Mathieu Bouchard

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). 

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.

 can be defined as the closeness or agreement among replicate results. 

 can be defined as the nearness of a result to the true or accepted value. The bull's-eye on the left in Figure 2 shows that several determinations can lead to high precision (the dots are close together), but poor accuracy (they missed the bull's-eye). This can often be the case with the pressed powder method of specimen preparation. The bull's-eye on the right shows both high precision (dots are close together), and high accuracy (they hit the bull's-eye). This is almost always the case with the fusion method of specimen preparation. Later on, we will discuss why this is so, and how to choose which method will give the fastest and most accurate result. It is also important to understand that, as stated before, XRF spectrometers produce intensities, which are converted into concentrations through a calibration curve. The intensities themselves can be of very high precision, and the theoretical precision can be calculated because it is equal to the square root of the total number of counts. It is therefore possible to determine if the spectrometer is performing properly by making a 10-shot precision test and comparing it to the theoretical precision of each element. This is highly recommended before preparing standards or unknowns, making intensity measurements, and performing the calibrations. 

Basic Concepts for XRF Sample Preparation

The general rules for XRF analysis apply to situations where the highest accuracy is desired; these rules include

		The specimen should be representative of the bulk sample

		The specimen must be homogenous and flat

		Standards and unknowns must be very similar (density, particle size, particle homogeneity, mass attenuation coefficient)

		Specimen preparation should have good reproducibility

		The specimen should remain stable before and during analysis

More specific considerations involving the physical properties of the specimen (and container, if liquids or loose powders are analyzed) include

		Surface film absorption characteristics (liquids)

		Particle size effects (loose and pressed powders) such as grain size effect, inter-mineral effect, and mineralogical effect

		Grinding curve analysis (pressed powders)

		Groove depth, smearing, and groove orientation (metals)

	As an ideal starting point, the specimen should have an analytical depth for each wavelength (energy) analyzed that provides 

infinite thickness. That is, the thickness of the sample will not affect the analysis. On a more practical note, the specimen should have an effective layer thickness that will provide at least 99% of the analysis. Figure 3 shows the concepts of infinite thickness and effective layer thickness. The wavelengths of interest are not excited in the white layer. They are excited in the light blue layer, but most of them are absorbed by the sample matrix. Wavelengths in the dark-blue layer are excited and escape from the specimen to take place further in the analytical process. Modern software has the capability to calculate the effective layer thickness, and such a calculation is shown in Table I. It is worthwhile to take note of the narrow depth (thickness) from which most of the analysis is taking place for each element. For instance, sodium is coming from a depth of only 4 Âµm, aluminum and silicon from around 10 Âµm, and all of it from only 200 Âµm. The average thickness of a human hair is about 100 Âµm, so it is evident that the surface of the prepared specimen cannot be touched, breathed on, or exposed to any conditions that could alter it. Moreover, the effective layer thickness for any given wavelength changes with the matrix. As an example, the effective layer thickness for iron K-alpha wavelength changes from 3000 Âµm (3 mm) in carbon to 11 Âµm in lead. Togel (4) gives the equation for calculating the effective layer thickness; the equation of calculation and geometry of the situation are shown in Figure 4. The problem of particle size effect is shown in Figure 5, where the specimen analyzed is neither homogenous nor representative in the effective layer analyzed for the wavelength of interest. This sample must be crushed and ground to obtain a representative, homogenous, effective layer thickness to be analyzed for the wavelength of interest shown (and for any longer wavelengths). Even then, the mineralogical effect may cause problems, which cannot be solved by any means other than fusion. We have seen first-hand the problems caused by the mineralogical effect when analyzing kyanite, sillimanite, and andalusite (three polymorphs of Al

). In their pure form, each has the same weight percent of silica and alumina; however, using one as a standard to analyze the other can result in analysis totals ranging from 75% to 125%! Figure 6 illustrates the mineralogical effect on iron intensities from minerals prepared as pressed briquettes having the same particle size and concentration of iron. Because the compositions of mineral deposits vary from one location to the next, in addition to substituting various elements as contaminants in the crystal structures, it is virtually impossible to closely match the matrix of standards to unknowns using the pressed powder technique; therefore highly accurate analyses at high concentration levels are difficult if not impossible for many natural materials. 

