Temper-Colour & Oxide-Growth Model

Temper Colours & Oxide Growth

Hold a polished metal at temperature; the model grows an oxide film (parabolic law, effective Arrhenius constants) and computes the interference colour of the air / oxide / metal stack (Fresnel + CIE 1931 observer, D65).

Hold temperature 300 °C

Time at temperature 10 min

what the polished surface
would look like

0 nm illustrative oxide thickness

Growth model: d = √(k_pt), k_p = k₀e^−Ea/RT · –

Bare polished metal — native film only.

Thickness → colour band for this metal (computed from the same optics)

Model honesty: colour = exact normal-incidence thin-film reflection of air / oxide / metal with representative constants (steel: oxide n≈2.35 on Fe N≈2.9−3.4i; Ti: TiO₂ n≈2.40 on Ti N≈2.7−3.8i), dispersion neglected, single uniform film, polished surface. Growth uses an effective parabolic–Arrhenius interpolation (steel Ea ≈ 40, Ti ≈ 60 kJ/mol) calibrated to reproduce familiar temper-colour charts; real thin-film low-T kinetics are Cabrera–Mott-like and alloy/finish/atmosphere-dependent. Real stainless-steel heat tint additionally depends on alloy grade, oxide composition, surface finish, exposure time and oxygen availability. Teaching tool, not metrology.