Electron crystallography

Electron crystallography

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Electron crystallography is a method to determine the arrangement of atoms in solids using a transmission electron microscope (TEM).

Comparison with X-ray crystallography


It can complement X-ray crystallography
X-ray crystallography
X-ray crystallography is a method of determining the arrangement of atoms within a crystal, in which a beam of X-rays strikes a crystal and causes the beam of light to spread into many specific directions. From the angles and intensities of these diffracted beams, a crystallographer can produce a...

 for studies of very small crystals (<0.1 micrometers), both inorganic, organic and protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s, such as membrane protein
Membrane protein
A membrane protein is a protein molecule that is attached to, or associated with the membrane of a cell or an organelle. More than half of all proteins interact with membranes.-Function:...

s, that cannot easily form the large 3-dimensional crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

s required for that process. Protein structures are usually determined from either 2-dimensional crystals (sheets or helices
Helix
A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...

), polyhedron
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

s such as viral capsids, or dispersed individual proteins. Electrons can be used in these situations, whereas X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

s cannot, because electrons interact more strongly with atoms than X-rays do. Thus, X-rays will travel through a thin 2-dimensional crystal without diffracting significantly, whereas electrons can be used to form an image. Conversely, the strong interaction between electrons and proteins makes thick (e.g. 3-dimensional > 1 micrometer) crystals impervious to electrons, which only penetrate short distances.

One of the main difficulties in X-ray crystallography is determining phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

s in the diffraction pattern. Because no X-ray lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

 exists, X-rays cannot be used to form an image of the crystal being diffracted, and hence phase information is lost. Fortunately, electron microscopes contain electron lenses
Electrostatic lens
An electrostatic lens is a device that assists in the transport of charged particles. For instance, it can guide electrons emitted from a sample to an electron analyzer, analogous to the way an optical lens assists in the transport of light in an optical instrument. The recent development of...

, and so the crystallographic structure factor phase information can be experimentally determined in electron crystallography. Aaron Klug
Aaron Klug
Sir Aaron Klug, OM, PRS is a Lithuanian-born British chemist and biophysicist, and winner of the 1982 Nobel Prize in Chemistry for his development of crystallographic electron microscopy and his structural elucidation of biologically important nucleic acid-protein complexes.-Biography:Klug was...

 was the first to realise that the phase information could be read out directly from the Fourier transform of an electron microscopy image that had been scanned into a computer, already in 1968. For this, and his studies on virus structures and transfer-RNA, Klug received the Nobel Prize for chemistry in 1982.

Radiation damage


A common problem to X-ray crystallography and electron crystallography is radiation damage
Radiation damage
Radiation damage is a term associated with ionizing radiation.-Causes:This radiation may take several forms:*Cosmic rays and subsequent energetic particles caused by their collision with the atmosphere and other materials....

, 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
Cryofixation
Cryofixation is a technique for fixation or stabilisation of biological materials as the first step in specimen preparation for electron microscopy...

 and imaging takes place at liquid nitrogen
Liquid nitrogen
Liquid nitrogen is nitrogen in a liquid state at a very low temperature. It is produced industrially by fractional distillation of liquid air. Liquid nitrogen is a colourless clear liquid with density of 0.807 g/mL at its boiling point and a dielectric constant of 1.4...

 or even liquid helium
Liquid helium
Helium exists in liquid form only at extremely low temperatures. The boiling point and critical point depend on the isotope of the helium; see the table below for values. The density of liquid helium-4 at its boiling point and 1 atmosphere is approximately 0.125 g/mL Helium-4 was first liquefied...

 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.

Protein structures determined by electron crystallography


The first electron crystallographic protein structure to achieve atomic resolution was bacteriorhodopsin
Bacteriorhodopsin
Bacteriorhodopsin is a protein used by Archaea, the most notable one being Halobacteria. It acts as a proton pump; that is, it captures light energy and uses it to move protons across the membrane out of the cell...

, determined by Richard Henderson
Richard Henderson (molecular biologist)
Richard Henderson FRS is a Scottish molecular biologist and pioneer in the field of electron microscopy of biological molecules.-Career:...

 and coworkers at the Medical Research Council
Medical Research Council (UK)
The Medical Research Council is a publicly-funded agency responsible for co-ordinating and funding medical research in the United Kingdom. It is one of seven Research Councils in the UK and is answerable to, although politically independent from, the Department for Business, Innovation and Skills...

