Self-pinning mechanism for grain boundary stabilization

TL;DR

The study tackles grain-growth stabilization in polycrystalline alloys by introducing self-pinning, where segregation at a moving grain boundary spontaneously forms solute-rich clusters that pin the boundary while lowering the GB free energy. Using a kinetic Monte Carlo framework that resolves segregation thermodynamics, diffusion, and GB migration, the authors demonstrate first-order transitions between solute-lean and solute-rich GB phases and the in situ formation of pinning clusters during boundary motion. The migrating GB exhibits intermittent pinning with a velocity-dependent solute drag, featuring a maximum drag at a characteristic velocity $V^*$ that depends on GB–solute interactions and bulk composition. These findings reveal a fundamental coupling between thermodynamic GB phase behavior and kinetic drag, suggesting alloy design should target GB phase stability to achieve intrinsic thermal stability without pre-existing second-phase inclusions.

Abstract

Previous research focused on two different mechanisms of microstructure stabilization in alloys: thermodynamic stabilization by reducing the grain boundary (GB) free energy and kinetic stabilization by suppressing the GB mobility by solute drag or embedded pinning particles. Here, we propose a new GB stabilization mechanism, called self-pinning, in which the segregation atmosphere of a moving GB spontaneously breaks into solute-rich clusters, which produce a strong pinning effect in addition to the free energy reduction resulting from the segregation. The cluster formation is caused by strong solute-solute attraction at GBs, leading to a first-order transformation between solute-lean and solute-rich GB phases. The effect is demonstrated by kinetic Monte Carlo simulations capturing segregation thermodynamics, GB dynamics, and solute diffusion. The self-pinning provides an intrinsic stabilization mechanism for suppressing grain growth that couples thermodynamics and kinetics. The mechanism obviates the need for pre-existing second phase inclusions, refocusing the alloy design on GB phase behavior.

Figures (5)

• Figure 1: (a) Illustration of the GB separation metric used in this work. A snapshot shows the detection of two GBs evolving under an applied driving force. The GB separation $\lambda$ is defined from the locations of the peaks of the structural order parameter $\phi(n)$. The lower panel shows the line-averaged $\langle\phi\rangle_{y}(x)$ profile with the peaks. (b) Representative configurations illustrating the correspondence between grain structure, the GB locator $\phi(n)$, and the solute distribution. Left: grain orientations with solute atoms overlaid. Center: spatial map of $\phi(n)$ highlighting the GB core and its local roughness. Right: solute distribution with the GB region defined as all sites within $\pm2$ lattice spacings of the GB core, distinguishing the solute atoms in the segregation atmosphere from those located inside the grains.
• Figure 2: Equilibrium GB segregation at $T=0.15$ and $J_{\mathrm{sg}}=-0.2$ for selected values of $J_{\mathrm{ssg}}$. (a) Segregation isotherms showing the amount of GB segregation $\Gamma$ as a function of bulk solute concentration $c_{g}$. The discontinuities indicate transformations between two GB phases. (b) Representative snapshot of the low-segregation GB state at $J_{\mathrm{ssg}}=-0.4$ and $c_{g}=0.01$, characterized by sparse solute decoration along the GB. (c) Representative snapshot of the high-segregation GB state at $J_{\mathrm{ssg}}=-0.4$ and $c_{g}=0.05$, exhibiting a dense, nearly continuous solute-rich segregated layer.
• Figure 3: Self-pinning mechanisms for two initially flat GBs in a binary system at $T=0.15$, $c_{g}=0.05$, $J_{\mathrm{sg}}=-0.2$, $J_{\mathrm{ssg}}=-0.4$, $J_{\mathrm{s}}=0$, and $F=0.2$, starting from an equilibrium configuration with solute segregation. Panels (a.1-4) show the temporal evolution of the GB configuration: (a.1) Initially, the GB motion is accompanied by drag of the segregation atmosphere. (a.2) Partial breakup of the solute atmosphere as the GB advances, accompanied by solute capture, phase separation, and clustering. (a.3) Pinning of the GB by solute clusters, leading to the development of local GB curvature and faceting. (a.4) Evolution into a quasi-steady regime characterized by fluctuations of the GB velocity and solute cluster morphology about a baseline configuration. (b) Evolution of the solute concentration profile at the timepoints of panels (a.1-4). (c) Zoom-in atomistic views of panels (a.1-4) highlighting the evolution of the GB structure, solute clustering, and faceting during the self-pinning process.
• Figure 4: Quantitative metrics of the system in Fig.\ref{['fig:self_pinning_qual']} describing (a) the GB velocity $V$, (b) Segregation $\Gamma$, (c) Number of clusters ($N_{\mathrm{C}}$) at the GBs, and (d) average clusters size ($S_{\mathrm{C}}$) at the GBs.
• Figure 5: Coupled evolution of GB mobility, solute drag, solute clustering, and solute segregation as a function of GB velocity at $T=0.15$ and $J_{\mathrm{sg}}=-0.2$, shown for three values of the solute--solute interaction parameter $J_{\mathrm{ssg}}=-0.2$, $-0.3$, and $-0.4$. (a) Driving force $F$ required to sustain a given GB velocity $V$ for segregating systems (circles) compared to the non-segregating reference case with $J_{\mathrm{sg}}=J_{\mathrm{ssg}}=0$ (squares). (b) Solute drag force $P$ exhibiting a pronounced maximum at a characteristic velocity $V^{\ast}$. (c) Average number of solute clusters along the GB, $N_{\mathrm{C}}$, showing a peak near $V^{\ast}$ that reflects the formation and subsequent breakup of solute-induced self-pinning structures during GB motion. (d) GB segregation, $\Gamma$, as a function of $V$, demonstrating a monotonic decrease with increasing velocity and a rapid collapse beyond $V^{\ast}$.