Incommensurate modulation in minute crystals revealed by combining high-resolution electron microscopy and electron diffraction

Abstract

Image processing combining high-resolution electron microscopy and electron diffraction is for the first time applied to the determination of incommensurate modulated structures. An image of a minute crystal of the high- T c superconductor Bi 2Sr 2Cacu 2O x is averaged and then transformed to an image of the average structure by a deconvolution technique based on the principle of maximum entropy. The image resolution is then enhanced to about 1 Å by the direct-method phase extension. All the unoverlapped atoms and their modulation are clearly seen in the final image.