Debye–Waller factor
= Debye–Waller factor
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The Debye–Waller factor suppresses coherent scattering because atoms fluctuate about their equilibrium positions. For Gaussian displacement $u$, the amplitude factor is $\langle e^{iqu}\rangle=\exp[-q^2\langle u^2\rangle/2]$ and the intensity factor is its squared modulus. It multiplies the lattice interference factor, so exact extrema of the full finite-lattice intensity need not coincide with the constructive-interference centers when this envelope varies appreciably.