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We present some theoretical results on the lattice vibrations that arenecessary for a concise derivation of the Debye-Waller factor in the harmonicapproximation. First we obtain an expression for displacement of an atom in acrystal lattice from its equilibrium position. Then we show that an atomicdisplacement has the Gaussian distribution. Finally, we obtain thecomputational formula for the Debye-Waller factor in the Debye model.

Lattice vibrations in the harmonic approximation