The failure of the free electron theory of metals

[ziadett]

I was woundering?

why did the free electron theory of metals fail (the free electron model)?

 

[ziadett]

why did the free electron theory of metals fail "the free electron of model"
my effort:
Because it was unable to answer why the mean free path of electrons reaches 20nm in a good conducting metal "like silver" in room tempereture.

 

[ziadett]

any answers

 

[nbo10]

Who said it failed?

 

[ZapperZ]

Who said it failed?

Ashcroft and Mermin did in the whole of Chapter 3 of their book "Solid State Physics".

Zz.

 

[Gokul43201]

why did the free electron theory of metals fail (the free electron model)?

The free electron model (as put forth by Drude, and modified by Sommerfeld and others) "failed" because for the most part, electrons aren't completely free. They interact with (i) the lattice, (ii) each other, and (iii) impurities. Drude incorporated (i) into his model in the form of a hard-sphere interaction, but completely neglected the other interactions. Sommerfeld made some corrections to this purely classical model, by ensuring that the electron gas obey Fermi statistics. This fixed some problems (like the overestimates of the electronic heat capacity), but still didn't cover for the missing interactions in the model.

The free electron model was understood to be an approximation, when it was proposed by Drude. The initial surprise was that it was far more successful than expected (eg: the Wiedemann-Franz Law), particularly in the case of the alkali and alkaline Earth elements.

Due to its limitations, the free electron model was unable to account for things like magnetoresistance, thermal dependence of conductivity, optical properties and the host of many body phenomena that result from electron-electron interactions being of importance.

 

[dimensionless]

Aren't the "free-electron theory" and the "free-electron model" the same thing?

You might try looking up the "nearly-free- electron model."

 

[inha]

Look up chapter three in Ashcroft&Mermin, it just happens to be named "Failures of the Free Electron Model" and probably contains more than enough information for you.

 

[Gokul43201]

This is a copy of an identical thread in Solid State Physics.

https://www.physicsforums.com/showthread.php?p=994086#post994086

Let's keep the discussion to one thread. I shall be requesting that the threads be merged or that one of them be locked.

 

[ZapperZ]

Thread merged.

ziadett : I strongly suggest you re-read the PF Guidelines that you have agreed to. There is a an explicit instruction that multiple posting is not allowed.

Zz.

 

[ziadett]

sorry man no more multiple posting from me any more