CogLabThe Cognition Lab

Physics simulations

Materials Atlas · physics workbench

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.

Research with AI →Metal equations of state →Methods & scientific foundations →
01 Define the system02 Review the method03 Calculate & check04 Compare & decide
Define your calculation

Crystal energy and vibrations

Explore a periodic crystal with a specified Lennard–Jones pair potential, energy-volume curve and vibration modes.

Scientific inputs
Method scope & sources

Monatomic FCC, BCC or simple-cubic crystals using explicit pair-potential parameters.

  • The element supplies mass and a label; it does not validate the selected potential
  • No electronic, magnetic, many-body or finite-temperature model
  • Unstable modes and an unbracketed minimum affect interpretation

ASE Lennard–Jones calculator ↗

Edit calculation inputs ↓
Calculated result

Ar mass · pair-potential crystal

Model calculation
Equilibrium volume per atom36.33ų/atom
Model energy per atom-0.081769eV/atom
Model bulk modulus3.0717GPa
EOS fit residual6.9406E-6eV/atom
Negative harmonic modes0
Sampled harmonic heat capacity at 300 K2.6125kB/atom
Energy per atom (eV/atom)
-0.0753832.2-0.07697134.395-0.07856236.591-0.08015338.786-0.08174440.982
Volume per atom (ų/atom)
Lennard–Jones energy–volume scan
Volume per atom: 32.2 ų/atom · Energy per atom: -0.07538 eV/atom

Interpret the result

  • Pairwise 12–6 Lennard–Jones potential, zero-temperature geometry, periodic monoatomic cubic structure.
  • Harmonic force constants from central differences at two displacements; masses use ASE elemental values.
  • Cv comes from the computed discrete harmonic frequencies; imaginary modes invalidate a stable harmonic thermodynamic interpretation.

Element selects atomic mass only. Lennard–Jones parameters are supplied inputs and do not describe arbitrary chemical bonding.

Two-by-two-by-two supercell modes are a discrete harmonic sample, not a converged phonon DOS or thermal conductivity.

The shifted-energy finite cutoff is part of the model; cutoffs and sampling need convergence for the target observable.

Numerical checks & provenance
Force-constant reciprocity1.6607E-10 ≤ 1E-5
Half-displacement force-constant refinement1.1774E-7 ≤ 0.0001
Translation invariance before projection1.5068E-10 ≤ 1E-5

Passing these checks verifies the stated numerical properties. Agreement with experiment requires a separate, condition-matched comparison.

Input SHA-256: e28203271c8466d5c8d05f70dc074b7fe146a40483a64649ce074a5293968889
Runner SHA-256: f27376d0f80371a1da4c926f1a21d43d841802e9f87bac7e876738ea78181e3d
atlas 1 · python 3.14.10 · numpy 2.5.4 · scipy 1.18.1 · ase 3.29.0
Calculated 11/12/2026, 2:03:23 AM · 0.38053 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

Bring the observable, conditions and result into a research plan with competing hypotheses and a test that can distinguish them.

Investigate this result →