Simulating Grain Nucleation with Circular Growth

In materials science, simulating grain nucleation and growth processes helps understand the microstructural evolution of metals or alloys. Grain nucleation refers to the formation of initial crystal nuclei under supercooled or supersaturated conditions, while circular growth describes the outward expansion of grains in an approximately circular pattern.

Grain Nucleation Nucleus formation typically follows a probability model with random distribution, where nucleation sites can be uniformly distributed or follow specific probability density functions. In simulation implementations, you can define the number of nuclei and their spatial distribution—for example, by generating initial nucleation points through random coordinate generation using functions like rand() or numpy.random.uniform() in a defined simulation domain.

Circular Growth Circular growth is commonly implemented using phase-field models or distance-transform methods. The phase-field model describes grain boundary movement through partial differential equations, while the distance-transform approach calculates the distance from each point to the nearest nucleus—if this distance is below a specified threshold, the point is assigned to that grain. This method is computationally efficient and ideal for simulating idealized circular growth scenarios. Key functions involve scipy.ndimage.distance_transform_edt for Euclidean distance mapping and threshold-based region growing algorithms.

Simulation Implementation Approach 1. Initialize nucleation points: Randomly generate multiple nucleation centers and record their coordinates using array-based data structures. 2. Compute distance field: For each pixel/voxel in the simulation area, calculate distances to all nuclei using vectorized operations, then identify the nearest nucleus through argmin or similar functions. 3. Growth control: Set growth rates or time steps to incrementally expand grain radii, updating grain boundaries via loop iterations or parallel processing. 4. Boundary handling: When grains meet, implement collision detection to halt growth and prevent overlap, forming clear grain boundaries through logical masking or nearest-neighbor checks.

This methodology enables the study of competitive grain growth and microstructural evolution in materials science research.