Grain-Growth Stagnation from Vacancy-Diffusion-Limited Disconnection Climb

TL;DR

Grain-growth stagnation in polycrystals is addressed by identifying vacancy-diffusion-limited disconnection climb as the governing mechanism. The authors extend the phase-field crystal (PFC) model to explicitly include vacancy diffusion and resolve grain-boundary migration on diffusive time scales. They show that vacancy diffusion controls the onset of stagnation and the stagnating grain size, with climb velocities increasing roughly linearly with a diffusion-control parameter $C$ and thresholds for activation. The framework links vacancy transport to disconnection dynamics, offering a tunable, scale-bridging modeling route and enabling control of stagnation in polycrystalline films and alloys. Overall, the work provides a mechanistic, scale-bridging description of GB migration that can inform strategies to stabilize or promote grain growth by tuning vacancy diffusion.

Abstract

Grain growth in polycrystals typically stagnates at long times. We identify disconnection climb, limited by vacancy diffusion, as a fundamental microscopic mechanism underlying this behavior. Using a phase-field crystal framework extended to model vacancy diffusion, we resolve grain-boundary migration on diffusive time scales and show that disconnection climb rates correlate with the characteristic grain size at which growth arrests. These results link vacancy transport, disconnection dynamics, and microstructural evolution, establishing vacancy diffusion as a key governing factor.

Figures (4)

• Figure 1: Controlling vacancy diffusion. (a) Crystal hosting a localized vacancy distribution illustrated by $\psi$ (left, upper half), $\langle \psi \rangle$ (left, lower half), and radial $\langle \psi \rangle$ over time (right). (b) Effective vacancy diffusivity $D=\partial s^2/(2\partial t)$ by varying $C$ with $C_0=3\cdot 10^4$, $D_0 = D(C_0)\approx 61$. (c) Crystal hosting a dislocation with Burgers vector aligned along $y$ axis (left) and $\langle \psi \rangle$ along the $x$ axis by varying $C$. (d) Effective diffusion length $s^2$ by varying $C$ with $s^2_0 = s^2(C_0) \approx 99$. (e) Hydrostatic stress $\sigma_{\rm H}=\sum_i \sigma_{ii}/2$ (left) and stress incompatibility field $\eta_{\mathrm{in}}$ (right) skogvoll2021dislocation of the dislocation in panel (c). (f) $\sigma_{\rm H}(x,0)$ for two values of $C$ at the bound of the considered range in this work with lattice unit $p=2\pi$. Model parameters are: $\kappa = 1$, $T = 0.3$, $\psi_0 =-0.35$, $\rho = 1$ and $\Gamma = 10^4$.
• Figure 2: The impact of vacancy diffusion on grain growth. (a) Evolution of the mean-squared grain size ($R^2$, upper half) and mean-squared grain size of stagnating microstructure (lower half) for various values of $C$ with $R^2_0=R^2(t=0)\approx 1.6\cdot 10^{4}$, $R^2_{S,0}=R^2_S(C=C_0)\approx 1.9\cdot 10^{4}$ and $C_0=3\cdot 10^4$. (b) Microstructure under investigation visualized by the relative orientation of grains $\Phi$. Insets show the density field $\psi$ (bottom left), the shear stress $\sigma_{xy}$ (bottom right), and the stress incompatibility field $\eta_\mathrm{in}$ (top left). (c) Time-sequenced snapshots of a microstructure detail illustrating GB and dislocation migration obtained by reconstructed atom positions (using OVITO toolkit stukowski2009visualization) with model parameters as in Fig. \ref{['fig:effVacDiff']}.
• Figure 3: The impact of vacancy diffusion on defect motion. (a) Dislocation glide and climb velocity for various values of $C$ with $v_0=v(C_0)\approx 2.7\cdot 10^{-3}$ and $C_0=1.08\cdot 10^6$ (linear scale as inset). (b) Disconnection climb velocity for various values of $C$ with $v_0(C=C_0)\approx 2.4\cdot 10^{-5}$ for $(b_\perp, -h_\perp)$, $v_0(C=C_0)\approx 2.0\cdot 10^{-5}$ for $(-b_\perp, -h_\perp)$ and $C_0=3.6\cdot 10^5$ (linear scale as inset) (c) Close-up of the atomic structure in a GB region hosting disconnections with Burgers vector and step height $(b_\perp, h_\perp)$ (upper half) and $(-b_\perp, -h_\perp)$ (lower half). Reconstructed atom positions are obtained using OVITO toolkit stukowski2009visualization with model parameters as in Fig. \ref{['fig:effVacDiff']}.
• Figure S-1: Grain counting routine based on the local orientations of individual grains. (a) Close-up of a polycrystalline configuration containing three individual grains (colored green, dark gray, and light gray, respectively). Grain boundaries and defects identified by applying a sharp threshold to the locally averaged density field $\langle \psi \rangle$ are highlighted in dark blue; the light blue regions indicate the broadened grain-boundary structure obtained by morphological opening. (b) Probability distributions $P(\Phi)$ (in $\%$) of the local orientation field $\Phi$ evaluated within each connected component, shown for the sharp grain-boundary detection (top row) and for the broadened grain-boundary structure (bottom row).