DETECTION LIMIT AND ESTIMATE OF UNCERTAINTY OF ANALYTICAL XRF RESULTS

X-Ray Fluorescence Analysis (XRF) is a nondestructive physical method used for chemical elemental analysis of materials in the solid or liquid state. The specimen is irradiated by photons or charged particles of sufficient energy to cause its elements to emit (fluoresce) their characteristic x-ray line spectra.The detection system allows determining energies of the emission lines and their intensities. Elements in a specimen are identified by their spectral line energies or wavelengths for qualitative analysis, and intensities are related to concentrations of elements providing opportunity for quantitative analysis. Computers are widely used in this field, both for automated data collection and for reducing the x-ray data to weight-percent and atomic-percent chemical composition or area-related mass. Email:marketing@medicilon.com.cn web:www.medicilon.com

1. Introduction' The basic requirement of quantitative X-ray fluorescence (XRF) analysis is first to prepare suitable specimens from the samples to be analyzed. Then, to measure the intensity Ip of the peak of the element to be determined (or analyte) since this intensity is related to the concentration by means of the calibration procedure. However, this analyte peak intensity must be first corrected for dead time, which is normally done automatically by contemporary instruments. If necessary, particularly for trace element determination, it must also be corrected for background beneath the peak, any spectral overlap(s) and blank. Finally, if necessary, the net intensity must be multiplied by the term Mis to correct for matrix effects. However, a description of this last step, and also calibration procedures, will be ignored in the present paper on the uncertainty associated with analytical XRF results, that having already been treated in other papers. We will consider, instead, how to estimate the uncertainty introduced in the analytical results during all these steps. . In quantitative XRF analysis, the global (or overall) uncertainty of an analytical result depends on the combination of errors introduced mainly by the sample preparation, the measurement of both peak and background intensities, the slope "m" of the calibration line and the corrections for matrix effects. All these errors can be grouped in two main categories. The first one is the random error, represented by the precision, which can arise, for example, from random fluctuations associated to the process of measurement of X-ray peak intensities. These are called counting statistical errors [(CSE). The other category is the systematic error, represented by the accuracy, whereby a certain bias is present in the results, as could happen if a badly determined calibration curve is used. Precision can be considered as a measure of the repeatability [4,8] (replicate determinations made under conditions as nearly identical as possible) of a result, while accuracy is a measure of the closeness of the results with its true value. As an analogy, if we have a ruler with an incorrectly engraved scale, we could repeat with precision the measurement of the length of an object, but the results will be inaccurate. The combination of these two types of errors, precision and accuracy, enables us to estimate the global uncertainty of each concentration to be determined. In practice, precision can be improved by controlling the random errors introduced during sample preparation and by the analytical instrument within the range of stability of the generator and of the X-ray tube, to such an extent that the main source of random errors remaining is due to counting statistical errors. Accuracy can also be improved to a large extent by controlling systematic errors introduced by sample preparation, the instrument itself and the calibration procedure. These errors can be reduced within certain limits by optimizing the use of the analytical instrument and by improving the reliability of the calibration procedure. As a result, only residual systematic errors due to the specimens themselves are then important, which are matrix effects (absorption and enhancement) and physical state effects (heterogeneity, surface, thickness, particle size, mineralogy). This paper deals mainly with the uncertainty introduced in a series of results by the random and systematic errors of all the mentioned sources. Some tools will be described hereafter for estimating this global uncertainty. However, the first subject to be treated is the detection limit in spite of both parameters, uncertainty of a result and detection limit, describe different characteristics of an analytical method. This first preliminary step is necessary for evaluating the total performance of an analytical system. It is also important to talk about this parameter because the expression "detection limit" is probably one of the most widely misunderstood in XRF analysis. Not only is there a general lack of agreement about the order of magnitude of detection-limit data, but also the international convention for calculating such data is not always respected and the way of naming them is questionable. The detection limit is usually defined as the smallest amount of an analyte that can be detected in a specimen. However, it is often misinterpreted as the smallest concentration of an analyte that can be determined with reliability in a given sample. Furthermore, the detection limit calculations are based on background measurements, which are below any peak intensity used for a possible determination. This paper attempts to clarify all this confusion. The basic philosophy behind the calculations of the different limit types is reviewed and a new realistic and representative way to name them is proposed. It must be emphasized that the terminology used here is presented to prevent ambiguity, but does not have any international ratification. Potts has already tried to do this, but without much success. Three types of limits are considered: the instrumental limit of detection, the limit of determination of a method and the theoretical or experimental analytical precision. General considerations for evaluating the uncertainty associated with the sample preparation will also be discussed. Finally, few comments on the way for reporting analytical results are presented. The analysts must absolutely employ an explicit way of reporting results and assessing the capabilities and limits of the analytical method. The present paper is not a proposal for a new terminology or new mathematical definitions for calculating detection limits applicable to all analytical techniques, but rather to show how the complex jargon of statisticians, often disconnected from the physical reality, should be adapted to the field of XRF analysis. We are more interested to supply to the XRF analyst the necessary tools for evaluating the quality of her/his results rather than getting international recognition. For a more general and thorough discussion on the subject, you may refer to the paper by the International Union of Pure and Applied Chemistry (IUPAC). This paper also contains other interesting references, which are not repeated here.