Alloy Phase Diagram Validation

alloy-phase-diagram-validation

A new Wang-Landau approach to obtain phase diagrams for multicomponent alloys — Takeuchi et al. (2016) (arXiv:1609.05292, 2016)

What this evaluates

Evaluates a Wang-Landau sampling method combined with cluster expansion for predicting thermodynamic phase diagrams of binary alloys. It probes the method's ability to capture ordering and phase-separation tendencies, and accurately reproduce experimental phase boundaries and transition temperatures.

Datasets

• Cu-Au alloy — total 183; splits: train (183)
• Pd-Rh alloy — total 71; splits: train (71)

Metrics

• cross-validation score (primary) — range: other
  • Mean absolute error between DFT-calculated formation energies and cluster expansion predictions for structures excluded from the ECI fitting set.
• phase diagram fidelity — range: other
  • Comparison of predicted temperature-composition (T-x) phase boundaries and transition temperatures against established experimental data (Okamoto et al.).

Input / output format

Input: Atomic configurations on an fcc lattice (supercells up to 32 atoms), chemical potentials (μ), and temperature (T).

Output: Effective Cluster Interactions (ECI), Helmholtz free energy F(T,x), equilibrium composition x, and T-x phase diagrams.

Scoring recipe

def evaluate_eci(dft_energies, ce_energies):
    return mean(abs(dft_energies - ce_energies))

def evaluate_phase_diagram(predicted_Tx, experimental_Tx):
    temp_error = abs(predicted_Tx['T_trans'] - experimental_Tx['T_trans'])
    boundary_match = compare_curves(predicted_Tx['x'], experimental_Tx['x'])
    return temp_error, boundary_match

Common pitfalls

• Neglecting non-configurational free energy (vibrational/electronic) shifts transition temperatures, though low-T phases remain qualitatively correct.
• Differential errors when converting T-μ diagrams to T-x diagrams, exacerbated by small simulation cell sizes.
• Phase-separation systems may lack clear heat capacity peaks, requiring common-tangent construction on Helmholtz free energy instead of peak detection.

Evidence (verbatim from paper)

We obtained 16 optimized ECI (see Fig.1(a)) with the prediction accuracy, a cross-validation score, of 1.1 meV/atom, which gives sufficient accuracy to capture the thermodynamic characteristics for Cu-Au alloy. Compared with our result and the experimental oneOkamotoet al.* (a)*, we confirmed that our method successfully describe the Cu-Au phase diagram that captures the thermodynamic characteristics of Cu-Au alloy.

Citation

@misc{takeuchi2016wanglandau,
  title={A new Wang-Landau approach to obtain phase diagrams for multicomponent alloys},
  author={Takeuchi et al. (2016)},
  year={2016},
  note={arXiv:1609.05292}
}

• arXiv: 1609.05292