# Are there energy bands for alloys?

• I
• Psinter

#### Psinter

In metals, there is a concept called the Fermi energy which you can calculate with the following:

Electron concentration in the solid:
$n = (valency)*\frac{N_{A}D}{M_{AT}}\\$
Where:
$n$ = electron concentration
$valency$ = number of valency electrons in the atom
$N_{A}$ = Avogadro constant
$D$ = element density
$M_{AT}$ = atomic mass

Energy of Fermi at absolute zero (0K):
$E_{F0} = (\frac{h^2}{2m_e})(\frac{3n}{\pi})^{\frac{2}{3}}(\frac{1}{q})$

Where:
$E_{F0}$ = energy of Fermi at absolute zero (0K)
$h$ = Plank's constant
$m_e$ = effective electron mass at rest
$n$ = electron concentration
$\frac{1}{q}$ = reciprocal of electron charge (to convert energy units to electron volts)

However, the math above is for a single element. Is there any quantum mechanical approach for the same concept, but in alloys where you have a metallic bonding and the same crystalline structure?

I want to know if there is such a thing as Fermi energy in such structures (alloys) that can be tackled mathematically in a quantum mechanical way. Such that one could describe conductivity properties of an alloy. Or if there are other models for that.

Yes, there is a Fermi level for alloys. It may not be so easy to calculate as in the simple model in your post.
Even for pure metals may be quite complicated actually.

Yes, there is a Fermi level for alloys. It may not be so easy to calculate as in the simple model in your post.
Even for pure metals may be quite complicated actually.
Hi,

How much more complex does it get? Any hints of what is it I'm after? A set of Equations and principles in the Fermi-Dirac statistics perhaps?

I've been reading a book which discusses those quantum mechanical principles in metals. So far so good, but I haven't found what I'm looking for which is in the end, finding Fermi energy levels of an alloy. That book discusses what happens with Fermi Energies in a metal to metal contact, but not an alloy.

I've already covered a wide range of principles, including the Fermi-Dirac statistics and other models with their equations and examples for specific elements. Still, I can't find what I'm looking for. Therefore my question: any hints?

Psinter
You can look up some papers. Calculating the Fermi surface of a metal is not trivial, as I said. Usually is done by numerical methods, I suppose.
From the hits below you can see that the concept is used for alloys. If you want to do your own calculations you may need to read some books.