[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

# The concept of inﬂuence coeﬃcients is used to

This preview shows pages 331–333. Sign up to view the full content.

The concept of inﬂuence coeﬃcients is used to describe the relationship between count rates and concentrations in a way that directly reveals the effect of the matrix on the count rates from the analyte element (Sect. 5.3). The general principle is that the “ideal” calibration curve is assumed to be in principle linear, however affected by matrix effects and thereby distorted (i.e., made nonlinear). By applying corresponding counteracting “corrections,” the experimental curve is again linearized. The coeﬃcients, which account for the extent of these (mathematical) corrections for each matrix element, are called empirical or theoretical inﬂuence coeﬃcients , respectively, depending on the method of their determination. The accuracy of empirical methods (where the inﬂuence coeﬃcients are determined by measuring standards) can be very high and is only limited by experimental issues (mainly the repeatability and reproducibility of the measurements and the specimen preparation procedure) and the quality of standards (reliability of the provided data and a close similarity of their com- position and preparatory method to that of the unknown material). In prac- tice, it is often diﬃcult (and expensive) to maintain the required quality and sometimes impossible to obtain or manufacture the standard specimens. Theoretical inﬂuence coeﬃcient methods are based on the classical set of FPs and their accuracy is comparable to that of any other FP method. Since the main time-consuming step is the computation of the inﬂuence coeﬃcients, routine analysis with precomputed sets of coeﬃcients is very fast. Compared to the empirical parameter method, the accuracy can be similar if the same set of standards is used. The high long-term stability of modern instruments allows precalibration for all elements in the factory with simple drift corrections on site. Analysis can thereby be carried out without actual standards (Sect. 5.7). Monte Carlo methods are sometimes employed for analyses of inhomoge- neous materials and for studying complex indirect excitation effects, such as

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
5 Quantitative Analysis 311 the excitation of light elements by photo-electrons and Auger-electrons. They are by their nature an FP method, but based on a statistical description of interactions rather than on a deterministic equation system. A brief introduc- tion to the principles of the method is given in Sect. 5.8. An important aspect of any analytical task is to estimate the resulting error in view of the chosen methodology (achievable trueness and precision) and the probable statistical error made in an individual measurement (Sect. 5.9). Following the demands of modern industrial networks for precise crite- ria, rules, guidelines, and definitions, internationally accepted standards have been set up not only for materials and manufacturing processes but also for analytical procedures. An introduction to standardized methods in XRF, as they are used for example in the petrochemical industry and in the cement industries, is given in Sect. 5.10.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern