## Colors of thin layers of materials

Hi everyone.

I have the following question: on passivated copper sheets used under high electric fields I found some color patterns I can't really explain. A possible explanation would be that there are some thin layers of material on top of pure copper, for instance the copper dioxide coming from the passivation, whose thickness changes, thus inducing interference patterns.
However, the equation for thin film interference (e.g. en.wikipedia.org/wiki/Thin-film_interference) depends on the angle of incidence of light:
2*n*d*cosθ = mλ,

where:
n = refraction index of the material
d = thickness of the layer
θ = incidence angle of incoming light
λ = light wavelength
m = integer number

So my assumption is that, if it really were all about thin layers of some material, depending on my position I should see different color patterns, and at some spots none!
However, as the colors on the surface of the copper sheets remain unchanged, no matter what position I'm looking from, I think it's not about thin layers, rather about pollutants.
Can somebody give me a clue?

Thank you very much!

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 Recognitions: Gold Member Welcome to PF, Jakobus. What is the purity (isolation?) of the environment? I'm guessing that you didn't simply get fingerprints on the thing. What sort of pollutants might make it through your quarantine system? It should be a small list.

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 Quote by jakobus However, the equation for thin film interference (e.g. en.wikipedia.org/wiki/Thin-film_interference) depends on the angle of incidence of light: 2*n*d*cosθ = mλ, where: n = refraction index of the material d = thickness of the layer θ = incidence angle of incoming light λ = light wavelength m = integer number
Hi Jakobus,
θ is the angle of the light ray inside the layer (the angle it encloses with the normal of the sheet). The oxides of cooper have very high refractive index, about 3. You know from Snell's law that nsinθ=sinα
where α is the angle of incidence from air. For n~3, θ does not exceed 20°, so 1>cos(θ)>0.94. You will not see much difference in the colour by changing your angle of view, but the colour does change with the thickness of the layer.

ehild

## Colors of thin layers of materials

Thank you very much you guys for your help! Ehild, this is really unexpected for me! I didn't think to do such a simple calculation!

Well, Danger, we are working in a clean room, where the environment is quite pristine and the air always remains at ≈20°C with ≈40% humidity, even less.
We made some X-Ray analysis on the foils with a SEM, and we found traces of sulfur, a little bit of silicon; Si however is always less than 1% of the total "scanned" mass. Also Carbon and Oxygen are present to varying degree, depending on the spot they may even reach 25% and 20% of the total mass respectively. However, if we look at the photos we made with the SEM, we basically see no signs of deposits nor structures whatsoever on the copper surface, as if it were quite pristine.
We are really puzzled.

Thanks!

Jakobus

 Recognitions: Homework Help If you find oxygen and carbon in various amounts on the surface I think the passivating layer can be copper carbonate or copper carbonate-hydroxide, maybe, some kind of oxide of copper. The basic copper carbonates can have different shades of blueish green, the carbonate is green, the oxide can be red or black. With the composition varying, the colour will change. ehild
 Hi Ehild, thank you very much for your answer. Yeah, I thought about that too. The problem is that, as far as I understand, the changes in the amount of the elements we found give no really clear answers, whether the colors are due to different chemical compositions or, maybe, thin films. However, there are so definite structures, almost every color from white to red to blue, in such an ordered way, something like concentric circles, that I find hard to believe that elements reacted differently or that they scattered differently depending on the spots on the foil. That's why I was thinking of thin films whose thickness varies. mmh....
 Do the colours appear to move across the surface when you change viewpoint or do they appear fixed to the surface? If it's an interferrence pattern I think it should move. If it's fixed perhaps it's local heating caused by standing waves??
 Hi CWatters, thank you! That is exactly my problem: I was also thinking about thin layers, but the colors don't move when changing position. So the question is: are colors fixed because they are not due to thin layers or because, as ehild put it, the angle doesn't play a big role? In fact you would have a cosθ, which would vary from 0.92 to 1, not a big difference! There is no heat, these are copper layers at room temperature exposed to high quantities of radiation and charged particles. The problem is that there is indeed sulfur and silicon on the surface; when we "photograph" the copper with the SEM, however, we do see some pollutants, but this is not strictly correlated to the color: there are colored regions where the surfaces appear to be as clean as the "pristine" ones and others that seem to have something on them, like a snow field. What a riddle!

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 Quote by jakobus However, there are so definite structures, almost every color from white to red to blue, in such an ordered way, something like concentric circles, that I find hard to believe that elements reacted differently or that they scattered differently depending on the spots on the foil. That's why I was thinking of thin films whose thickness varies. mmh....
In that case, they are very probable due to some thin film. Do the colours appear after irradiation? What are the charged particles you the sheets are bombed?

ehild