mat-grand-canonical-mc

Grand Canonical Monte Carlo

Goal

To perform Grand Canonical Monte Carlo (GCMC) simulations using cluster expansion models to study composition-dependent thermodynamics and generate temperature-composition (T-x) phase diagrams. GCMC allows the system composition to vary by controlling the chemical potential ($\mu$) instead of fixing composition directly.

Background

In the canonical ensemble (fixed N, V, T), Monte Carlo simulations explore configurational space at a fixed composition. In contrast, the grand canonical (or semigrand canonical) ensemble allows composition to fluctuate in response to specified chemical potentials. This is particularly useful for:

• Mapping phase diagrams (composition vs. temperature)
• Identifying miscibility gaps and phase transitions
• Studying composition-dependent thermodynamics
• Exploring equilibrium compositions at different chemical potentials

For binary alloys (e.g., Cu-Ag), we typically control the chemical potential difference Δμ = μ_A - μ_B by setting one species to μ = 0 and varying the other.

Workflow

Step 1: Load a Trained Cluster Expansion

Start with a trained cluster expansion model. You can train one using the ml-cluster-expansion skill or use an existing model.

# Load the cluster expansion
from smol.cofe import ClusterExpansion

ce = ClusterExpansion.load("path/to/cluster_expansion.json")
print(f"Loaded CE with {len(ce.cluster_subspace)} clusters")

Step 2: Run Chemical Potential Sweep

Use the run_gcmc_sweep.py script to perform systematic sweeps of chemical potential at different temperatures.

# Env: smol-agent
python .agents/skills/mat-grand-canonical-mc/scripts/run_gcmc_sweep.py \
    --ce_file cluster_expansion.json \
    --supercell 3 3 3 \
    --temperatures 400 600 800 1000 \
    --mu_min -0.4 \
    --mu_max 0.4 \
    --num_mu_points 20 \
    --steps 50000 \
    --equilibration_steps 10000 \
    --element Ag \
    --output_dir gcmc_results/