Mass fractionation factor

The implicit assumption in this correction is that both mass fractionation factors P, e.g., for Cu and Zn, are different, but will be changed by the same constant upon switching between sample and standard solutions. Again, this assumption has better chances of being correct if purihcation of the sample is efficient. For isotopic ratios not too far from unity (e.g., Cu/ Cu, Zn/ Zn, Te/ Fe), a precision of 0.05%o can be achieved (Marechal et al. 1999 Zhu et al. 2000 Beard et al. 2003). For larger ratios, the obtainable precision is 0.2-0.4%o. 

When written in full, the numher of unknowns is the sum c + e + r, where c is the number of active cups, e the number of elements for which the value h is needed, and r the number of ratios to measure. We first show how to use a standard solution (or a mixture of standards of different elements) of known isotopic compositions to determine the cup efficiencies. The unknowns are the efficiencies A for each cup and the mass fractionation factors/(or h for other laws). The system of equations is particularly compact since Equation (59) now reduces to ... 

Note that mass fractionation factor 6 for power law and the cup efficiency factor K are completely cancelled out in (10.34). However, readers may find that if we use linear law or exponential law, the fractionation factors cannot be completely eliminated by division. 

The spike in most cases is single spike, but it can be double spike. Single spike method provides the information of the concentration of the sample, whereas the double-spike method can yield the concentration of the sample and the mass fractionation factor that can be used to calculate the true isotopic ratios in the sample. Take Pb isotope as an example. Natural Pb samples have 1.4% ° Pb, 24.4% ° Pb, 22.1% ° Pb and 52.4% ° Pb. A single spike is made by artificially concentrating one of the minor Pb isotopes, for example Pb. A double spike is made by artificially concentrating two minor isotopes. For example, we can concentrate Pb and b isotopes to make ° Pb- Pb double spike or concentrate Pb and Pb to make Pb- ° Pb double spike. 

Marechal et al. [40] defined a generalized law for the mass fractionation factor p ... 

Calculation of the mass fractionation factor p from experimental data provides insight into whether thermodynamic or equilibrium as opposed to kinetic effects are at the origin of the mass-dependent isotope fractionation, although often the fractionation is shown to be of mixed origin. For example, Wombacher et al. 

For example, if a carbonaceous sample (S) is examined mass spectrometrically, the ratio of abundances for the carbon isotopes C, in the sample is Rg. This ratio by itself is of little significance and needs to be related to a reference standard of some sort. The same isotope ratio measured for a reference sample is then R. The reference ratio also serves to check the performance of the mass spectrometer. If two ratios are measured, it is natural to assess them against each other as, for example, the sample versus the reference material. This assessment is defined by another ratio, a (the fractionation factor Figure 48.2). 

Throughout this discussion we have used the numerical fraction of molecules in a class as the weighting factor for that portion of the population. This restriction is not necessary some other weighting factor could be used equally well. As a matter of fact, one important type of average encountered in polymer chemistry is the case where the mass fraction of the ith component is used as the weighting factor. Defining the mass of material in the ith class as mj, we write... 

Assuming that the gluing of particles of different sizes is performed randomly with their surface area as decisive parameter, for various homogeneous particle size fractions and for different particle size mixtures, the theoretical mass gluing factors and the distribution of the resin solid content can be calculated. 

Accuracy for all thorium measurements by TIMS is limited by the absence of an appropriate normalization isotope ratio for internal correction of instrumental mass fractionation. However, external mass fractionation correction factors may be obtained via analysis of suitable thorium standards, such as the UC-Santa Cruz and IRMM standards (Raptis et al. 1998) for °Th/ Th, and these corrections are usually small but significant (< few %o/amu). For very high precision analysis, the inability to perform an internal mass fractionation correction is probably the major limitation of all of the methods for thorium isotope analysis discussed above. For this reason, MC-ICPMS techniques where various methods for external mass fractionation correction are available, provide improved accuracy and precision for Th isotope determinations (Luo et al. 1997 Pietruszka et al. 2002). 

Fig. 1. Left panel. Post-explosive yields versus mass of the Ge isotopes for a 25 M of solar composition by [10]. Arrows represent a production factor of 200 over the initial mass fraction of each isotope. Right panel. Logaritmic abundances relative to O and to solar ratio observed in the DLA-B/FJ0812+32 System (dust corrected) [5]. The observed [Zn/O] value is represented by a full square.

When metallicity decreases, the opacity decreases and the stars are more compact. For instance the radius of a 20 Mq star on the ZAMS is decreased by about a factor 4 when its metallicity passes from 0.020 in mass fraction to 0. Due to the decrease of the opacities, the radiative driven stellar winds are also weaker [5]. 

The maximum height and diameter for the fire occur when all of the fuel bums out at t = tb- The mass of the fireball at that time includes all of the fuel (mF) and all of the air entrained (me) up to that height. The mass of air entrained can be related to the excess air factor, n, the stoichiometric oxygen to fuel mass ratio, r, and the ambient oxygen mass fraction, To2j00. Thus the fireball mass at burnout is... 

The isotope fractionation factor and mass-dependency of fractionation... 

Figure 4. Illustration of mass-dependent fractionation of Mg isotopes, cast in terms of 5 values. 5 Mg and 5 Mg values based on Mg/ Mg and Mg/ Mg ratios, respectively. A common equilibrium fractionation model, as defined by exponential relations between a values (fractionation factors) for different isotope ratios, is shown in the gray line. A simple linear relation, where the slope is proportional to the mass difference of the isotope pair, is shown in the black line. Additional mass-dependent fractionation laws may be defined, and all are closely convergent over small ranges (a few per mil) in isotope compositions at 5 values that are close to zero.

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