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- W3021286370 abstract "Metals and semiconductors have crystal lattices with a well-defined translational symmetry. Most important among the crystal lattices are the simple cubic, body-centered cubic, and face-centered cubic structures, the diamond structure, and the hexagonal close-packed structure.The structure of the crystal of which a substance is composed determines the properties of the wave functions of electrons moving through the crystal. Free-electron wave functions are periodic with respect to the crystal lattice if the wave vector k belongs to the reciprocal lattice, which may be constructed using the primitive vectors of the original crystal lattice. The reciprocal lattice of the simple cubic lattice is itself a cubic lattice, while the reciprocal lattice of the bcc lattice is a fcc lattice and the reciprocal lattice of the fcc lattice is a bcc lattice.According to Bloch’s theorem, the translational symmetry of the lattice implies that each wave function, which is a solution of Schrodinger equation, has an associated wave vector k. The vector k is a vector in the reciprocal lattice, which, like the crystal itself, consists of a multitude of basic cells. The unit cell of the reciprocal lattice is called the Brillouin zone. Each electron having a wave vector k interacts with the electron with a wave vector k′, which is the mirror image of k across the boundary of the Brillouin zone. This simple model of the interaction of electrons in a crystal allows us to understand the bandgap of solids and to classify materials into insulators, metals, and semiconductors.Graphene and carbon nanotubes, which have appeared recently, are complex material with properties of metals and semiconductors." @default.
- W3021286370 created "2020-05-13" @default.
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- W3021286370 date "2015-01-01" @default.
- W3021286370 modified "2023-09-24" @default.
- W3021286370 title "Electronic Structure of Solids" @default.
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- W3021286370 doi "https://doi.org/10.1016/b978-0-12-800734-1.00008-1" @default.
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