Formerly of Thermo Electron Corp. NITON Analyzers, is now a consultant living in Atibaia, SÃ£o Paulo, Brazil.

Volker Thomsen

An overview of the chemical analysis process is presented. The actual spectrometric instrumental analysis is only one part of the process. Equally important are sampling, sample preparation, and analysis of the results. A "Third Law of Spectrochemical Analysis" is proposed to augment those introduced by the authors in a previous tutorial (1).

The process of chemical analysis consists of several steps, beginning with the taking of the sample and followed by sample preparation. The sample is subjected to the analytical method and we arrive at a result (Figure 1).

The flowchart shown in Figure 1 is quite general and all steps are of equal importance. More detailed flowcharts are available (2). 

The handling of the sample is one of the most important aspects of chemical analysis, and yet, often it is simply considered a means to an end. Scant thought is given to the fact that without appropriate sample treatment, it is not possible to obtain good analytical results from even the best-calibrated instrument. 

We can think of sample handling as a two-step process, as in the flowchart in Figure 1: sample collection (sampling) followed by sample preparation. In spectrochemical analysis, the sample is then introduced to a spectrometer in order to determine the analyte or analytes of interest. 

The first step, sample collection, is often outside of the control or expertise of the analyst, and yet this process can make or break the actual analysis. Sampling should provide a truly representative subsection of the whole sample, in a fairly small specimen. Let us consider some examples.  

Molten metal is held in a furnace until the chemistry is correct for the alloy being prepared. These furnaces range in size from small laboratory types (maybe a few kilograms of metal) up to the huge arc furnaces used in the manufacture of iron and steel that can contain 200 tons at one time (Figure 2). Obviously, there is a question as to how representative a sample weighing perhaps 100 g is of 200 tons of metal. Generally speaking, larger furnaces require more than one sample and have several sampling points to provide a better idea of the true metal composition and homogeneity of the melt. 

The molten metal should be well mixed, and any slag floating on the top of the metal must be removed before sampling. The sample ladle and sample mold should be manufactured of a material and shape appropriate for the task. Once a sample is poured into the mold, it should be cooled according to the type of metal. In some cases, this can involve quenching in a bucket of cold water, while in other instances, the sample should be allowed to cool slowly.

Differences in cooling times affect the crystal formation (grain structure) in the solidifying metal, and this can have a significant impact on the results of the analysis. Compositional variations can arise for a number of reasons, such as that metals might be soluble in one another in the liquid state, but only have limited solubility in the solid state. On solidification, these components begin to segregate to form discrete phases of differing composition. The most common way to prevent this occurring is very rapid cooling of the sample, which minimizes the grain size. The sample itself is still heterogeneous, but on a size that is now very small compared with that examined by the spectrometer.

Water samples typically are collected in screw-top containers, and again, suitable steps must be taken to ensure a representative sample. The containers used must be well cleaned before the sample collection to prevent contamination of the sample. In collecting from a lake or river (Figure 3), samples often are taken at different depths. Depending upon the type of analysis required, these samples can either be kept separate (for depth analysis) or can be mixed to give a "total" analysis.

For the analysis of tap water, it generally is recommended that the faucet be turned on and water allowed to flow for a couple of minutes before a water sample is collected. This is to collect water that is representative of what is being delivered to the house, and does not indicate, for example, how much lead is picked up overnight while water sits in the pipe from the main to the house.

Depending upon the type of analysis required, preservation of the sample might be required by the addition of a small amount of acid or by placing it in a refrigerator. The specimen labels must be of a suitable material to prevent loss of identifying marks should they get wet or cold during the sampling or storage steps.

Soil sampling is another example of the collection of a tiny amount of material compared with the total amount under consideration. In general, it is appropriate to remove leaf pieces and other organic matter from the soil surface. Scoop a representative soil sample, remove rocks and stones, and place the remaining soil in polyethylene bags.

Note that soil sampling often can involve sampling from different depths of the soil, and the different layers from the soil need to be kept in separate bags if a depth profile is required (for example, looking to see how far a contaminant has penetrated the soil). Any large pieces should be broken up and the sample roughly mixed. It might be necessary to reduce sample size, either in the field or in the laboratory. Appropriate techniques, such as manual "cone and quarter" methods or the mechanical use of a sample splitter (riffle splitter), can be used to decrease the sample to a manageable size (3).

