Infinite Number Of Layers Research Articles

X-Ray Plane Wave Dynamic Reflection at a Laminar Crystalline Medium in the Bragg Case

The problem of dynamic reflection of X-ray monochromatic plane waves at a laminar crystalline medium consisting of N plane-parallel and crystalline layers of equal thickness is considered. A formula for the dependence of reflectivity on the angle of incidence is obtained. The case of an infinite number of layers is considered. The boundaries of the ranges of total reflection of the incident wave are found in dependence on the layer thickness and the shift of the crystalline layer lattices with respect to each other. [Russian Text Ignored.]

Lattice relaxation around positive muon in copper

A model to study the local structure and geometry of condensed matter was applied to the lattice dilatation of Cu if a μ+ is implanted interstitially. The model system consists of a finite cluster of atoms embedded in the spherically symmetric part of the potential of the rest of the material. The calculations were calibrated with crystalline Cu using a cluster of 6 atoms and 0, 6 or a practical infinite number of layers around this central cluster. It is found that 6 layers are enough to deseribe the boundary conditions that the material imposes to the selected central cluster. Afterwards it was applied to a cluster of a central μ+ and 6 octahedrally disposed Cu. The equilibrium geometries, electronic configurations, electronic densities of states are presented and compared with μSR.

Dynamic tomography

Dynamic tomography is a radiographic procedure that allows details in a thin layer within the patient to be examined. This layer can be moved at will throughout the patient. Thus, details lying in an infinite number of layers can be scrutinized one layer at a time. Eight underexposed radiographs are made under rigid controls. Each film receives one fourth of a normal exposure. The “in focus” layer of details is about 0.5 mm. thick. Various future applications of the technique are discussed.

Adsorption on nonporous solids

It is a well-known fact that the two-parameter BET equation gives too high adsorption values at x (or p/ p 0) > 0.35. The reason for this is the assumption that at x = 1 an infinite number of layers are adsorbed. Experimental data for nonporous adsorbents show that the number of adsorbed layers close to x = 1 is far from infinite; in fact, it is in the vicinity of 5 or 6. A modified BET equation is derived, employing a third parameter k, which is a measure of the attractive force field of the adsorbent. The equation is identical with one derived by Anderson in 1946, but the model on which it is based, the derivation, and the method of application are different. Examples of the application of the modified BET equation are presented, and certain conclusions are drawn about the BET parameters v m and c.

Spiral Pits on Silicon Carbide

THE dislocation theory of crystal growth1 suggests that the crystal growing at low supersaturation in the presence of a single dislocation is not composed of an infinite number of layers stacked on each other as ideally considered, but is a helicoid with the dislocation line as its axis and the point of emergence of the dislocation at the top. The observation of a growth hill in the form of a ‘spiral staircase’ on a number of crystals reported in recent years2 has amply substantiated the theoretical predictions. Silicon carbide crystals have afforded evidence3 of a large variety of spiral growths, for example, monomolecular as well as microscopic, and interaction of spiral growth due to two or more dislocations of same as well as of opposite sign. In some cases, hitherto unobserved, silicon carbide crystals exhibit spirally terraced pits. Fig. 1 shows a phase-contrast micrograph of a spirally terraced pit. It is easy to decide with the fringes of equal chromatic order that this feature is a pit. The step height of this terraced pit as determined from high-dispersion Fizeau fringes corresponds to 27 ± 2 A., which is the repeat distance of this crystal identified by X-rays as 33 R (Ramsdell's symbol).