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Diffusion into a solid
Calculate a concentration profile, gradient and uptake for a maintained surface concentration.
Method scope & sources
Analytical Fickian diffusion into a homogeneous semi-infinite solid.
- Constant diffusivity at the supplied temperature
- Initially uniform concentration and fixed surface concentration
- No concentration-dependent diffusivity, reaction or moving boundary
One Hour
Interpret the result
- Semi-infinite, one-dimensional Fickian diffusion with a fixed surface concentration and uniform initial concentration.
- D is constant in space, concentration and time. Temperature records the condition of supplied D; no Arrhenius parameters are inferred.
- Concentrations retain the declared amount-density, mass-density or fraction basis; trapping, reactions, stress coupling and finite-film boundaries are excluded.
Numerical checks & provenance
Passing these checks verifies the stated numerical properties. Agreement with experiment requires a separate, condition-matched comparison.
Input SHA-256: a631d730c9fa7f6d47dedb791f3434b2378cdb786a5f46ce788f75db6dfbeb07
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 · 0.022724 s
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