Elemental concentration calculation

Ema data can be quantitated to provide elemental concentrations, but several corrections are necessary to account for matrix effects adequately. One weU-known method for matrix correction is the 2af method (7,31). This approach is based on calculated corrections for major matrix-dependent effects which alter the intensity of x-rays observed at a particular energy after being emitted from the corresponding atoms. The 2af method corrects for differences between elements in electron stopping power and backscattering (the correction), self-absorption of x-rays by the matrix (the a correction), and the excitation of x-rays from one element by x-rays emitted from a different element, or in other words, secondary fluorescence (the f correction). 

Fluxes of volatile elements (CO2, S, As) and other elements (Hg, Mn, Ba) due to hydrothermal activities at back-arc basins were calculated. Probably the hydrothermal flux of minor elements concentrated in Kuroko deposits (Sb, Tl, etc.) is large compared with those from midoceanic ridges. CO2 flux from back-arc basins is estimated to be large compared with that from midoceanic ridges. 

The procedure is schematically shown in Fig. 34.29. Equation (34.10) represents a homogeneous system of equations with a trivial solution r, = 0. Because component / is absent in the concentration vector, this component does not contribute to the matrix T °. As a consequence the rank of T is one less than its number of rows. A non-trivial solution therefore can be calculated. The value of one element of r, is arbitrarily chosen and the other elements are calculated by a simple regression [17]. Because the solution depends on the initially chosen value, the size (scale) of the true factors remains undetermined. By repeating this procedure for all columns c, (t = 1 to p), one obtains all columns of R, the entire rotation matrix. 

The sources of uncertainty in NAA analysis are well understood, and can be derived in advance, modelled and assessed experimentally. There are two main kinds of interferences in the calculation of trace-element concentrations by INAA. The first one is formation of the same radionuclide from two different elements. Another kind of interference is from two radionuclides having very close y lines. Whenever interferences occur, the radionuclide of interest can be carried through a post-irradiation radiochemical separation without the danger of contamination. 

Using the temperature and electron density as fitting parameters, within a range established from measurements from known samples, the ratio nx /nx may be obtained and the concentration of element x calculated using... 

A unique feature of the ion microprobe is the potential to measure both elemental concentrations and isotopic ratios in the same spot. This capability was particularly valuable in the present study since the possible correlations between the 26Mg/24Mg and Al/Mg ratios are central to the interpretation of Mg isotopic anomalies. The Al/Mg ratio is calculated from the... 

Table 1.10. Isotope ratios and elemental concentrations (ppm ) used for the three-component mixing calculation shown in Figure 1.9.

The first three fluxes can be calculated by multiplying the biolimiting element concentration (C) by the annual water transport (p) that is,... 

Figure 3-24 Calculated diffusion-couple profiles for trace element diffusion and isotopic diffusion in the presence of major element concentration gradients using the approximate approach of activity-based effective binary treatment. The vertical dot-dashed line indicates the interface. The solid curve is the Nd trace element diffusion profile (concentration indicated on the left-hand y-axis), which is nonmonotonic with a pair of maximum and minimum, indicating uphill diffusion. The dashed curve is the Nd isotopic fraction profile. Note that the midisotopic fraction is not at the interface.

In order to consolidate the separate concentrations of soil elements, a soils concentration was calculated by summing the elemental concentrations plus their presumed oxide concentration. These oxide forms are Al203,Si02,K20,Ca0,Ti02, and Fe203. For the coarse particles, this soils concentration accounted for 60% of the coarse gravimetric mass, with a correlation coefficient between the two of 0.90. For the fine particles, soils accounted for only 25% of the fine gravimetric mass, and the two were poorly correlated. 

Example. Plot the variations in trace element concentrations in instantaneous melt and extracted melt for an incompatible element with Dq = 0.02 during fractional melting. From Eq. (2.7) for extracted melt and Eq. (2.8) for instantaneous melt, when = 0.02, we can calculate the source-normalized concentrations C / Q and / Cq at different degrees of melting in Fig. 2.1. 

Element standards were grouped into four standard libraries, corresponding to the four decay counting times. Decay time boundaries for each standard library are shown in Table II. In each library, at least two elements were calculated from different standards. These two standards represented different concentrations, counting geometries, dead times, decay times, and sample matrices. Visual inspection of the computer listing provided a rapid spot check for computer program malfunctions. 

The ratio /spectrophotometric measurement, and the value of a is then calculated from eq. (3.5) to yield the desired absorption constant. The numerous absorption constants found in the literature arise from the choice of quantities incorporated in the constant b. Some of the terms most commonly used to express absorption in minerals are summarized in table 3.2. Note that optical densities (O.D.), representing the direct output from many spectrophotometers, lack specificity about sample thickness and element concentrations. Absorption coefficients (a) indicate that sample thicknesses have been measured or estimated. Molar extinction coefficients (e) require chemical analytical data as well as knowledge of sample thicknesses. 

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