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Concept
Modèle de l'électron libre
Résumé
In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
Given its simplicity, it is surprisingly successful in explaining many experimental phenomena, especially
the Wiedemann–Franz law which relates electrical conductivity and thermal conductivity;
the temperature dependence of the electron heat capacity;
the shape of the electronic density of states;
the range of binding energy values;
electrical conductivities;
the Seebeck coefficient of the thermoelectric effect;
thermal electron emission and field electron emission from bulk metals.
The free electron model solved many of the inconsistencies related to the Drude model and gave insight into several other properties of metals. The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role. The model can be very predictive when applied to alkali and noble metals.
In the free electron model four main assumptions are taken into account:
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 , 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.
Source officielle
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