Crystallographic image processing
Encyclopedia
Crystallographic image processing (CIP) is a set of methods for determining the atomic structure of crystalline matter from high-resolution 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.
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 exit-wave 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. Exit-wave function reconstruction 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 pseudo-potential 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 exit-wave 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 Cs0.5[Nb2.5W2.5O14] shows the advantages when both methods are linked in one study .
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 . This idea was picked up by the research group of Sven Hovmöller which proved that the metal framework partial structure of the heavy-metal oxide K8-xNb16-xW12+xO80 could be determined from single HREM images recorded at Scherzer defocus . In later years the methods became more sophisticated so that also non-Scherzer images could be processed . One of the most impressive applications at that time was the determination of the complete structure of the complex compound Ti11Se4, which has been inaccessible by X-ray crystallography . Since CIP on single HREM images works only smoothly for layer-structures 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
HFe2Al9Si4O4 and more recently to determine the structures of the huge quasicrystal
approximant phase ν-AlCrFe and the structures of the complex zeolites TNU-9 and IM-5 .
A few computer programs are available which assist to perform the necessary steps of processing. The most common programs are CRISP , VEC and the EDM package .
EDM (free for non-commercial purposes) - a ready to go version of EDM is implemented on the elmiX Linux live CD
Transmission electron microscopy
Transmission electron microscopy is a microscopy technique whereby a beam of electrons is transmitted through an ultra thin specimen, interacting with the specimen as it passes through...
). The term was created in the research group of Sven Hovmöller at Stockholm University
Stockholm University
Stockholm University is a state university in Stockholm, Sweden. It has over 28,000 students at four faculties, making it one of the largest universities in Scandinavia. The institution is also frequently regarded as one of the top 100 universities in the world...
during the early 1980s and became rapidly a label for this approach.
HREM image contrast and crystal potential reconstruction methods
Many beam HREM images are only directly interpretable in terms of a projected crystal structureCrystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
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
Contrast transfer function
The contrast transfer function is a type of optical transfer function that affects images collected in an transmission electron microscope. The contrast transfer function must be corrected in the images in order to obtain high resolution structures in three-dimensional electron microscopy,...
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 exit-wave 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. Exit-wave function reconstruction 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 pseudo-potential 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 exit-wave 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 Cs0.5[Nb2.5W2.5O14] shows the advantages when both methods are linked in one study .
Brief history of crystallographic image processing
Aaron KlugAaron 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...
suggested in 1979 that a technique that was originally developed for structure determination of 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:...
structures can also be used for structure determination of inorganic crystals . This idea was picked up by the research group of Sven Hovmöller which proved that the metal framework partial structure of the heavy-metal oxide K8-xNb16-xW12+xO80 could be determined from single HREM images recorded at Scherzer defocus . In later years the methods became more sophisticated so that also non-Scherzer images could be processed . One of the most impressive applications at that time was the determination of the complete structure of the complex compound Ti11Se4, which has been inaccessible by X-ray crystallography . Since CIP on single HREM images works only smoothly for layer-structures 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
Staurolite
Staurolite is a red brown to black, mostly opaque, nesosilicate mineral with a white streak.-Properties:It crystallizes in the monoclinic crystal system, has a Mohs hardness of 7 to 7.5 and a rather complex chemical formula: 2Al94O204...
HFe2Al9Si4O4 and more recently to determine the structures of the huge quasicrystal
Quasicrystal
A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry...
approximant phase ν-AlCrFe and the structures of the complex zeolites TNU-9 and IM-5 .
Crystallographic image processing of high-resolution 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 ).- Selecting the area of interest and calculation of the Fourier transformFourier transformIn mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
(= 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 factorsStructure factorIn condensed matter physics and crystallography, the static structure factor is a mathematical description of how a material scatters incident radiation...
. - Calculating the pseudo-potential map by Fourier synthesis with corrected (structure factor) amplitudes and phases (done in Real space)
- Determining 2D (projected) atomic co-ordinates (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 , VEC and the EDM package .
Links
CRISP (commercial)EDM (free for non-commercial purposes) - a ready to go version of EDM is implemented on the elmiX Linux live CD