Ores and rock samples are notoriously inhomogeneous. Multiple samples often are required from either rock (drill) face or core samples so that a good average can be obtained. Rocks must be crushed (for example, using a jaw-crusher), or alternatively, the fine powder produced when using a rotary air blast–reverse circulation drilling rig can be collected and is ideal for the task. If crushing is required, this might have to be done in several steps using different types of mechanical crushers to reduce the fragment size gradually. However, there is a risk of contamination from grinding surfaces, and this should be determined before using a particular grinder. Some rocks (especially silicate type) can be broken up more easily if they undergo a heating and cooling cycle first.

In all cases, the samples must be well identified, and any appropriate chain-of-custody documentation used. The collection of a perfect sample is for naught if you don't know from where it came. The sample containers must be clean so that the risk of contamination is minimized, and containers should not be reused unless they are cleaned thoroughly to prevent cross-contamination.

The second step is the actual sample preparation, which is the process by which a rough sample is manipulated to produce a specimen that can be presented to the spectrometer.

Metal samples for arc/spark spectrometry or X-ray fluorescence (XRF) analysis require a technique to produce a clean, flat surface. This can be achieved through the use of a milling machine or lathe (typically for nonferrous metals) or by grinding (typically for ferrous alloys including nickel and cobalt superalloys).

Lathe and milling machine tools should be kept sharp to prevent smearing and reduce heating of the sample during this step. Some operators keep different tool heads for different metal types in shops where multiple alloy types are analyzed to prevent cross-contamination.

Grinding belts and disks should be of a suitable material to prepare the sample and should not contain elements that might be of interest; for example, alumina (aluminum oxide) and zirconia (zirconium oxide) papers can deposit aluminum and zirconium, respectively, on the sample surfaces. Typically, 60-grit grinding paper is used for arc/spark spectrometry, while XRF analysis might require a more polished surface. The grinding paper should be replaced when changing from one base metal to another (such as from stainless steels to cobalt alloys) to prevent cross-contamination.

Samples that are not suitable for milling or grinding might require a manual surface cleaning with a piece of emery paper, or at the very least, cleaning the surface with a detergent or solvent to remove oil and grease.

Dissolution is required for atomic absorption spectrometry (AAS), inductively coupled plasma (ICP), photometry, and classical wet chemical methods such as gravimetry and titrimetry. The sample can be dissolved using an appropriate solvent to dissolve or extract the element or elements of interest. The solvent can be an acid or a combination of acids, an alkali, or an organic solvent. This typically requires heating, either using a hot plate or microwave oven. More difficult to dissolve samples can be fused to form a glass sample that subsequently can be dissolved in acid.

Depending upon the chemical behavior of the elements to be analyzed as well as the other elements that are present in the sample, more than one dissolution technique might be required for the analysis of all elements. The choice of appropriate solvent is critical because it must dissolve the element of interest reliably, but it might cause changes in viscosity (and therefore droplet size formation) in the solution, so care must be observed in matching solvent strengths in samples and standards.

Some acids can attack the spectrometer sample introduction system, so appropriate materials must be selected. For example, hydrofluoric acid (HF) dissolves glass, so a sample introduction system of HF-resistant material must be used. Also, depending upon the type of (spectrochemical) analysis, other chemicals (such as supressors and releasing agents) also can be added. Note that dissolution by its very nature dilutes the sample considerably, so that some additional steps might be required to concentrate the sample before or after dissolution.

Not all digestion methods are considered to be "total digestion" methods. For example, the often-used EPA Method 3050B (Acid Digestion of Sediments, Sludges, and Soils) is one of the most commonly used digestion procedures because it uses a relatively innocuous acid and oxidizer (nitric acid and hydrogen peroxide). However, this is a partial digestion method only. Some critical elements (such as Ag, Cr, Pb, Sb, and Tl) can be left behind in the residue and are therefore unavailable for analysis. It also should be noted that the element of interest is unlikely to extract at the same rate from sample to sample. Therefore, while a particular series of samples might show (for example) an 80% recovery rate, you might well have samples that give only a 35% or a 65% recovery in a different batch.

The digestion method (EPA Method 3052) is considered a total digestion; however, it does use the more aggressive and dangerous hydrofluoric acid in addition to nitric acid. Basically, if there is a residue left behind after a digestion process, then there is a likelihood that your element of interest is partially or totally in that residue.

An example of this is noted in the National Institute of Standards and Technology (NIST) Certificate of Analysis for Standard Reference Material 2586. Table I shows the certified mass fractions with uncertainties for four elements and also the mean, minimum, and maximum range values obtained when using a partial digestion method. Additional information from the certificate is available on the NIST website.

