Nearlyfreeelectronmodellen

The Nearly Free Electron Model (NFEM) describes conduction electrons in a crystalline metal as nearly free particles moving in a weak periodic potential produced by the ion cores. It sits between the free-electron gas and full band theory, providing a tractable way to understand how lattice periodicity shapes the electronic structure.

Under a periodic potential, Bloch's theorem yields electronic states as Bloch waves and energies that form bands E_n(k). For weak V, perturbation theory shows that where E0(k) equals E0(k+G) at a Brillouin zone boundary, a band gap opens. The gap size is set by the Fourier component V_G of the lattice potential, and away from zone boundaries the dispersion remains approximately parabolic, giving a free-electron-like Fermi surface with an effective mass m*.

The Kronig-Penney model in one dimension illustrates the idea, while in three dimensions the approach uses Fourier components V_G to predict the band structure. The NFEM explains metallic properties in simple metals such as alkali metals and some noble metals and provides a transparent link between the free-electron gas and full band theory.

Limitations include the reliance on a weak lattice potential and the neglect of electron–electron interactions; it does not capture strong bonding or correlation effects. Consequently, its applicability is greatest for metals with nearly free electrons and it serves as a stepping-stone to more comprehensive band calculations, including more detailed nearly free-electron approximations and ab initio methods.