Depth distribution function

Since the composition of the unknown appears in each of the correction factors, it is necessary to make an initial estimate of the composition (taken as the measured lvalue normalized by the sum of all lvalues), predict new lvalues from the composition and the ZAF correction factors, and iterate, testing the measured lvalues and the calculated lvalues for convergence. A closely related procedure to the ZAF method is the so-called ())(pz) method, which uses an analytic description of the X-ray depth distribution function determined from experimental measurements to provide a basis for calculating matrix correction factors. 

The depth distribution function, 4>(p r) represents the X-ray intensity per unit mass depth (pz), relative to that in an isolated thin layer, and is of the form illustrated in Figure 5.12. 

Emission depth distribution function (EDDF), 24 89 Emission intensity, 14 835 Emission rate enhancement spectrum,... 

Temperature variations cause to shift, thereby accessing different positions of the basin-depth distribution function (11). In any event < (j8) identifies the set of basins preferentially inhabited at the chosen temperature. As will be shown in Section V, <7(0) for low molecular weight substances in the liquid state tends to fall in the range 1 to 10 (see also Stillinger, 1998 Speedy, 1999). 

Quantification of AES and XPS has been a challenge for many years, but substantial progress has been made [5, 6]. We will focus here on two subjects that are very important for quantitative measurements by these techniques, first, it is often necessary to obtain different measures of the surface sensitivity of AES and XPS, such as those that are required for a quantitative analysis, a measurement of an overlayer-film thickness, and a statement of sampling depth. The following four terms can be used for these purposes the IMEP, the EAL, the mean escape depth (MED), and the information depth (ID). We show why these terms are conceptually different as well as often numerically different, for this purpose, it is useful to first introduce the concept of the depth distribution function (DDE) for the detected signal. We give information on five databases available from the... 

In another approach, which was previously mentioned, the mass thickness, or depth distribution of characteristic X-ray generation and the subsequent absorption are calculated using models developed from experimental data into a < )(p2) function. Secondary fluorescence is corrected using the same i flictors as in ZAP. The (pz) formulation is very flexible and allows for multiple boundary conditions to be included easily. It has been used successfully in the study of thin films on substrates and for multilayer thin films. 

The information available on UV-susceptibility of different developmental stages in kelps indicate the unicellular zoospores as being most sensitive (Wiencke et al. 2000, 2004). However, zoospore UV-sensitivity varies species-specifically as a function of depth distribution of the sporophyte, i.e. kelps from shallow water are more tolerant than plants from deeper vertical positions. Consequently, any increase in UVB-induced spore mortality will result in impaired reproductive success and finally reduce fitness of the population. In addition, elevated UVB will penetrate deeper into the water column, which may result in a shift of the upper distribution limit of seaweed communities to deeper waters (Wiencke et al. 2006). 

The use of traditional rod and piston pumps continues at many LNAPL recovery locations, particularly at refineries and distribution terminals. These units are usually powered by single-speed electric motors and have adjustable stroke lengths to control the pumping rate. When installed with the intakes set at the optimum pumping depth, they function fairly well. The primary advantage of rod and piston pumps is that the smooth slow stroke rate can pump mixtures of product and water without creating a significant emulsion. 

Dimensionless well depth Velocity of a particle Steady-state distribution function Dimensionless frequency (for electrolyte solutions)... 

Fig. 9.14 Values of F(y) for a 6-in-diameter, 20 1 IVD extruder at constant flow rate (500 lb/h) with screw speed as a parameter. Simulation was made for a square pitched screw with a constant channel depth of 0.6 in. [Reprinted by permission from G. Lidor and Z. Tadmor, Theoretical Analysis of Residence Time Distribution Functions and Strain Distribution Functions in Plasticating Extruders, Polym. Eng. Sci., 16, 450-462 (1976).]...

The depth distribution of the Sr/Ca ratios of the recrystallized calcites in these sediments was calculated from the Sr2+/Ca2+ concentrations in the pore waters and appropriate values of the strontium distribution coefficient as a function of temperature from 5-25°C, where... 

The intensity calculation is based on the knowledge of qKpr), the primary X-ray intensity distribution function as a function of mass depth pz (Fig. 8.9). Some experimental calculations of (iKp ) have been conducted using the tracer method proposed by Castaing. These measurements have only covered a limited number of experimental situations but have enabled adjustment of the parameters used in simulations by the Monte Carlo method or matrix effect correction models using a parameterisation of the function [Pg.164]

Figure 8.9 Diagrammatic representation of the function

To calculate the foam cell size distribution function we consider, following Mihira an isolated cell foam structure model (Fig. 24). Let r be a true cell radius, and s the radius of sectional circles on the cut surface X, f and s their mean values, of and of their mean square deviations, and f(r) and f(s) their distribution functions. We will denote by x the depth of a cell dissected by the plane X (Fig. 24) and calculate the probability P(r,x) of cells having a radius in the range from r to (r + dr) and a depth from x to (x + dx). The probability P(r) for the cells dissected by the plane X to have a radius r is ... 

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