Detailed Calculations of Thermal Diffuse Scattering

Abstract Convergent beam electron diffraction (CBED) produces a diffraction pattern from a single point on the specimen using a focused probe in the scanning transmission electron microscope (STEM). Because the incident wavefunction is a focused probe, each diffraction spot is enlarged to a disk the size of the objective aperture. Thermal vibration in the specimen reduces the intensity of the diffraction disks and introduces scattering in between the disk. This normally forbidden scattering between the diffraction disks is referred to as thermal diffuse scattering (TDS). The effects are most pronounced at large scattering angles, where TDS scattering can greatly reduce the intensity of the higher order Laue zone (HOLZ) lines. Previous work on modeling the TDS intensity involved the so-called frozen phonon method and the Einstein model of lattice vibration. The Einstein model assumes that each atom in the specimen vibrates independently of every other atom in the specimen and possible correlations among adjacent atoms are ignored.