Areal concentrations

Three common uses of RBS analysis exist quantitative depth profiling, areal concentration measurements (atoms/cm ), and crystal quality and impurity lattice site analysis. Its primary application is quantitative depth profiling of semiconductor thin films and multilayered structures. It is also used to measure contaminants and to study crystal structures, also primarily in semiconductor materials. Other applications include depth profilii of polymers, high-T superconductors, optical coatings, and catalyst particles. ... 

Figure 20. Summary of phosphorus cycle in southern Lake Michigan. Values in boxes are areal concentrations (milligrams/square meter) values on arrows are fluxes (milligrams/square meter per year). Areal concentrations are based on the mean depth (85 m) of the water column.

A summary of our most recent studies on biologically mediated decay is shown in Figure 5. In situ H202 decay was determined by using the natural logarithm of the nighttime areal concentration plotted versus time. The decay rate constant was taken as the slope of the line. Decay rate constants calculated using in situ values were similar to water samples incubated in bottles kept in the dark in the laboratory. The decay rate constants seemed to correlate with bacteria numbers. 

In deriving Eq. (36), and hence Eq. (38), it was assumed that the induction time is dominated by the time required to accumulate a critical areal concentration of cation vacancies (i.e., the formation time of the vacancy condensate). However, as evident from Fig. 33, the induction time may exceed the vacancy condensation time by the amount required for the film to dissolve locally and rupture. We previously lumped these effects into the relaxation time, r, and for the pitting of metals such as iron, copper, nickel, and stainless steels, which form very thin barrier layers, this approximation appears to be reasonable, in that Eq. (36) accounts for the experimental data very well. It is possible, however, to envision a case where the time... 

The areal concentration of major carbonate-cemented zones can reflect the location of incipient structural closure during the time of carbonate cementation, rather than the modern-day closure, as exemplified by the Angel Field case study. 

Using a simple model based upon the one-dimensional diffusion equation, it was shown [101] that the areal concentration of [60]PCBM molecules C at a distance x from the semiconductor-dielectric interface could be described as a function of... 

Depending on the film thickness and the experimental conditions, ERD can provide areal concentration (atom cm ) and/or concentration ratio of elements present. A sensitivity in the ppm region with a depth resolution of some 10 nm and a depth range of 1 pm is obtained in standard ERD set-ups. 

Fig. 2. Critical areal concentration, infinite slab—full HiO reflection.

From these data, an envelope of minimum values can be obtained. As can be seen, critical Systems extend to <2 g/llter. (However, if the critical mass is plotted as a function of the H/Pu ratio, the normal solution curve is the most limiting.) Althoue the absolute minimum critical mass is still at 30 g/liter and in a normal solution, the critical areal concentration for the slab Is less for the low-plutonium-concentration/low-water content mixtures than for the normal solution. 

The kinetics of H2 formation (and other surface reactions) via the Langmuir-Hinshelwood (diffusive) mechanism can be treated by rate equations, as in Eq. (1.52), or by stochastic methods.There are two main objections to the former approach it does not handle random-walk correctly and it fails in the limit of small numbers of reactive species. The latter objection is a far more serious one in the interstellar medium because dust particles are small, and the number of reactive atoms and radicals on their surfaces can be, on average, less than unity. Nevertheless, with rare exceptions, the few large models of interstellar chemistry that include surface processes as well as gas-phase chemistry do so via the rate equation approach, so we discuss it here. In the treatment below, we do not use the ordinary units of surface chemistry — areal concentrations or mono-layers — but instead refer to nmnbers of species on the mantle of an individual but average grain. Numbers can be converted to bulk concentrations, as used in Eq. (1.52), by multiplication by the grain number density n. ... 

Zno.9Mno.1O/ZnO heterostructure grown on c-plane sapphire by PLD n/a 8.8x10 (areal concentration cm ) 130 [165]... 

A] (voluminal or areal) concentration of component A A amount of component A a lattice parameter... 

Rp average areal resistance offered by the concentration potential between the enrichment and depletion compartments, ohm-cm ... 

Areal Variation. One objective of the sampling comparison studies was to determine the variation in TCDD concentration over a small area to estimate the error associated with a grab sample concentration. Accordingly, a one-square-yard area was selected adjacent to a previously sprayed road. The center of the test area was about 6 feet from a sprayed road shoulder. This one-square-yard area was divided into nine one-square-foot areas. Using clean spoons and knives, a single scoop was collected from the center of each one-square-foot area down to a depth of 2 inches. The data are presented in Figure 1. 

The large areal variation in environmental TCDD concentrations is confirmed by the analytical data resulting from using the four different methods to obtain samples at depth. An examination of Figure 3 which presents road centerline data from two 15-foot segments shows variations in the upper six inches ranging, from 295 to 895 and from 2.1 to 1020. 

Since the nuclear and electronic scattering cross sections for alpha particles are well known, the relative concentrations of the elements and their depth profiles can be easily obtained. The relative element concentrations are determined by the relative scattering intensities. The depth profile is obtained from the energy spread of the scattered particles, which lose energy before and after the nuclear collision, by inelastic scattering with electrons. The knowledge of the elements areal density and of the film thickness allows the determination of film density. 

In order to simplify the situation, we assume that our porous sample under investigation covers the bottom of an open straight-walled can and fills it to a height d (Figure 1). Such a sample will exhibit the same areal exhalation rate as a free semi-infinite sample of thickness 2d, as long as the walls and the bottom of the can are impermeable and non-absorbant for radon. A one-dimensional analysis of the diffusion of radon from the sample is perfectly adequate under these conditions. To idealize the conditions a bit further we assume that diffusion is the only transport mechanism of radon out from the sample, and that this diffusive transport is governed by Fick s first law. Fick s law applied to a porous medium says that the areal exhalation rate is proportional to the (radon) concentration gradient in the pores at the sample-air interface... 

The equation for determination of the sulfide produced in terms of the resulting concentration in the bulk water phase based on the areal sulfide production rate is ... 

C 2-, = sulfide concentration at the start of the sewer section (gS m-3) ra = areal sulfide production rate (gS m-2 h-1)... 

Following Equation (2.6), the concentration profile with depth z of any non-adsorbed substrate in an areally homogeneous system is given by ... 

Fig. 16.28 Dissolved-phase concentration plumes showing 0.5, 0.15, and 0.015 (and 0.0015 for last four TCM dates) contours. The inner, darkest shade contour is the maximum concentration. The source is 1 m upgradient of the 1 X 1.5 m areal faces shown here, and groundwater flow directions relative to north (normal to source face) are also shown. Reprinted with permission from Rivett MO, Feenstra S (2005) Dissolution of an emplaced source of DNAPL in a natural aquifer setting. Environ Sci Technol 39 447 55. Copyright 2005 American Chemical Society...

Lakewide Hg Accumulation. Mercury accumulation rates can be calculated for individual core sites as the product of the 210Pb-based sediment accumulation rate and Hg concentration in different strata. If enough cores are analyzed, whole-lake Hg inputs can be calculated by weighting the Hg flux of each core by the portion of the depositional basin it represents. In this study we calculate Hg loading for each lake on an areal basis for two time-stratigraphic units—modem (roughly the last decade) and preindustrial (before 1850)—according to eq 2 ... 

When P in the nepheloid zone was excluded from the integrations, areal total P concentrations increased from 733 mg/m2 in mid-April to 845 mg/m2 in mid-July, and then declined to 630 mg/m2 by late November. 

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