Table I: Recovery using partial digestion method 

For rock, soil, and other geological samples, sample preparation often means reducing the sample size further using appropriate splitting methods. Note that care must be taken to keep the sample representative in terms of particle size so as to avoid biasing the values obtained. The best way to remove these biases is to take a representative sample and dry, grind, and sieve it so that all the particles are of a similar size (Figures 4–6). The sample should then be mixed well before taking the subsample for analytical work.

It is important to be aware that the element of interest might preferentially be found associated with one particle size rather than another. In rock samples, this is because of the different physical properties of minerals (such as hardness, cleavage, and crystal habit), which have been shown to cause preferential concentration at different particle sizes. In other words, if a rock is crushed for sampling purposes, then some analytes might concentrate in either the larger or smaller particle sizes. 

In soil samples, this is caused by differences in chemical or physical binding (adsorption) of the soil constituents. Colloidal particles (such as clay) show a far greater tendency to adsorb ions and molecules than the noncolloidal constituents such as silt and sand. Therefore, if the analyte is associated more closely with the very fine (<125 μm) particles within a soil specimen, then the results might be biased either high or low, depending upon how the sample is prepared. If more fine material is weighed and dissolved, then the readings will be higher than the "true" result. If a higher percentage of coarser particles is taken, then the reading will be lower than the "true" result. As mentioned earlier, grinding and sieving a sample to a consistent particle size and then mixing the powder thoroughly reduces these errors. 

Sample preparation for XRF analysis requires making the particle size of the sample as small and homogeneous as possible. Particle size has a profound effect on X-ray analysis, especially with the elements of atomic number Z < 22, due to the weak penetrating power of these X-rays. This might mean the relatively simple process of drying, grinding, sieving, and cupping the specimen before analysis. However, ground samples also might be mixed with a binding agent and pressed into a pellet. Alternatively, the sample might undergo a fusion (with sodium or lithium tetraborate) and form a glass bead that can be analyzed subsequently (4).

Articles

The authors present an overview of the chemical analysis process.

The Chemical Analysis Process

In this article, we discuss the basic premises that underlie the science of spectrochemistry, which has been humorously referred to as a "black art" by some. We present the two primary "laws" of spectrochemistry and some of the consequences thereof. What follows relates to elemental analysis by atomic spectrometry, including atomic emission, atomic absorption, and X-ray fluorescence. Although molecular spectrometry and mass spectroscopy are not addressed, with fairly straightforward edits, these "laws" should be applicable in these fields as well. 

All atoms emit and absorb radiation at various wavelengths of the electromagnetic spectrum, which are unique for each element. 

Figure 1:  Gustav Robert Kirchoff (left) and Robert Bunsen.			

The emission and absorption spectra provide a "fingerprint" of the sample, that is, a qualitative analysis. This was first discovered in 1860 by Gustav Robert Kirchoff (1824–1887) and Robert Wilhelm Bunsen (1811–1899) and published in their landmark paper (1). They discovered cesium (1860) and rubidium (1861) using their new technique.  

Thereafter, several more elements were discovered using their new method of spectral analysis: thallium in 1861 by Sir William Crookes (1832–1919) and indium in 1863, by German professor of physics Ferdinand Reich (1799–1882) and German metallurgical chemist Theodor Richter (1824–1898). In fact, the names of these first four newly discovered elements come from the Latin for the primary color of their spectral lines. Thus, cesium is from the Latin 

, meaning "blue of the upper part of the sky." Rubidium derives from the Latin 

, meaning "deep red." Thallium comes from 

, or "sprouting green shoot." Indium is from the Latin 

				In 1868, the element helium was discovered through its characteristic spectral lines in the spectrum of the sun (found independently by Pierre Janssen of France and Sir Joseph Norman Lockyer of England). It was named for the Greek term for sun "helios." 

In the year 1869, Dmitri Mendeleev introduced his "periodic law" in which he predicted several as yet undiscovered elements. Three were discovered by spectroscopic means by French, Scandinavian, and German chemists and named after the regions of their discoverers: gallium (Paul Emile Lecoq de Boisbaudran, 1875), scandium (Lars Fredrik Nilson, 1879), and germanium (Clemens Winkler, 1886).  

Figure 2:  X-ray energy spectrum of Lanthanum, 241Am radioisotope excitation.			

