mat-grain-boundary

Grain Boundary Energy Calculation

Goal

To compute the specific grain boundary energy ($\gamma_{GB}$, J/m²) for a series of coincidence site lattice (CSL) grain boundaries using Machine Learning Interatomic Potentials. This enables:

• Identification of low-energy special grain boundaries (Σ3, Σ5, Σ7, ...)
• Anisotropy analysis of GB energy as a function of misorientation angle
• Input data for polycrystalline simulations (phase-field, kinetic Monte Carlo)

The grain boundary energy is defined as:

$$\gamma_{GB} = \frac{E_{GB} - N \cdot E_{bulk}}{2 A}$$

where $E_{GB}$ is the total energy of the GB supercell, $N$ is the number of atoms, $E_{bulk}$ is the DFT/MLIP energy per atom of the relaxed bulk, and $A$ is the interfacial area (one GB, periodic cell contains two identical GBs hence the factor of 2).

Instructions

1. Select Foundation Potential

GB calculations benefit from accurate interatomic forces. Prefer r2SCAN-level models for energy accuracy:

• MACE-MH-1 with matpes_r2scan head (recommended)
• CHGNet-MatPES-r2SCAN-2025.2.10-2.7M-PES (MatGL)
• TensorNet-MatPES-r2SCAN-v2025.1-PES (MatGL, faster)

Refer to ml-foundation-potentials.

2. Relax Bulk Reference

Perform a high-accuracy bulk relaxation to obtain $E_{bulk}$.

# Env: matgl-agent
mcp_matgl_load_model(model_name="CHGNet-MatPES-r2SCAN-2025.2.10-2.7M-PES")
mcp_matgl_relax_structure(
    structure_data="bulk.cif",
    relax_cell=True,
    fmax=0.005,
    output_dir="bulk_relaxation/"
)

Record the final energy per atom ($E_{bulk}$) from the relaxation output JSON.

3. Generate Grain Boundary Structures

Use pymatgen's GrainBoundaryGenerator to create CSL grain boundary supercells for a range of Σ values and rotation angles.

# Env: base-agent
python .agents/skills/mat-grain-boundary/scripts/create_grain_boundary.py \
    --bulk bulk_relaxation/relaxed_structure.cif \
    --rotation-axis 0 0 1 \
    --max-sigma 29 \
    --min-slab-size 10.0 \
    --vacuum 0.0 \
    --output-dir gb_structures/