• Applicable to various samples, including solids • Relatively rapid and easy to learn • Semiquantitative results can be obtained from many samples without use of standard s; most standards may be kept for long periods of time, because most applications are for solids • Instrumentation is relatively inexpensive Limitations • Detection limits for bulk determinations are normally a few ppm to a few tens of ppm, depending on the x- ray energy used and the sample matrix composition • For thin-film samples, detection limits are approximately 100 ng/cm 2 • Not suitable for elements of atomic number less than 11 unless special equipment is available, in which case elements down to atomic number 6 may be determined Capabilities of Related Techniques • Inductively coupled plasma optical emission spectroscopy and atomic absorption spectrometry have better detection limits for most elements than x-ray spectrometry and are often better choic es for liquid samples; elements of low atomic number can be determined using these techniques X-ray spectrometry, or x-ray fluorescence, is an emission spectroscopic technique that has found wide application in elemental identification and determination. The technique depends on the emission of characteristic x-radiation, usually in the 1 - to 60-keV energy range, following excitation of atomic electron energy levels by an external energy source, such as an electron beam, a charged particle beam, or an x-ray beam. In most sample matrices, x-ray spectrometry can detect elements at concentrations of less than 1 μg/g of sample (1 ppm); in a thin film sample, it can detect total amounts of a few tenths of one microgram. Initially, x-ray spectrometry found wide acceptance in applications related to metallurgical and geochemical analyses. More recently, x-ray spectrometry has proved valuable in the analysis of environmental samples, in the determination of sulfur and wear elements in petroleum products, in applications involving forensic samples, and in measurements of electronic and computer-related materials. Roentgen discovered x-rays in 1895. H.G.J. Moseley developed the relationships between atomic structure and x-ray emission and in 1913 published the first x-ray spectra, which are the basis for modern x-ray spectrometry. Moseley recognized the potential for quantitative elemental determinations using x-ray techniques. The development of routine x- ray instrumentation, leading to the x-ray spectrometer known today, took place over the following decades. Coolidge designed an x-ray tube in 1913 that is similar to those currently used. Soller achieved collimation of x-rays in 1924. Improvements in the gas x-ray detector by Geiger and Mueller in 1928 eventually led to the design of the first commercial wavelength-dispersive x-ray spectrometer by Friedman and Birks in 1948. More recently, other detectors, such as the germanium and the lithium-doped silicon semiconductor detectors, have resulted in modified x-ray spectrometer designs. Modern energy-dispersive instrumentation facilitates qualitative identification of elements in various samples. The information content of an energy dispersive x-ray spectrum is among the highest obtainable from inorganic materials in a single measurement. The position and intensity of the spectral peaks provide qualitative and quantitative information, and the intensity of the background yields information on bulk composition of the sample matrix. X-ray spectrometry is one of the few techniques that can be applied to solid samples of various forms. Although most x- ray spectrometers are in laboratories, many are finding application in routine analyses for production and quality control and in specialized tasks. Growth in the capability and economy of microcomputer technology will enhance these applications. Many of these same principles, practices, and instrumentation developments are common to electron microscopy and electron microprobe analysis. Acknowledgement The author wishes to thank Tracor X-Ray Inc., Mountain View, CA, for permission to use material from "Fundamentals of X-Ray Spectrometry as Applied to Energy Dispersive Techniques" by D.E. Leyden. X-Ray Spectrometry Donald E. Leyden, Department of Chemistry, Colorado State University Electromagnetic Radiation Electromagnetic radiation is an energy form that may be propagated through space and may interact with atoms and molecules to alter their energy state. Both properties are important to spectroscopy. Electromagnetic radiation exhibits behavior that requires two theories to explain. The wave theory describes behavior of electromagnetic radiation, such as refraction, reflection, diffraction, and scatter. Radiation is defined as an energy form consisting of two orthogonal waves, each having the same frequency and wavelength. One is an oscillating electric field, and the other an