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Lattice Vibration II - Coggle Diagram

- - - - The simplest crystal is the one dimensional chain of identical atoms with identical masses M connected by identical springs of spring constant K.
      - Chain consists of a very large number of identical atoms with identical masses
      - Atoms are separated by a distance of "a".
      - Atos move only in a direction parallel to the chain.
      - Only nearest neighbours interact (short-range forces).
  - - - The result is periodic in k and the only unique solutions that are physically meaningful correspond to the values in the range -π/a ≤ k ≤ π/a
- - - - The cos term forces the group velocity down to zero at the edge of the first Brillouin zone (k=π/a)
        
        There is a standing wave with no net propagation in this limit.
- - - - Any wavelength shorter that this can be mapped onto a wavelength longer than 2a, due to the periodicity of the lattice
        
        Shorter wavelength are physically identical with some longer wavelength.
        
        That means the configuration of the system will look the same.