Towards 3D image-based nanocrystallography by means of transmission electron goniometry

Abstract

It is well known that the crystallographic phase and morphology of many materials changes with the crystal size in the tens of nanometer range and that many nanocrystals possess structural defects in excess of their equilibrium levels. A need to determine the ideal and real structure of individual nanoparticles, therefore, arises. High-resolution phase-contrast transmission electron microscopy (TEM) and atomic resolution Z-contrast scanning TEM (STEM) when combined with transmission electron goniometry offer the opportunity of develop dedicated methods for the crystallographic characterization of nanoparticles in three dimensions. This paper describes tilt strategies for taking data from individual nanocrystals "as found", so as to provide information on their lattice structure and orientation, as well as on the structure and orientation of their surfaces and structural defects. Internet based java applets that facilitate the application of this technique for cubic crystals with calibrated tilt-rotation and double-tilt holders are mentioned briefly. The enhanced viability of image-based nanocrystallography in future aberration-corrected TEMs and STEMs is illustrated on a nanocrystal model system.

Image-based nanocrystallography with online database support

“…Tilt protocol applications are discussed by P. Fraundorf and co-workers in refs. [6,7,25,26] and Moeck et al [5,27,28].…”

“…The applications of such protocols are special cases of the more general transmission electron goniometry [5,28] since the latter delivers the transformation matrix between the crystallographic coordinate system of the crystal under investigation and the Cartesian coordinate system of the electron microscope. This matrix and its derivatives serve as the basis for many kinds of crystallographic analyses.…”

Towards Generalized Noise-level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

“…Since about 80 % of the -information‖ in a crystal structure resides in structure factor phases and only about 20 % in structure factor amplitudes [120], this is a distinct advantage of the direct space imaging approach. The tomography approach [22] combined with discrete goniometry [121][122][123] is also applicable in atomic resolution HRTEM in order to obtain information in 3D. Another peculiarity of the direct space imaging approach is that the magnitudes of the complex structure factors can be obtained directly from Fourier transforms of the images so that strictly linear least-squares refinements can be undertaken.…”

Crystal Structure Visualizations in Three Dimensions with Database Support

“…Since the NCD is being developed to support not only materials science education but also image-based nanocrystallography in general (i.e. methods that determine both structure and morphology of nanocrystals from images [20][21][22] in transmission electron microscopes), visualizations in 3D of the entries in this database are crucial. For a start, we provide 3D visualizations [18] by means of Jmol applets for the structural information that is contained in the entries of the COD, Figs.…”

“…The option to Reset to (the) original orientation also exist. In the future, we will add more crystallographic functionality to the display of structures in order to support image-based nanocrystallography [20][21][22] so that the NCD can become a free internet based research support tool in addition to providing world wide support for materials science and engineering, crystal physics, crystal chemistry, and mineralogy education.…”