Low magnification differential phase contrast imaging of electric fields in crystals with fine electron probes

• Measuring electric fields by on-axis electron diffraction is explored by simulation.
• Electron channelling reduces deflection predicted by the phase object approximation.
• First moment measurements cannot distinguish electric fields from specimen mistilt.
• Segmented detector estimates are fairly insensitive to camera length and orientation.

To correlate atomistic structure with longer range electric field distribution within materials, it is necessary to use atomically fine electron probes and specimens in on-axis orientation. However, electric field mapping via low magnification differential phase contrast imaging under these conditions raises challenges: electron scattering tends to reduce the beam deflection due to the electric field strength from what simple models predict, and other effects, most notably crystal mistilt, can lead to asymmetric intensity redistribution in the diffraction pattern which is difficult to distinguish from that produced by long range electric fields. Using electron scattering simulations, we explore the effects of such factors on the reliable interpretation and measurement of electric field distributions. In addition to these limitations of principle, some limitations of practice when seeking to perform such measurements using segmented detector systems are also discussed.