The Debye–Waller factor, also known as the thermal factor or the static form factor, quantifies the effect of atomic vibrations on the scattering of neutrons or X-rays by a crystalline material. Specifically, it describes how much the intensity of scattered X-rays or neutrons is reduced due to the thermal motion of atoms within a crystal lattice. In a crystalline solid, atoms are not stationary but vibrate about their equilibrium positions due to thermal energy.
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The Debye–Waller factor suppresses coherent scattering because atoms fluctuate about their equilibrium positions. For Gaussian displacement , the amplitude factor is 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.