Electron crystallography
Electron crystallography is a method to determine the arrangement of atoms in solids using a
Comparison with X-ray crystallography
It can complement
One of the main difficulties in X-ray crystallography is determining
Radiation damage
A common problem to X-ray crystallography and electron crystallography is radiation damage, by which especially organic molecules and proteins are damaged as they are being imaged, limiting the resolution that can be obtained. This is especially troublesome in the setting of electron crystallography, where that radiation damage is focused on far fewer atoms. One technique used to limit radiation damage is electron cryomicroscopy, in which the samples undergo cryofixation and imaging takes place at liquid nitrogen or even liquid helium temperatures. Because of this problem, X-ray crystallography has been much more successful in determining the structure of proteins that are especially vulnerable to radiation damage. Radiation damage was recently investigated using MicroED[4][5] of thin 3D crystals in a frozen hydrated state.
Protein structures determined by electron crystallography
The first electron crystallographic protein structure to achieve atomic resolution was
Application to inorganic materials
Electron crystallographic studies on inorganic crystals using high-resolution electron microscopy (HREM) images were first performed by Aaron Klug in 1978[13] and by Sven Hovmöller and coworkers in 1984.[14] HREM images were used because they allow to select (by computer software) only the very thin regions close to the edge of the crystal for structure analysis (see also crystallographic image processing). This is of crucial importance since in the thicker parts of the crystal the exit-wave function (which carries the information about the intensity and position of the projected atom columns) is no longer linearly related to the projected crystal structure. Moreover, not only do the HREM images change their appearance with increasing crystal thickness, they are also very sensitive to the chosen setting of the defocus Δf of the objective lens (see the HREM images of GaN for example). To cope with this complexity methods based upon the Cowley-Moodie multislice algorithm[15][16] and non-linear imaging theory[17] have been developed to simulate images; this only became possible[18] once the FFT method was developed.[19]
There was a serious disagreement in the field of electron microscopy of inorganic compounds; while some have claimed that "the phase information is present in EM images" others have the opposite view that "the phase information is lost in EM images". The reason for these opposite views is that the word "phase" has been used with different meanings in the two communities of physicists and crystallographers. The physicists are more concerned about the "electron wave phase" - the phase of a wave moving through the sample during exposure by the electrons. This wave has a wavelength of about 0.02-0.03 Ångström (depending on the accelerating voltage of the electron microscope). Its phase is relative to the phase of the undiffracted direct electron beam. The crystallographers, on the other hand, mean the "crystallographic structure factor phase" when they simply say "phase". This phase is the phase of standing waves of potential in the crystal (very similar to the electron density measured in X-ray crystallography). Each of these waves have their specific wavelength, called d-value for distance between so-called Bragg planes of low/high potential. These d-values range from the unit cell dimensions to the resolution limit of the electron microscope, i.e. typically from 10 or 20 Ångströms down to 1 or 2 Ångströms. Their phases are related to a fixed point in the crystal, defined in relation to the symmetry elements of that crystal. The crystallographic phases are a property of the crystal, so they exist also outside the electron microscope. The electron waves vanish if the microscope is switched off. In order to determine a crystal structure, it is necessary to know the crystallographic structure factors, but not to know the electron wave phases. A more detailed discussion how (crystallographic structure factor) phases link with the phases of the electron wave can be found in.[20]
Just as with proteins, it has been possible to determine the atomic structures of inorganic crystals by electron crystallography. For simpler structure it is sufficient to use three perpendicular views, but for more complicated structures, also projections down ten or more different diagonals may be needed.
In addition to electron microscopy images, it is also possible to use electron diffraction (ED) patterns for crystal structure determination.
Recent progress for structure analysis by ED was made by introducing the Vincent-Midgley
Crystal structures determined via electron crystallography can be checked for their quality by using first-principles calculations within density functional theory (DFT). This approach has been used to assist in solving surface structures[32] and for the validation of several metal-rich structures which were only accessible by HRTEM and ED, respectively.[33][34]
Recently, two very complicated zeolite structures have been determined by electron crystallography combined with X-ray powder diffraction.[35][36] These are more complex than the most complex zeolite structures determined by X-ray crystallography.
References
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Further reading
- Zou, XD, Hovmöller, S. and Oleynikov, P. "Electron Crystallography - Electron microscopy and Electron Diffraction". IUCr Texts on Crystallography 16, Oxford university press 2011. http://ukcatalogue.oup.com/product/9780199580200.do ISBN 978-0-19-958020-0
- Downing, K. H.; Meisheng, H.; Wenk, H.-R.; O'Keefe, M. A. (1990). "Resolution of oxygen atoms in staurolite by three-dimensional transmission electron microscopy". Nature. 348 (6301): 525–528. S2CID 4340756.
- Zou, X.D.; Hovmöller, S. (2008). "Electron crystallography: Imaging and Single Crystal Diffraction from Powders". Acta Crystallographica A. 64 (Pt 1): 149–160. PMID 18156680.
- T.E. Weirich, X.D. Zou & J.L. Lábár (2006). Electron Crystallography: Novel Approaches for Structure Determination of Nanosized Materials. Springer Netherlands, ISBN 978-1-4020-3919-5
External links
- Interview with Aaron Klug Nobel Laureate for work on crystallograph electron microscopy Freeview video by the Vega Science Trust.
- Raunser, S; Walz, T (2009). "Electron Crystallography as a Technique to Study the Structure on Membrane Proteins in a Lipidic Environment". Annual Review of Biophysics. 38 (1): 89–105. PMID 19416061.