 Laboratory of Molecular Biology
Laboratory of Molecular Biology
The Laboratory of Molecular Biology is a research institute in Cambridge, England, which was at the forefront of the revolution in molecular biology which occurred in the 1950–60s, since then it remains a major medical research laboratory with a much broader focus.-Early beginnings: 1947-61:Max...

 in 1990. However, already in 1975 Unwin and Henderson had determined the first membrane protein structure at intermediate resolution (7 Ångström), showing for the first time the internal structure of a membrane protein, with its alpha-helices standing perpendicular to the plane of the membrane. Since then, several other high-resolution structures have been determined by electron crystallography, including the light-harvesting complex
Light-harvesting complex
A light-harvesting complex is a complex of subunit proteins that may be part of a larger supercomplex of a photosystem, the functional unit in photosynthesis. It is used by plants and photosynthetic bacteria to collect more of the incoming light than would be captured by the photosynthetic reaction...

, the nicotinic acetylcholine receptor
Nicotinic acetylcholine receptor
Nicotinic acetylcholine receptors, or nAChRs, are cholinergic receptors that form ligand-gated ion channels in the plasma membranes of certain neurons and on the postsynaptic side of the neuromuscular junction...

, and the bacterial flagellum
Flagellum
A flagellum is a tail-like projection that protrudes from the cell body of certain prokaryotic and eukaryotic cells, and plays the dual role of locomotion and sense organ, being sensitive to chemicals and temperatures outside the cell. There are some notable differences between prokaryotic and...

.



Application to inorganic materials


Electron crystallographic studies on inorganic crystals using high-resolution electron microscopy (HREM) images were first performed by Aaron Klug
Aaron Klug
Sir Aaron Klug, OM, PRS is a Lithuanian-born British chemist and biophysicist, and winner of the 1982 Nobel Prize in Chemistry for his development of crystallographic electron microscopy and his structural elucidation of biologically important nucleic acid-protein complexes.-Biography:Klug was...

 in 1978 and by Sven Hovmöller and coworkers in 1984. 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
Crystallographic image processing
Crystallographic image processing is a set of methods for determining the atomic structure of crystalline matter from high-resolution electron microscopy images obtained in a transmission electron microscope...

). 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 Michael O'Keefe started in the early 1970s to develop image simulation software which allowed to understand an interpret the observed contrast changes in HREM images.

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 related 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.

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. The utmost care must be taken to record such ED patterns from the thinnest areas in order to keep most of the structure related intensity differences between the reflections (quasi-kinematical diffraction conditions). Just as with X-ray diffraction patterns, the important crystallographic structure factor phases are lost in electron diffraction patterns and must be uncovered by special crystallographic methods such as direct methods
Direct methods (crystallography)
In crystallography, direct methods are a family of methods for estimating the phases of the Fourier transform of the scattering density from the corresponding magnitudes...

, maximum likelihood or (more recently) by the charge-flipping method. On the other hand, ED patterns of inorganic crystals have often a high resolution (= interplanar spacings with high Miller indices) much below 1 Ångström. This is comparable to the point resolution of the best electron microscopes. Under favourable conditions it is possible to use ED patterns from a single orientation to determine the complete crystal structure. Alternatively a hybrid approach can be used which uses HRTEM images for solving and intensities from ED for refining the crystal structure.

Recent progress for structure analysis by ED was made by introducing the Vincent-Midgley precession technique for recording electron diffraction patterns. The thereby obtained intensities are usually much closer to the kinematical intensities, so that even structures can be determined that are out of range when processing conventional (selected area) electron diffraction data.

Crystal structures determined via electron crystallography can be checked for their quality by using first-principles calculations within density functional theory
Density functional theory
Density functional theory is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure of many-body systems, in particular atoms, molecules, and the condensed phases. With this theory, the properties of a many-electron system can be determined by...

 (DFT). This approach was for the first time applied for the validation of several metal-rich structures which were only accessible by HRTEM and ED, respectively.

Recently, two very complicated zeolite
Zeolite
Zeolites are microporous, aluminosilicate minerals commonly used as commercial adsorbents. The term zeolite was originally coined in 1756 by Swedish mineralogist Axel Fredrik Cronstedt, who observed that upon rapidly heating the material stilbite, it produced large amounts of steam from water that...

structures have been determined by electron crystallography combined with X-ray powder diffraction. These are more complex than the most complex zeolite structures determined by X-ray crystallography.

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
  • K. H. Downing, H. Meisheng, H.-R. Wenk & M. A. O'Keefe (1990). "Resolution of oxygen atoms in staurolite by three-dimensional transmission electron microscopy." Nature 348, p. 525 - 528.
  • Zou, X.D. and Hovmöller, S. (2008). "Electron crystallography: Imaging and Single Crystal Diffraction from Powders." Acta Crystallographica A 64, p. 149-160.
  • T.E. Weirich, X.D. Zou & J.L. Lábár (2006). Electron Crystallography: Novel Approaches for Structure Determination of Nanosized Materials. Springer Netherlands, ISBN 978-1402039195

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