Gases, Liquids, Loose Powders, and Metals

The analysis of gases is not practical with an XRF spectrometer, although it is possible. To be sure, there are many other analytical techniques better suited to this task. The specimen preparation for liquids and loose powders is a matter of choosing the appropriate equipment and accessories, and it is better demonstrated in a workshop environment such as at the annual XRF course at ICDD in Newtown Square, Pennsylvania (5), or at the Denver X-ray Conference Workshop on XRF Sample Preparation (6). Metals are also a matter of trial and error, with the properties of hardness and smearing weighing heavily on the choice of cutting tool, sanding device, or sanding material (7). In any case, the surface should be renewed whenever it has changed, and that depends on the element and the material it is in. Selecting the sample spinner on the spectrometer will remove the problem of groove orientation affecting intensities. And in any case, the same fundamental concepts of infinite thickness and effective layer thickness (described above) apply no matter the physical state of the material.

Now that the question of "How long should I grind?" has been answered, we can take a closer look at the grinding and pressing (also known as 

) process. There are many different types of grinding equipment, and the size of the specimen and briquette have to be taken into consideration when choosing one, as well as the standard sizes and characteristics of the manufacturer of the XRF instrument being used. The typical size of a briquette made for a typical XRF spectrometer ranges from 30 to 40 mm in diameter, and involves about 5 g of sample and 1 g of binder. Figure 7 shows a briquette (pressed pellet) of cement. The powder was poured into an aluminum cap to provide stability to the pellet. Also shown are the ring, puck, and container in which the specimen was ground. The weight and motion of the ring and puck mill are quite efficient for reducing most oxide materials down to about 30â40 Âµm particle size in about 3â4 min. Grinding further will lead to agglomeration of the particles, thus defeating the purpose of the grinding exercise. Adding a binder is necessary for the stability of the briquette, depending on the friability of the material. Anzelmo and colleagues (8) describe adding a grinding aid that greatly facilitates the uniformity of the particle size reduction, eliminates contamination from the grinding media and from the sample sticking to the grinding media, speeds up the cleaning process, and reduces dust during the cleaning process. Manual or automatic presses operating between 20,000 lb and 40,000 lb have been found adequate as long as the time of the pressing procedure remains constant. After the grinding equipment, additives, and backing equipment are decided on, the final step is to determine the optimum grinding time, given the goal of achieving the correct effective layer thickness for all wavelengths of interest. Figure 8 shows plots of grinding time versus intensity for various briquettes. The intensities are changing with different grinding times, so in addition to finding the time to achieve the appropriate effective layer thickness for each wavelength of interest, it is desirable to find a time when intensities are not changing drastically with time. 

When should one use the pressed powder technique? When parameters such as high speed of analysis, low skill level for preparation, small concentration range of calibration, and lowest limit of detection are involved, the pressed powder technique may serve the purpose adequately. The technique can be especially useful when working with man-made products, because the material being analyzed is well known and characterized when the process is working correctly; secondary standards can be collected and analyzed by wet and alternative methods to provide "matrix matched" standards, allowing the prospect of a highly accurate analysis. A problem arises with the technique when the process is not working correctly, and the unknowns are then not matrix matched. This presents a challenging if not unacceptable situation to a process control situation requiring accurate analyses.

The borate fusion technique shown in Figure 9 consists of mixing a ground sample with a borate flux (lithium or sodium) inside a 95% platinum, 5% gold crucible, heating to about 1000 Â°C with agitation until the flux melts, and then dissolving the sample homogeneously in the flux (10). The choice of lithium borate or sodium borate depends on the application, but lithium borates are more commonly used because of the greater retention of moisture on the surface of the glass disks with sodium borate flux, and the desire to analyze for sodium. Lithium borates exist as lithium tetraborate (Li

