 Crystallographic image processing

Crystallographic image processing (CIP) is a set of methods for determining the atomic structure of crystalline matter from highresolution electron microscopy (HREM) images obtained in a transmission electron microscope (TEM). The term was created in the research group of Sven Hovmöller at Stockholm University during the early 1980s and became rapidly a label for this approach.
Contents
HREM image contrast and crystal potential reconstruction methods
Many beam HREM images are only directly interpretable in terms of a projected crystal structure if they have been recorded under special conditions, i.e. the so called Scherzer defocus. In that case the positions of the atom columns appear as black blobs in the image. Difficulties for interpretation of HREM images arise for other defocus values because the transfer properties of the objective lens alter the image contrast as function of the defocus. Hence atom columns which appear at one defocus value as dark blobs can turn into white blobs at a different defocus and vice versa. In addition to the objective lens defocus (which can easily be changed by the TEM operator), the thickness of the crystal under investigation has also a significant influence on the image contrast. These two factors often mix and yield HREM images which cannot be straightforwardly interpreted as a projected structure. If the structure is unknown, so that image simulation techniques cannot be applied beforehand, image interpretation is even more complicated. Nowadays two approaches are available to overcome this problem: one method is the exitwave function reconstruction method, which requires several HREM images from the same area at different defocus and the other method is crystallographic image processing (CIP) which processes only a single HREM image. Exitwave function reconstruction ^{[1]} ^{[2]} provides an amplitude and phase image of the (effective) projected crystal potential over the whole field of view. The thereby reconstructed crystal potential is corrected for aberration and delocalisation and also not affected by possible transfer gaps since several images with different defocus are processed. CIP on the other side considers only one image and applies corrections on the averaged image amplitudes and phases. The result of the latter is a pseudopotential map of one projected unit cell. The result can be further improved by crystal tilt compensation and search for the most likely projected symmetry. In conclusion one can say that the exitwave function reconstruction method has most advantages for determining the (aperiodic) atomic structure of defects and small clusters and CIP is the method of choice if the periodic structure is in focus of the investigation or when defocus series of HREM images cannot be obtained, e.g. due to beam damage of the sample. However, a recent study on the catalyst related material Cs_{0.5}[Nb_{2.5}W_{2.5}O_{14}] shows the advantages when both methods are linked in one study ^{[3]}.
Brief history of crystallographic image processing
Aaron Klug suggested in 1979 that a technique that was originally developed for structure determination of membrane protein structures can also be used for structure determination of inorganic crystals ^{[4]} ^{[5]}. This idea was picked up by the research group of Sven Hovmöller which proved that the metal framework partial structure of the heavymetal oxide K_{8x}Nb_{16x}W_{12+x}O_{80} could be determined from single HREM images recorded at Scherzer defocus ^{[6]}. In later years the methods became more sophisticated so that also nonScherzer images could be processed ^{[7]}. One of the most impressive applications at that time was the determination of the complete structure of the complex compound Ti_{11}Se_{4}, which has been inaccessible by Xray crystallography ^{[8]}. Since CIP on single HREM images works only smoothly for layerstructures with at least one short (3 to 5 Å) crystal axis, the method was extended to work also with data from different crystal orientations (= atomic resolution electron tomography). This approach was used in 1990 to reconstruct the 3D structure of the mineral staurolite HFe_{2}Al_{9}Si_{4}O_{4} ^{[9]} ^{[10]} and more recently to determine the structures of the huge quasicrystal approximant phase νAlCrFe ^{[11]} and the structures of the complex zeolites TNU9 ^{[12]} and IM5 ^{[13]}.
Crystallographic image processing of highresolution TEM images
The principal steps for solving a structure of an inorganic crystal from HREM images by CIP are as follows (for a detailed discussion see ^{[14]}).
 Selecting the area of interest and calculation of the Fourier transform (= power spectrum)
 Determining the defocus value and compensating for the contrast changes imposed by the objective lens (done in Fourier space)
 Indexing and refining the lattice (done in Fourier space)
 Extracting amplitudes and phase values at the refined lattice positions (done in Fourier space)
 Determining the origin of the projected unit cell and determining the projected (plane group) symmetry
 Imposing constrains of the most likely plane group symmetry on the amplitudes an phases. At this step the image phases are converted into the phases of the structure factors.
 Calculating the pseudopotential map by Fourier synthesis with corrected (structure factor) amplitudes and phases (done in Real space)
 Determining 2D (projected) atomic coordinates (done in Real space)
A few computer programs are available which assist to perform the necessary steps of processing. The most common programs are CRISP ^{[16]} ^{[17]}^{[18]}, VEC ^{[19]} ^{[20]} and the EDM package ^{[21]}.
Links
EDM (free for noncommercial purposes)  a ready to go version of EDM is implemented on the elmiX Linux live CD
References
 ^ A. Thust, M.H.F. Overwijk, W.M.J. Coene, M. Lentzen (1996) “Numerical correction of lens aberrations in phase retrieval HRTEM” Ultramicroscopy 64, 249  264.
