Question for Physicists: Metallic lustre in Non-Metals

[exchemist]

On my recent trip to the London Natural History Museum I was struck by the number of minerals that, while not metals, nevertheless have a metallic sheen or lustre. Iron Pyrite (FeS₂), "Fool's Gold" is a classic example. Semiconductor metalloid elements also have this property.

I'm aware that metals have this lustre due to the freedom of movement of electrons in the conduction band, which are (in simplistic terms) set into sympathetic oscillation by incident light. However in these non-metals and metalloids, the bonding electrons should by rights be in the valence band and thus not available to move freely in the way necessary to reflect incident light. 

Hence to my question: in semiconductors, i.e. materials with a relatively narrow band gap, is there some degree of thermal population of the conduction band, by promotion of electrons from the valence band?  This is the only way I could think of to explain the metallic surface appearance of these non-metal compounds.

Grateful for a physicist's advice.  

[KJW]

1 hour ago, exchemist said:

is there some degree of thermal population of the conduction band

It's my understanding that's how semiconductors work. It's why the conductivity of semiconductors increases with temperature instead of decreases like normal conductors.

 

Edited Sunday at 08:20 PM by KJW

[exchemist]

32 minutes ago, KJW said:

It's my understanding that's how semiconductors work. It's why the conductivity of semiconductors increases with temperature instead of decreases like normal conductors.

 

Aha. I wasn’t sure if the band gap was small enough to be bridged by thermal effects, but if it is, that would account for it. I suppose that should mean the metallic sheen on these materials should disappear at cryogenic temperatures. I wonder if anyone has observed that.

[KJW]

46 minutes ago, exchemist said:

Aha. I wasn’t sure if the band gap was small enough to be bridged by thermal effects, but if it is, that would account for it. I suppose that should mean the metallic sheen on these materials should disappear at cryogenic temperatures. I wonder if anyone has observed that.

I don't know if thermal excitation is necessary for a metallic lustre. The energy of visible photons may be sufficient to bridge the band gap. And because of the almost continuum of energy levels, reflections would occur over a broad spectrum, appearing as an opaque metallic lustre.
 

 

[exchemist]

2 minutes ago, KJW said:

I don't know if thermal excitation is necessary for a metallic lustre. The energy of visible photons may be sufficient to bridge the band gap. And because of the almost continuum of energy levels, reflections would occur over a broad spectrum, appearing as an opaque metallic lustre.
 

 

Hmm. How would photon absorption work in this case? I presume if thermal excitation can work then the equivalent photon absorption would be in the IR rather than the visible. Whereas reflection presumably is elastic, with no energy absorption. So perhaps there is an IR absorption band which pumps the conduction band and then the resulting population of the conduction band produces reflection in the visible. 
 

By the way I’ve now found something that says that, in semiconductors, valence band electrons can absorb a phonon and be thereby excited to the conduction band. So this would be the thermal excitation mechanism. 

[KJW]

1 hour ago, exchemist said:

I presume if thermal excitation can work then the equivalent photon absorption would be in the IR rather than the visible.

As I see it, the band gap is the minimum energy difference between the bands, whereas the width of the bands themselves can increase the energy difference that is accessible. A 1 eV band gap corresponds to an infrared photon of wavelength 1240 nm, whereas a 4 eV band gap considered to be an insulator corresponds to an ultraviolet photon of wavelength 310 nm. Thus, the band gap of a semiconductor is thermally accessible, whereas the band gap of an insulator is not visibly accessible. I was unable to locate data on band widths, so I can't at present say that the energy difference between the bands admits visible photons.

 

 

1 hour ago, exchemist said:

reflection presumably is elastic, with no energy absorption.

I'm guessing that there is an immediate absorption and lossless reemission that is due to the continuum of energy differences between the bands. This is different to refraction and different to absorption by non-metallic materials. However, I must say that the details are getting somewhat beyond me. Have you ever seen rhodamine B? It forms shiny dark green crystals and a violet solution (and violet smears in trace amounts on a white benchtop). I find this intriguing.

 

 

[swansont]

1 hour ago, KJW said:

As I see it, the band gap is the minimum energy difference between the bands, whereas the width of the bands themselves can increase the energy difference that is accessible. A 1 eV band gap corresponds to an infrared photon of wavelength 1240 nm, whereas a 4 eV band gap considered to be an insulator corresponds to an ultraviolet photon of wavelength 310 nm. Thus, the band gap of a semiconductor is thermally accessible, whereas the band gap of an insulator is not visibly accessible. I was unable to locate data on band widths, so I can't at present say that the energy difference between the bands admits visible photons.

1 eV is not a thermal photon. kT for 300K is 0.026 eV

e^-E/kT (probability of excitation) is going to be quite small

[exchemist]

7 hours ago, swansont said:

1 eV is not a thermal photon. kT for 300K is 0.026 eV

e^-E/kT (probability of excitation) is going to be quite small

 

Hmm. As I understand it, near IR ~1eV, mid IR ~0.1eV and far IR ~ 0.01eV. I recall from the specific heat of diatomic gases that vibrations - which give rise to near IR absorption bands - are not appreciably excited at 300K, which fits with what you say. Whereas rotational spectra are in the far IR.

