Page 243 - Inorganic Mass Spectrometry - Fundamentals and Applications

Mass
Isotope ~~~ut~on Spectrometry 229
fortunately, however, low abundance and high enrichment equate to high cost, fre-
is
quently making the best solution impracticable; in cases where cost prohibitive,
another stable isotope of greater natural abundance than that of the smallest must
be chosen. It is for this reason, for example, that enriched 42Ca (0.65% natural
abundance) and %2a (2.09%) are more often used than 46Ca (0.004%); the cost of
of
enriched 46Ca is many times higher than that the other isotopes.
All of the considerations discussed lead naturally to the question of what
price the analyst pays for this less-than-ideal spikeisample ratio. In most cases,
error in the measurement of Rm makes the largest contribution to analytical uncer-
tainty; the isotopic compositions of sample and spike are usually well known in
comparison to R,. The matter of error propagation in isotope dilution analyses has
been extensively treated by Adriaens et al., [ 131, and Patterson et al. used Monte
Carlo simulation to study the problem [14]. Using propagation of error laws,
Heumann derived the following relationship with which to calculate Itopt, the op-
timum spike-to-sample ratio (neglecting cost and availability) [S]:

where the terms are as defined for Eq. (5.7). The factor by which error is multi-
plied for given isotopic enrichments is illustrated for thallium in Fig. 5.2. Tnspec-
tion of Fig. 5.2 reveals that relatively large deviations from the optimum sample-
to-spike ratio can be tolerated in most analyses; in addition, the greater the
enrichment of the spike isotope, the less sensitive the analysis is to deviation from
optimum. With spikes of 80% or more enrichment in 203Tl, sample-to-spike ratios
from 0.1 to 10.0 should give acceptable results. In critical applications where highly
accurate concentration measurements are desired, is advisable to obtain an esti-
it
mate of the sample concentration to use in dete~ning how much spike to add.
This analysis, of course, need not be by isotope dilution mass spectrometry; a less
time-consuming and less expensive method would be preferred in most cases.
Enriched stable isotopes for use as spikes are available from several sources;
Oak Ridge National Laboratory sells them for most solid elements [ 151.

The literature on isotope dilution is so voluminous that it is impossible to cover
It
the subject thoroughly in a single chapter. is in fact tantamount to impossible to
locate all relevant papers, let alone read them. There are also questions arising from
the definition of “inorganic.” Elemental assay has traditionally been an inorganic
discipline and analysis of, say, body fluids biological. The question is where, for
example, to place analysis lead in human serum. The area into which such analy-
of
ses fall depends on whether is the analyte or the sample that is used for the def-
it