Large unit cells

An experimental teclmique that is usefiil for structure studies of biological macromolecules and other crystals with large unit cells uses neither the broad, white , spectrum characteristic of Lane methods nor a sharp, monocliromatic spectrum, but rather a spectral band with AX/X 20%. Because of its relation to the Lane method, this teclmique is called quasi-Laue. It was believed for many years diat the Lane method was not usefiil for structure studies because reflections of different orders would be superposed on the same point of a film or an image plate. It was realized recently, however, that, if there is a definite minimum wavelengdi in the spectral band, more than 80% of all reflections would contain only a single order. Quasi-Laue methods are now used with both neutrons and x-rays, particularly x-rays from synclirotron sources, which give an intense, white spectrum. 

Figure BT2T4 illustrates the direct-space and reciprocal-space lattices for the five two-dimensional Bravais lattices allowed at surfaces. It is usefiil to realize that the vector a is always perpendicular to the vector b and that is always perpendicular to a. It is also usefiil to notice that the length of a is inversely proportional to the length of a, and likewise for b and b. Thus, a large unit cell in direct space gives a small unit cell in reciprocal space, and a wide rectangular unit cell in direct space produces a tall rectangular unit cell in reciprocal space. Also, the hexagonal direct-space lattice gives rise to another hexagonal lattice in reciprocal space, but rotated by 90° with respect to the direct-space lattice.

Computational solid-state physics and chemistry are vibrant areas of research. The all-electron methods for high-accuracy electronic stnicture calculations mentioned in section B3.2.3.2 are in active development, and with PAW, an efficient new all-electron method has recently been introduced. Ever more powerfiil computers enable more detailed predictions on systems of increasing size. At the same time, new, more complex materials require methods that are able to describe their large unit cells and diverse atomic make-up. Here, the new orbital-free DFT method may lead the way. More powerful teclmiques are also necessary for the accurate treatment of surfaces and their interaction with atoms and, possibly complex, molecules. Combined with recent progress in embedding theory, these developments make possible increasingly sophisticated predictions of the quantum structural properties of solids and solid surfaces. 

Because of the high vapor pressure of the metals EUB4 and YbB4 are difficult to obtain. However, this factor is not sufficient to explain why EUB4 cannot be prepared an equally important factor may be the large unit cell resulting for a 2+ oxidation... 

From these observations Zachariasen concluded that glass can be thought of as an infinitely large unit cell containing an infinite number of atoms. The difference between the crystalline and the vitreous state is, therefore, found in the presence or absence of periodicity - what we would now describe as long range order , which is a fundamental property of a crystalline structure. This theory explains many of the differences between glasses and crystals, such as ... 

At a high degree of supersaturation, the nucleation rate is so high that the precipitate formed consists mostly of extremely small crystallites. Incipiently formed crystallites might be of a different polymorphous form than the final crystals. If the nucleus is smaller than a one-unit cell, the growing crystallite produced initially is most likely to be amorphous substances with a large unit cell tend to precipitate initially as an amorphous phase ("gels"). 

By using slightly different words, approximants are translationally normal crystal compounds generally with large unit cells that contain condensed, highly symmetric building blocks such as dodecahedra and icosahedra and have compositions close to those of related quasicrystals. 

One big problem, which arises mainly in crystals with rather large unit cells, is the overlapping of reflections. This prevents an accurate measurement of the local integrated intensities of a large number of reflections. A solution to this problem can be the 2D pattern decomposition method, which is based on the same principles as in X-ray powder diffraction. This method takes into account the dependence of intensities on the particle orientation function and the size of microcrystals. It is therefore necessary to establish the mathematical formalism that describes the dififiaction pattern taking into account these parameters. 

Due to the large unit cell of v- AlCrFe, many atoms overlap in every projection. Images have to be combined to obtain a 3D potential map in order to resolve the individual atoms. Two important steps are needed for 3D reconstruction converting the 2D indices into 3D indices and putting all images into a common origin. 

CCD detectors use a phosphor to convert the incoming X-ray to visible light, which is in turn detected by the CCD chip. During this conversion process, the apparent size of an X-ray reflection increases, a phenomenon known as the point-spread factor. Typically, this change in reflection size does not present a significant challenge. In extreme cases (i.e. large unit cell dimensions or a very short sample to detector distance), however, it can lead to overlaps between adjacent reflections. When overlaps do occur, diffraction data can be recorded... 

Note also that the possibility of continuous readout will be very important for large unit cells, allowing reflection overlap to be minimized and signal-to-noise to be further improved. At present, neither technology is quite mature. 

Rossmann, M. G. (1979). Processing oscillation diffraction data from very large unit cells with an automatic convolution technique and profile fitting. /. Appl. Cryst. 12, 225-238. 

Seeded crystals grow in the orthorhombic space group C222j and diffract to a resolution of up to 6 A (Fig. 8). They have relatively small, densely packed unit cells of 215 300 590 A, in contrast to the open structure and the large unit cells of the... 

The traditional approach for structure solution follows a close analogy to the analysis of single-crystal XRD data, in that the intensities 1(H) of individual reflections are extracted directly from the powder XRD pattern and are then used in the types of structure solution calculation (e.g. direct methods, Patterson methods or the recently developed charge-flipping methodology [32-34]) that are used for single-crystal XRD data. As discussed above, however, peak overlap in the powder XRD pattern can limit the reliability of the extracted intensities, and uncertainties in the intensities can lead to difficulties in subsequent attempts to solve the structure. As noted above, such problems may be particularly severe in cases of large unit cells and low symmetry, as encountered for most molecular solids. In spite of these intrinsic difficulties, however, there have been several reported successes in the application of traditional techniques for structure solution of molecular solids from powder XRD data. 

The N,N -dimethyl-l,3-propanediamine complex of cellulose, prepared from ramie, requires a large unit-cell, with a - 3.364 nm, b (chain axis) = 1.026 nm, c = 3.040 nm, and /3 = 32.74°. One diamine molecule per two /3-D-Glcp residues exists in the complex. 

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