). It is not necessary to melt the sample, so temperatures above 1100 Â°C are not necessary and can adversely affect the retention of volatiles and flux. A nonwetting agent (bromide or iodide) can be added when integrated into the flux, or independently, depending on the application. All oxides dissolve in borate flux, so it is essential to make sure the sample is oxidized. Metals alloy with the platinum forming a eutectic, which lowers the melting point of the platinum and results in its destruction. If the sample is not oxidized fully, it may be necessary to add an oxidizer to the sampleâflux mixture, and heat at a lower temperature to start, and then raise the temperature after the oxidation process has taken place. Careful observation of the oxidation process will allow commonly analyzed volatiles such as sulfur (9,10) and even chlorine to be analyzed. After the sample is completely dissolved in the flux, the casting process can be performed by pouring the melt into a heated 95% platinum, 5% gold mold. This particular alloy of platinum is chosen to prevent wetting (sticking) of the bead to the mold. The cast glass disk is cooled quickly at first to freeze the bead in the amorphous (glass) state, and then it is cooled faster over a period of time with forced air to relieve the stresses in the glass disk from the initial drop in temperature when first cast and to allow the bead to be retrieved by hand for analysis. The entire process is shown in Figure 10. Glass disks made from different materials and cast into molds of different sizes are shown in Figure 11 along with their crucibles. 

The process can be performed manually with a Meker burner and a ring stand or with a good muffle furnace. Automatic fusion machines, electric or gas (propane or natural gas), can produce multiple glass disks automatically depending on how many positions they have (typically one to six). For the highest sample throughput, it is possible to use a robot to automate the entire process, including the weighing and flux dispensing step. 

	The advantages of fusion are listed below:

		Provides excellent homogeneity and flatness

		Creates perfectly matrix matched standards and unknowns

		Allows for matrix correction when previously not possible

		Can use with the synthetic standards for calibrations, when reference standards are otherwise not available

Easy to produce "defendable" analyses (traceable to International Primary Reference Standards)

		Can provide wide-range (universal) calibrations

		Should be used whenever it is not known if the standards and unknowns are not matrix matched. This is often the case when working with materials from nature (minerals mining, clays, ores, geological, and soils). It is also used in the case where man-made products are mixed with other man-made products and also products from nature such as blended cements, catalysts, electronic materials, and high-tech composite materials.

	Fusion should be used whenever it is not known if the standards and unknowns are matrix matched. This is often the case when working with materials from nature, such as mining samples, minerals, clays, ores, geological, soils, wastes, and environmental samples. It is also used in the case where man-made products are mixed with other man-made products and also with products from nature such as blended cements, polymers with additives, catalysts, electronic materials, and high-tech composite materials. 

These samples are difficult if not impossible to matrix-match with standards. An everyday example of this problem is the analysis of SiO

 in raw mix used in the manufacturing of cement (9,10). The plot on the left in Figure 12 shows the calibration curve made for SiO

 in raw mix from three cement plants (denoted by the triangle, circle, and x symbols). The scatter around the line is unacceptable and cannot even be made into straight lines by separating out each plant. Mathematical interelement corrections will not improve this situation because the problem is not from absorption-enhancement effects; it is from the mineralogical effect and can only be solved by fusion. The middle plot shows that the points have now moved very close to the line after fusion, giving acceptable accuracy expectations when analyzing unknowns. The plot on the right shows even more improvement after mathematical corrections are applied. Mathematical corrections are now possible because the larger, dominating error from the mineralogical effect has been removed, allowing the smaller error from absorption enhancement to be reduced (and to be able to see the improvement).

	The choice of specimen preparation for XRF analysis is critical to achieving the accuracy desirable. The choice between pressed 

powder briquettes and fused glass disks is actually easy to make when one knows whether the samples are matrix-matched or not. If the standards and unknowns are not known with certainty to be matrix-matched, then fusion is the safe choice to ensure that a ridiculous analysis is not reported. For more detail about the concepts and practices of these techniques, we recommend attending the training course and workshop noted in references 5 and 6.

Articles

X-ray Fluorescence Spectroscopy, Part II: Sample Preparation

This column installment is the first in a series describing the educational components and processes necessary in learning the technique of X-ray fluorescence (XRF) spectroscopy. Here, we discuss the main areas of training necessary for a good foundation in the analytical methodology of XRF spectroscopy. The installment begins with the place of XRF in the analytical instrumentation spectrum and defines its capabilities and compares them to other elemental analysis techniques. Then a description of a general spectrometer is provided so that the different types and capabilities of the various XRF spectrometers can be listed and understood. This leads to a discussion of the conceptual physics that occurs during XRF analysis, including the physics of the interactions occurring inside the sample that are not related to the spectrometer. 