 ^ L.J. Allen, W. McBride, N.L. O’Leary & M.P. Oxley (2004) “Exit wave reconstruction at atomic resolution” Ultramicroscopy vol. 100, 91104.
 ^ J. Barthel, T.E. Weirich, G. Cox, H. Hibst, A. Thust (2010) “Structure of Cs_{0.5}[Nb_{2.5}W_{2.5}O_{14}] analysed by focalseries reconstruction and crystallographic image processing” Acta Materialia vol. 58, 37643772. article
 ^ Klug, A. (1979) „Image Analysis and Reconstruction in the Electron Microscopy of Biological Macromolecules“, Chemica Scripta vol. 14, 245256.
 ^ L.A. Amos, R. Henderson, P.N.T. Unwin (1982) “ThreeDimensional Structure Determination by Electron microscopy of TwoDimensional Crystals” Prog. Biophys. Molec. Biol. vol. 39, 183231. article
 ^ Hovmöller, S., Sjögren, A., Farrants, G., Sundberg, M., Marinder, B.O. (1984) “Accurate atomic positions from electron microscopy”, Nature vol. 311, 238241. article
 ^ X.D. Zou, M. Sundberg, M.Larine, S. Hovmöller (1996) “Structure projection retrieval by image processing of HREM images taken under non optimum defocus conditions” Ultramicroscopy vol. 62, 103121.article
 ^ Weirich, T. E., Ramlau, R., Simon, A., Hovmöller, S., Zou, X. (1996) “A crystal structure determined with 0.02 Å accuracy by electron microscopy”, Nature vol. 382, 144146. article
 ^ Downing, K. H., Meisheng, H., Wenk, H. R., O’Keefe, M. A. (1990) “Resolution of oxygen atoms in staurolite by theeedimensional transmission electron microscopy”, Nature vol. 348, 525528. article
 ^ Wenk, H. R., Downing, K. H., Meisheng, H., O’Keefe, M. A. (1992) “3D Structure Dertermination from ElectronMicroscope Images: Electron Crystallography of Staurolite”, Acta Cryst. vol. A48, 700716.
 ^ Zou, X. D., Mo, Z. M., Hovmöller, S., Li, X. Z., Kuo, K. H. (2003) “Threedimensional reconstruction of the νAlCrFe phase by electron crystallography”, Acta Cryst vol. A59, 526539. article
 ^ F. Gramm, C. Baerlocher, L.B. McCusker, S.J. Warrender, P.A. Wright, B.Han, S.B. Hong, Z. Liu, T. Ohsuna & O. Terasaki (2006) "Complex zeolite structure solved by combining powder diffraction and electron microscopy" Nature 444, 7981. article
 ^ J. Sun, Z. He, S. Hovmöller, X.D. Zou, F. Gramm, C. Baerlocher & L.B. McCusker (2010) "Structure determination of the zeolite IM5 using electron crystallography" Z. Kristallogr. vol. 225, 77–85. article
 ^ X.D. Zou, T.E. Weirich & S. Hovmöller (2001) “Electron Crystallography  Structure determination by combining HREM, crystallographic image processing and electron diffraction.” In: Progress in Transmission Electron Microscopy, I. Concepts and Techniques, X.F. Zhang, Z. Zhang Ed., Springer Series in Surface Science. Vol. 38, Springer 2001, 191 – 222. ISBN 9783540676812
 ^ T. E. Weirich, From Fourier series towards crystal structures  a survey of conventional methods for solving the phase problem; in: Electron Crystallography  Novel Approaches for Structure Determination of Nanosized Materials, T. E. Weirich, J. L. Lábár, X. Zou, (Eds.), Springer 2006, 235  257.
 ^ S. Hovmöller (1992) “CRISP: crystallographic image processing on a personal computer” Ultramicroscopy vol. 41, 121–135.
 ^ S. Hovmöller, Y.I. Sukharev, A.G. Zharov (1991) “CRISP  A new system for crystallographic image processing on personal computers” Micron and Microscopica Acta vol. 22, 141–142.
 ^ H. Zhang, T. Yub, P. Oleynikov, D.Y. Zhao, S. Hovmöller & X.D. Zou (2007) “CRISP and eMap: software for determining 3D pore structures of ordered mesoporous materials by electron crystallography” Studies in Surface Science and Catalysis vol. 165, 109112.
 ^ Z. Wan, Y. Liu, Z. Fu, Y. Li, T. Cheng, F. Li, H. Fan (2003) Visual computing in electron crystallography. Zeitschrift für Kristallographie: Vol. 218, Issue 4 Electron Crystallography, pp. 308315. doi: 10.1524/zkri.218.4.308.20739
 ^ Li XueMing , Li FangHua & Fan HaiFu 2009 A revised version of the program VEC (visual computing in electron crystallography) Chinese Phys. vol. B18, 2459. doi: 10.1088/16741056/18/6/056
 ^ R. Kilaas, L.D. Marks & C.S. Own (2005) “EDM 1.0: Electron direct methods” Ultramicroscopy vol. 102, 233237.
Further reading
see also the Wiki on Electron Crystallography
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