Isotope ratio calculation

Detector saturation can effect both quantitative and qualitative data analysis, and each of these effects should be appreciated. The effect on sample quanti-tation is intuitive, where for instance a twofold increase in sample concentration produces a less than twofold increase in response. This will cause a flattening of calibration curves at higher concentrations. For API techniques, source saturation (or ion suppression) is another source of response saturation independent of detector saturation. Detector saturation can also effect qualitative measurements such as mass accuracy and isotope ratio calculations. In the former, when a mass spectral peak that has some finite resolution stalls to saturate the detector the peak-top calculations that provide the m/ measurement of the peak will become ambiguous. Likewise, it is possible that as one isotope of an ion starts to saturate the detector, adjacent isotopes in the distribution will still provide a linear response. The result of this is that incorrect isotope ratios will be obtained. Changes in relative isotope ratios of individual spectra across a chromatographic peak is an indicator of possible detector saturation. 

The recoveries of the methods were determined by spiking the sediment with known levels of each of the CBs. Spiking was either on a single level in triplicate or on three levels in at least singlefold. In case of recovery values over 100% no corrections have been on the final CB contents in the sediment. In case of recovery values under 100% corrections have been made. Data for CBs with recoveries significantly differing from 100% were discussed and possibly rejected. When isotope dilution with labelled CBs was applied, results were not corrected for recovery (isotope ratio calculation principle). Recoveries ranged from ca. 70 to 110%. 

B [%] represents the concentration decrease expected along a theoretical streamline plug flow without mixing and a single degradation process with a constant isotope fractionation factor. Co is the concentration of contaminants in the source area and Q is the concentration of contaminants along the flow path. R is the isotope ratio calculated ... 

Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) is also used to study nuclear materials. Commonly, samples are introduced into an ICP-MS via an aerosol. However, LA has become the sample introduction technique of choice for solid samples and those samples that cannot be easily aero-solubilized [100]. Nanosecond LA coupled to an ICP-TOF-MS can rapidly screen nuclear and nonnuclear solid samples for a wide array of nuclides and isotopes (nuclides of the same element) [101]. LA-ICP-MS is also used to analyze uranium oxide [102-103] these studies determine the ratios of U-235, U-236, and U-238 isotopes in the sample from microgram sample quantities. Isotopic ratio calculations are essential to determine if the sample is natural or of human origin. 

The Oklo Phenomenon. Naturally occurring uranium consists mainly of and fissionable The isotopic ratio can be calculated from the relative decay rates of the two isotopes. Because decays faster than the isotopic ratio decreases with time. In 1997, the isotopic abundance of 235u... 

The Mattauch-Herzoggeometry (Fig. 3.20) enables detection of several masses simultaneously and is, therefore, ideal for scanning instruments [3.49]. Up to five detectors are adjusted mechanically to locations in the detection plane, and thus to masses of interest. Because of this it is possible to detect, e. g., all isotopes of one element simultaneously in a certain mass range. Also fast, sensitive, and precise measurements of the distributions of different isotopes are feasible. This enables calculation of isotope ratios of small particles visible in the image. The only commercial instrument of this type (Cameca Nanosims 50) uses an ion gun of coaxial optical design, and secondary ion extraction the lateral resolution is 50 nm. 

The gross flux of carbon from atmosphere to ocean is thus ca. 80 Pg C/yr. There are several complications with the above calculation. The isotopic ratios must be steady-state values, which are unavailable due to the changes resulting from atmospheric atom bomb testing. The few available pre-bomb measurements from the late 1950s (Broecker et ah, 1960) together with determinations in corals (Druffel and Linick, 1978) are invaluable tools for determin-... 

Table 9.4. C N molar ratios (calculated and measured), total C and N content and stable carbon and nitrogen isotope data from bacteria, their growth medium (nutrient broth), and from collagen (infected and non-infected marten bone). The bacteria for inoculation were raised on nutrient broth (nb), with/without additives.

Table 11.2. Model calculations of weighting functions for fractionation of carbon isotope ratios (in %o) from dietary nutrient biochemical fractions to tissue biochemical fractions.