oscillating magnetic field, thus producing the term electromagnetic radiation. In a vacuum, the velocity of propagation of the wave through space is the speed of light (c = 3 × 10 10 cm/s). This leads to an important fundamental relationship: λν= c (Eq 1) This expression states that the product of the wavelength (λ) of electromagnetic radiation and its frequency (ν) is equal to its velocity. The wavelength of electromagnetic radiation varies over many orders of magnitude. For example, radio waves in the normal AM broadcast band have wavelengths of several hundred meters. By contrast, x-rays useful in spectroscopy range from 0.01 to 10 nm. Not all properties of x-rays can be adequately described by the wave theory. As physicists began to understand the quantum nature of the energy levels of atoms and molecules, the requirement for a different description of electromagnetic radiation became increasingly clear. The basic need was to describe the energy content of radiation that could interact with matter to cause the observed discrete energy changes. The energy content of electromagnetic radiation is proportional to frequency: E = hν (Eq 2) where the proportionality constant, h, is known as Planck's constant. Because the relationship in Eq 1 also holds, substitution of: (Eq 3) in Eq 2 yields: (Eq 4) Substitution of numerical quantities for h and c results in: (Eq 5) where E is in keV, and λ in angstroms (1 A o = 0.1 mn). This expression relates the energy content of photon quanta to the wavelength of the corresponding electromagnetic radiation. For example, a rhodium Kα x-ray has a wavelength of 0.0614 nm (0.614 A o ), which corresponds to an energy of 20.2 keV. As a result of Eq 5, radiation may be discussed in terms of wavelength or energy interchangeably. For wavelength-dispersive spectrometry, it is often more convenient to use wavelength units, but for energy-dispersive x-ray spectrometry (EDS), the energy description is more convenient. Clearly, interconversion is simple. Several commonly used descriptions of the characteristics of x-rays are significant. The proper meaning of the intensity of electromagnetic radiation is the energy per unit area per unit time; however, the number of counts per unit time from the detector is frequently used as intensity. Because the area is the active area of the detector used, and time is an adjustable parameter, the use of counts is a practical description of x-ray intensity. The terms hard or soft x-rays are often used to differentiate x-rays of short (0.01 to 0.1 nm, or 0.1 to 1 A o ) and long (0.1 to 1 nm, or 1 to 10 A o ) wavelengths, respectively. X-radiation falls in the high-energy region of the electromagnetic spectrum. Although modern commercial x-ray spectrometers incorporate many safety features, awareness of proper procedures (Ref 1, 2) as well as local and national codes for installation, inspection, and safety precautions is necessary. References cited in this section 1. A.H. Kramers, Philos. Mag., Vol 46, 1923, p 836 2. R.T. Beatty, Proc. R. Soc. London, Ser. A, Vol 89, 1913, p 314 X-Ray Spectrometry Donald E. Leyden, Department of Chemistry, Colorado State University X-Ray Emission X-rays are generated from the disturbance of the electron orbitals of atoms. This may be accomplished in several ways, the most common being bombardment of a target element with high-energy electrons, x-rays, or accelerated charged particles. The first two are frequently used in x-ray spectrometry directly or indirectly. Electron bombardment results in a continuum of x-ray energies as well as radiation characteristic of the target element. Both types of radiation are encountered in x-ray spectrometry. Continuum. Emission of x-rays with a smooth, continuous function of intensity relative to energy is called continuum, or bremsstrahlung, radiation. An x-ray continuum may be generated in several ways. However, the most useful is the electron beam used to bombard a target in an x-ray tube (tubes used in x-ray spectrometry will be discussed below). The continuum is generated as a result of the progressive deceleration of high-energy electrons impinging on a target, which is a distribution of orbital electrons of various energies. As the impinging electrons interact with the bound orbital electrons, some of their kinetic energy is converted to radiation; the amount converted depends on the binding energy of the electron involved. Therefore, a somewhat statistical probability exists as to how much energy is converted with each interaction. The probability of an impinging electron interacting with an orbital electron of the target element should increase with the atomic number of the element; thus, the intensity of the continuum emission should increase with the atomic number of the target element. Further, the probability of an interaction increases with the number