Model Detection Limits

Model Detection Limits

This menu item will allow the user the estimate the 99% confidence (3 sigma) values for the minimum concentration detected based on a specified the unknown count time or the count time required to detect a specified concentration. This will allow the user to design the required analytical setup for trace element determinations based on a given set of intensities from the standard on-peak and unknown background measurements.

The expression for minimum detection concentration is:

The expression for counting time required for the detection of the given concentration is:

where:               is the intensity of the background in cps/nA (divide the unknown counts by beam current)

               is the count time used for the unknown background or peak measurement (must be equal)

               is the beam current used for the unknown measurement in nA

               is the concentration of the element in the standard in weight percent (wt. %)

               is the intensity of the standard in cps/nA (divide the standard intensity by standard beam current)

              is the unknown concentration in weight percent (wt. %)

Note that all calculations are performed at 3 sigma (standard deviations) and assume that the background and peak measurement count times on the unknown are equal. There is no correction for unknown ZAF correction, but it could easily be applied by simply multiplying the ZAF factor times the resulting concentration or count time.

Remember that weight percent can be converted to ppm (parts per million) using the following expression:

Therefore, 0.010 wt. % is equal to 100 ppm or 0.001 wt. % is equal to 10 ppm.

Note the calculation assumes that the counting time used for the unknown peak and background measurements are equal. This is usually the case for trace elements since at zero concentration both the peak and off-peak measurements have equal statistical weight. Note also that the unknown background time is the sum of both the high off-peak and low off-peak count times so that:

where:               is the count time for the on-peak measurement

               is the count time for the high off-peak measurement

                is the count time for the low off-peak measurement

               is the count time for the combined high and low off-peak measurements (used in the above calculations)