MrTitanium Presents
a short article on the physics of
Anodized Titanium Color
Original article © by , 2002

There is no dye in the colors brought out in titanium, niobium, or tantalum.
The colors are produced by controlled application of a fairly simple law of physics. The same law that explains the rainbow colors seen in oil on wet pavement

Background bullets (a review of basic refraction and reflection from high-school physics):
  • When 2 parallel continuous waves of the same frequency collide, the resulting wave will be the same frequency, and somewhere between the sum of the sizes of the two incident (starting) waves, and completely flat. If the crest of one lines up with the trough of the other, they cancel out. If the peak lines up with the peak, then they reinforce.
  • Light, which is made up of energy packets called photons, can also be modeled as light waves. A beam of light can be accurately visualized as waves in the (proven non-existent) interstellar ether, like water waves propagate on water.
  • Visible light has wavelengths from 350nm (blue) to 700nm (red). Between these falls the full rainbow spectrum of visible light.
    nm = nano-meters: 25,400,000 nm = 1", 1,000 nm = 1 micron, 1/10nm = 1 Å is the diameter of a hydrogen atom.
  • White light is made up of all colors together in particular proportions; similar to a black-body radiation skewed bell curve peaking at blue-green. The solar spectral distribution is what we call white.
  • When there is a transparent dielectric material (dielectric = insulator, like glass, water, quartz, titania) in contact with air, light will reflect off of the boundary with an efficiency proportional to the sine of the incident angle and to the dielectric constant (density, sort of) of the material. The farther the angle is from straight on, the better the surface reflection.
  • Light reflects from metals. Duh, you say?
    Look at a reflection from a tight angle to a mirror. Notice how it doubles? You are seeing the reflection from both the dielectric glass, and from the metal silver

How it Works:

Okay, so we know that a clear layer on metal is like a mirror (or vice-versa). There are really 2 reflections.
So, if a light wave of a single frequency hits the mirror, it reflects once from the clear part, and once from the metal. When they come out, they run into each other. What happens?
Right. They interfere with each other. If the dielectric is thick enough, like several wavelengths of light or more, nothing noticeable happens. All the interesting effects are statistically cancelled out.
However, if the distance the light has to travel through the dielectric to bounce off of the metal and back up to where it hits the first reflection is between ½ and 2 or so times the wavelength, then the interference gets interesting. If, for example, the total length (twice the thickness) is about half the length of the wavelength of red light, then it is also about the full wavelength of blue light. So, blue light will be reinforced, and red will be cancelled! Since white is made up of all colors, the blue end of the rainbow comes back out, and the red gets lost.

Voila! Color. Maybe this illustration will help:
Graphic of wave interference
The shorter blue wavelength reflects of the surface, and off the metal.
The interior wave travels a full wavelength farther than the first reflection, so they reinforce.
The longer red wave travels the same distance, but that's only ½ of its wavelength, so it cancels out.
When all the colors which are in white bounce off this double layer, what you see is blue.

Rainbow line

Some more details:


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