After one goes through the process of evaluating different types of X-ray fluorescence (XRF) spectrometers, and then purchases one, the next task is learning how to use it. Operation of the instrument has now been reduced to pushing one button for production laboratory operation with the vendor initially supplying the program setup and calibration necessary to facilitate this method of analysis for the main bread and butter operations of the laboratory. However, when a new material appears on the task list, and the operator must build a program and calibrate the XRF system by themselves, that is when the fun starts. It soon becomes clear that a basic foundation of X-ray physics, as well as some knowledge of how to build a "general application," will be necessary to prepare the instrument to give the most accurate and precise analysis possible and to have confidence in the analysis should it be challenged. 

There are not as many resources for acquiring an education in XRF as one might think if the goal is to build a solid foundation of concepts and experience in the necessary areas of X-ray physics, instrumentation hardware, XRF (vendor specific) software, and applications knowledge (Figure 1). Many good texts are available from experts in the field (1–3) and articles about the subject give good guidance (4,5), but slogging through them is not desirable in the high productivity, "little time to do things" world of today. Manufacturers normally provide customer user courses, but from necessity they must focus on the particular hardware components of their instrument, which vary from vendor to vendor, and on the operation of their particular software, which even varies from model to model within a manufacturer's product line. This leaves little time for the fundamental X-ray principles and even less time for suggesting generalities between applications: Many concepts can be taught about "Element X," rather than speaking about a specific element. In fact, the typical beginner is frustrated by the discussion of "Element X," desiring to speak about the specific elements dealt with in his or her everyday operations instead. Eventually, however, as certain general concepts are applied and practiced, the advantages of learning this way become apparent. Ultimately, all parties concerned realize that there is a lot to learn and that it will take a long time to learn it well. To do so, many basic concepts must be taught first, as is so with any scientific endeavor based on physics, mathematics, and chemistry. 

So, the hope of the vendors is to give enough training in the typical one-week course to allow the attendee to return to his or her laboratory and produce results with a new XRF system. Having been in this situation for the better part of 27 years with X-ray manufacturers, and having been responsible for customer training for most of that time, this author (J.A.A.) can vouch for this description of the teaching and learning process with confidence. This is an unfortunate situation for which there is no alternative in the industrial world. Furthermore, the study of the XRF discipline is so rich and varied, that it is only after a great deal of study, application, and trial and error, that one begins to accumulate enough knowledge to accelerate the process of learning. Therefore, after a student acquires a certain amount of knowledge regarding his or her specific hardware and software, it is possible and hoped for that the user can or will now "bootstrap" himself along. Often, this results in uncertainty about how to develop a new method and uncertainty about the numbers that are produced when using it. In the United States, a course has been designed to expand the user's knowledge into the areas of the fundamental physics and general applications, thus allowing a more confident approach to setting up a new specific application and trusting the numbers it generates (6). 

The Place of XRF in the Grand Unified Theory of Physics — The Electromagnetic Spectrum

It is useful to first determine the place of the X-ray technique in the overall world of physics and chemistry. We start with the 

 (GUT) of physics (as good a place as any to start), which describes the universe in terms of the four fundamental forces of nature (the strong nuclear force, the weak nuclear force, the electromagnetic spectrum, and gravity). Now we can narrow our discussion to the electromagnetic spectrum (Figure 2). Nature provides a continuous range of wavelengths (or energies) on which many instrumental techniques are based. As can be seen, the X-ray region occupies an area of high energy and short wavelengths, which range approximately from 0.01 to 20 nm. It is important to note the inverse relationship between wavelength and energy. This phenomenon can cause many a problem during the initial learning period if not understood and remembered. 

