The free electron theory of metals, initially proposed by Drude and later modified by Sommerfeld, failed to accurately describe electron behavior in conductive materials such as silver. Key limitations include its inability to account for interactions with the lattice, electron-electron interactions, and impurities, which are crucial for understanding phenomena like magnetoresistance and thermal conductivity. Ashcroft and Mermin detail these failures in Chapter 3 of their book "Solid State Physics," emphasizing that the model was an approximation that surprisingly succeeded in some areas, such as the Wiedemann-Franz Law.
PREREQUISITESStudents and researchers in solid-state physics, materials scientists, and anyone interested in the limitations of classical models in explaining electron behavior in metals.
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)?