The physics workbench

See how a crystal responds.

Explore the energy landscape of four metals. Inspect every calculated point, understand the model behind it, and run your own volume scans.

Aluminum · reference calculation

Energy & volume

Calculated · EMT · 0 K

Compress or expand an ideal crystal. The energy minimum estimates its preferred volume; the curvature measures resistance to compression.

Lattice parameter3.994 ÅConventional FCC unit cell

Equilibrium volume15.93 Å³/atomFitted energy minimum

Bulk modulus39.6 GPaModel estimate at 0 K

Computed samplesFitted equilibrium volume

Lines between samples guide the eye. Energy is relative to the fitted minimum, not an isolated-atom reference.

Sample 7 of 1316.6075 Å³/atom3.38129 meV/atom relative to fitted minimum

Inspect the 13 computed samples

Absolute energies use the EMT potential’s energy reference.
Sample	Volume (Å³/atom)	Energy (eV/atom)	Relative energy (meV/atom)
1	15.27892875	-0.0014328762	3.45045960
2	15.50036250	-0.0033955182	1.48781760
3	15.72179625	-0.0045360166	0.34731919
4	15.94323000	-0.0048815949	0.00174086
5	16.16466375	-0.0044666156	0.41672015
6	16.38609750	-0.0033278310	1.55550482
7	16.60753125	-0.0015020476	3.38128821
8	16.82896500	0.0009750092	5.85834500
9	17.05039875	0.0040692609	8.95259670
10	17.27183250	0.0077485971	12.63193292
11	17.49326625	0.0119831316	16.86646742
12	17.71470000	0.0167455084	21.62884420
13	17.93613375	0.0220113551	26.89469089

Method, numerical checks & provenance

ASE’s effective-medium theory potential evaluates an ideal face-centered cubic crystal at 0 K. A stabilized jellium equation of state fits 13 volumes over ±8%. The fit residual is 0.0000051321 eV/atom. It measures fit error, not uncertainty against experiment.

Energy minimum: Inside sampled range · positive curvature
Energy–stress consistency: 2.132e-11 ≤ 0.00001 eV/Å³
Finite-difference force check: 4.132e-10 ≤ 0.0001 eV/Å
Supercell energy agreement: 5.662e-15 ≤ 1e-7 eV/atom
Engine: ASE 3.29.0 · NumPy 2.5.4 · SciPy 1.18.1
Calculated: 2026-11-12 · 01:05:53 UTC
Input SHA-256: d3a90e940a55a44a9f4c811cf7ef6a5cc9ad84b968ff1bac23d97972e428e568
Worker SHA-256: 4c14dfddcb3696be2ad35f0a4fb02ef0ba2716d654f3d571b6a2f883cd78e47c

These checks establish numerical consistency within this model. Experimental accuracy and property uncertainty have not been quantified for this run.

Read the EMT method ↗

Your calculations

Run a volume scan

Choose a metal and sample its energy over a small range of crystal volumes.

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Know the model

A precise, narrow lens.

Effective-medium theory (EMT) is a fast empirical potential for metallic bonding. These calculations describe ideal, face-centered cubic Al, Cu, Ag and Au at 0 K.

Read the lattice size, equilibrium volume and resistance to uniform compression.
Numerical checks verify forces, stress and the fitted minimum within the model.
Temperature, defects, melting, electronic properties and chemical reactions are outside this recipe.

Calculated values are model predictions. Compare with appropriate experiments or higher-fidelity calculations before using them in a research decision.

Method documentation ↗