Volume 225, Issue 2-3 - Precession Electron Crystallography

Precession Electron Diffraction (PED) offers a number of advantages for crystal structure analysis and solving unknown structures using electron diffraction. The current article uses many-beam simulations of PED intensities, in combination with model structures, to arrive at a better understanding of how PED differs from standard unprecessed electron diffraction. It is shown that precession reduces the chaotic oscillatory behavior of electron diffraction intensities as a function of thickness. An additional characteristic of PED which is revealed by simulations is reduced sensitivity to structure factor phases. This is shown to be a general feature of dynamical intensities collected under conditions in which patterns with multiple incident beam orientations are averaged together. A new and significantly faster method is demonstrated for dynamical calculations of PED intensities, based on using information contained in off-central columns of the scattering matrix.

The structure of an intermediate form of tin oxide was investigated by precession electron diffraction. The results support a revised version of a layered, vacancy-ordered structure for Sn 3 O 4 proposed in the preceding literature. The lattice parameters were found to be consistent with a monoclinic cell which is a distorted superlattice of the cassiterite structure. Zero-order Laue zone (ZOLZ) Patterson maps, phased projections and phases measured from a [001] first-order Laue zone (FOLZ) conditional Patterson map all support the proposed modification to the tin coordinates over the unmodified form. The results of kinematical refinement were not satisfactory, although weak features found in the Patterson maps were consistent with the oxygen atoms being located close to the previously proposed positions.

Simulations suggest that the strong phase object approximation of dynamical scattering may allow extracting crystallographic phase information from single 2D electron diffraction patterns of 3D protein crystals using probabilitistic procedures. Unlike other phasing methods, the procedure does not requires any additional knowledge – like real space images, atomicity, non-crystallographic symmetry, the presence or location of disordered solvent or the availability of a support with a known structure. In specific cases, the availability of precession electron diffraction data can further improve the phases.

The structure of the complex zeolite IM-5 ( Cmcm , a = 14.33(4) Å, b = 56.9(2) Å, c = 20.32(7) Å) was determined by combining selected area electron diffraction (SAED), 3D reconstruction of high resolution transmission electron microscopy (HRTEM) images from different zone axes and distance least squares (DLS) refinement. The unit cell parameters were determined from SAED. The space group was determined from extinctions in the SAED patterns and projection symmetries of HRTEM images. Using the structure factor amplitudes and phases of 144 independent reflections obtained from HRTEM images along the [100], [010] and [001] directions, a 3D electrostatic potential map was calculated by inverse Fourier transformation. From this 3D potential map, all 24 unique Si positions could be determined. Oxygen atoms were added between each Si–Si pair and further refined together with the Si positions by distance-least-squares. The final structure model deviates on average 0.16 Å for Si and 0.31 Å for O from the structure refined using X-ray powder diffraction data. This method is general and offers a new possibility for determining the structures of zeolites and other materials with complex structures.

Texture diffraction data in pioneering Russian electron crystallographic studies inspired the invention of modern precession methods for collecting single crystal data. (Although oblique texture patterns contain overlapped reflections, the similarity to precession methods is a result of averaging intensities over an angular distribution of crystallites within the large area sampled by the incident electron beam.) Using texture diffraction amplitudes originally measured by Vainshtein, the crystal structure of diketopiperazine has been re-determined using automated direct methods ( SIR97 ) and refined by block diagonal least squares. This determination was carried out in parallel with an equivalent direct methods study of a larger X-ray data set from the same material published by Degeilh and Marsh, followed by least squares refinement, reproducing the original results. After both refinements, the electron crystallographic bonding parameters for heavy atoms are found to be similar to derived X-ray crystallographic parameters. On the other hand, C–H and N–H distances are more accurately determined by electron crystallography than by X-ray crystallography since the light atom positions are more easily detected in ensuing maps. Surprisingly the least squares refinement against the electron diffraction data did not require a restraint on the magnitude of atomic incremental movement; moreover the atomic temperature factors could be refined, producing results that were more reasonable than expected from the very low overall B value found from a Wilson plot.

A new method for collecting complete three-dimensional electron diffraction data is described. Diffraction data is collected by combining electron beam tilt at many very small steps, with rotation of the crystal in a few but large steps. A number of practical considerations are discussed, as well as advantages and disadvantages compared to other methods of collecting electron diffraction data.

An automated technique for the mapping of nanocrystal phases and orientations in a transmission electron microscope is described. It is primarily based on the projected reciprocal lattice geometry that is extracted from electron diffraction spot patterns. Precession electron diffraction patterns are especially useful for this purpose. The required hardware allows for a scanning-precession movement of the primary electron beam on the crystalline sample and can be interfaced to any older or newer mid-voltage transmission electron microscope (TEM). Experimentally obtained crystal phase and orientation maps are shown for a variety of samples. Comprehensive commercial and open-access crystallographic databases may be used in support of the nanocrystal phase identification process and are briefly mentioned.

The foundations of precession electron diffraction in a transmission electron microscope are outlined. A brief illustration of the fact that laboratory-based powder X-ray diffraction fingerprinting is not feasible for nanocrystals is given. A procedure for structural fingerprinting of nanocrystals on the basis of structural data that can be extracted from precession electron diffraction spot patterns is proposed.