326
M. Mantler
Count-rate ratios.
In almost all practical applications, count-rate ratios are
used rather than absolute counts. Such ratios are built with the count rates
from the same element in another specimen, which can be a standard of any
composition, or a pure element. The main advantage is that thereby a number
of unknown or less accurately known factors cancel, namely all factors included
in
G
i
of (5.11), as well as any scaling constant in the absolute photon ﬂux
of the primary radiation (which is rarely ever known in practice), and the
detection eﬃciency, which is omitted in (5.11). Note that the factors
g
J
and
g
K
in the secondary and tertiary excitation terms in (5.17) and (5.18) do
not cancel. In this chapter, all count-rate ratios are relative to pure elements
unless otherwise indicated:
R
i
=
N
i
N
(
i
)
.
(5.19)
(Non-) Necessity of measuring pure element counts.
It is not necessary to
actually measure pure elements in order to obtain count-rate ratios relative
to pure elements. This is an important point because several elements cannot
be produced or analyzed by reasonable means, in pure form. Assume that the
counts from a specimen,
N
i,S
, and a standard,
N
i,St
, have been measured.
Then the count-rate ratio of the standard,
R
i,St
, relative to a pure element
can be computed by FP methods, and the count-rate ratio of the specimen,
R
i,S
, relative to a pure element obtained from (see also Sect. 5.3.1 and (5.31)):
R
i,S
=
N
measured
i,S
N
extrapolated
(
i
)
=
N
measured
i,S
N
measured
i,St
·
R
computed
i,St
.
(5.20)
Requirement and selection of additional standards.
While one standard is re-
quired in order to build relative intensities, additional standards can improve
the accuracy of the analysis. Standards with a similar composition as the
unknown are called
local standards
. A single local standard pins the cali-
bration curve to the point defined by this standard and its measured count
rates. When several standards are used, an average calibration factor can be
computed. This is achieved by computing pure element count rates for each
analyte line and standard, and averaging these values. The observed standard
deviation of these data should match the expected uncertainty of the certi-
fied chemical composition, eventual preparatory inconsistencies, and the error
introduced by counting statistics. Sets of standards that give larger errors
should not be used.
Instead of local standards, standards with widely varying composition may
be employed with advantage. These are
global standards
. The same as given
earlier applies with respect to averaging and consistency. A weighting factor
may be introduced for each standard, which matches the differing statisti-
cal reliability of low and high element counts. Note that reanalyzing sets of