Computer simulations of two-dimensional and three-dimensional ideal grain growth

Area of Science:

• Materials Science
• Computational Physics
• Metallurgy

Background:

• Grain growth is a fundamental process in materials science, influencing material properties.
• Existing simulation methods face challenges with computational efficiency and scalability.
• Understanding grain size distribution and topological effects is crucial for materials design.

Purpose of the Study:

• To develop an efficient phase-field simulation scheme for grain growth.
• To investigate ideal grain growth in 2D and 3D using large-scale simulations.
• To validate theoretical models like the von Neumann-Mullins law and Hillert theory.

Main Methods:

• Developed an efficient phase-field computation scheme for grain growth simulations.
• Conducted large-scale, coalescence-free simulations in 2D and 3D.
• Analyzed grain size distributions and validated against established laws (von Neumann-Mullins, Hillert).

Main Results:

• Achieved high computational efficiency independent of orientation variables.
• Observed distinct steady-state grain size distributions in 2D and 3D.
• 3D simulations showed excellent agreement with the Hillert 3D theory for ideal grain growth.
• Confirmed the 3D growth law from smaller-scale Surface Evolver simulations.

Conclusions:

• The developed phase-field simulation is efficient and accurate for modeling grain growth.
• The Hillert theory accurately describes 3D ideal grain growth.
• Simulation results provide insights into the relationship between grain topology and growth rate in 3D.