Mat Grain Boundary

Grain Boundary Energy Calculation

<!-- mcp-tools-note -->

[!NOTE] Steps written server.tool are MCP tool calls: matgl.load_model is the load_model tool of the matgl server (mcp__matgl__load_model, or mcp__plugin_atomistic-skills_matgl__load_model when installed as a plugin). Without a connected server, run the same tools from the shell. Tools named in one command share a process, so a model loaded by load_model stays loaded:

${CLAUDE_SKILL_DIR}/../../venv/run mlip python -m src.mcp_server.cli matgl load_model key=value relax_structure key=value
${CLAUDE_SKILL_DIR}/../../venv/run cpu python -m src.mcp_server.cli base search_materials_project_by_formula key=value

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-PES-MatPES-r2SCAN-1M-2026.9 (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 $E_{bulk}$.

matgl.load_model(model_name="CHGNet-PES-MatPES-r2SCAN-1M-2026.9")
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.

${CLAUDE_SKILL_DIR}/../../venv/run cpu python ${CLAUDE_SKILL_DIR}/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/

Key parameters:

The script writes one CIF per unique GB, with filename format sigma{Σ}_{angle:.1f}deg_{hkl}.cif.

[!TIP] For a first survey use --max-sigma 13 (gives Σ1, Σ3, Σ5, Σ7, Σ9, Σ11, Σ13). Increase to 29 for more complete misorientation curves.

4. Relax Grain Boundary Structures

Relax all generated GB structures. Do NOT relax the cell in directions parallel to the GB plane — use relax_cell=False to fix the in-plane lattice vectors and only relax atomic positions.

matgl.load_model(model_name="CHGNet-PES-MatPES-r2SCAN-1M-2026.9")
matgl.relax_structure(
    structure_data="gb_structures/",
    relax_cell=False,
    fmax=0.02,
    output_dir="gb_relaxations/"
)

[!IMPORTANT] relax_cell=False is required. The in-plane lattice vectors of the GB supercell are fixed by the CSL geometry and must remain constant to preserve the grain boundary orientation.

5. Calculate Grain Boundary Energies

${CLAUDE_SKILL_DIR}/../../venv/run cpu python ${CLAUDE_SKILL_DIR}/scripts/calculate_gb_energy.py \
    --bulk-energy-per-atom -4.567 \
    --gb-relaxation-dir gb_relaxations/ \
    --output-dir gb_results/

The script reads the JSON output from each relaxation, applies the GB energy formula, and generates:

• gb_energy_results.json — Σ, angle, area, $\gamma_{GB}$, and provenance per boundary
• gb_energy_vs_angle.png/svg — plot of $\gamma_{GB}$ (J/m²) vs. misorientation angle (°)
• gb_summary_table.csv — CSV for further analysis