The discussion revolves around the failure of the free electron theory of metals, specifically questioning the limitations of the free electron model in explaining various physical phenomena related to electron behavior in metals.
The discussion is active, with participants providing insights and references to literature. Some have suggested looking into specific chapters of relevant texts for more detailed information, while others have pointed out the need for clarity on terminology. There is no explicit consensus on the failure of the theory, as some participants question the assertion itself.
Participants mention specific constraints such as the limitations of the free electron model and its inability to account for various phenomena, indicating a focus on theoretical understanding rather than practical solutions.
nbo10 said:Who said it failed?
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.ziadett said:why did the free electron theory of metals fail (the free electron model)?