
How much Oxide makes a color

Basic Numbers Needed to Find the Answer  

Titanium dioxide numbers
TiO_{2} specific gravity = 4.2 g/cc TiO_{2} refractive index = 2.7 TiO_{2} moleweight = 47.87 + (2 x 16) = 79.87g/mole 
Relevant Physical Constants
Avogadro's Number = 6.02 x 10^{23} Electrons per Coulomb = 6.24 x 10^{18} => 1 Coulomb = 1 ampsecond Approximate Wavelength of titanium colors  bronze = 3 x 10^{5} cm  blue = 4 x 10^{5} cm  yellow = 6 x 10^{5} cm  purple = 7 x 10^{5} cm  green (second order) = 10 to 12 x 10^{5} cm 
Assumptions for this approximate number:
Steps to calculate the volume of oxide under these ideal conditions and the amount of electricity needed:
Example:
Let's turn a 1 square centimeter flat piece of titanium yellow:
Ignoring edges, that gives us 2 cm^{2}
oxideVolume = area * (wavelength / 2) / refractiveIndex
= 2 * (6 x 10^{5} / 2) / 2.7
= 2.22 x 10^{5} = 0.0000222 cc
oxideMass = oxideVolume * specGrav
= 2.22 x 10^{5} cc * (4.2 g/cc)
= 9.32 x 10^{5} = 0.0000932 g
oxideMolecules = oxideMass / moleWt * Avagadro
= 9.32 x 10^{5} g) / (79.87 g/mole) * 6.02 x 10^{23}
= 7.0 x 10^{17} = 700,000,000,000,000,000 molecules
ampseconds = 4 * oxideMolecules / ElectronsPerCoulomb
= 4 * (4.5 x 10^{21}) / (6.24 x 10^{18})
= .45 ampseconds or 100 ma for 4.5 seconds
BUT in the real world, you probably need several times that much for
reasons alluded to in the Assumptions section above.
Also, the current starts high, and drops exponentially fast as the oxide builds up.
Check out my anodizing page for more detailed instructions on coloring titanium with an anodizer.
Check out my physics page for how the color actually works.
Read my titanium details page for information about the history, chemistry, and so forth of element 22
Please use this forum post to ask me a question. 
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