ThermodynamicsAdvanced Level
Defect Concentration Tool
Estimate equilibrium concentration of point defects (vacancies) in a crystal lattice at different temperatures.
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Vacancy Concentration
Equilibrium point defects in crystal lattice
Enter valid inputs to calculate defects.
Formula: Point Defect Thermodynamics
Nv / N = exp(-Qv / (kB · T))
Where:
Nv=Number of equilibrium vacancies (atoms/m³)
N=Total atomic lattice sites (atoms/m³)
Qv=Vacancy formation activation energy (eV/atom or J/mol)
kB=Boltzmann constant (8.617e-5 eV/K)
T=Absolute temperature (K)
Scientific Assumptions & Methodology
- Applies to equilibrium vacancy state where Gibbs free energy is minimized.
- Ignores vacancy-vacancy interactions, which is valid for dilute defect concentrations.
- Assumes vibrational entropy contributions are negligible (or bundled into Qv).
Limitations & Educational Warnings
- Represents equilibrium states only. Rapid quenching (fast cooling) will 'freeze in' non-equilibrium vacancy populations.
- Approximate atomic density presets assume isotropic elemental solids.