Thermal vibrations in convergent-beam electron diffraction

The frozen phonon technique is introduced as a means of including the effects of thermal vibrations in multislice calculations of CBED patterns. This technique produces a thermal diffuse background, Kikuchi bands and a Debye–Waller factor, all of which are neglected in the standard multislice calculation. The frozen phonon calculations match experimental silicon (100) CBED patterns for specimen thicknesses of up to at least 550 Å. The best-fit silicon r.m.s. vibration amplitude at near room temperature was determined to be 0.085 (5) Å. As an independent check of validity, a comparison of calculated CBED, experimental CBED and electron energy loss spectroscopy (EELS) data was also performed. The frozen phonon technique provides an improved theoretical basis for the simulation of CBED and therefore annular dark field scanning transmission electron microscope imaging.