Fig. 2.43. Graphical illustration of sulfur isotope values of HiS (left axis and. solid line) produced during basalt-seawater interaction at various water/rock ratios. Calculations assume that seawater sulfate is mostly removed as anhydrite, that any residual sulfate is reduced by iron oxidation in reacting basalt, and that there is quantitative leaching of basaltic sulfide and homogeneous mixing of both sulfides. Dashed line...

The age equation. Because of extremely low initial °Th/ U ratios in surface corals, we first present the version of the °Th age equation calculated assuming an initial condition of °Th/ U = 0. Below, we present tests that indicate that this assumption holds for most surface corals. We then present a variant of this equation, which relaxes the criterion that initial °Th/ U = 0, but requires some knowledge of initial °Th/ Th values. It may be necessary to employ this second equation in unusual cases involving surface corals, with deep-sea corals, and in some other marine and lacustrine carbonates. The °Th age equation, calculated assuming (1) initial 230Th/238u = ("2) all changes in isotope ratios are the result of radioactive decay and... 

A quick glance at Equations (1) through (5) shows sources of error that contribute to error in age, presuming that the assumptions used in calculating the equations hold (initial condition assumptions and the closed-system assumption). These include errors in the decay constants/half-lives, errors in the measurement of the pertinent isotope ratios, and in the case of Equation (3), the error in our estimate of initial °Th/ Th. Relationships among error in half-lives, laboratory standardization procedures, and °Th age are discussed in detail by Cheng et al. (2000b). 

L234 are about 3 per mil lower than those calculated with commonly used X234 values, hence the revised modem sea water of 145.8 1.7 per mil (Cheng et al. 2000b), compared to earlier values about 3 per mil higher. In general half-lives are now known precisely enough so that their contribution to error in age is comparable to or smaller than typical errors in isotope ratios (determined with mass spectrometric techniques). 

There are a few developments on the horizon that will increase our ability to date bones and teeth reliability. Both y- and a-spectrometric methods can measure Pa/ U and °Th/U and concordance between dates calculated using the two can provide a measure of reliability. However, the discordance between the two is not very sensitive to different uptake regimes, and it is difficult to resolve, for example, bones that have undergone EU from those that have undergone LU with the analytical errors commonly encountered in measurements by y- and a-spectrometry. On the other hand, it has been shown recently that TIMS can measure both isotopic ratios with a precision usually better than 1% (Edwards et al. 1997). TIMS measurements of Pa/ U and °Th/U have yet to be routinely applied to dating fossil remains, but in the future, concordance between the two decay series will provide further evidence of the validity of a particular uptake model to a particular sample. 

Not giving the isotope ratios and errors actually used in age or isochron calculations (for example, data tables with only °Th/ Th, °Th/ " U, and 234y/238u j-atios but using Th/ Th- W Th and U/ Th- W Th isochrons) so that the reader cannot reproduce the calculations ... 

Atomic isotopes help detection so that the shift for 13 CO is perfectly predictable and isotope ratios are known from various sources, as we shall see later on. The change in the rotational constant with reduced mass is easily calculated and hence the change in the frequency of the J = J = 0 can be calculated, as we saw in Section 3.3. 

Chapter 8 describes a similar one-dimensional chain of identical reservoirs, but one that contains several interacting species. The example illustrated here is the composition of the pore waters in carbonate sediments in which dissolution is occurring as a result of the oxidation of organic matter. I calculate the concentrations of total dissolved carbon and calcium ions and the isotope ratio as functions of depth in the sediments. I present... 

This is the expression I use to calculate isotope ratios. The rate of change of delta is the influx of the abundant isotope times the delta of the source minus the outflux times the delta of the sink minus an extra term, delta times the rate of change of the amount of the abundant isotope (=// - fo), with the whole expression divided by the amount m of the abundant isotope. The isotope ratio in die standard, s, does not enter the expression, nor do the units, whether per mil or percent. 

The study of isotopes makes it necessary to introduce a further refinement in the general method of solution. I have been using a test of the relative increment to adjust the time step. The relative increment is the change in a dependent variable divided by the value of that variable. This is not a useful test, however, when the value of the variable approaches zero, because the test requires progressively smaller time steps. None of the variables I considered in previous chapters has approached zero, and so there has been no problem with this test. But carbon isotope ratios of seawater have delta values near zero, and a problem may occur when calculating these values. I have modified subroutine CHECKSTEP to permit a flexible response to this situation. 

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