Specific lattice

Raman spectroscopy is sensitive to ordering arrangements of crystal structures, the effect depending on the type of order. Ordering atoms onto specific lattice sites in... 

An additional advantage of the proxy approach is that the relationship between a U-series element and its proxy is unlikely to be significantly modified by the presence of water. Wood and Blundy (2002) have shown that water can have the effect of either increasing or decreasing partition coefficients due to the combined effect of water on melting temperatures and component activities in melts. For the same reason water can fractionate one valence group from another. It will not, however, produce fractionation between different-sized ions of the same valence entering a specific lattice site. The principal effect of water on the proxy relationship lies in the lower temperature at which hydrous processes tend to occur, relative to anhydrous processes. This is readily accounted for by the presence of temperature in the denominator of Equation (8). 

In addition to the point defects that occur at specific lattice sites, there are types of defects, known as extended defects, that extend over a region of the crystal. The three most important types of extended... 

With regard to the geometry, a classical difficulty is the fact that the surface structure may differ considerably from the bulk. Only if surface and bulk structure are closely related may it be expected that specific crystal phases are responsible for active and selective oxidation. Otherwise these properties cannot be attributed to a specific lattice structure. 

PAC atomic probes (e.g., mIn or mHf) possess a nuclear quadrupole moment and a magnetic dipole. Even if no field acts on the PAC nucleus, the successive emission of the y-photons through an intermediate state exhibits an appreciable angular anisotropy between the emission directions. If the (isolated) nucleus is then brought into a perturbing field (e.g., on a specific lattice site which is next to a vacancy), the angular anisotropy becomes time-dependent due to the precession of the nuclear spin. For example, if the PAC nucleus in the crystal is exposed to a (static) electric... 

Consider the A-B binary system. If A and B form a random solid solution with, say, 10 atom percent B, the probability of finding a B atom on any specific lattice site is just 0.1. Under certain conditions, however, B atoms may favour certain specific sites than die test. B atoms will then preferentially position themselves on these specific sites. The probability of finding B atoms in these sites will greatly increase. This type of arrangement is referred to as an ordered structure. The process in which a random disordered solid solution is rearranged into an ordered solid solution is called an order-disorder transition. 

The percolation probability (q) for the lattice models is defined as the probability that a given site (or bond) belongs to an infinite open cluster (47). It is fundamental to percolation theory that there exists a critical value qc of q such that 9(q) = 0 3t q < qc, and (q) > 0 if > qc. The value qc is called the critical probability or the percolation threshold. Mathematical methods of calculating this threshold are so far restricted to two dimensions, consistent with the experience in the field of phase transitions that three-dimensional problems in general cannot be solved exactly (12,13). Almost all quantitative information available on the percolation properties of specific lattices has come from Monte Carlo calculations on finite specimens (8,11,12). In particular. Table I summarizes exactly and approximately known percolation thresholds for the most important two- and three-dimensional lattices. For the bond problem, the data presented in Table I support the following well-known empirical invariant (8)... 

These are the monochromator crystal materials that are used extensively for macromolecular crystallography at SR sources. The wavelength of the reflected beam from the monochromator can be calculated from the specific lattice plane spacing and the angle of reflection. 

Similar to adsorption on real surfaces, kinetic models based on involvement of lateral interactions and more specifically lattice gas models have been developed in literature. In the widely used lattice gas model the relationships between the rate of an elementary reaction and coverage is complex and cannot be written in a closed form when this model is used. 

Ionic doping of crystalline samples is presently achieved by coprecipitation [291-293]. Thin films are doped by gasing lead alloys with HN3 [294]. No techniques have been reported for quantitatively controlling dopant concentrations or occupying specific lattice sites. 

A simple translation is represented by the operation (E, T yJ, where E is the identity (represented by a unit matrix), and = wa + i b + wc, a vector of the translation lattice. Translational symmetry allows us to arrange a large number of identical molecules or atoms in such a way that they are all strictly equivalent provided that the crystal is infinitely large (or large compared to the shortest translations). The atoms or molecules on the surface of a crystal are equivalent to each other if they form a two-dimensional translation lattice, i.e. planar faces parallel to specific lattice planes in the three-dimensional lattice (Bravais law. Section 1.4.2). 

As the draw ratio increases, arcs first develop from the circular reflections at right angles to the draw direction and then point-shaped reflections in wide-angle X-ray pictures (Figure 5-35). The reciprocal length of an arc is a measure, therefore, of the extent of orientation of the crystallites, or, more precisely, the specific lattice planes. Arcs at various positions in the X-ray diagram correspond to the different lattice planes. Thus, an orientation factor / exists for each of the three spatial coordinates, and this is related to the angle of orientation P via... 

After all of the neutron losses that enter into e chain reaction have been evaluated for a specific lattice, with the exception of the loss by leakage from the exterior of the system, the size to which the system is to be built to effect a self-sustaining chain reaction has to be determined. The size at which the neutrons gained equal the neutrons lost is known as the critical size. The operating size is somewhat larger than the critical size. 

There is a variety of laser systems, the gain media of which consist of centres incorporated in a solid. The nature of these centres can be different, e.g. transition metal ions or electrons trapped in a lattice vacancy. Anyway the gain medium is associated with some specific lattice defects randomly distributed in a periodic structure. Since the wavelength of the radiation involved in the laser process is large compared to the lattice unit cell or the defect diameter, the periodicity of the crystal structure is not relevant. 

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