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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

Binary mixing and phase separation

Explore free energy, binodal coexistence and spinodal instability in a symmetric regular solution.

Scientific inputs
Method scope & sources

Ideal configurational entropy with a constant symmetric interaction energy.

  • A model binary system, not an assessed material phase diagram
  • Constant interaction parameter and equal lattice-site basis
  • No ordering, elastic strain, pressure or additional phases

MIT thermodynamics of materials ↗

Edit calculation inputs ↓
Calculated result

Phase Separating

Model calculation
Symmetric-model critical temperature1,082.5K
Supplied interaction energy18,000J/mol
Mixing free energy (J/mol)
2,771.101,186.20.25-398.670.5-1,983.50.75-3,568.41
Mole fraction B
Mixing free energy at 300 KMixing free energy at 1400 K
Mole fraction B: 0 · Mixing free energy: 0 J/mol

Interpret the result

  • Binary symmetric regular solution with composition-independent, temperature-independent interaction Ω.
  • Ideal configurational entropy; one disordered phase and no ordered compounds, magnetism, elastic coherency or competing crystal structures.
  • Ω is a supplied physical parameter. A material formula alone does not determine it.

This is a model phase diagram, not an assessed CALPHAD database or measured phase diagram.

Numerical checks & provenance
Common-tangent chemical-potential equality1.1116E-14 ≤ 1E-8
A/B exchange symmetry7.5791E-17 ≤ 1E-12
Pure-component mixing energy0 ≤ 1E-12 J/mol

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

Input SHA-256: 71e5ac473ae4fc0913d7086112278b94ed8ed4f830cb28830fb15396bc60921b
Runner SHA-256: f27376d0f80371a1da4c926f1a21d43d841802e9f87bac7e876738ea78181e3d
atlas 1 · python 3.14.10 · numpy 2.5.4 · scipy 1.18.1
Calculated 11/12/2026, 2:03:23 AM · 0.001575 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.

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