Structures of nanometre-size crystals determined from selected-area electron diffraction data

Abstract

The structure of a new modi®cation of Ti 2 Se, the -phase, and several related inorganic crystal structures containing elements with atomic numbers between 16 and 40 have been solved by quasi-automatic direct methods from singlecrystal electron diffraction patterns of nanometre-size crystals, using the kinematical aproximation. The crystals were several thousand times smaller than the minimum size required for single-crystal X-ray diffraction. Atomic coordinates were found with an average accuracy of 0.2 A Ê or better. Experimental data were obtained by standardized techniques for recording and quantifying electron diffraction patterns. The SIR97 program for solving crystal structures from three-dimensional X-ray diffraction data by direct methods was modi®ed to work also with two-dimensional electron diffraction data.

Electron crystallography without limits? Crystal structure of Ti45Se16redetermined by electron diffraction structure analysis

“…The internal R factor of symmetry-related re¯ections in the merged data set was only 11%, which con®rms that the crystal was suf®ciently well aligned along the [010] direction. Similar to the previous study (Weirich et al, 2000), the data were phenomenological corrected for dynamical diffraction using the approximation |F hkl | G I hkl .…”

“…In a recent study, it was shown that metal-rich inorganic crystal structures containing elements with atomic numbers between Z = 16 and 40 can be solved by quasi-automatic direct methods from single-crystal electron diffraction patterns using the kinematical approximation (Weirich et al, 2000). According to this study, the most complex structures that have been solved from electron diffraction data are Ti 8 Se 3 (Weirich et al, 1996b) and Ti 11 Se 4 , which contain 22 and 23 atoms per asymmetric unit.…”

“…Besides the new phases -Ti 2 Se (Weirich et al, 2000), Ti 8 Se 3 , Ti 11 Se 4 and Ti 9 Se 2 (Weirich Simon & Po È ttgen, 1996), another previously unknown titanium selenide, Ti 45 Se 16 , was identi®ed in the TiÀSe system (Weirich, Duppel et al, 1996).…”

Protein structure determination by electron diffraction using a single three-dimensional nanocrystal

“…On average, dynamical diffraction is anticipated to affect weaker reflections more than strong reflections. Thus, on average, weak spots close to intense spots will become more intense, whereas intense spots close to weak spots will hardly be affected (Weirich et al, 2000). Assuming an expected complexvalued error E(h) that is uncorrelated to F(h), we can infer a hyperbolic relationship between the expected value of h|F o |i and |F c |,…”

Transmission electron microscopy analysis of some transition metal compounds for energy storage and conversion

“…To obtain 2D HRTEM images, one often needs to tilt the sample to an on-axis orientation so that the incident beam coincide with a crystallographic axis, enabling the diffraction of various crystal planes and interference between transmitted beam and diffracted beams. Meanwhile, a corresponding diffraction pattern encoding diffracted amplitudes can be obtained [23][24][25]. The phase preserved in HRTEM images can be combined with the amplitude contained in electron diffraction patterns to discover the atomic structural features [26], although, in comparison with X-ray and neutron diffraction methods, the atomic positions in crystals determined by HRTEM are not so accurate.…”