EFFICIENCY AND EVALUATION - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 390

Figure6.3. Dependence of precision and accuracy represented by a percentage deviation, on the
net intensity measured for the analyte peak. The net intensity for the internal standard was assumed
to be 10 000 counts and the spectral background was estimated to 500 counts. Figure from Ref. [8],
reproduced with permission. Copyright1996, John Wiley and Sons.

take these relations into account, it follows that

s

N x b N b ; x

N is b

N b ; is

s rel c x (6.8)

2 2

N x b N b ; x N is b N b ; is

This relationship is illustrated in Figure 6.3 for a typical set of intensity
values. The background intensities are assumed to be 500 for both the analyte
and internal standard; the net intensity of the internal standard is set to 10 000,
and that of the analyte is varied between 100 and 1 000 000. The concentration
of the analyte does not appear explicitly but is proportional to the associated
net intensity N x . Determinations significantly above the detection limit can be
carried out with a precision of 1-5%.
The deviations between the actual determinations and the nominal values,
which characterize the accuracy of an analytical method, will surpass these
values. From Equation 4.12, they can be estimated according to

s

s rel

N x
N is

S x
S is

a rel a rel c is

a rel c x (6.9)

where s rel ( N x / N is ) is the aforementioned relative standard deviation, a rel ( S x /S is )
is the relative uncertainty in the determination of the relative sensitivities, and