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Solution of 3 d lattice equation of motion solution

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Unformatted text preview: ntical. Solution of 3-D Lattice Equation of Motion Solution Phonon Dispersion in FCC with 2 Atom Basis Phonon http://debian.mps.krakow.pl/phonon/Public/phrefer.html Approaches to Calculating Electronic Bandstructure Bandstructure Nearly Free Electron Approximation: • Superposition of a few plane waves Cellular Methods (Augmented Plane Wave): • Plane wave between outside rs • Atomic orbital inside rs (core) Pseudopotential Approximation: • Superposition of plane waves coupled by pseudopotential k.p: • Superposition of bandedge (k=0) wavefunctions Tight-binding Approximation (LCAO): • Superposition of atomic orbitals Band Formation in 1-D Solid Band Simple model for a solid: the one-dimensional solid, which consists of a single, infinitely long line of atoms, each one having one s orbital available for forming molecular orbitals (MOs). When the chain is extended: The range of energies covered by the MOs is spread This range of energies is filled in with more and more orbitals The width of the range of energies of the MOs is finite, while the number of molecular orbitals is infinite: This...
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