In 1911, the English physicist Charles Glover Barkla (1877–1944) discovered that each element has its own characteristic X-ray spectrum. (He was awarded the Nobel Prize for this discovery in 1917.) This extended the range of applicability of spectral analysis into the X-ray region of the electromagnetic spectrum. The X-ray energy spectrum of lanthanum is shown in Figure 2. (Note: for better comparison with the optical emission spectrum of Figure 3, Planck's law provides the conversion E(keV) = 1.24/λ (nm). Thus, the x-axes run from 1 keV ~ 1.24 nm to 60 keV ~ 0.02 nm.) 

Figure 3:  An optical emission spectrum of aluminum.			

In 1922, the Hungarian György Von Hevesy (1885–1966) and Dutchman Dirk Coster (1889–1950), working in Bohr's laboratory in Copenhagen, discovered hafnium, the first element identified by its X-ray spectrum. (Von Hevesy received the 1943 Nobel Prize in Chemistry for work on using isotopes as tracers to study chemical processes.) 

The number of spectral lines per element varies widely over both atomic number and region of the electromagnetic spectrum. Table I shows the numbers of spectral lines of the elements in the optical emission region from 200 to 1000 nm (3) for the neutral atom and singly ionized species. The number of spectral lines in this region varies by over three orders of magnitude. For comparison, the principal X-ray spectral lines for these elements also are listed (4).

Table I:  Numbers of spectral lines of the elements			

The "emit and absorb" in the above statement of the "First Law" is a consequence of Kirchoff's Law of Radiation (1859). This can be stated as, "For a given element, the wavelengths of emission and absorption are the same." This is, of course, an indication that the electron transition is between the same energy levels, merely in opposite directions. 

Thus, it is clear that we can characterize the presence or absence of any element from a spectrum of the sample. Now we move from the qualitative to the realm of quantitative analysis. 

 The intensity of the spectral line of the element is proportional to the concentration of that element. 

This allows quantitative analysis and permits the generation of calibration curves. The following quote is from the International Union of Pure and Applied Chemistry (IUPAC): 

 In general, the relation of the measure 

. A graphical plot of the analytical function, whatever the axes used, is called the 

 For one-component systems or multicomponent systems for which interelement effects can be neglected, the measure 

 of element I can be expressed as a function of concentration 

) . . . . These functions are called the 

; the graphs corresponding to these functions are called 

 and are determined by observations on reference samples of known concentrations. 

) . . . , are often used; their corresponding graphs are called 

. These curves are derived from analytical calibration curves by interchanging the 

 . . . axes. The distinction between analytical evaluation and analytical calibration functions can at first seem superfluous. This distinction can be trivial in the case of analysis for one-component systems, but assumes importance for multicomponent systems when the measures for the individual component are interdependent because of various interelement effects. (2) 

We propose three "corollaries" to this Second Law, as the issues involved affect the measured spectral line intensities: 

 There exists background radiation across all wavelengths of the electromagnetic spectrum. 

Therefore, background correction might be necessary so that we are dealing with net peak intensity. This concept of spectral background radiation is also crucial to a proper understanding of detection limits (5). 

 The radiation emitted by atoms of the sample may be absorbed by other atoms of the same element within the sample. This is called self-absorption. 

Sensitive spectral lines are most prone to self-absorption, thus limiting the range of concentration that can be determined using that particular spectral line. This phenomenon is responsible for the curvature of calibration curve and in extreme cases cause the curve to actually turn back on itself (called "self-reversal"). 

 The sample matrix may affect the intensity of the spectral line of the analyte. This is the so-called "interelement" effect. 

The definition of "matrix" might be unclear when using multielement spectrometric techniques: It is everything else other than the single element of interest when considering analytes one at a time. The matrix can affect the measured intensities in three ways: chemically, physically, and spectrally. 

 These generally occur when the analyte forms a new compound with very different thermochemical characteristics. One of the most common of these in flame atomic absorption spectrometry (FAAS) is the signal depression of alkaline earth elements in the presence of phosphate. Chemical interferences rarely occur in inductively coupled plasma–optical emission spectrometry (ICP-OES) due to the high temperature of the plasma that can decompose those compounds that are thermally stable within a flame. However, one chemical effect (formation of an insoluble salt of the analyte by the addition of an inappropriate acid) will affect all liquid analysis due to the removal of the element of interest. Bad chemistry is not correctable.  

