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*Electron concentration in the solid*:

[itex]

n = (valency)*\frac{N_{A}D}{M_{AT}}\\

[/itex]

Where:

[itex]n[/itex] = electron concentration

[itex]valency[/itex] = number of valency electrons in the atom

[itex]N_{A}[/itex] = Avogadro constant

[itex]D[/itex] = element density

[itex]M_{AT}[/itex] = atomic mass

*Energy of Fermi at absolute zero (0K)*:

[itex]E_{F0} = (\frac{h^2}{2m_e})(\frac{3n}{\pi})^{\frac{2}{3}}(\frac{1}{q})[/itex]

Where:

[itex]E_{F0}[/itex] = energy of Fermi at absolute zero (0K)

[itex]h[/itex] = Plank's constant

[itex]m_e[/itex] = effective electron mass at rest

[itex]n[/itex] = electron concentration

[itex]\frac{1}{q}[/itex] = 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.