Asymmetries in electron Compton profiles of silicon — a coherence effect

Electron Compton scattering in crystals in the case of large Ewald spheres is treated both theoretically and experimentally. The incident and scattered probe electron is represented by a sum of Bloch waves in the crystal leading to interference terms in the scattering cross section. The interference terms show a shift towards lower energies with respect to the diagonal Compton profile which depends only on the reciprocal lattice vectors of the excited Bragg reflexions. For a symmetric two-beam case the expression for the cross section is evaluated and it is shown that in contrast to the case of a small Ewald sphere the interference terms cannot be extracted from an experiment. For silicon the cross section is evaluated numerically for a (220) two-beam case and compared to experimental data from a transmission electron microscope. The agreement between theory and experiment is excellent and the shift of the interference terms with respect to the diagonal Compton profile can be observed in the measured profile.