An oxidation record, mistaken for a thermometer
The Color That Was Not a Temperature
The straw, purple and blue that run across heated steel are not the steel glowing and not a unique thermometer reading. They are light interfering in an oxide film only tens of nanometres thick. Color can reveal that film, but the same film records both time and temperature, so a familiar workshop color chart hides an inverse problem with more than one answer.
Put nanometres on the steel
The 98 nm ceiling is deliberate. Fujimura reported agreement with a uniform Fe3O4 layer only below 100 nm.
Reflected spectrum under CIE illuminant C
This curve is the physical result. The large swatch is only an sRGB rendering of its CIE XYZ coordinates.
Model locus and Fujimura's measured chromaticity points
Line: the model from 0 to 98 nm. Dots: 19 x,y measurements transcribed from Fujimura's table 2, not sampled from a modern color chart.
Layer one · the optical thing
The color is a ruler for a film
Light reflects from the air-oxide boundary and again from the oxide-steel boundary. The two returns acquire a thickness-dependent phase difference. Across white light, some wavelengths cancel more strongly than others. The page evaluates the complex Fresnel coefficient at every plotted wavelength, then folds the reflected spectrum through the CIE 1931 2 degree observer.
The film model does not use temperature. Its input is the thickness d; its oscillating term contains 2π(n + ik)d / λ. Fujimura used polished S15C and S45C steel plates, heated them in argon, and colored them during rapid cooling in still air. For films assigned thicknesses under 100 nm, his measured spectrophotometric chromaticities lay close to the calculated single-layer Fe3O4 locus. Above that, he reported the measurements moving inward from the theory. This calculation inherits his optical constants and preparation; it is not a universal morphology model for steel heat tint. That is why this control stops at 98 nm.
It is useful, and sharply limited. The measured color can locate a place on a thickness locus under specified illumination and observer functions. It does not yet tell you what thermal history grew the film.
Layer two · the inverse problem
Now hold the color still
One color, an entire time-temperature contour
Curves reproduce McAdam and Geil's power-law slopes and anchors digitized from their figures 16 to 18. The shaded width is the declared ±10 °C graph-reading uncertainty, not optical-constant uncertainty.
These are oxidation experiments in air on the stated 1939 specimens. They are not modern tempering recommendations. The control stays inside the published graph range.
At the default blue setting, the iron curve passes through about 164 °C at 100,000 minutes. Drag the same point left to 10 minutes and it rises above 300 °C. The chromium steel follows another contour again. A single visible class therefore admits many temperature-time pairs, and alloy composition moves the family of pairs.
The color is an oxidation record at the surface. Metallurgical tempering is a bulk transformation. Under one controlled recipe the two may correlate, but they are not identical quantities. A universal temper-color-to-temperature table tries to invert a map that has thrown away time, alloy, atmosphere, surface preparation, illumination and the observer.
The check, with teeth
All figures below are recomputed in this browser. The offline verifier repeats them and also string-matches the share surface.
Independent route
Recursive complex Fresnel amplitudes versus Fujimura's printed Heavens closed form.
Published anchor
A perfect reflector under the pinned tables must recover illuminant C at x=0.3101, y=0.3162.
Control on the control
Reverse the film's absorption sign. The checker must reject the resulting gain spectrum above R=1.
Historical chromaticity points
Recompute RMS and maximum CIE 1976 color difference for Fujimura's 19 measured x,y,Y points with model-assigned thicknesses below 100 nm.
Thermal forward check
Recover each of six published power exponents from two points on its live contour.
Reachable bounds
Sweep every reader setting: passive reflectance stays in [0,1], and all contour temperatures remain finite.
Free choices
- Normal incidence, a perfectly smooth and uniform Fe3O4 film, and an optically semi-infinite steel substrate.
- Fujimura's own 1972 wavelength formulas for film and steel optical constants, not modern values chosen to improve the fit.
- CIE illuminant C and the CIE 1931 2 degree observer, both pinned at 10 nm intervals from 380 to 780 nm.
- Bradford adaptation from illuminant C to D65 for the display swatch, followed by explicit sRGB clipping. The plotted spectrum and x,y values are upstream of that display choice.
Uncertainties and limits
- Fujimura's x,y,Y values and assigned thicknesses are transcribed from table 2. The 1972 paper does not supply uncertainty bars for them.
- The thermal exponents come from McAdam and Geil's table 2. One temperature anchor per curve was digitized from figures 16 to 18 with a declared ±10 °C reading band.
- The historical steel curves describe particular specimens, polished surfaces and air exposures. A different heat, finish or atmosphere can move them.
- Fujimura found Fe3O4 and Fe2O3 by electron diffraction and called the structure complex. Raman had already warned that vivid tempered-steel colors may require more surface structure than an ideal continuous film. The single-layer result here is limited to Fujimura's stated thin-film regime.
Why the historical points are not a modern calibration chart
Fujimura's table pairs measured chromaticity with thickness values assigned through the paper's own optical model. It supports the local model-locus claim, but it is not an independent profilometer measurement of film thickness. McAdam and Geil's contours were built from visually identified interference-color classes, not from Fujimura's later nanometre assignments. This page therefore keeps the optical locus and the thermal contours as two linked but distinct instruments.