depinning mechanisms for $\langle111\rangle$ screw dislocations in BCC alloys. (a) Formation of a cross-kink (jog) arising from the intersection of kinks nucleated on different slip planes along the same screw-dislocation line. (b) In classical strengthening models, depinning of a cross-kink is commonly assumed to occur via defect-assisted cutting, accompanied by the formation of vacancy or interstitial debris suzuki1980solidRao2019ModelingSolutionHardeningMaresca2020TheoryScrewDislocation. (c) The present work reveals additional depinning pathways, including lateral cross-kink migration, loop emission, and other three-dimensional dislocation-line rearrangements, that become operative at low strain rates and for long dislocation line lengths. Solid and dashed blue lines denote dislocation segments on the $(\bar{1}0\bar{1})$ and $(\bar{1}10)$ slip planes, respectively; this convention is adopted consistently in all subsequent dislocation-line segment representations.
• Figure 2: Illustration of the hyperdynamics framework and the determination of key parameters used in this study. (a) Schematic representation of the hyperdynamics method Voter1997HyperdynamicsAcceleratedMolecular. The solid curve denotes the original potential-energy surface, while the dashed curve represents the biased potential with elevated basin energies and unchanged transition states. (b) Simulation supercell containing an embedded $\langle111\rangle$ screw dislocation used in the present study. The same $X$--$Y$--$Z$ coordinate system is adopted for all subsequent dislocation-structure visualizations. (c) Evolution of $\eta^{\mathrm{Mises}}_{\mathrm{max}}$ defined in Eq. \ref{['eq:StrainBoost_StoppingFunction']} for a Nb single crystal with a pre-existing screw dislocation at 300 K. (d) Corresponding evolution of $\eta^{\mathrm{Mises}}_{\mathrm{max}}$ for a NbMo alloy containing a pre-existing screw dislocation at 300 K.
• Figure 3: Simulation results for $\langle111\rangle$ screw dislocations with a line length of 15 nm. Shear stress–strain ($\sigma_{yz}$–$\gamma_{yz}$) responses at different applied strain rates for (a) pure Nb, (b) pure Mo, and (c) equiatomic NbMo alloy. (d) Dislocation configurations in NbMo immediately before and after $\sigma_{yz}$ drops at a high strain rate of $5.0\times10^{7}\ \mathrm{s^{-1}}$, illustrating defect generation during cross-kink depinning. (e) Corresponding dislocation configurations in NbMo at a low strain rate of $1.0\times10^{4}\ \mathrm{s^{-1}}$, shown immediately before and after $\sigma_{yz}$ drops.
• Figure 4: Simulation results for screw dislocations with a line length of 20 nm. Shear stress–strain ($\sigma_{yz}$–$\gamma_{yz}$) responses at different applied strain rates for (a) pure Nb, (b) pure Mo, and (c) the NbMo alloy. (d) Dislocation configurations in the NbMo alloy immediately before and after $\sigma_{yz}$ drops under a high strain rate of $5.0\times10^{7}\ \mathrm{s^{-1}}$. (e) Dislocation configurations in the NbMo alloy immediately before and after $\sigma_{yz}$ drops under a low strain rate of $1.0\times10^{4}\ \mathrm{s^{-1}}$.
• Figure 5: Simulation results for screw dislocations with a line length of 50 nm in pure Nb, pure Mo, and dilute Nb–Mo alloys. Shear stress–strain ($\sigma_{yz}$–$\gamma_{yz}$) responses for (a) pure Nb and $\text{Nb}_{0.99}\text{Mo}_{0.01}$, and (b) pure Mo and $\text{Nb}_{0.01}\text{Mo}_{0.99}$. Dislocation and defect configurations immediately before and after depinning in pure Mo at strain rates of (c) $\dot{\gamma}_{yz} = 5.0\times10^{7}\ \mathrm{s^{-1}}$ and (d) $\dot{\gamma}_{yz} = 1.0\times10^{4}\ \mathrm{s^{-1}}$.