Calculator Inputs
The page stays in a single-column flow, while the form uses a responsive grid: three columns on large screens, two on medium, and one on mobile.
Example Data Table
| System | Type | Solute Input | Host Density | Solute Density | Host Lattice | Solute Lattice | Temperature | Notes |
|---|---|---|---|---|---|---|---|---|
| Cu-Ni | Substitutional | 10 wt% | 8.96 g/cm³ | 8.90 g/cm³ | 3.615 Å | 3.524 Å | 1200 K | Near-ideal metallic mixing example. |
| Ag-Au | Substitutional | 25 mole% | 10.49 g/cm³ | 19.32 g/cm³ | 4.086 Å | 4.078 Å | 1000 K | Very small size mismatch. |
| Fe-C | Interstitial | 0.8 wt% | 7.87 g/cm³ | 2.26 g/cm³ | 2.866 Å | 3.567 Å | 1100 K | Interstitial expansion coefficient matters strongly. |
Formula Used
This calculator combines composition conversion, ideal molar-volume mixing, simple lattice estimation, configurational entropy, and a Hume-Rothery style compatibility screen.
For weight-percent input:
n_solute = wt_solute / M_solute
n_host = wt_host / M_host
x_solute = n_solute / (n_solute + n_host)
For mole-percent input:
x_solute = mole_percent / 100
wt_solute = [x_solute × M_solute] / [x_solute × M_solute + (1 − x_solute) × M_host] × 100
Average molar mass:
M_mix = (1 − x) × M_host + x × M_solute
Ideal molar volume and density:
V_mix = (1 − x) × (M_host / ρ_host) + x × (M_solute / ρ_solute)
ρ_mix = M_mix / V_mix
Substitutional lattice estimate (Vegard-style):
a_mix = (1 − x) × a_host + x × a_solute
Interstitial lattice estimate:
a_mix = a_host × (1 + k × x)
Atomic size misfit:
Misfit (%) = [(r_solute − r_host) / r_host] × 100
Configurational entropy:
ΔS_mix = −R [x ln(x) + (1 − x) ln(1 − x)]
Gibbs free energy of mixing:
ΔG_mix = ΔH_mix − T × ΔS_mix
These equations are useful for fast screening. Real solid solutions may deviate because of ordering, magnetic effects, non-ideal interactions, phase boundaries, and temperature-dependent structure changes.
How to Use This Calculator
- Enter a system name for your alloy or crystal pair.
- Select substitutional or interstitial solid solution behavior.
- Choose whether the entered composition is weight percent or mole percent.
- Fill in molar mass, density, lattice parameter, and atomic radius for both components.
- Enter temperature and estimated enthalpy of mixing for thermodynamic screening.
- Provide valence, electronegativity, and crystal-structure match to improve compatibility assessment.
- Click the calculate button to show results above the form.
- Review the result table, chart, assessment text, then export to CSV or PDF if needed.
Frequently Asked Questions
1) What does this solid solution calculator estimate?
It estimates composition conversion, density, lattice parameter, lattice strain, configurational entropy, Gibbs free energy of mixing, and a practical compatibility score based on common solid-solution screening rules.
2) When should I choose substitutional instead of interstitial?
Choose substitutional when solute atoms replace host atoms on lattice sites. Choose interstitial when small atoms occupy gaps between host atoms and mainly expand the host lattice.
3) Does a negative Gibbs free energy guarantee a single phase?
No. Negative mixing free energy suggests favorable mixing at the entered temperature, but it does not guarantee a single phase. Ordering, kinetics, phase diagrams, and competing compounds still matter.
4) Why is size misfit important?
Large atomic size mismatch increases local strain energy. That often lowers solubility, raises defect stress, and can encourage ordering, clustering, or second-phase formation instead of a broad solid solution.
5) Why does the calculator ask for valence and electronegativity?
These values support a quick Hume-Rothery style check. Similar valence and moderate electronegativity differences often favor broader substitutional solubility, while large differences may promote compound formation.
6) Can I use this tool for ceramics or ionic solids?
Yes, but carefully. The screening logic is most natural for metallic systems. Ceramic, ionic, and covalent solids often need charge-balance constraints, defect chemistry, and more detailed thermodynamic models.
7) Why might experimental density differ from the estimate?
The tool uses ideal molar-volume mixing. Experimental density can differ because of vacancies, porosity, phase separation, thermal expansion, non-ideal volume changes, and measurement conditions.
8) What is a good workflow for practical use?
Start with literature values for both species, test several compositions, inspect the graph trends, compare compatibility score with free-energy sign, then verify promising systems using phase-diagram or experimental data.