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Why Aren't Superconductors Perfect Mirrors?

11/09/2008 4:22 PM

Here's some food for thought: the degree to which a metal reflects light is closely related to how well the metal conducts electricity (why?). Other materials -- dielectric mirrors, for example -- reflect light by means of a related, but different mechanism which we won't cover here. We're talking only about conductors. Specifically superconductors. They conduct electricity perfectly; hence the name "superconductor."

Turns out most superconductors don't reflect light all that well. The worst offenders are those high-temp superconducting ceramics (1-2-3, et al), which range from grey to black no matter what the temperature. But that roll of tin/aluminum foil in your pantry? It probably beats 'em all hands-down and with plenty to spare.

Why is that? Anyone care to explore this little oddity?

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#1

Re: Why Aren't Superconductors Perfect Mirrors?

11/09/2008 6:10 PM

The premise is flawed. Conductivity and reflectivity are unrelated. Would you rather have a copper mirror or a stainless steel mirror? Case closed.

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#2
In reply to #1

Re: Why Aren't Superconductors Perfect Mirrors?

11/09/2008 7:01 PM

"Conductivity and reflectivity are unrelated."

Indeed. How about a Teflon mirror and a copper mirror? Which would you prefer? And why do metals reflect light like...well...metals? Surely you know.

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#3
In reply to #2

Re: Why Aren't Superconductors Perfect Mirrors?

11/09/2008 10:12 PM

Again a flawed premise. The original post stated that we would not consider dielectrics. Teflon is one of the most highly insulating materials known.

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#4

Re: Why Aren't Superconductors Perfect Mirrors?

11/10/2008 4:38 AM

Hello TheVoices

<"....superconductors. They conduct electricity perfectly....">

Incorrect in fact.

There is no superconductor which is absolutely perfect, there will be at least one lattice bond which is incomplete.

Kind Regards....

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#5
In reply to #4

Re: Why Aren't Superconductors Perfect Mirrors?

11/10/2008 10:24 AM

Congrats he All Blacks proved that Wales had a few in complete bonds on Saturday.

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#6

Re: Why Aren't Superconductors Perfect Mirrors?

11/10/2008 11:40 AM

I gave answers earlier that apparently didn't make the point adequately. At frequencies well below that of light, in the radio frequency spectrum, it is as the original post states - conductivity determines the degree of reflection. The degree of reflection is proportional to the ratio of the traveling electromagnetic wave impedance (377 Ohms in free space) to the reflecting surface impedance. The lower the surface impedance, the better the reflection. Nothing gets absorbed. But as you get beyond microwave frequencies, the skin depth is so shallow that absorption plays an increasing role in what happens at the material surface. For green light at 500 nanometers, the skin depth is 27 nm. Consider that value is only a couple orders of magnitude larger than the diameter of an atom. You are getting effects at light frequencies that are totally negligible at radio frequencies. Also, when we speak of light, we think of white light, which contains an entire spectrum of colors. Therefore it is important for a mirror substance to equally reflect all colors of the spectrum. That is why in my one post I said compare the reflection of stainless steel to that of copper. Copper absorbs more of the blue-green and reflects red, whereas stainless steel reflects without such filtering. A more precise example would be aluminum vs. copper. Aluminum conductivity is less than that of copper, precisely 0.6 that of copper, but it makes a much better mirror because it is not red. Silver is used for mirrors not because its conductivity is better than that of copper (which is true) but because it is color distortion free. And while silver costs more than aluminum as a bulk material, silver is cheaper to plate on glass, and it takes very little silver to make the mirror, so that manufacturing costs totally dominate material costs.

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#7
In reply to #6

Re: Why Aren't Superconductors Perfect Mirrors?

11/10/2008 2:58 PM

Hello emc_c

from me

Good explanation.

For readability of a Post, could you consider spacing them out in future.

Kind Regards....

EDIT: This Post should have been off-topic, but I am unable to Edit it to make it off-topic - Sorry.

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#8
In reply to #6

Re: Why Aren't Superconductors Perfect Mirrors?

11/10/2008 3:31 PM

I concur - you beat me to it, but it's worth a GA vote! It's all in the surface, how that surface reacts to the specific wavelengths of the electromagnetic spectrum, and the (for lack of a better term) electrocrystalline structure of that surface. Reflecting visible light (as a typical mirror) is really no different (apart from frequency response) to radar signals reflecting off of an aircraft (both aluminum in some cases). Electrical conductivity is not a surface effect, and depends on a different sort of crystal lattice structure - one that provides electrons that can move, and 'holes' for them to move through. So-called superconductors exhibit extremely low resistance, but that does not make them mirrors any more than having a yellow color makes mustard spicy. It just isn't a related property. If it were, lemon custard would be spicy too.

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#10
In reply to #6

Re: Why Aren't Superconductors Perfect Mirrors?

11/12/2008 12:55 PM

Hi emc c,

what is the reflecting surface impedance?

I know the impedance X to be equal to the square root of permittivity/(magnetic permeability).

Magnetic permeability being near 1 (? also at these frequencies?),

how can you define or measure permittivity at these frequencies - or only possible by reflectance?

