Quantitative analysis of twist boundaries and stacking faults in Bi-based superconductors by parallel recording of dark-field images with a coherent electron source

Abstract

Using a 300-keV transmission electron microscope equipped with a field-emission gun, we study grain boundaries by forming a coherent electron probe 100--200 \ensuremath{\mu}m above the specimen and observe in the diffraction mode the angular distribution of the transmitted electrons within the convergent beam disks. We studied Bi-based high-temperature superconductors containing stacking faults and twist grain boundaries with accompanying displacements perpendicular to the boundary plane. We observed strong intensity oscillation from the planar faults even when they were viewed edge on, in agreement with model calculations. At twist boundaries we observed rigid body translation normal to the boundaries as large as $0.03\ifmmode\pm\else\textpm\fi{}0.01\mathrm{nm},$ and determined the displacement vector associated with the addition or subtraction of one bilayer of $({\mathrm{CuO}}_{2}+\mathrm{Ca})$ to be $0.320\ifmmode\pm\else\textpm\fi{}0.002\mathrm{nm}$ for the intrinsic and extrinsic layers in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8},$ as well as for the intrinsic layer in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{10}.$ We also briefly address the possibility of determining the profile of the inner potential across grain boundaries using this coherent electron probe.