Atoms arrangement within

Considering only scattering at small momentum transfers, we may neglect the detailed atomic arrangements within e.g. a monomer or a solvent molecule and take into account only the scattering length densities pM or ps of such scattering units... 

The atomic arrangement within the unit cell is more difficult to determine than the cell dimensions. Trial structures deduced from these dimensions and a knowledge of the chain conformation,... 

Intercalation reactions (14.1) represent the ideal case there is an increase in the inter-layer distance while the carbon atom arrangement within the layers remains unchanged. However, during intercalation of cations from polymer [25] and solid [26] electrolytes, ternary phases (M (solv)yC /C (solv)yX ) are produced because the solvent from the electrolyte is also accepted into the carbon lattice. 

Considerations concerning the atomic arrangements within the schee-lite structure reveal that the removal of cations from the A positions... 

In the present study we have used a thin, well-ordered atomically flat alumina film grown on a NiAl(llO) single crystal surface as a model support [27]. The atomic arrangement within line defects of this film have recently been investigated [28]. In addilion, Ihere exists a proposed structure of the film based on X-ray diffraction data which is controversially debated at the moment [29]. The structure and size of the oxide-supported metal particles were controlled utilizing nucleation and growth of vapor deposited metal atoms under ultrahigh vacuum conditions. 

To show how diffraction of X-rays by a crystal may be used to determine the atomic arrangement within that crystal (see Chapter 6). 

The geometry of a crystal is defined with respect to a given lattice by picturing the crystal as made of periodically repeating unit cells. The atomic structure within the cell is a property of the particular structure (e.g. each cell can contain one or more molecules, or several atoms arranged within the cell volume in some given way), however, the cells themselves are assigned to lattice points that determine the periodicity. This periodicity is characterized by three lattice vectors, a, z = 1,2,3,... 

The symmetry of the atomic arrangement within the crystal can be described by space group theory, that is, the theory of the various ways of arranging objects in three dimensions such that a continuation of the symmetry operations gives the next unit cell and so forth (24). For protein molecules, which are by nature asymmetric, the important symmetry operations are rotation axes and screw axes. An object is said to have an n-fold rotation axis if, when an object is rotated (360/n)0, it appears like the original. For isolated objects, by point group theory, n may have any value. On the other hand, if the object is in a crystal (with its regular... 

The intensities of the Bragg diffracted beams or reflections, 1, are determined by the atomic arrangement within the unit cells. This gives the relative positions of the atoms and thereby also information about bonding, distances and angles between the individual atoms in the crystalline compound. Mathematically this can be described as ... 

Every crystalline phase in a sample has a unique powder diffraction pattern determined from the unit cell dimensions and the atomic arrangement within the unit cell. It can be considered a fingerprint of the material. Thus, powder diffraction can be used for phase identification by comparing measured data with diffraction diagrams from known phases. The most efficient computer searchable crystallographic database is the PDF-4 from the International Centre for Diffraction Data (ICDD) [3]. It is used by very efficient computer-based search-processes. In 2007 the PDF-4-i- database contains information about Bragg-positions and X-ray intensities for more than 450000 compounds, out of which there are about 107 500 data sets with atomic coordinates. New entries are added every year. The positions of the peaks in the measured pattern have to be determined. This can be done manually, but effective, fast and reliable automatic peak search methods have been developed. The method can obviously be successful only if the phases in the sample are included in the database. However, the database can also help to determine unknown phases if X-ray data exist for another isostructural compound albeit with a different composition. 

Nevertheless, the theory, as it emerged from Laurent s work, remained incomplete.. It still made use of radicals as units, and the question of molecular structure was evaded rather than answered. For a proper answer, one had to face up to the question What is the actual atomic arrangement within the radicals themselves ... 

The termination of a solid by a surface modifies the atomic surroundings in terms of the atomic coordination and the distribution of conduction electrons. It is then to be expected that the equilibrium positions of the surface atoms will change in order to minimize the surface free energy. If the entire surface layer is shifted collectively inward or outward, the surface is said to be relaxed (contracted or expanded). If the atomic arrangement within the surface plane changes, the surface is said to be reconstructed. Both relaxation and reconstruction phenomena can be analyzed by ion scattering. 

Mineraloids. The mineraloids are naturally occurring substances having a structure which can be partially crystalline or noncrystalline, i.e., solids with an irregular atomic arrangement within the solid. For instance, compounds such as obsidian, opal, amber or succinite are defined as mineraloids. 

The entire group of symmetry operators that completely describes the symmetry of the atomic arrangements within a crystal is called the space group. It has been shown that there are 230 space... 

The overall intensities of the peaks are related to the abundance of each phase in the sample. For each phase, the relative intensities may be determined by the calculation of structure factors, multiplicity factors, preferred orientation, and Lorentz/polarization factors. The latter two are normally tabled as a function of the scattering angle. The atomic arrangement within the cell also influences individual peak intensities via structure factor. 

Trends in adsorbate-induced relaxations on hcp(OOOl) are less clear than on fcc(lll), cf. Table 5. Perhaps the effects seen on fcc(l 11) do not carry over to hcp(OOOl), or the effects on hcp(OOOl) are more sensitive to details of the atomic arrangements within the various unit cells. A more exhaustive analysis and comparison of the results on a single metal, Ru(OOOl) [97M1], also suggests that structural trends may be difficult to extract for this one metal, and thus even more so for the class of hcp(OOOl) surfaces. 

Figure 13.1 Schematic illustration of the atomic arrangement within the zinc blende structure. This structure is derived by combining two fee lattices shifted by 1/4 of the diagonal length along the [111] direction with respect to one another. In the case of binary compounds, each of these fee lattices is populated with only cations or anions.

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