Nevertheless it is clear that in semiconductors there must be some thermal excitation of electrons across a band gap ~1eV, to account for the increase in electrical conductivity of these materials with temperature - and to account for their metallic sheen, which is what sparked my original interest. Perhaps the issue is that we are seeing the effect of the tail of the Boltzmann distribution, i.e. we should be thinking of this on a logarithmic scale. One may not need too many charge carriers to see an increase in conductivity on a logarithmic scale -  and the development of a superficially metallic appearance.

I suppose one has to look at the distribution of phonon energies in a solid and see if the high energy tail end of these can reach ~1eV at 300K.    

 

 

 

Edited Monday at 09:19 AM by exchemist

[exchemist]

10 hours ago, KJW said:

As I see it, the band gap is the minimum energy difference between the bands, whereas the width of the bands themselves can increase the energy difference that is accessible. A 1 eV band gap corresponds to an infrared photon of wavelength 1240 nm, whereas a 4 eV band gap considered to be an insulator corresponds to an ultraviolet photon of wavelength 310 nm. Thus, the band gap of a semiconductor is thermally accessible, whereas the band gap of an insulator is not visibly accessible. I was unable to locate data on band widths, so I can't at present say that the energy difference between the bands admits visible photons.

 

 

I'm guessing that there is an immediate absorption and lossless reemission that is due to the continuum of energy differences between the bands. This is different to refraction and different to absorption by non-metallic materials. However, I must say that the details are getting somewhat beyond me. Have you ever seen rhodamine B? It forms shiny dark green crystals and a violet solution (and violet smears in trace amounts on a white benchtop). I find this intriguing.

 

 

Right, now I feel I'm starting to grasp this. 

I've now found this very informative link, which explains a lot of what we have been discussing: https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Introduction_to_Inorganic_Chemistry_(Wikibook)/10%3A_Electronic_Properties_of_Materials_-_Superconductors_and_Semiconductors/10.05%3A_Semiconductors-_Band_Gaps_Colors_Conductivity_and_Doping

 So indeed the conductivity is orders of magnitude lower than for a typical metal, consistent with the idea that thermal population of the conduction band is due to just the very tail end of the Boltzmann distribution. There's also a discussion of colours, which touches on what you were saying about photon absorption - and the link to how LEDs work which, thinking about it, is obviously the converse process. 

Anyway I think, subject to any further comments either of you may have, that I have the answer to my original question about metallic lustre of non-metallic compounds. I see for instance that iron pyrite, "fool's gold" has a band gap of 0.95eV, and in fact it is a semiconductor being studied for photovoltaic applications! 

My undergraduate chemistry focused on the populated bonding orbitals , i.e. the valence band, without giving much attention to the (nominally) empty antibonding orbitals, which merge to form the conduction band in an extended solid array. We didn't study solid state physics at all really. But when you think about it, as one descends a Group in the Periodic Table and the principal quantum number goes up, the orbital overlap between a pair of atoms gets less efficient, so the splitting in energy between bonding and antibonding orbitals grows less. And so we get a narrower band gap and start to see semimetallic properties, due to start of thermal population of the conduction band - bingo!  

Cool stuff. 

[swansont]

3 hours ago, exchemist said:

 

Hmm. As I understand it, near IR ~1eV, mid IR ~0.1eV and far IR ~ 0.01eV. I recall from the specific heat of diatomic gases that vibrations - which give rise to near IR absorption bands - are not appreciably excited at 300K, which fits with what you say. Whereas rotational spectra are in the far IR.

Nevertheless it is clear that in semiconductors there must be some thermal excitation of electrons across a band gap ~1eV, to account for the increase in electrical conductivity of these materials with temperature - and to account for their metallic sheen, which is what sparked my original interest. Perhaps the issue is that we are seeing the effect of the tail of the Boltzmann distribution, i.e. we should be thinking of this on a logarithmic scale. One may not need too many charge carriers to see an increase in conductivity on a logarithmic scale -  and the development of a superficially metallic appearance.

I suppose one has to look at the distribution of phonon energies in a solid and see if the high energy tail end of these can reach ~1eV at 300K.    

Some excitation, yes. The peak of room-temperature photons is longer than 10 microns, but shorter wavelengths exist in the spectrum, as you note. The function is exponential, so increasing temperature will increase the excitation probability.

But the color is probably due to what visible photons do to it, as with all things that have a color.

[exchemist]

48 minutes ago, swansont said:

Some excitation, yes. The peak of room-temperature photons is longer than 10 microns, but shorter wavelengths exist in the spectrum, as you note. The function is exponential, so increasing temperature will increase the excitation probability.

But the color is probably due to what visible photons do to it, as with all things that have a color.

For sure. But it was the metallic sheen I was trying to account for - which I think is now clear.