Debye-Waller factor

The Debye-Waller factor expresses the magnitude of thermal vibrations (lattice vibrations) of atoms, called B factor. B is given by and expressed in units of Ų, where is the mean square amplitude of an atom due to thermal vibration. The angular dependence of scattering amplitude (θ or k dependence) of an atom for X-rays, neutrons and electrons, is given by the following equation.

Here, F is the atomic scattering amplitude without thermal vibration, and (λ: the wavelength of a quantum wave, θ : half angle of the scattering angle). Due to the B factor, the amplitude of the scattering (Bragg reflection) is attenuated at high scattering angles (at θ or large k). As the temperature of a specimen is lowered, thermal vibrations are reduced and the value of B becomes small. As a result, the decrease in the amplitude of high order reflections is suppressed and the intensities of those reflections are increased, making them easier to observe.

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