 These can be caused by particle size, viscosity, density, temperature, and so forth. In liquid solutions, they occur as the physical characteristics of the solution to be measured change (such as surface tension, and vapor pressure), which has an effect on the sample uptake and vaporization. For example, determination of elements by ICP-OES in seawater compared with standards in deionized water will result in very different values, due to differences in density, surface tension, and viscosity, which change nebulization characteristics between the two solutions. Physical effects also are seen in X-ray fluorescence (XRF), in which particle size has a large impact on the lighter (Z < 22) elements.  

 Because of the large numbers of spectral lines, spectral line overlaps might be encountered. Line overlaps are considerably more prevalent in the optical region of electromagnetic spectrum as compared with the X-ray region (see Table I), although line overlaps do occur in XRF. The severity of overlap will depend upon the instrument resolution. Note that a line overlap will result in too much intensity for a spectral line, which gives a positive bias. The answer is to select an alternate spectral line or make an interelement correction. 

 These interelement effects often are referred to as "line overlaps" (spectral interferences) and "matrix effects," the physical and chemical effects noted earlier. 

The correction of interelement effects to ensure the proper relationship between measured analyte intensity and concentration can be accomplished in several ways: 					

Matrix matching of calibration standards and unknowns, or, in simple terms, comparing like to like. An example is the "alloy family calibrations" of arc/spark OES. The "method of standard additions" (MSA), used primarily in AAS and ICP-OES, can be considered as an extension of matrix matching. The standard and sample are matched perfectly, because the standard is incorporated in the sample.

The use of an "internal standard" to compensate for these effects is common in arc/spark-OES and somewhat less so in ICP-OES. The intensity of the analytical line is ratioed to that of an appropriate internal standard line. The internal standard spectral line should be homologous with the analytical spectral line (6). In arc/spark, the internal standard is typically the base element. In ICP-OES, the internal standard is typically something not found in the original sample, for example, scandium. This element is added to the solution before analysis. This ratioing technique also is applied to XRF in Compton normalization, in which the analyte line intensity is ratioed to the scatter peak. Note that this technique requires simultaneous multielement capability so that it is inherently unsuitable for use in AAS.

Dilution of the sample. For example, the dilution of a seawater sample effectively reduces the differences in nebulization characterisitics in ICP-OES. Similarly, the preparation of a lithium tetraborate fusion bead removes matrix effects in XRF samples. Note, however, that this technique reduces the concentration of the analyte, so that this element must be present at reasonably high concentrations to begin with.

"Buffering" involves the addition of an excess of a competing anion, a technique used often in FAAS. An example is the analysis of calcium in the presence of phosphate, in which the addition of lanthanum interferes and prevents the formation of calcium pyrophosphate.

Mathematical Corrections: A line overlap correction for analyte element "A" is of the form: 

				corrected intensity A = uncorrected intensity A - 

 is the correction factor. Other matrix effects can be corrected by an equation of the form:  

				 corrected intensity A = uncorrected intensity A [1 ± 

 * (intensity of interfering element)].			

 Note that we could just as well use the concentration of the interfering element rather than its intensity. 					

In X-ray spectrometry, matrix effects can be corrected by the fundamental parameters approach. This is a mathematical calibration based upon the characteristics of the incident X-ray beam, sample mass absorption coefficients, excitation–sample–detector geometry, energy of the fluorescent X-rays returning to the detector, and so forth (7). Although this fundamental parameters calibration allows for absorption and enhancement effects to be minimized, it does not compensate for physical effects such as particle size.

Some types of corrections are more predominant in one technique than another. Mathematical corrections typically are used in simultaneous multi-element techniques in which signals generated at the same time can be compared. Chemical corrections often are used in the single-element FAAS technique because the method may not work otherwise. 

Spectrochemistry develops logically from the two primary laws presented here: Each element has its own unique spectral signature, and the intensity of the spectral line of an element is proportional to the concentration of the element present in the sample. 

There might be alternative logical structures for the science of spectrochemisty. For example, one could approach the subject from the point of view of method development. Then the "first law" might be: "Choose an appropriate spectral line for the application." Presented here is our proposal. 

The authors would like to thank John Goulter and David Mercuro for their review and helpful comments. 

 are with Thermo Electron NITON Analyzers, Billerica, Massachusetts.  

In this article, the authors discuss the basic premises that underlie the science of spectrochemistry, which has been humorously referred to as a "black art" by some.

