7.3 Detection limits
Detection limit (DL) is the lowest amount of an analyte to be examined in a test material that can be detected and regarded as different from the blank value (with a given probability), but not necessarily quantified. In fact, two risks must be taken into account: false positives (the risk α of considering the element is present in test material when its quantity is null) and; false negatives (the risk β of considering a substance is absent from a substance when its quantity is not null).
Detection limits are important for several reasons:
From a "legal" point of view, regulatory bodies impose strict rules and definitions, and the statement about presence or absence of a substance can have serious consequences.
From an analytical point of view, DLs serve to compare performance of methods and instruments as well as to know if a method is applicable for a certain purpose.
The evaluation of the detection limits requires a careful assessment, based on statistics approach and on the specifics of EDXRF analysis.
The detection limits are usually expressed in units of calculated weight fraction (or grams per square centimetre). The latter is achieved by evaluating the noise counts in the formula used to calculate the weight fraction (or areal deposit).
(for thin samples)
(for thick samples)
As the measured counts N depend on the time of measurement (N = I × tmeas) the detection limits are directly proportional to the square root of the noise, inversely proportional to the instrumental sensitivity S and inversely proportional to the square root of the measurement time tmeas.
The noise signal in EDXRF can include different non-correlated contributions. In the more general case, its combined standard deviation can be expressed using the rules for error propagation:
where:
NCnt are the counts of the spectral continuum under the peak (usually calculated for an interval of channels corresponding to full width at one tenth of the peak maximum, FWTM).
Np-sp are the counts of instrumental background (e.g. spurious peak originated from the excitation of the same element in some constructive materials of the spectrometer chamber). Np-sp can be determined if measuring a sample with an effective atomic number close to that of the unknown, but surely not containing the given element. In the case of using some sample support (e.g. cups or filters) it reflects the signal arising from the impurities of the element in the sample support material.
Nsp-int are the counts of another overlapping peak. The peak fitting procedure provides the closest to experiment modelled solution, but does not remove the inherent counting statistic error of the overlapping peak.
Nblank is an additional contribution for the case of complex sample preparation procedures, and reflects the counts of a blank sample prepared following all the steps of sample preparation. It includes the contribution of impurities from chemical reagents used in the sample preparation.
Reference: R. Padilla Álvarez, D. Hernández Torres, A. Markowicz, D. Wregzynek, E. Chinea Cano, S. A. Bamford, Quality management and method validation in EDXRF analysis, X-Ray Spectrometry 36 (2007) 27.