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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, [1] 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.
Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m −3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.
The SI unit of temperature is the kelvin (K), but using the above relation the electron temperature is often expressed in terms of the energy unit electronvolt (eV). Each kelvin (1 K) corresponds to 8.617 333 262... × 10 −5 eV; this factor is the ratio of the Boltzmann constant to the elementary charge. [6]
Spin density is electron density applied to free radicals. It is defined as the total electron density of electrons of one spin minus the total electron density of the electrons of the other spin. One of the ways to measure it experimentally is by electron spin resonance, [14] neutron diffraction allows direct mapping of the spin density in 3D ...
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. [1] The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point.
Under the free electron model, the electrons in a metal can be considered to form a uniform Fermi gas. The number density / of conduction electrons in metals ranges between approximately 10 28 and 10 29 electrons per m 3, which is also the typical density of atoms in
Under the free electron model, the electrons in a metal can be considered to form a Fermi gas.The number density / of conduction electrons in metals ranges between approximately 10 28 and 10 29 electrons/m 3, which is also the typical density of atoms in ordinary solid matter.
ε 0 is the permittivity of free space, k B is the Boltzmann constant, q e is the charge of an electron, T e and T i are the temperatures of the electrons and ions, respectively, n e is the density of electrons, n j is the density of atomic species j, with positive ionic charge z j q e