The Laws of Spectrochemistry

X-rays are attenuated as they pass through matter. That is, the intensity of an X-ray beam decreases the farther it penetrates into matter. Basically, each interaction of an X-ray photon with an atom of the material removes an X-ray from the beam, decreasing its intensity. 

The amount of decrease in intensity of the X-ray beam depends upon two factors: 					

A characteristic of the material called its "absorption coefficient" (

The intensity decreases exponentially with the distance traveled, or

 is the initial X-ray beam intensity. Note that this exponential decay of photon intensity applies in the optical region of the electromagnetic spectrum as well. In this region, it is known as the Beer–Lambert law.  

 absorption coefficient. Note that the term μ , by conventional nomeclature, is often referred to as the 

. These two coefficients are related by the density of the material (ρ) as μ = 

An interesting application of this equation is to determine the depth of penetration of X-rays. The attenuation length is defined as 

the depth into the material where the intensity of the X-rays has decreased to about 37% (1/

, sometimes called Euler's number or Napier's constant, is the base of natural logarithms, or 

 ≈ 2.7183.] Then, substituting into Equation 1, we get 

This also is referred to as the "mean free path" of the X-rays. 

Cd radioisotope source of X-rays with an energy of 22.1 keV, how far do these penetrate a piece of pure iron, (atomic number 26)? From Table I, we find the mass absorption coefficient for iron at 22.1 keV is μ = 18.2 cm

 = 0.007 cm = 0.07 mm = 70 μm. A comparison of this depth for the same incoming X-ray energy both for lighter and heavier elements is shown in Table I. 

Measuring the Mass Absorption Coefficient

Figure 1: Attenuation of X-ray intensity. 

We need a source of X-rays — the radioisotope Cd-109 or an X-ray tube, for example — and a detector such as a Geiger counter. Place a piece of foil of thickness 

 between the source and detector and measure the radiation intensity 

, as shown in Figure 1. Now place a second piece of foil with a thickness 

 in the path and measure the new intensity 

For example, we use an X-ray tube run at 35 kV and a 0.025-mm thick piece of copper foil. With one foil thickness, our Geiger counter measures 185,000 counts per minute (cpm). When the foil is doubled and the measurement repeated, we find a count rate of about 155,000 cpm. The density of copper is 8.94 g/cm

The accepted value for the mass absorption coefficient of copper at this energy is approximately 7.0 cm

/g. This is a reasonable agreement given the rather crude experimental set-up in which the Geiger counter used had a low-resolution analog readout meter. 

When a sample contains more than one component, the total mass absorption coefficient is the sum of the individual coefficients, each multiplied by the weight fraction present. That is,   

Consider an alloy containing 70% Ni and 30% Mo. What is the mass absorption coefficient of this sample at an excitation energy of 22.1 keV (

Mo)(μMo) = (0.7)(23.8) + (0.3)(61.9) = 35.3 cm

The mass absorption coefficient of a material is energy dependent. In general, this coefficient decreases with increasing energy of the penetrating X-rays. Figure 2 shows a plot of the mass absorption coefficient for molybdenum from about 7 to 35 keV. 

Figure 2: Mass absorption coefficient of molybdenum.  

Note, however, that we do observe sharp increases in this coefficient at certain energies. These discontinuities occur at the minimum energies for excitation of a particular electron shell, that is, at the binding energies. For example, in Figure 2, we find a discontinuity at about 20 keV. This is the K-shell electron binding energy.  			

These discontinuities in the mass absorption coefficient are called "absorption edges." After an absorption edge, the general decrease with increasing energy continues. 

Figure 3 presents the energy dependence of the mass absorption coefficient of Molybdenum in the more traditional log–log format. Also evident are the L absorption edges at about 2.5, 2.6, and 2.9 keV. These correspond to the electron binding energies of the three L-shell subshells.  

Figure 3: LogÃ¢ÂÂlog plot of mass absorption coefficient of molybdenum. 			

The attenuation of X-rays by matter is a specific example of the more general phenomenon of the attenuation of electromagnetic radiation by matter. In the optical region of the E–M spectrum, this phenomenon finds significant spectrometric application in the form of the Beer–Lambert law.   

In this X-ray tutorial, the authors attempt to answer the frequently asked question, "How deep do the X-rays penetrate my sample?"

Tutorial: Attenuation of X-Rays By Matter

A diagrammatic view of the concept of detection limits is presented that effectively shows its relationship to the reproducibility of measurements on the blank.

Limits of Detection in Spectroscopy (PDF)