ThermodynamicsCore Level
Diffusion Calculator
Calculate temperature-dependent diffusion coefficients and model depth concentration profiles using error functions.
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m²/s
Calculated Coefficient
Arrhenius kinetic rate D = D0 * exp(-Q/RT)
Enter valid inputs to compute D.
Formula: Arrhenius Rate Equation
D = D0 · exp(-Q / (R · T))
Where:
D=Diffusion coefficient (m²/s)
D0=Pre-exponential factor (m²/s)
Q=Activation energy (J/mol, kJ/mol, eV/atom)
R=Gas Constant (8.314 J/mol·K) / k_B (8.617e-5 eV/K)
T=Absolute temperature (K)
Scientific Assumptions & Methodology
- Fick's Second Law for one-dimensional semi-infinite solid holds.
- Surface concentration Cs is assumed to be constant throughout diffusion.
- Diffusion coefficient D is independent of composition/concentration.
Limitations & Educational Warnings
- Does not solve finite-source (Gaussian) boundary conditions.
- Assumes isotropic structure, excluding grain boundary or surface diffusion enhancements.