Before going further, it is necessary to make sure the choice of instrumental technique will solve the analytical task at hand. Because XRF is blessed with many unique capabilities (Table I), it has become the technique of choice for many applications requiring accurate elemental analysis for the purpose of meeting tight specifications at high concentration levels. These applications include cement, mining, geology, catalysts, oils, plastics, steel, iron, high alloys, super alloys, precious metals, nonferrous metals, ferro-alloys, and many others. The attributes that bring it to the top of the list for these applications are 					

the wide range of elements it is capable of determining on a routine basis (Na through U); 

the wide range of concentrations it is capable of analyzing (parts per million to 100%); 

fast and easy sample preparation for most materials analyzed;

the ability to achieve better precision with increasing concentration (0.1%) in very short analysis times; and 

a relatively simple spectrum that, unlike many other techniques, has relatively few analytical wavelengths from which to choose, thus providing a spectrum that is uncluttered and free of line overlaps. 

Figure 3: XRF emission lines of iron.						

Although line overlaps can be removed by a plethora of mathematical methods, the best approach and most accurate analyses are obtained using analytical lines that are free of line overlap. An example of the simplicity of the XRF spectra is shown in Figure 3. The analytical lines most commonly used for XRF analysis are the K-alpha and K-beta lines. There are only five other iron lines that might possibly be used for analysis, but usually they are not. In fact, eight is the highest number of lines that can be used for analysis for the highest atomic numbered elements. In contrast, the spark emission lines for iron are shown in Figure 4. This spectrum, like those of many of the elements analyzed using other spectroscopic techniques, has thousands of lines, making the choice of line to be analyzed very difficult, and matrix dependent. The difficulty can be imagined from a multicomponent matrix containing many elements, all of which generate thousands of lines. Keeping this in mind, a review of the capabilities of the some of the most common instrumental techniques for elemental analysis (Table II) will narrow the analyst's choice quickly to the best instrument for the task at hand. 

Figure 4: Spark emission lines of iron.			

The next concept to be understood when learning and choosing the XRF technique is the spectrometer configuration type. Most hardware configurations of XRF instrumentation are relegated to either wavelength-dispersive XRF (WDXRF or just WDX), and energy-dispersive XRF (EDXRF or just EDX). Figures 5 and 6 show the different concepts and component configurations used with these two different XRF spectrometer types. The EDX system excites a sample using an X-ray tube, generating characteristic radiation for each element in the sample. A portion of that radiation is directed to a detector, which serves the purpose of determining the energy of each characteristic X-ray generated (qualitative analysis) and the number of X-ray photons per second for each energy (quantitative analysis) simultaneously. A computer containing various algorithms converts the intensity (number of photons per second) for each element to concentration. 

Table II: Comparison of analytical techniques			

The WDXRF system operates in a similar fashion, except that an analyzing crystal is inserted between the sample and the detector for the purpose of separating (resolving) the different wavelengths (energies), and then directing those wavelengths to the detector individually, one at a time in sequence (sequential WDXRF spectrometer). These two different configurations have different advantages and disadvantages and will be discussed in a future column installment. 

Figure 5: X-ray fluorescence spectrometers - energy-dispersive XRF (EDX, EDXRF).			

It is useful now to consider the concept of a "general" spectrometer (Figure 7). A modern "general" spectrometer is composed of components such as a source, a sample area, a dispersion device, a detector, processing electronics, a microprocessor, and possibly a computer and printer. Different individual sources are designed and used to generate all of the wavelengths (energies) in the electromagnetic spectrum for the various instrumental techniques and at different power levels. In the case of XRF, sealed X-ray tubes are capable of power levels ranging from 1 to 4000 W. The dispersion devices can be gratings, natural crystals, or layered synthetic microstructures. XRF uses the latter two. Detector types range from gas filled to solid state and even charge-coupled devices (CCD) for XRF. The microprocessors serve as the interface with the human operator and direct and coordinate all of the operations of the spectrometer, including capturing the data, processing it, or sending it to a computer for processing, or a network for distribution and storage. Some of the more important fundamental laws of physics that allow these components to perform their functions are listed in Table III and will be discussed in a future installment. 

Figure 6: X-ray fluorescence spectrometers - wavelength-dispersive XRF (WDXRF).			

