Skip to content

Interatomic potentials for monoatomic metals from experimental data and ab initio calculations

Evidence and attribution

Authority of statements

Prose sections below (Summary, Methods, Findings, etc.) are curated summaries of the publication identified by doi, title, and pdf_path in the front matter above. They are not new primary claims by this wiki.

For definitive numerical values, reaction schemes, and interpretations, use the peer-reviewed article (and optional records under normalized/papers/ when present)—not this page alone.

Summary

The paper develops embedded-atom method (EAM) potentials for Al and Ni by fitting to a joint database of experimental observables and ab initio energies of many alternative crystal structures, with a distance rescaling step to improve consistency between experiment and theory. An alternating fit–test loop compares ab initio structural energies to EAM predictions so the parameterization stays accurate within the limits of the EAM functional form. The resulting potentials reproduce elastic constants, phonons, vacancy formation and migration, stacking faults, surfaces, and relative stabilities across a range of coordinations—aimed at defect, grain-boundary, and dislocation simulations. The motivation is that simple pair fits often fail when coordination changes away from fcc bulk, which is precisely the regime encountered near defect cores.

Methods

This paper reports interatomic potential development and validation only (no molecular dynamics production runs).

Force-field lineage and functional form (checklist A)

  • Form: Embedded-atom method (EAM) / glue model: total energy as a pair sum plus embedding \(F(\bar\rho)\) with atomic density \(\rho\) summed over neighbors (Eqs. (1)–(2) in the article). Al and Ni are parameterized in parallel for consistent comparative use (intended also as building blocks toward Ni–Al compounds, as stated in the introduction).
  • Parametrization: cubic splines for \(V(r)\) and \(\rho(r)\) with a shared cutoff \(r_c\) and smooth cutoff function; embedding \(F(\bar\rho)\) chosen so an effective-pair gauge can be enforced to simplify elastic constants (Sec. III.B–III.C).

Training / reference data

  • Experimental database (Sec. III.A.1): equilibrium lattice parameter, cohesive energy, elastic constants \(c_{11},c_{12},c_{44}\), vacancy formation energy (aligned with the data used by Voter–Chen reference potentials), plus vacancy migration energy, intrinsic stacking fault energy, phonon dispersions, and constraints on surface energies and an empirical equation of state (Rose et al.) anchored at \(a_0\), \(E_0\), and bulk modulus.
  • Ab initio structural energies (Sec. III.A.2): first-principles LAPW, all-electron, general crystal potential; exchange–correlation: Perdew–Wang parametrization of LDA within Kohn–Sham DFT; Brillouin-zone integration via Monkhorst–Pack meshes (modified for low-symmetry cells); Fermi smearing at 2 mRy; authors state a large basis and k-point mesh such that energies converge to better than ~0.5 mRy/atom.
  • Spin treatment: Al calculations spin-restricted; Ni treated with spin-polarized LDA by iterating from an initial moment (Sec. III.A.2).
  • Crystal prototypes and distances: energies for fcc, hcp, bcc, simple hexagonal, simple cubic, L12, and diamond structures; hcp taken at ideal c/a; Al additionally includes A15 (\(\beta\)-W); Ni A15 omitted for computational limitations. Each structure evaluated at three nearest-neighbor distances: 0.95R₀, R₀, and 1.1R₀ (Sec. III).
  • Experiment vs theory alignment: rescaling of distances in the ab initio vs EAM comparison (Eq. (4)) to reduce inconsistency between experimental and ab initio reference volumes; effect on elastic constants discussed explicitly for Al LAPW elastic constants vs experiment (Sec. III).

QM reference (checklist C, as used to build the FF database)

  • Clusters / finite systems: not the focus; the QM block is periodic LAPW structural energies as above.

Optimization / fitting (checklist A)

  • Optimizer: Nelder–Mead simplex with many random starts (Sec. III.C).
  • Objective: minimize weighted sum of relative squared deviations from target properties; weights encode reliability and intended defect applications (Sec. III.C).
  • Fit vs test split: hcp/bcc/diamond ab initio energies included in the fit (via Eq. (4)); other structural energies and tests (including rms metrics reported in Sec. IV/V) used for testing stages; alternating fit/test strategy emphasized in the abstract.

Findings

  • Bulk and harmonic properties: for both Al and Ni, the fitted potentials reproduce the targeted equilibrium properties, elastic constants, and phonon branches substantially better than the Voter–Chen reference in several columns of the paper’s Tables I–II (quantitative comparisons tabulated there).
  • Nonfcc stability and coordination: potentials reproduce relative energies of hcp/bcc/diamond-like prototypes and predict sensible trends for vacancy, interstitial, stacking fault, unstable stacking fault, grain-boundary, and surface energies relative to the reference potentials; authors highlight improved \(\gamma_\mathrm{us}\) values as relevant to dislocation nucleation (discussion around Fig. 3 and Tables I–II).
  • Testing-stage structural-energy rms: authors quote ~0.06 eV (Al) and ~0.15 eV (Ni) rms deviations for ab initio vs EAM structural-energy tests (Sec. IV/V), interpreted as a practical accuracy ceiling for EAM transferability across the sampled coordination range.
  • Transferability caveat: agreement for structural energies is best near equilibrium nearest-neighbor conditions and degrades for more extreme coordinations (e.g., discussion of diamond and surface energies); surfaces are systematically underestimated, consistent with known EAM limitations (Fig. 4 / surface discussion).
  • Future / limitations (authors): emphasize EAM form limits and the need for high-quality, broad QM structural databases; no MD validation trajectories are reported in the article itself.

Limitations

  • Accuracy is bounded by the EAM ansatz; chemically complex environments (alloys, charge transfer) require other models.
  • Heavy reliance on the quality and breadth of the DFT reference set used in the fit.

Relevance to group

Foundational interatomic potential methodology in the same empirical-MD ecosystem as later reactive and ReaxFF work; useful historical context for metal parameterization culture and QM-informed fitting.

Citations and evidence anchors

  • DOI: https://doi.org/10.1103/PhysRevB.59.3393 — Phys. Rev. B 59, 3393 (1999).