[Paper Review] A unified theory of grain growth in polycrystalline materials

Jianfeng Hu, Xianhao Wang+4 more|arXiv (Cornell University)|Dec 14, 2018

Microstructure and mechanical propertiesMaterials Science61 references3 citations

TL;DR

This paper presents a unified, nonlinear theoretical model for grain growth in polycrystalline materials that explains normal, abnormal, and stagnant grain growth behaviors by redefining the relationship between grain boundary migration and capillary driving force. The model reveals that the classical linear relationship is a special case, and experimental data from SrTiO3 validate its predictive power for microstructural evolution.

ABSTRACT

Grain growth is a ubiquitous and fundamental phenomenon observed in the cellular structures with the grain assembly separated by a network of grain boundaries, including metals and ceramics. However, the underlying mechanism of grain growth has remained ambiguous for more than 60 years. The models for grain growth, based on the classically linear relationship between the grain boundary migration and capillary driving force, generally predict normal grain growth. Quantitative model for abnormal grain growth is lacking despite decades of efforts. Here, we present a unified model to reveal quantitatively how grain growth evolves, which predicts the normal, abnormal and stagnant behaviors of grain growth in polycrystalline materials. Our model indicates that the relationship between grain boundary migration and capillary driving force is generally nonlinear, but will switch to be the classically linear relationship in a specific case. Furthermore, the grain growth experiments observed in polycrystalline SrTiO3 demonstrates the validity of the unified model. Our study provides a unified, quantitative model to understand and predict grain growth in polycrystalline materials, and thus offers helpful guides for the microstructural design to optimize the properties of polycrystalline materials.

Motivation & Objective

• To resolve the long-standing ambiguity in grain growth mechanisms in polycrystalline materials over the past 60 years.
• To address the lack of quantitative models for abnormal grain growth despite decades of research.
• To develop a unified framework that predicts normal, abnormal, and stagnant grain growth behaviors in polycrystalline systems.
• To establish a nonlinear relationship between grain boundary migration and capillary driving force as the fundamental mechanism, with the classical linear model as a limiting case.

Proposed method

• Derivation of a nonlinear constitutive relation between grain boundary migration velocity and capillary driving force, replacing the classical linear assumption.
• Incorporation of geometric and energetic constraints of grain boundaries in polycrystalline networks to model collective behavior.
• Use of a generalized mobility function to capture the transition between different growth regimes (normal, abnormal, stagnant).
• Validation of the model against experimental data from polycrystalline SrTiO3, where grain size evolution was measured under controlled conditions.
• Numerical simulation of grain growth dynamics under varying boundary mobility and curvature conditions to demonstrate regime transitions.
• Analysis of the critical conditions under which the nonlinear model reduces to the classical linear relationship.

Experimental results

Research questions

• RQ1 What is the true nature of the relationship between grain boundary migration and capillary driving force in polycrystalline materials?
• RQ2 Why has quantitative prediction of abnormal grain growth remained elusive despite extensive research?
• RQ3 Under what conditions does the classical linear model of grain growth emerge as a special case of a more general nonlinear framework?
• RQ4 How can a single theoretical model account for the coexistence of normal, abnormal, and stagnant grain growth regimes?
• RQ5 What experimental evidence supports the proposed nonlinear unified theory of grain growth?

Key findings

• The relationship between grain boundary migration and capillary driving force is fundamentally nonlinear, with the classical linear model being a specific limiting case.
• The unified model successfully predicts the emergence of normal, abnormal, and stagnant grain growth regimes based on material-specific boundary mobility and curvature conditions.
• Experimental data from polycrystalline SrTiO3 show excellent agreement with model predictions, confirming its validity across different growth behaviors.
• The model identifies critical thresholds in boundary mobility and curvature that determine the transition between growth regimes.
• The nonlinear formulation resolves long-standing inconsistencies in grain growth theory and provides a quantitative basis for microstructural design in materials engineering.