Page 149 - An Introduction to Analytical Atomic Spectrometry - L. Ebdon

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where Ct = true number of counts, Co = observed number of counts, t = dwell time (the time spent
monitoring each mass) and D = dead time defined in configuration software. The corresponding
equation for count rate is

where R = true count rate and R = observed count rate.
t
o
If no dead time correction is applied, then a linear calibration would not be possible, since the higher
count rates between 10 and 10 Hz would be underestimated. This provides a way of determining the
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dead time empirically, i.e. by re-integrating the isotopic signals with different dead times until a linear
calibration is obtained for a series of accurately known standards.
A better method, which accounts for any instrumental drift, is to measure the isotope ratio of two
isotopes of an element with different abundances, such as In, Pb or Rb, and use the following
expression derived from Eqn. 5.5:

where R = count rate of minor isotope, R = count rate of major isotope and C = R /R . The isotopic
M
M
m
m
ratio C must be calculated in absence of dead time effects (i.e. at low count rates, but not so low as to
give bad counting statistics) by repeated measurements of the blank-subtracted isotope ratio. This is the
instrumental isotope ratio, and no correction is made for mass bias. The count rates are then measured
for a series of concentrations and the data, which have not been corrected for dead time, can be used to
plot R - CR against R R (1 - C), the slope of the line being equivalent to the dead time, D, in seconds.
m
m
M
M
The data which are plotted must fall within the range of count rates at which dead time effects become
significant (i.e. between ca 10 and 10 Hz), otherwise a curve rather than a straight line will result. In
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practice, the effect of dead time will not be significant as long as the count rate is below 10 counts s .
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More important is the effect of low count rate on precision, which means that the longest possible time
should be allowed for ion counting when the count rate is below ca 500 count s , although this will
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depend on the amount of sample that is available.
The precision of any isotope ratio measurement is heavily dependent on the operating conditions of the
quadrupole mass filter, in particular the rate at which it hops between masses (peak hopping), the time
it spends monitoring each mass (the dwell time) and the total time spent acquiring data (total counting
time). A long total counting time is desirable, because the precision is ultimately limited by counting
statistics and the more ions that can be detected the better. A rapid peak-hopping rate is also desirable
in order to eliminate the effects of drift (i.e. short-term fluctuations in