Editing Free electron model (section)

==Ideas and assumptions==

In the free electron model four main assumptions are taken into account:<ref name=":5" group="Ashcroft & Mermin">{{Harvnb|Ashcroft|Mermin|1976|pp=60}}</ref>
*Free electron approximation: The interaction between the ions and the valence electrons is mostly neglected, except in boundary conditions. The ions only keep the charge neutrality in the metal. Unlike in the Drude model, the ions are not necessarily the source of collisions.
*[[Independent electron approximation]]: The interactions between electrons are ignored. The electrostatic fields in metals are weak because of the [[screening effect]].
*Relaxation-time approximation: There is some unknown scattering mechanism such that the electron probability of collision is inversely proportional to the relaxation time <math>\tau</math>, which represents the average time between collisions. The collisions do not depend on the electronic configuration.
*[[Pauli exclusion principle]]: Each quantum state of the system can only be occupied by a single electron. This restriction of available electron states is taken into account by [[Fermi–Dirac statistics]] (see also [[Fermi gas]]). Main predictions of the free-electron model are derived by the [[Sommerfeld expansion]] of the Fermi–Dirac occupancy for energies around the [[Fermi level]].

The name of the model comes from the first two assumptions, as each electron can be treated as [[free particle]] with a respective quadratic relation between energy and momentum.

The crystal lattice is not explicitly taken into account in the free electron model, but a quantum-mechanical justification was given a year later (1928) by [[Bloch's theorem]]:<!-- Is this Bloch theorem? We must check the validity of this paragraph --> an unbound electron moves in a periodic potential as a free electron in vacuum, except for the [[electron mass]] ''m<sub>e</sub>'' becoming an [[effective mass (solid-state physics)|effective mass]] ''m*'' which may deviate considerably from ''m<sub>e</sub>'' (one can even use negative effective mass to describe conduction by [[electron hole]]s). Effective masses can be derived from [[band structure]] computations that were not originally taken into account in the free electron model.{{Cn|date=April 2024}}