Simulation of Thermal Diffuse Scattering Including a Detailed Phonon Dispersion Curve

Thermal vibration of the atoms in a crystal give rise to a diffuse background in the diffraction pattern (in between the normal allowed Bragg reflections). The Einstein model for phonon vibrations in a crystal leads to Gaussian statistics for the phonons. However the Einstein model ignores the possibility of correlation between the atoms. An accurate model of the phonon dispersion curves for silicon is used to generate a set of more accurate random atomic displacements. These displacements are used in a multislice-style simulation to gauge the validity of the Einstein approximation. The phonon dispersion curve yields a small additional oscillatory structure in the thermal diffuse scattering (TDS) pattern. This doeso not produce significant changes in the ADF-STEM (annular dark field scanning transmission electron microscope) image signal, but could have a large impact on convergent beam measurements of bond charges.