What mechanism is changing the permittivity (peaking?) of copper and gold and no other metal in the visible?

What about the influence of resistance?

What about the influence of thin absorbed layers (water, oxide) on the metal?

I saw the color of copper changing a lot from red to silvery-red on ultra-smooth (Rt=10nm) and ultra-precision metal cutting.

Thanks for help and explanations

RHABE

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#11
In reply to #10

Re: Why Aren't Superconductors Perfect Mirrors?

11/12/2008 1:54 PM

Answers as best as I can...

1) The reflecting surface impedance at radio frequencies (rf) is the resistivity of the metal. Absorption doesn't have to be taken into account. But as I pointed out in the previous post, at light frequencies one skin depth is getting down to the level of atomic distances, and then the rf model doesn't work so well.

2) The impedance you cite as being the square root of the ratio of permittivity to permeability relates to the impedance of a wave traveling in a dielectric medium. The impedance thus calculated is of the wave impinging on the reflecting metallic surface. It does not describe the metal itself.

3) In the rationalized MKS system of units (SI) magnetic permeability for a non-ferromagnetic material is 4*pi* 10^-7 Henries per meter. Ferromagnetic materials have a higher value of permeability, which is a multiple of the basic value. That multiple is called the relative permeability. The number you cite as " near 1" is the relative permeability of a non-ferromagnetic material.

4) How would one measure relative permeability at light frequencies? I don't know the answer to that. The reason I don't know the answer is I'm not sure why you would need to know. The permeability would have no measurable effect on the interaction of light with the metal. Permeability decreases skin depth at radio frequencies, but as we have seen skin depth is already insignificant at light frequencies, so calculating the skin depth including a non-unity relative permeability seems pointless.

5) Regarding this: "What mechanism is changing the permittivity (peaking?) of copper and gold and no other metal in the visible?" Don't understand question. I think of metals in terms of resistance and permeability, not in terms of permittivity.

6) The resistance of a metal is a factor in its reflectivity at radio frequencies, as previously noted. At light frequencies, also as previously noted, it is but one of many factors.

7) Dielectrics forming on a metal surface due to corrosion or other processes will have a dramatic effect on reflectivity. In fact, the properties of the dielectric deposit totally dominate in determining the new reflectivity - the base metal no longer factors in at all.

8) One of the factors affecting the degree of perceived reflectivity is how specular the reflection is, again as noted previously. It is not surprising that increased surface smoothness would change the observed reflections, but I myself have never seen copper as smooth as you cite. I'll bet many of the people who have waded through this thread would be interested in a picture.

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#12
In reply to #11

Re: Why Aren't Superconductors Perfect Mirrors?

11/12/2008 4:52 PM

Hi,

1) The reflecting surface impedance at radio frequencies (rf) is the resistivity of the metal.

So what is different in much higher frequencies except skin depth and resistivity to be taken within this skin depth, respective to be integrated (?) by current density over depth. ?

2), 3) agreed.

4) 5): I had in my mind permittivity but if resistivity is working, why is resistivity going up this much in the blue region of the (for us) visible spectrum that gold and copper exhibit "color".

7) Dielectrics forming on a metal surface due to corrosion or other processes will have a dramatic effect on reflectivity.

I thought about very thin oxide (or else) films of 0.2 to 200nm thickness. Seems to be difficult to calculate? Especially if oxides may be partially conducting, as for copper.

8) ... interested in a picture.

ordinary fotos show "perfect mirror surfaces", laser-reflection spots show stray-light generated by roughness, stylo profiler shows 10nm roughness filtered by stylo shape, differential-interference-contrast-mikrofotos show steps at grain-boundaries not resolved by best optical microscopes. If of interest I can get some of these.

RHABE

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#13
In reply to #12

Re: Why Aren't Superconductors Perfect Mirrors?

11/12/2008 6:34 PM

1) At light frequencies, the wave is not only interacting with the conductivity of the material as a whole, but the wavelength interacts with energy levels of the electrons. This is also the answer to your question 4 & 5: different materials absorb in different portions of the spectrum.

2) A semi-conductive oxide layer whose thickness was small relative to a wavelength would not have the total effect I described based on a thick nonconductive oxide. In my experience, oxide layers are not as smooth as the metal sheet on which they grow, hence the specularity of the reflection suffers. I imagine that if one intentionally grew an oxide layer (as is done in IC manufacturing) that smoothness could be controlled and specularity would not suffer.

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#14
In reply to #13

Re: Why Aren't Superconductors Perfect Mirrors?

11/13/2008 3:30 AM

Hi,

1) so the absorbed power at blue wavelengths is exciting electrons, and then? converted to radiation orheat?

2) I did aluminum-nitride on aluminum on highly polished silicon. Roughness of crystalline nitride (50nm) is added to very low roughness of aluminum (10nm), silicon having nearly perfect smoothness.

Remaining original question: If in ordinary metals the conductivity is defining reflectivity, what is defining reflectivity in superconductors?

RHABE

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#9

Re: Why Aren't Superconductors Perfect Mirrors?

11/10/2008 7:05 PM

Nice work! Thanks to all of you. I learned a lot from this thread!

Kind regards,

TV

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