Elementary Layers Research Articles

The propagation of radiation in capillary-porous colloidal bodies

We present a solution for the problem of the distribution of spectral radiation fluxes through the thickness of a layer and the quantity of radiant energy absorbed by the elementary layers at a specific depth in capillary-porous colloidal bodies. We have demonstrated that the solution is found to be in good agreement with experiment.

Calculation of the Penetration of Gamma Rays Through Two-Layer Slabs

The method of invariant imbedding has been applied to the problem of penetration of gamma rays through two-layer slabs and turned out to be accurate and less time-consuming than the Monte Carlo method. A series of calculations was made for two-layer slabs of water, iron, and lead for plane oblique sources. An approximate formula for synthesizing the buildup factor of a composite slab from those of elementary layers is derived from numerical solutions by modifying the formula originally proposed by Kalos.

Defauts structuraux dans les carbones graphitables effets des traitements thermiques—partie II

Shapes and intensities of two-dimensional reflexions ( hk) can be used to evaluate the lattice distortion of elementary carbon layers in their plane and the rate of interstitial carbon atoms. The results show that the rate of interstitials t supplies the fundamental basis of classification for graphitized samples of different origin. Layer distortions are amplified effects of the presence of interstitial atoms.

Defauts structuraux dans les carbones graphitables effets des traitements thermiques — partie I

Graphitized samples, with the same degree of graphitization g show great differences in some physical properties. It is clear that we must associate to g another structural parameter. Study of six series of samples of different origin show that the distortion parameter δ c which measures the distortion of elementary carbon layer upright its mean plane, gives an interesting basis of classification. The evolution of δ c presents a striking parallelism with the lattice thermal expansion.

Electron-Optical Study of Smectites

AbstractThe combined use of electron microscopy and of selected area diffraction (SAD) has been applied to the study of montmorillonites from Wyoming and from Camp-Berteaux, of nontronite, and of hectorite. The study shows that only the elementary layers of the Wyoming montmorillonite and of the nontronite are single two-dimensional crystals. The elementary layers of the montmorillonite from Camp-Berteaux are formed by edge-to-edge associations of very small elements with mutual orientations of about 60° or multiples of 60°. The layers of hectorite are formed by edge-to-edge association of laths with fluctuations of orientation of the order of 10° rotation around adjoining edges. The SAD patterns of Wyoming montmorillonite show that the single layer plane symmetry group of this mineral is c1m1; nontronite layers belong to the symmetry group c2mm. The study of thick particles shows that in turbostratic smectites the layers are stacked with mutual rotations around the perpendicular to their plane. This mode of stacking explains the absence of hkl reflections. High resolution diffraction (HRD) patterns obtained with sample inclined to the electron beam show that only the structure of hectorite approaches the ideal model; nontronite and montmorillonite exhibit appreciable distortions with respect to the ideal model. HRD diagrams provide precise information for the refinement of the crystal structures of smectites

Derivation of absorption coefficients from reflection spectra for dyed wool cloth

The Girin-Stephanov theory is used. The reflection coefficient for an elementary layer is derived from Fresnel's formula for normal incidence, as modified by a factor for the proportion of the area taken up by fibers.

Etude cinetique de l'oxydation en milieu liquide des carbones graphitables

All carbons are oxidized to CO 2 by a hot mixture of H 2SO 4 and Ag 2 Cr 2 O 7. A study of the kinetics of the reaction shows that the oxidation rates vary within a ratio of 1 to 1000 according to the state of graphitization. The lowest rate constant k 1 is found with soft carbons treated between 1000 and 1200°C. The highest constant k″ 3 is observed with natural graphite or artificial graphite with a degree of graphitization in the region of 1. In a partially graphitized carbon (treated between 1500 and 2800°C) four rate constants k 1, k 2, k' 3 and k″ 3 are observed to be simultaneously involved, the two extreme values being identical with those mentioned above. The oxidation kinetics thus enable the presence of four structural forms F 1, F 2, F' 3, F″ 3 to be detected, and their proportions measured. Each form corresponds to a particular state of the elementary carbon layer (the nature of the structural defects). The results of the kinetic analysis are discussed in relation to the physical properties and the data from X-ray studies.

Influence of Light Scattering in a Photographic Layer on the Exposure of the Uppermost Elementary Layer

AbstractTheory and experiments show that the effective exposure in the uppermost elementary layer (i.e., the uppermost layer of grains) of a photographic emulsion coating is I+88R times (R=reflexion factor of the emulsion) as high as the exposure caused by an incident flux of “parallel” light. The experiments show that in determining the exposure increase by means of a substitute layer (which stands for the genuine elementary layer for the experiment) the physical properties of this layer are of decisive importance; an inappropriate choice of this layer will yield exposure values which are lower than those applying in the elementary layer.

