Predicting Fermi Surface from Chemical Formula

In summary, the conversation discusses the prediction of band crossings in the compound LaFeAsO based on the chemical formula and the valency of each element. The main focus is on the role of Fe, which is determined to be the main contributor due to its half-filled d-orbitals. The conversation also highlights the importance of understanding inorganic chemistry in the study of solid state physics.
  • #1
tylerscott
28
0
Hi, I was hoping I could get some things cleared up. Recently my Solid State professor mentioned that we could simply, from the chemical formula, predict where the band crossings are going to be. For example, take LaFeAsO. Since La has a valency of +3, Fe of +3, As of -3, and O of -2, he deducted from the lattice (which is more or less cubic), that the band crossings are going to be primarily from the Fe. However, I'm completely lost as to why. Any help is appreciated!
 
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  • #2
This is a mainly ionic compound. Did you pay attention in your chemistry class? Then you should be able to name the valence orbitals of these elements and their occupation in the ions. For which element in your list aren't they neither full nor empty?​
 
  • #3
So, La is 5d1, Fe is 3d6, As is 4p3, and O is 2p4. So Fe is close to half filling. But, so is As and O. So can we just say the bandstructure will compose of mostly Fe because of the half filling? Therefore, it is highly metallic and also the binding energy of the 3d6 should be much smaller?
 
  • #4
You didn't count well. Take in mind that these are ions.
 
  • #5
So Fe is 3d8. La is 5d3. On the right track?
 
  • #6
No. Neutral La has 5d1 6s2, so La 3+ has none. Neutral Fe has 3d6 4s2, so what do you get for Fe 3+?
 
  • #7
I'm afraid I'm quite rusty in my chemistry here. So, Fe 3+ would be 3d5. However, I'm not sure where the 3+ for La is coming from (unless it's just because its a common oxidation state). How can one assume that the most common oxidation state is the right one to choose?
 
  • #8
Solid state physics is in some respect inorganic chemistry specialized to molecules of infinite size. So you better polish your inorganic chemistry.
Lanthanum has almost exclusively oxidation state 3+ just like oxygen mostly 2-. Iron mostly 2+ or 3+ and arsenic 3-, 3+ or 5+.
The only reasonable combination to make this compound neutral is thus O 2-, As 3-, La 3+ and Fe 3+. Hence the valence shells on O and As are completely filled while the one of La is completely empty. If you form bands from these atomic states, they will be filled or empty, too. This leaves as the main suscpect only Fe whose d-orbitals are only partially filled and partially degenerate in a cubic environment (cf Ligand field theory).
 

1. What is the significance of predicting Fermi surfaces from chemical formula?

Predicting Fermi surfaces from chemical formula is important because it allows scientists to understand the electronic properties of materials, such as their conductivity, magnetism, and superconductivity. By knowing the Fermi surface, researchers can also make predictions about a material's potential uses and applications.

2. How is the Fermi surface predicted from a chemical formula?

The Fermi surface can be predicted using theoretical models and computational methods. These methods take into account the chemical composition and crystal structure of a material, as well as the electronic interactions between atoms, to calculate the shape and size of the Fermi surface.

3. Can the Fermi surface be experimentally measured?

Yes, the Fermi surface can be experimentally measured using techniques such as angle-resolved photoemission spectroscopy (ARPES) and de Haas-van Alphen oscillations. These methods allow researchers to directly observe the electron energy levels and momentum distribution on the Fermi surface.

4. Are there any limitations to predicting Fermi surfaces from chemical formulas?

One limitation is that the predictions are based on theoretical models and may not always accurately reflect the real-world properties of a material. Additionally, predicting the Fermi surface of complex materials with multiple elements and crystal structures can be challenging and may require more advanced computational methods.

5. How can predicting Fermi surfaces contribute to materials research?

Predicting Fermi surfaces can provide valuable insights into the electronic properties of materials, which can aid in the development of new materials with desired properties. It can also help in understanding and predicting the behavior of materials under different conditions, such as temperature and pressure, and guide the design of more efficient and functional materials.

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