Effects of atomic thermal vibration in a crystal on the diffracted intensities is described by the Debye-Waller factor (DWF). In general, DWF is a 3×3 symmetric matrix with six independent elements. For isotropic atomic vibration or atoms with cubic site symmetry, a single DWF B suffices:
here s=sinθb/λ. DWFs are among the refined parameters in structure analysis in x-ray or neutron diffraction. The accuracy of DWF in such measurements often depends on the quality of the crystal. In quantitative electron diffraction, accurate DWF is needed for 1) converting Fourier coefficients of potential to that of charge density, 2) comparison with theoretical calculations of static crystals, 3) estimation of high order structure factor and absorption coefficients.
DWF can be determined from measured amplitude of high order structure factors where the effects of bonding is minimal and DWF largest. Fig. 1 shows a plot of logrithmitic of ratios of measured MgO electron structure factors and calculated ones without temperature factor.