Ionospheric reflection processes for long radio waves—II

In a previous paper ( Westcott , 1962), the reflection process of very long waves within an ionospheric medium was considered. The Darwin-Hartree microscopic theory of re-radiation was used to derive formulae for 1. (i) the contribution by an elementary layer of a horizontally stratified ionosphere to the reflected field below the medium and 2. (ii) the integrated contribution to the reflected field due to a finite layer. These formulae were developed for a vertically incident wave and applied to an exponential isotropic ionosphere. In this paper the formulae are extended to determine the effect of oblique incidence on the reflection process and the results obtained are complementary to those obtained in the previous paper. For vertically polarized waves it is shown that the pole occurring at the level of zero refractive index in the full wave equations can seriously affect the reflection process at very low frequencies. As the wave frequency increases through the band 8–128 kc/s, with incidence at 60° it is shown that even when small collision frequencies are assumed the effect of the pole diminishes. The results then become very similar to those obtained for horizontally polarized waves where the main reflections occur from the level at which the Booker function q is zero.

Ionospheric reflection processes for long radio-waves—I

At the present time no established theory exists for the reflection process of long radio waves from an ionospheric medium. After a brief discussion of the Darwin-Hartree microscopic theory of re-radiation, formulae are derived for 1. (i) the contribution by an elementary layer of a horizontally stratified ionosphere to the reflected field below the medium 2. (ii) the integrated contribution to the reflected field due to a finite layer. The formulae are applied to an exponential isotropic ionosphere for a vertically incident wave. For short waves the level at which the refractive index vanishes has long been regarded as the reflection level. This level when computed for very long waves is found to be much lower than the level at which the maximum reflection density occurs. The agreement between the two definitions is shown to improve with increasing wave frequency.

LONG DISTANCE V.H.F. FIELDS: I. PARTIAL REFLECTION FROM A STANDARD ATMOSPHERE

Reliable propagation of V.H.F. waves and microwaves from high power transmitters to distances of several hundred miles beyond optical range has been demonstrated by an ever increasing number of experiments during the last ten years. The fields which have been observed have consistently been many times greater than the field strengths predicted by the "effective radius" theory. The present paper will be published in two parts. In Part I the theory that the phenomenon can be explained solely in terms of "partial internal reflection" from elementary layers of a dielectric distribution where the rate of decrease of (μ – 1) with height is everywhere continuous and of the same order of magnitude as in a "standard" atmosphere is carefully examined and found to be untenable. In Part II, the case where the distribution contains "sharp layers" (i.e., local regions where (μ – 1) changes relatively rapidly with height) is examined and it is found that these could cause the phenomenon. However, in view of the other characteristics of the observed field, it is concluded that the effect in question is probably more usually due to scattering of the electromagnetic waves from atmospheric turbulence.

On the Theory of Flame Propagation

A new theory of flame propagation in slow inflammation is proposed which considers that the highly energized atoms or radicals formed in the flame front play a more important rôle than heat conductivity in bringing the unburned gas to the reacting state. A small number of atoms or radicals diffuse over into the unburned phase, there initiating the chemical reaction. This and other considerations allow one to propose that the sum of thermal and chemical energy per unit mass of gas in all layers from the burned phase to the unburned phase is constant. The fundamental equation for the velocity V of the flame is derived simply from the fact that the number of molecules of combustible gas entering the reaction zone (flame front) in unit time equals the number reacting in the zone in the same time. If the flame front extends from xu to xb and the unburned gas enters it at a rate just sufficient to maintain the flame front stationary, then for 1cm¯2 cross section the equation reads: VNc(u)= ∫ TuTb−∂Nc∂tdxdTdTwhere V is the flame speed which is identical with the volume of unburned gaseous mixture (under initial conditions) entering the reaction zone per sec.; Nc(u) is the concentration of combustible gas in molecules/cc in the unburned phase; and Tb and Tu are temperatures of the completely burned and unburned gases at xb and xu, respectively. This equation, in addition to the postulates that the sum of thermal and chemical energy per unit mass remains constant and that the rate of change of concentration of the various gas constituents in an elementary layer due to mass flow, diffusion and chemical reaction is zero, allows a solution of the problem. The theory is applied to explosions of mixtures of ozone gas and oxygen. Ozone decomposes to oxygen, with evolution of heat. With the help of the postulate that the total energy per unit mass is constant, the terms ∂Nc/∂t and dx/dT can be expressed as functions of temperature alone, and the above equation can be solved. In view of certain simplifications the calculated velocities are considered to be in satisfactory agreement with the experimental velocities. The theory furnishes knowledge of the structure of the flame front. A particular explosion is analyzed. The width of its flame front is shown to be about 10-3 cm. The temperature distribution, the distribution of the concentrations of various molecular and atomic species, and the rate of reaction throughout the flame front are given. The authors add an appendix, which includes a critical analysis of the essential differences between the present theory and previous theories of other investigators.