So following through the notes and the book simultaneously, it seems that chapter 15 isn't really touched on. This is probably because it doesn't introduce too many new concepts, but gives multiple examples of band structure in different metals. One thing that I decided to check up on was the noble metals. I've heard it mentioned a few times, but at this stage had never known what exactly distinguishes a metal as being noble.
This wasn't entirely helped by the fact that there seem to be different definitions, the general definition given in the quick blurb on wiki states that a metal is noble as long as it is resistant to corrosion and oxidation in moist air. However, the definition in physics for a noble metal is somewhat different, and it talks about them on pages 288-293. The only three metals that meet these requirements to be noble are copper, gold and silver.
Essentially, these three elements inner electron shells are all filled, and can be ignored in all further calculations. The outer electrons are all found in six energy bands around the fermi energy. However, at (essentially) all k values, 5 of these bands are located in a very small energy range, just beneath the fermi energy. Meanwhile the sixth band wanders all over the place. However, it's not a case of following the path of one band that goes across a wide range of energies, but all the bands seem to take turns moving about. It just happens that whilst one band is wandering about, the other five bands are all located very close together (approximately 2-5eV beneath the fermi energy). This isn't the case always, there are some moments where all six bands lie within this range, but for the most part this is how it works.
Because of this structure, it's usual to classify the 5 close bands as the f-bands, and the wandering level as the 4s band. This 4s band's energy closely resembles the lowest free electron band of a face centred cubic crystal, and it is this band that gives the metal its various properties. The diagram on page 289 shows all of this in more detail.
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I recall mentioning Chapter 15 in an earlier blog post/comment!
ReplyDeleteThe distinction of noble metal seems strange - I've not come across this before either.
For the non-noble metals, the model described was the tight-binding model.
The difference given between potassium and copper is unclear -- they both have one electron alone with the rest of the shells filled?
I'm still not clear with the description given in A&M...
Noble metals are called as such because they are analogous to noble gases (e.g. helium, argon, etc.) which have full outer shells. It is interesting how those properties differ between actual noble elements and these 'noble metals', too, since noble gases are generally bad conductors unlike silver, copper and gold (which are the opposite). Although it probably wouldn't have seemed strange before someone did a rigorous physics model of matter....
ReplyDeleteNot having read the A&M description yet, from lectures I recall that the d-orbitals are much farther out spatially than f-orbitals. So, for copper, with a full d-orbital, the s-orbital electron isn't very far out from the rest of the electrons. In contrast, potassium or other alkali metals, have closer f-orbitals filled, and so their s-orbital electron is much farther away from the atom. So I guess (assuming my recollections are right!) that this is why they show different behaviour: alkali metals have much less tightly bound electrons. But also, just because copper usually has 10 electrons in the d-orbitals doesn't mean that under certain conditions an electron won't 'retreat' back to the s-orbital since they're close in energy, so the model should reflect this.
As a side note, it does seem easier to talk about s/d/f/p orbitals than L = 0, 1, 2, etc.. What does everyone else think?
The analogy of nobel metals to nobel gases makes sense with regards to a filled outer shell.
ReplyDeleteSince outer band is full, this could be thought of a zero conduction electron, so we would expect poor reactivity, which we do have, e.g. gold jewellery.
The conduction is an interesting point - one oould expect a full outer band to have fewer conduction electrons, hence less conductivity?
We're familiar from high school chemistry with the s, p, d, f orbitals.
Histroically, sharp, principal, diffuse, fundamental reffering to the appearance of the spectral lines.
The L = 0, 1, 2,... seems like a convenience from quatum...I'm willing to take the convenience...
Interesting that you mention potassium and copper, they're the two they mention the book for comparison! :)
ReplyDeleteAs Josh said, it has everything to do with the d-band. In fact the physics definition of a noble metal requires that the highest occupied d-band is completely filled. This requirement is relaxed for other definitions of a noble metal, where up to 10 or so elements then meet the requirements.
(Sidenote, if a significant portion of metals meet this requirement, can they truly be referred to as being noble, by the definition of the word?)
As the Argon configuration is entirely stable, the potassium and copper atoms can thus be described by the electrons 4s1 and 3d10,4s1 respectively. For a single electron, only one energy band is required to be filled, and it behaves like a free electron from all reports.
Meanwhile, for the 11 electrons outside of the stable Argon configuration for copper 6 bands are required as a minimum (as each band can accomodate 2 electrons). These 6 bands take the structure as I described above, which gives the noble metals their distinctive features.
Nice post. I this post very much and thanks for sharing.
ReplyDeleteClick here for more details about Nobel Metals.