Choosing only the components to make an XRF system, the spectrometer can be configured for bulk analysis to support production of primary materials such as steel, high alloys, cement, catalysts, nonferrous materials, oil and fuels, and plastics. Recent XRF configurations include handheld spectrometers used for metal sorting and mining prospecting, as well as environmental and toxic metal screening. Thin-film applications, wafer fabrication processing applications, microanalysis, automated systems eliminating human interaction from sampling to delivery of analysis, and other custom, noncommercial, specialized, industrial, or proprietary "homemade" XRF system configurations that populate the industrial world have been well established for decades.  

Figure 7: Concept of a general spectrometer.			

Qualitative, Quantitative, and Standardless Analysis — Data Reduction

With the advent of automated elemental identification software routines, manual identification of the elements by the operator for qualitative analysis became less and less popular. The development of capable, standardless analysis software further hastened the decline of manual identification to the point that manual identification of the spectrum is nearly extinct. Nevertheless, the reliability of automated identification becomes problematic below 100 ppm and human abilities begin to outperform automated software routines at that level. In many cases, it may be necessary to closely inspect an automated qualitative analysis before reporting or it may be necessary to simply perform it manually because of the complexity of the matrix. In these cases, knowledge of the basics of qualitative analysis is required and these skills are often neglected because of time restraints. 

Standardless analysis has varying degrees of accuracy depending on the matrix, and it is best for the novice XRF operator to learn what those capabilities are and, in general, why they are limited. For instance, accuracies on steel over a very wide range can approach an impressive 1% relative. However, when analyzing pressed powders the error can balloon to 5%, and even 10% relative, again depending on the matrix. The implementation of the sample preparation method for different matrices is paramount to the accuracy that can be achieved and, once again, this topic needs to be well understood and practiced if there will be any hope to achieve an accurate analysis. The choice between pressed powder and fusion sample preparation is quite important. The fundamental physics and chemistry of these preparation methods as well as when and when not to use them will be the topic of a future installment. 

After the data have been processed to remove detector curvature, missing dead time counts, drift correction phenomena, and line overlap problems, the intensities (in counts per second) can be converted to weight percent concentrations by means of a calibration curve constructed from reference standards and intensities from the XRF system. Because XRF is a comparative technique, the rule of thumb is that the more the matrix of the standards is like the matrix of the unknowns, the higher the accuracy will be. For this reason, the method of preparation of both the standards and the unknowns is paramount to achieving the highest accuracy possible. After the operations described previously have been performed to acquire corrected intensities, there are several different conversion algorithms beyond straight line regression that make corrections for the interelement effects (absorption and enhancement) occurring in the sample before the characteristic intensities even get to the rest of the spectrometer. A good grasp of both mathematical and statistical concepts is necessary in choosing the appropriate algorithm for calibration to keep the operator from reporting grossly incorrect results. The theoretical process of using the fundamental parameter method of processing the data has become more and more popular and should also be learned and kept in the operator's bag of tools. 

Finally, the topics of precision and accuracy, counting statistics, random and systematic error, analysis of variance, multiple regression, and limit of detection (LOD) need to be understood in terms of what they mean, and how to calculate them. 

After all of these concepts are presented, explained, discussed, and practiced, the XRF student is ready to face the real life laboratory and the challenges of producing accurate and credible numbers with the XRF spectrometer. The next installment will discuss the fundamental X-ray physics concepts taking place in the sample and the XRF spectrometer. 

 Principles and Practices of X-ray Spectrometric Analysis, 2nd ed.

 X-ray Fluorescence Spectrometry, 2nd ed.

 (John Wiley & Sons, New York, New York, 1999). 

 (Springer-Verlag, New York, New York, 1969).  

(5) J.A. Anzelmo and A.I. Buman, "Evaluation Criteria for Wavelength Dispersive XRF Instrumentation," 

International Scientific Communications, Fairfield, New Jersey, 1988. 

(6) ICDD XRF Clinic, "Practical X-ray Fluorescence," annual, Newtown Square, Pennsylvania, 

 is a Technical Representative (M.Sc. Chemist) with Corporation Scientifique Claisse in Quebec City, Quebec, Canada. 

The main areas of training necessary for a good foundation in the analytical methodology of XRF spectroscopy are discussed.

Mathieu Bouchard

Articles

X-ray Fluorescence Spectroscopy, Part II: Sample Preparation

X-ray Fluorescence Spectroscopy, Part I: The Educational Essentials