of electrons per unit time in the beam, or flux. Therefore, the intensity of the continuum increases with electron beam current (I), expressed in milliamperes. Moreover, the ability of the impinging electrons to interact with tightly bound electrons of the target element increases with the kinetic energy of the bombarding electrons. Because the kinetic energy of the electrons in the beam increases with acceleration potential, the integrated intensity of the continuum should increase with electron acceleration potential (V), expressed in kilovolts. Finally, the maximum energy manifested as x-ray photons equals the kinetic energy of the impinging electron, which in turn relates to acceleration potential. These concepts can be approximated quantitatively (Ref 1, 2): (Eq 6) I int = (1.4 × 10 -9 )IZV 2 (Eq 7) Other relationships have been proposed. Differentiation of an expression given by Kulenkampff (Ref 3) yields an expression that demonstrates that the energy of the maximum intensity in the continuum lies at approximately two thirds the maximum emitted energy. The shape of the continuum predicted by Eq 6 and 7 is approximate. These functions do not include the absorption of x-rays within the target material or absorption by materials used for windows in the x-ray tube and detectors. Therefore, some modification of the intensity distribution may occur especially at low x-ray energies. Characteristic Emission. Most of the electrons impinging on a target interact with the orbital electrons of the target element in nonspecific interactions and result in little or no disturbance of the inner orbital electrons. However, some interactions result in the ejection of electrons from these orbitals. The resulting vacancies, or holes, represent high-energy unstable states. If the orbital vacancies are in the innermost shells, electrons from outer shells cascade to fill them, resulting in a lower energy and more stable state. The energy released by the process may be manifested as x-rays. Each of the transitions that may occur lead to the emission of sharp x-ray lines characteristic of the target element and the transition involved. These characteristic radiation lines are emitted with the continuum. The relationship between the elements and the characteristic spectrum will be discussed below. References cited in this section 1. A.H. Kramers, Philos. Mag., Vol 46, 1923, p 836 2. R.T. Beatty, Proc. R. Soc. London, Ser. A, Vol 89, 1913, p 314 3. H. Kulenkampff, Ann. Phys., Vol 69, 1923, p 548 X-Ray Spectrometry Donald E. Leyden, Department of Chemistry, Colorado State University X-Ray Absorption X-rays impinging on a specimen undergo two important interactions with the elements of the specimen: absorption and scatter. Absorption of the radiation may occur by specific interactions that are significant in sample excitation in x-ray spectrometry or by more general interactions that influence the emitted x-ray intensity from the sample. Scatter of x-rays leads to background intensity in the observed spectra. Mass Absorption. When an x-ray beam passes through a material, the photons (electromagnetic fields) may interact in nonspecific ways with electrons in the orbitals of the target elements, attenuating the intensity of the x-ray beam. The interactions may lead to photoelectric ejection of electrons or scatter of the x-ray beam. In either case, the overall result is frequently described in terms of an exponential decrease in intensity with the path length of the absorbing material: (Eq 8) where Iλ, is the intensity of a beam of wavelength λ after passing through a length x (cm) of an absorber, I o is the initial intensity of the beam, μ/ρ is the mass absorption coefficient of the absorber (cm 2 ), and ρ is the density of the absorber (g/cm 3 ). The mass absorption coefficient is characteristic of a given element at specified energies of x-radiation. Its value varies with the wavelength of the x-radiation and the atomic number of the target element. These relationships will be discussed in the section "Mass Absorption Coefficients." The photoelectric effect is the most important of the processes leading to absorption of x-rays as they pass through matter. The photoelectric effect is the ejection of electrons from the orbitals of elements in the x-ray target. This process is often the major contributor to absorption of x-rays and is the mode of excitation of the x-ray spectra emitted by elements in samples. Primarily as a result of the photoelectric process, the mass absorption coefficient decreases steadily with increasing energy of the incident x-radiation. The absorption versus energy curve for a given element has sharp discontinuities. These result from characteristic energies at which the photoelectric process is especially efficient. Energies at which these discontinuities occur will be discussed in the