Crystal structure determination of K 2O·7Nb 2O 5 by combining high-resolution electron microscopy and electron diffraction

Abstract

With an image deconvolution procedure based on the principle of maximum entropy, positions of metallic atoms in crystal of K 2O·7Nb 2O 5 have been determined from a single high-resolution electron microscope image and from the combination of the image and the electron diffraction pattern. The function of image decovolution is to transform an image taken under an arbitrary defocus condition into the structure image. The structure images restored from two original images taken under much different defocus conditions show almost the same contrast. In the restored structure images, niobium and potassium atoms appear as black dots with larger and smaller contrast, respectively. The positions of oxygen atoms have been determined by the phase-extension technique developed in X-ray crystallography. Moduli of structure factors up to H = 1 Å p-1 were obtained from the electron diffraction pattern, while phases within H ⩽ (1.9 Å) p-1 were derived from Fourier transform of the electron microscope image after deconvolution. The Sayre equation was used to extend the phase from (1.9 Å) p-1 to 1 Å p-1 and to retrieve the phases of those reflections within (1.9 Å) p-1, which were rejected in image deconvolution owing to unreliable values of the contrast transfer function. Fourier synthesis was used to improve the quality of the image after phase extension. The final structure image reveals clearly all atoms in the unit cell.