[Paper Review] The Role of Surface Tension and Mobility Model in Simulations of Grain Growth

Tiago Salvador, Selim Esedoḡlu|arXiv (Cornell University)|Jul 26, 2019

Metallurgy and Material Forming17 references4 citations

TL;DR

This study uses large-scale threshold dynamics simulations to investigate how surface tension and mobility models affect grain growth in polycrystalline materials. In 2D, grain size distributions are insensitive to model choice, but in 3D, anisotropic reduced mobilities significantly alter the stationary grain size distribution, while the misorientation distribution function rapidly converges to the Mackenzie distribution regardless of initial conditions.

ABSTRACT

We explore the effects of surface tension and mobility models in simulations of grain growth using threshold dynamics algorithms that allow performing large scale simulations, while naturally capturing the Herring angle condition at junctions and automatically handling topological transitions. The results indicate that in two dimensions, the different surface tension / mobility models considered do not play a significant role in the stationary grain size distribution. However, in three dimensions, there is a substantial difference between the distributions obtained from the same three models, depending on whether the reduced mobilities are isotropic or anisotropic. Additional results show that in three dimensions, the misorientation distribution function of a grain network with random orientation texture returns to the close vicinity of the Mackenzie distribution even if started very far from it.

Motivation & Objective

• To investigate the influence of surface tension and mobility models on grain growth dynamics in polycrystalline materials.
• To determine whether different surface tension and mobility combinations affect the stationary grain size distribution (GSD) in 2D and 3D.
• To examine the asymptotic behavior of the misorientation distribution function (MDF), particularly its convergence to the Mackenzie distribution under non-equilibrium initial conditions.
• To compare simulation results with experimental data and assess model consistency.
• To develop and apply a novel algorithm for generating initial grain networks with perturbed MDFs while preserving random texture.

Proposed method

• Employed a threshold dynamics algorithm for the Mullins continuum model of grain boundary motion, enabling large-scale simulations with automatic topological transition handling.
• Used three distinct surface tension and mobility models: (i) Read-Shockley surface tension with isotropic mobility, (ii) Read-Shockley surface tension with reciprocal mobility (anisotropic junction angles), and (iii) isotropic surface tension and mobility (symmetric 120° junctions).
• Applied a steepest descent procedure on the L² norm of the difference between the regularized MDF and a target distribution to generate initial grain networks with non-Mackenzie MDFs while maintaining uniform orientation distribution.
• Simulated grain growth in both 2D and 3D using the threshold dynamics method, tracking evolution of GSD and MDF over time.
• Regularized the MDF using a Gaussian kernel to smooth discrete misorientation angle data, enabling quantitative comparison with theoretical distributions.
• Validated results against experimental data from literature and analyzed isoperimetric ratios to assess grain shape evolution.

Experimental results

Research questions

• RQ1 Does the choice of surface tension and mobility model significantly affect the stationary grain size distribution in 2D and 3D grain growth simulations?
• RQ2 How do anisotropic versus isotropic reduced mobilities influence the final grain size distribution in three dimensions?
• RQ3 Can a misorientation distribution function (MDF) that starts far from the Mackenzie distribution evolve toward it in 3D grain growth simulations?
• RQ4 To what extent do junction angles and mobility anisotropy affect grain shape statistics such as isoperimetric ratios?
• RQ5 How do different initial MDF configurations impact the long-term evolution of grain network statistics?

Key findings

• In 2D, the stationary grain size distribution is nearly identical across all three surface tension and mobility models tested, indicating insensitivity to model choice.
• In 3D, the grain size distribution differs significantly between the model with anisotropic reduced mobilities (model ii) and the two with isotropic reduced mobilities (models i and iii), showing that reduced mobility anisotropy plays a key role.
• The grain size distribution from model (i) with Read-Shockley surface tension and isotropic mobility is consistent with experimental data, despite substantial variation in measurements.
• The misorientation distribution function (MDF) in both 2D and 3D simulations converges rapidly to a very close vicinity of the Mackenzie distribution, even when initialized far from it, provided the initial texture is random.
• The MDF evolution is nearly identical between models (i) and (ii), despite their different junction angles, suggesting that isotropy of reduced mobilities is more critical than junction angle symmetry.
• Grain shape statistics, such as isoperimetric ratios, show strong dependence on the choice of surface tension and mobility model, particularly in 3D.