section "Absorption Edges" in this article. Scatter. When x-ray photons impinge on a collection of atoms, the photons may interact with electrons of the target elements to result in the scatter of the x-ray photons, as illustrated in Fig. 1. Scatter of x-rays from the sample is the major source of background signal in the spectra obtained in x-ray spectrometry. The scatter of x-rays is caused mainly by outer, weakly held electrons of the elements. If the collisions are elastic, scatter occurs with no loss of energy and is known as Rayleigh scatter; if inelastic, the x-ray photon loses energy to cause the ejection of an electron, and the scatter is incoherent. The path of the x-ray photon is deflected, and the photon has an energy loss or a longer wavelength. This is Compton scatter. Fig. 1 Rayleigh and Compton scatter of x- rays. K, L, and M denote electron shells of principal quantum number 1, 2, and 3, respectively; is the angle between the incident and scattered rays. Scatter affects x-ray spectrometry in two ways. First, the total amount of scattered radiation increases with atomic number because of the greater number of electrons. However, samples with low atomic number matrices exhibit a larger observed scatter because of reduced self-absorption by the sample. Second, the ratio of Compton-to-Rayleigh scatter intensity increases as the atomic number of the sample matrix decreases. The energy loss associated with Compton scatter results in a predictable change in the wavelength of the radiation: (Eq 9) where ∆λ cm is the change in wavelength (cm), h is Planck's constant (6.6 × 10 -27 erg · s), m e is the electron mass (9.11 × 10 -28 g), c is the velocity of electromagnetic radiation (3 × 10 10 cm/s), and is the angle between the scattered and incident x-ray paths. Substitution of the above values into Eq 9 yields: ∆λ= 0.0243(1 - cos ) (Eq 10) Because most x-ray spectrometers have a primary beam-sample-detector angle of approximately 90°, = 90° and cos = 0. Therefore, for many spectrometers: ∆λ= 0.024 A o (Eq 11) This is known as the Compton wavelength. In energy-dispersive systems, the Compton shift may be more conveniently represented: (Eq 12) where E and E' are the x-ray energies in keV of the incident and scattered radiation, respectively. For a spectrometer with beam-sample-detector geometry of 90°, a Compton-scattered silver Kα line (22.104 keV) from a silver x-ray tube will be observed at 21.186 keV. The intensity of the Compton scatter of the characteristic lines from the x-ray tube can be useful in certain corrections for matrix effects in analyses. X-Ray Spectrometry Donald E. Leyden, Department of Chemistry, Colorado State University Relationships Between Elements and X-Rays Absorption. X-ray photons may interact with orbital electrons of elements to be absorbed or scattered. The relationship between absorption and the atomic number of the element is important in selecting optimum operating conditions for x- ray spectrometry. Mass absorption coefficients differ for each element or substance at a given energy of x-ray and at each energy of x- ray for a given element or substance. Because of the greater probability of interaction with orbital electrons, the mass absorption coefficient increases with the atomic number of the element of the target material. At a given atomic number, the mass absorption coefficient decreases with the wavelength of the x-radiation. This is illustrated in the log-log plot of mass absorption coefficient versus wavelength for uranium given in Fig. 2, which also shows discontinuities in the relationship at certain wavelength values. These result from specific energies required for the photoelectric ejection of electrons from the various orbitals of the atom and are characteristic of the element. Fig. 2 X-ray absorption curve for uranium as a function of wavelength. A detailed analysis of data similar to those shown in Fig. 2 for many elements confirms the relationship: (Eq 13) where Z is the atomic number of the target element, λ is the wavelength of the incident x-ray, and K is the variable at each absorption edge of the target element. Absorption edges, which are discontinuities or critical points in the plot of mass absorption versus wavelength or energy of incident x-radiation, are shown in Fig. 2. Absorption-edge energy is the exact amount that will photoeject an electron from an orbital of an element. Figure 3 shows the electron shells in an atom. The familiar K, L, and M notation is used for the shells of principal quantum number 1, 2, and 3, respectively. The lower the principal quantum number, the greater the energy required to eject an electron from that shell. As shown in Fig. 3, the wavelength of an x-ray that can eject an L electron is longer (of less energy) than that required to eject an electron from the K shell. That is, the K- absorption