Surface Energy Calculation

Goal

To determine the surface energy ($\gamma$) of different crystallographic planes (hkl) and construct the equilibrium crystal shape (Wulff shape) using structural relaxation with Machine Learning Interatomic Potentials (MLIPs).

Instructions

1. Select Level of Theory: Choose the target accuracy level for surface energy calculations.

   • Recommended: r2SCAN-level foundation potentials for high accuracy in inorganic systems.
   • Examples: CHGNet-MatPES-r2SCAN-2025.2.10-2.7M-PES (MatGL), TensorNet-MatPES-r2SCAN-v2025.1-PES (MatGL), or MACE-MH-1 with matpes_r2scan head.
   • See ml-foundation-potentials for detailed guidance.

2. Relax Bulk Reference: Perform a high-accuracy relaxation of the bulk material to serve as the reference energy.

   # 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=0.01,
       output_dir="bulk_relaxation/"
   )
   

   Note: Record the final energy per atom ($E_{bulk}$).

3. Generate Slabs: Create oriented slabs for the target (hkl) planes.

   # Env: base-agent
   python .agents/skills/mat-surface-energy/scripts/create_slabs.py \
       --bulk bulk_relaxation/relaxed_structure.cif \
       --max_index 1 \
       --min_thickness 10.0 \
       --vacuum 15.0 \
       --output slabs/
   

   This script generates slabs for all unique planes up to the specified max_index.

4. Relax Slabs: Perform structural relaxation on all generated slabs.

   # Env: matgl-agent
   mcp_matgl_load_model(model_name="CHGNet-MatPES-r2SCAN-2025.2.10-2.7M-PES")
   mcp_matgl_relax_structure(
       structure_data="slabs/",
       relax_cell=False,  # DO NOT relax cell for slabs (fixed area)
       fmax=0.02,
       output_dir="slab_relaxations/"
   )
   

   Important: Keep the unit cell fixed (relax_cell=False) to maintain the target surface area.

5. Calculate Surface Energy: Compute the surface energy for each plane.

   # Env: base-agent
   python .agents/skills/mat-surface-energy/scripts/calculate_surface_energy.py \
       --bulk_energy_per_atom -4.567 \
       --slab_dir slab_relaxations/ \
       --output surface_energies.json
   

   Surface energy is calculated as: $$\gamma = \frac{E_{slab} - N \cdot E_{bulk}}{2A}$$ where $E_{slab}$ is the total energy of the slab, $N$ is the number of atoms in the slab, $E_{bulk}$ is the energy per atom of the bulk, and $A$ is the surface area.

6. Generate Wulff Shape: Construct the Wulff shape from the calculated surface energies.

   # Env: base-agent
   python .agents/skills/mat-surface-energy/scripts/generate_wulff.py \
       --energies_json surface_energies.json \
       --bulk bulk_relaxation/relaxed_structure.cif \
       --output wulff_shape.png
   

Examples

Example 1: Aluminum (fcc) Surface Energy

# Generate slabs up to index 1 (100, 110, 111)
python .agents/skills/mat-surface-energy/scripts/create_slabs.py --bulk Al.cif --max_index 1

# Load and run relaxations using CHGNet
mcp_matgl_load_model(model_name="CHGNet-MatPES-r2SCAN-2025.2.10-2.7M-PES")
mcp_matgl_relax_structure(structure_data="Al.cif", relax_cell=True, output_dir="bulk_relax")
mcp_matgl_relax_structure(structure_data="slabs/", relax_cell=False, output_dir="slab_relax")

# Calculate and generate Wulff shape
python .agents/skills/mat-surface-energy/scripts/calculate_surface_energy.py --bulk_energy_per_atom -3.36 --slab_dir slab_relax/
python .agents/skills/mat-surface-energy/scripts/generate_wulff.py --energies_json surface_energies.json --bulk Al.cif

Constraints

• Cell Relaxation: Do NOT relax the unit cell during slab relaxation. The surface area must remain constant to match the bulk reference.
• Vacuum: Ensure sufficient vacuum (typically >15 Å) to avoid interactions between periodic images.
• Slab Thickness: Ensure sufficient slab thickness (typically >10 Å) to recover bulk-like behavior in the center of the slab.
• Consistency: Use the SAME MLIP and convergence settings for both bulk and slab relaxations.

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Author: Bowen Deng Contact: GitHub @learningmatter-mit