Model. Compare. Investigate.
Work from molecular geometry, crystal structure, processing conditions or a material stack. Inspect the physics, compare calculated results, and turn uncertainty into the next research question.
Neutral defects in a crystal
Construct a vacancy or interstitial, relax its local geometry and account for formation energy against an explicit chemical potential.
Method scope & sources
Monatomic neutral defects under a specified Lennard–Jones model, with immutable before/after structures.
- Explicit pair-potential and chemical-potential reference
- Neutral defects only; no electronic charge corrections
- Finite supercells and local relaxation need size and convergence checks
Neutral vacancy · periodic pair model
Interpret the result
- Neutral defect with explicit atom-count change and compatible total-cell energy normalization.
- Identical pair potential and periodic cell for bulk and defect; atom positions may relax while cell vectors remain fixed.
- Formation energy uses E_defect − E_bulk − Σ ΔN μ; no Fermi-level or charged-cell correction is included.
Uniform Lennard–Jones bonding is an explicitly supplied model; an element label does not establish defect accuracy for real chemistry.
The cell is fixed and periodically repeats the defect. Finite-size interactions and chemical-potential uncertainty require separate convergence and evidence.
The chemical potential is user-supplied with a declared reference; textual provenance is not an independent verification of that reservoir.
Meeting a force threshold establishes stationarity, not a stable minimum. High-symmetry interstitials may be saddle points; a defect Hessian or perturbed multi-start relaxation is needed to test stability.
Numerical checks & provenance
Passing these checks verifies the stated numerical properties. Agreement with experiment requires a separate, condition-matched comparison.
Input SHA-256: e34b8b12305f78febebea5f6b26dd49134b7028a46c0c95937d60ccfd5d96daf
Runner SHA-256: f27376d0f80371a1da4c926f1a21d43d841802e9f87bac7e876738ea78181e3d
atlas 1 · python 3.14.10 · numpy 2.5.4 · scipy 1.18.1 · defects_sha256 0245994c7e3ad6257a618393814b9c3c319125205a00b1751003d8efb60afa41 · ase 3.29.0
Calculated 11/12/2026, 2:07:51 AM · 0.074023 s
Test the explanation
Compare a numerical refinement or a different physical assumption. Agreement within one model does not establish agreement with experiment.
Build the investigation
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