Multiscale Modeling of Abnormal Grain Growth: Role of Solute Segregation and Grain Boundary Character

TL;DR

This work addresses the challenge of predicting abnormal grain growth (AGG) by linking atomic-scale solute segregation energetics at grain boundaries to mesoscale grain-growth dynamics in $\alpha$-Fe. It introduces a multiscale approach that couples DFT-derived segregation energies for nine solutes along the $<110>$ axis with CLS-based solute drag and anisotropic phase-field simulations to capture AGG across three symmetric tilt GB types: $\sum 3 (\bar{1}11)$, $\sum 3 (11\bar{2})$, and $\sum 9 (\bar{2}21)$. Key findings show that low-energy $\Sigma 3$ boundaries generally have higher mobility and weaker drag, while AGG emerges only when high-mobility GBs occur in a mixed-boundary environment (roughly 10–30%), producing crown-like grain morphologies; the GB type distribution critically governs AGG. The results provide a predictive framework for tailoring grain growth via strategic solute design and GB engineering in advanced Fe-based alloys, with broad implications for performance and processing.

Abstract

Abnormal grain growth (AGG) influences the properties of polycrystalline materials; however, the underlying mechanisms, particularly the role of solute segregation at the grain boundary (GB), are difficult to quantify precisely. This study demonstrates a multiscale framework that integrates atomic-scale segregation energetics (using density functional theory) with mesoscale grain growth dynamics (using phase-field model) to investigate AGG, using $α$-Fe as an example system. Multisite segregation energies are calculated for symmetric tilt grain boundaries (STGBs) along the $\langle 110 \rangle$ axis for nine different solutes (Co, Cr, Mn, Mo, Nb, Ni, Ti, W, and V), encompassing three different types of coincident site lattice (CSL) boundaries: $\sum 3 (11\bar{2})$, $\sum 9 (\bar{2}21)$, and $\sum 3 (\bar{1}11)$. The model takes into account the effect of solute drag on GB mobility, estimated using a bulk solute concentration of 0.1 at\%. The results demonstrate that AGG originates due to GB anisotropy, the extent of which largely depends on the type of solute atom present. Such a complex dependence necessitates using a multiscale model to understand AGG comprehensively. In general, low-energy $Σ3$ boundaries are found to have higher mobility and show preferential growth for most of the solutes, other than Co. The study reveals how the distribution of GB types significantly influences AGG. When 10-30\% of the GBs are high-mobility type, crown-like morphologies are observed, leading to AGG. These findings underscore the critical role of GB chemistry and crystallography in governing AGG, and the model can be generalized to provide a predictive framework for controlling grain growth through strategic solute design in advanced alloys.

Figures (10)

• Figure 1: GB structures for STGBs, where the dotted red line denotes the center of the GB, having width $l_{GB}$. Segregation energies are calculated by placing a single solute atom at various segregation sites, highlighted in blue. The topmost structure corresponds to a twin boundary, while the remaining ones are symmetric tilt boundaries. The structures were visualized using VESTA VESTA.
• Figure 2: Site-wise segregation energies as a function of distance from the GB center. Note that, magnitude of $E_{seg}$ is relatively small in case of low energy $\Sigma 3(11\overline{2})$.
• Figure 3: (Left) Bar plot illustrates the segregation energy spectrum across different segregating sites [Figure \ref{['fig:schematic']}]. Yellow lines denote the value of effective segregation energy $E_0$ [Equation \ref{['eq:solute_excess_CLS']}]. The circles represent the diffusivity of the respective element in $\alpha$-Fe. (Right) Grain boundary mobility [Equation \ref{['eq:mobility']}] of $\alpha$-Fe with 0.1% solute concentration at 850 K.
• Figure 4: Mobility of the three STGBs, from top to bottom: $\sum 3 (11\bar{2})$, $\sum 9 (\bar{2}21)$, and $\sum 3 (\bar{1}11)$). Variation of mobility as a function of: (a) temperature (at a constant bulk Cr concentration of 0.1%) and (b) bulk Cr concentration (at a constant temperature of 850 K). Similar plots are given for the rest of the solute atoms in Figures S3-S10, SM.
• Figure 5: (Top) Initial equiaxed microstructure with nearly equal-sized grains generated from Voronoi tessellation. (Bottom) Different grain shapes: (a) Grain with fewer than six sides. Such grains will disappear in later time steps. (b) Six-sided stable grains. (c) Crown-type morphology with a very large number of sides. Such a morphology is observed when a very large grain is surrounded by several small grains, resulting in abnormal grain growth. Note that the initial microstructure mainly has 5 to 7-sided grains, most of which are 6-sided.