edge energy (K abs ) is greater than the L-absorption edge energy (L abs ) for a given element. Fig. 3 Photoejection of K electrons by higher energy radiation and L electrons by lower energy radiation. The photoelectric process leads to the unstable electronic state, which emits characteristic x-rays, as illustrated in Fig. 4. Figure 4(a) shows a plot of absorbance versus energy for radiation lower in energy than the x-ray region. In this case, photon energy is used to promote electrons from low-lying orbitals to higher ones. The transition is from a stable quantized state to an unstable quantized state. The atom, ion, or molecule that is the target defines the energy difference. The sample absorbs only photons with energy very close to this energy difference. The result is the familiar absorption peak found in visible, ultraviolet, and other forms of spectroscopy. Fig. 4 Excitation of electronic energy levels. (a) Transition between two quantized energy levels. (b) Photoejection of electrons by x-radiation Figure 4(b) illustrates radiation in the x-ray energy range. The electron is ejected from a stable low-lying orbital of a given quantized energy level to the continuum of energy of an electron removed from the atom. Any excess energy in the x-ray photon is converted to kinetic energy of the ejected electron (measurement of the kinetic energy of these electrons is the basis of x-ray photoelectron spectroscopy). Therefore, instead of the absorption peak shown in Fig. 4(a), an absorption edge or jump is observed when the x-ray photon energy is sufficient to photoeject the electron. Selection of the x-ray photon energy for excitation of the elements in the sample will be based on these considerations. For example, 8.98-keV x-rays are required to photoeject the K (1s) electrons from copper, but x-rays of only approximately 1.1 keV are required for the 2s or 2p electrons. For magnesium, the values are 1.3 and 0.06 keV, respectively. The energy of the absorption edge of a given orbital increases smoothly with the atomic number of the target element. X-Ray Spectrometry Donald E. Leyden, Department of Chemistry, Colorado State University Emission The photoelectric effect is an x-ray absorption mechanism by which unstable states in the electron orbitals of atoms are created. Once the vacancies in the inner orbitals are formed, relaxation to the stable ground state may occur by the emission of x-rays characteristic of the excited element. Figure 5 illustrates excitation and emission for the photoejection of a K (1s) electron of copper. Figure 5(a) shows a plot of mass absorption coefficient of copper versus x-ray energy from 0 to 20 keV, with K abs at 8.98 keV. Figure 5(b) depicts an electronic energy level diagram for copper. Irradiation of copper with an x-ray of just greater than 8.98 keV will photoeject an electron from the K shell. This is an ionization of the copper atom from the inner shell rather than the outer valence electrons, as is the case with chemical reactions. The energy of the 1s electron is shielded from the state of the valence electrons such that the absorption-edge energy and the energy of the emitted x-rays are essentially independent of the oxidation state and bonding of the atom. [...]... standards The results are summarized in Table 3 Table 3 Cement analysis for NBS 634 Oxide Concentration, % Given Empirical corrections XRF-11(a) PC-XRF(b) MgO 3. 30 3. 16 3. 16 3. 19 AlO 5.21 5.01 5.00 5.05 SiO2 20. 73 20.45 20 .10 20 .35 SO3 2.21 2.54 2 .30 2 .32 K2O 0.42 0. 43 0.41 0 .35 CaO 62.58 62.55 63. 34 64. 03 FeO 2.84 2. 83 2.81 2.84 (a) See Ref 17 (b) See Ref 18 Table 3 shows a comparison of three methods of... wavelength-dispersive spectrum of an AISI Type 34 7 stainless steel taken with a wavelength-dispersive x-ray spectrometer Approximately 30 min were required to obtain this spectrum Additional information on wavelength dispersive x-ray instrumentation and applications is available in Ref 4, 5, 6, 7, 8 Fig 7 Wavelength-dispersive x-ray spectrum of AISI type 34 7 stainless steel Philips PW-1 410 sequential x-ray...Relative intensity E, keV LIII → K(2P3/2 → 1S1/2) 63 8.047 Kα2 LII → K(2P1/2 → 1S1/2) 32 8.027 Kβ1 MIII → K(3P3/2 → 1S1/2) 10 8.9 03 K 3 MII → K(3P1/2 → 1S1/2) 10 8.9 73 Kβ5 MV → K(3D5/2 → 1S1/2 . L III → K(2P 3/ 2 → 1S 1/2 ) 63 8.047 Kα 2 L II → K(2P 1/2 → 1S 1/2 ) 32 8.027 Kβ 1 M III → K(3P 3/ 2 → 1S 1/2 ) 10 8.9 03 Kβ 3 M II → K(3P 1/2 → 1S 1/2 ) 10 8.9 73 Kβ 5 M V → K(3D 5/2 → 1S 1/2 . Vol 46, 19 23, p 836 2. R.T. Beatty, Proc. R. Soc. London, Ser. A, Vol 89, 19 13, p 31 4 3. H. Kulenkampff, Ann. Phys., Vol 69, 19 23, p 548 X-Ray Spectrometry Donald E. Leyden, Department. (6.6 × 10 -2 7 erg · s), m e is the electron mass (9.11 × 10 -2 8 g), c is the velocity of electromagnetic radiation (3 × 10 10 cm/s), and is the angle between the scattered and incident x-ray