This installment of "Atomic Perspectives" is the second in a series describing the educational components and processes necessary
in teaching and learning the technique of X-ray fluorescence (XRF) spectroscopy. Although three of the four states of nature
(gas, liquid, and solid) are discussed briefly, the focus is on the sample preparation of bulk solid materials. Because of
the advances in XRF instrumentation hardware and software as well as algorithm knowledge and selection for mathematical corrections,
selection of an appropriate sample preparation technique is the major source of error in the most exacting quantitative analyses.
The discussion begins with the fundamental assumptions necessary to prepare a bulk powder material for the best possible accuracy
during quantitative analysis. Analysis of error is considered to show where sample preparation fits in the scheme of things.
Then we discuss the physics involved during the excitation and emission processes and consider the major sources of error
in preparing powders. Finally, the basics of grinding, pressing, and the fusion method of sample preparation are described.

The analytical process involved in producing an X-ray fluorescence (XRF) spectrochemical analysis of bulk materials (such
as samples from ore deposits, ship cargo holds, quarries, coal seams, rail cars, manufacturing processes, and production lines)
can be described as following four main categories: representative sampling and subsampling from the bulk, taking an aliquot
from the subsample from which a specimen for analysis is prepared, generating net intensities from the specimen in an XRF
spectrometer, and converting the net intensities into concentrations through a calibration curve. As shown in Figure 1 (1),
the XRF technique can analyze most any material. The question is how much effort if any should go into the preparation of
the specimen (the portion that is actually analyzed). As described in the previous installment of this column series on XRF
spectroscopy (2), the reason to determine the elemental composition at high concentration of many materials with an XRF spectrometer
is that the technique has the capability to produce the highest accuracy and precision possible. To achieve that goal, it
is necessary when perfecting the method to review the sources of error and the amount that each may contribute (equation 1).

Figure 1: An assortment of materials that can be analyzed by XRF. Adapted with permission from Bruker.

Equation 1, the analysis of variance, shows contributions of the various components making up the analysis system. Analysis
of variance (3) shows that the total error is equal to the square root of the sum of the squares of error of the individual
components of the error; that is, the error from the counting statistics, the power source, the spectrometer, the macro sampling
process, the specimen preparation process, the reference standards used for calibration, the type of correction algorithms
applied and the decisions made when making those corrections, and everything else. Everything else can include the temperature,
humidity, vibration, and dust in the laboratory and surroundings. These components contribute both random and systematic error.
It is the job of the analyst performing the method development to minimize random errors and remove the systematic errors,
which are generally quite large and easy to remove by an experienced spectroscopist. In fact, because of the advances made
in the stability of the generators, tubes, and electronics, the accuracy of the goniometers, and the empirical and theoretical
correction algorithms available in the software, the largest error now comes from standard selection, sampling, and specimen
preparation. Therefore, the choice of method and application of technique when performing the specimen preparation is of paramount
importance to the final accuracy of the analytical method. Notice the word accuracy is used here and not precision. In fact,
it is possible when using XRF to choose a method where the precision will be very high but the accuracy will not be acceptable.
The differentiation between precision and accuracy needs to be well understood when working with XRF, and will be discussed
below.

If the goal is to achieve the highest accuracy possible, it is absolutely necessary to understand the concepts involved. For
sure, the XRF technique for quantitative analysis is a comparative technique. That is, by virtue of using calibration curves,
the ratio technique, or type standard technique, the closer the standards used are to the mineralogy, particle homogeneity,
particle size, and matrix characteristics of the unknown, the more accurate the analysis will be. Let us call this "The Golden
Rule for Accuracy in XRF Analysis." Conversely, the farther standards and unknowns are from each other in the above listed
characteristics, the less accurate the analysis will be. This is a certainty.