Periodic Potential of Crystals
- Practical Electron Microscopy and Database -
- An Online Book -

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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.
 

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The scattering potential of the crystal is given by,

          scattering potential of the crystal --------------------------------- [2205a]
where,
          τn -- The atomic co-ordinate for the nth atom,
          fq -- The atomic scattering factor,
          Vc -- The volume of the supercell,
          ħq -- The momentum transfer.

In crystals, a periodic potential appears because the ions are arranged with a periodicity of their Bravais lattice. The periodic potential can be given by,

          U(r + R) = U(r) ----------------------------------- [2205b]

where,
          R -- The lattice vector.

This potential can be applied into the Schrödinger equation,

          Schrödinger equation ------------------- [2205c]

In these cases, the electrons in the crystals are no longer free electrons, but are now called Bloch electrons.

 

 

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