4.3.4. Detection Limits

It is important to determine the "detection limit" when reporting trace element concentrations. There are many ways of expressing the detection limit. Some variations arise because of unstated distinctions between what can be detected with what certainty and what can be measured with reasonable precision.

Detection limits are a function of the background counts in the unknown and the peak counts in the standard. Recall that the corrected counts (C_corr) and standard deviations are:

Using these relationships, the error associated with C_corr is:

For detection, the corrected X-ray peak height produced by an element must be greater than the error associated with it by some factor, z:

We will define the detection limit as:

where z = 2.3 at the 99% confidence level, and 1.6 at the 95% level.

Near the detection limit C_pk is approximately equal to C_bkg, so we may write:

We have defined detection limit in terms of counts, but our real interest is in the absolute concentration that it represents. It is not necessary to make any matrix corrections (see Quantitative Analysis), because the concentrations of interest are so small that the corrections applied to them would be negligible. Recall,

Substituting, we get,

Let K equal the counts per unit time per unit concentration (convenient units for K are cps/wt% element and cps/wt% oxide). We can rewrite the detection limit expression to yield concentration:

Which simplifies to:

Background rate is determined on the unknown and K on the standard. At the 95% and 99% confidence levels, z equals 1.6 and 2.3, respectively. Note that counting 4 times longer on background halves the detection limit (Figure 4.3.4a). Increasing the accelerating voltage or sample current may also decrease the detection limit. Do not report values less than the detection limit. Also note that the precision near the detection limit is very poor.

Figure 4.3.4a. Detection limit as a function of counting time.

One must not assume that since a value exceeds the detection limit that the element is really present. Good detection limits depend on accurate determination of the background (Figure St-4). If the background is nonlinear (sloping or curved), the analysis of trace concentrations of an element is very difficult. The locations are which backgrounds are determined must be free of spectral interference from the peak of interest or other peaks. It is also important to be sure that the positions used to calculate background do not span an absorption edge, which can put a "step" in the background.

 

Figure 4.3.4b. Determination of background. (a) Linear interpolation between two off-peak measurements BG1 and BG2. The interpolated estimate of background (B) is subtracted from the measured peak height (P). With linear backgrounds, a background slope may be determined and either background measurement used to calculate the value under the peak. (b) Background measurements must be free from spectral interferences. BG1 lies beneath an interfering peak. (c) Discontinuities in the background continuum, such as an absorption edge, also may result in erroneous background determinations. (d) Non-linear backgrounds are also a potential problem in determining background. The calculated background (B') is significantly higher than the true background (B) (after Williams 1987).