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In solid-state physics, the free electron model is a simple model for the behaviour of valence electrons in a crystal structure of a metallic solid. It was developed 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. The free electron empty lattice approximation forms the basis of the band structure model known as nearly free electron 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 heat capacity; * the shape of the electronic density of states; * the range of binding energy values; * electrical conductivities; * thermal electron emission and field electron emission from bulk metals. ==Ideas and assumptions== As in the Drude model, valence electrons are assumed to be completely detached from their ions (forming an electron gas). As in an ideal gas, electron-electron interactions are completely neglected. The electrostatic fields in metals are weak because of the screening effect. The crystal lattice is not explicitly taken into account. A quantum-mechanical justification is given by Bloch's Theorem: an unbound electron moves in a periodic potential as a free electron in vacuum, except for the electron mass ''m'' becoming an effective mass ''m *'' which may deviate considerably from ''m'' (one can even use negative effective mass to describe conduction by electron holes). Effective masses can be derived from band structure computations. While the static lattice does not hinder the motion of the electrons, electrons can be scattered by impurities and by phonons; these two interactions determine electrical and thermal conductivity (superconductivity requires a more refined theory than the free electron model). According to the Pauli exclusion principle, each phase space element (Δk)3(Δx)3 can be occupied only by two electrons (one per spin quantum number). 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Free electron model」の詳細全文を読む スポンサード リンク
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