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X-Ray Fluorescence 10.1 INTRODUCTION

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10 X-Ray Fluorescence 10.1 INTRODUCTION The potential use of x rays for qualitative and quantitative elemental assay was appreciated soon after x rays were discovered. The early applications used Geiger-
10 X-Ray Fluorescence 10.1 INTRODUCTION The potential use of x rays for qualitative and quantitative elemental assay was appreciated soon after x rays were discovered. The early applications used Geiger- Mueller tubes and elaborate absorber arrays or crystal diffraction gratings to measure x rays. Later, advances in semiconductor detectors and associated electronics opened up the field of energy-dispersive x-ray fhmrescence (xrf) analysis for general elemental assay. XRF analysis is based on the fact that the x rays emitted from an ionized atom have energies that are characteristic of the element involved. The x-ray intensity is proportional to both the elemental concentration and the strength of the ionizing source. Photon ionization, which is achieved using either an x-ray tube or radioisotope, is most applicable to the nondestructive assay of nuclear material. Other methods of ionization are generally prohibitive because of the physical size and complexityof the ionization source. XRF analysis is a complementary technique to densitometry (Chapter 9). Densitometry measures photons that are transmitted through the sample without interaction, whereas XRF measures the radiation produced by photons that interact within the sample. As indicated by Figure 10.1, densitometry is usually better suitkd for measuring samples with high concentrations of the element of int.tmx%whenk XRF is the more imeful tekhnique for measuring samples with lower The lite~t~ on XRF analysis includes several general references (Refs, 1 through 4) that prbvide a thorough discussion of the method, with extensive bibliographies and information ~ at&nuation correction procedures and both erkgy- and XRF. 313 314 M. C. Miller 30 I t i, I.,,,,,,,,.il, X-ray Fluorescence (XRF) A Absorption-Edge Densitometry (K) Uranium Concentration (g/l) Fig Solution assay precision vs uranium concentration for ppical XRFmeasurements (squares) and absorption-edge densitometry measurements (triangles) THEORY x-ray Production Section 1.3 of Chapter 1 contains a brief discussion of x-ray production, X rays originate from atomic electron transitions and are element-specific. In the stable atom, electrons occupy discrete energy levels that are designated (in order of decreasing binding energy) K, Ll, L2, L3, Ml,... Ms, Nl,... N7, and so forth. The binding energy is the energy that must be expended to remove an electron from a given orbit. The vacancy thus created is filled by an electron from an outer orbit. The resultant loss in potential energy may appear as an x ray whose energy is equal to the difference in the binding energies of the two electron states. For example, if a uranium K electron is removed from the atom and an eleetron from the L3 level falls into itsplace, the energy of the emitted x ray is kev ( kev minus kev). The x ray produced by this transition is designated Knl. The K-series x rays are produced by outer electrons filling a K-shell vacancy. Each x-ray transition has a specific probability or intensity. The K-to-L3 transition is the most probable, and other intensities are usually expressed relative to Kal. Figure 10.2 depicts the transitions invoived in the production of the most abundant K and L x rays. Table 10-1 presents the major K and L lines of uranium and plutonium, along with their relative intensities. Figures 10.3 and 10.4 show the K and L x-ray spectra of uranium. X-Ray Fluorescence 315 M L 11 I I I I C.K Ttm,$tbn 4 Fig Diagram of energy levels showing the atomic transitions that produce the major K and L x rays. (C.K. = Coster Kr6nig).~ Kal a2 I P Fluorescence Yield All ionizations do not result in x-ray emission. The Auger effect is a competing mechanism ofatomic relaxation. Inthisprocess, theatom regains energy stability by emitting an outer shell electron. The ratio of the number of emitted x rays to the total number of ionizations is called the fluorescence yield w~,where i designates the shell involved. Fluonxcence yield increases with atomic number and is greater than 95% for K x rays of elements with Z 78 (see Figure 10.5). For a given element, the fluorescence yield decreases from the K series to the L and M series. The fluorescence yield can be approximated by (Ref. 1) wi = Z4/(Ai + Z4) (lo-1) where Ai is approximately 106 for the K shell and 108 for the L shell Photon Transmission For a photon to eject an electron, the photon energy must be greater than or equal to the electron binding energy. For example, to ionize K electrons of plutonium, the energy of the excitation photon must be at least kev. 316 M. C. Miller Table Energies and relative intensities of the major K and L x rays of uranium and plutonium Energies in kev Transition Uranium Plutonium Line (FinaI - Initial) (%)b (%) Kal K -L3 Ka2 K -L2 K/31 K -Ms K/?3 K -Mz KD2 K - N2,3 L3 - M5 La2 L3 - M4 Lf12 L3 - N5 L, L3 - Ml L2 - M4 L71 L2 - N4 L1 - M3 L1 ~M (100) (61.9) (22.0) (1 1.6) , (12.3) (100~ (lo) (20) (l-3) (50) (1-10) (1-6) (3-5) (100) (62.5) (22.2) (11.7) , (12.5) (100) (10) (20) (1-3) (50) (1-10) (l-6) (3-5) Calculated from Table of Isotopes, Appendix 111(L lines) (C. M. Lederer and V. S. Shirley, Eds., 7th ed. [John Wiley& Sons, Inc., New York, 1978]). bintensities relative to either Kal or Lal in percent. Approximate only (from Ref. 4). The fraction of photons, F, that interact with the atomic electrons of a particular materird is given by F = 1 exp( ~px) (lo-2) where p = mass attenuation coefficient p = density of sample x = thickness of sample. If one plots the mass attenuation coefficient vs photon energy for a given element, sharp discontinuities (known as absorption edges ) are observed. Figure 10.6 shows the mass attenuation coefficient for uranium and plutonium. The edges indicate the sudden decrease in the photoelectric cross section for incident photon energies just below the binding energy of that particular electron state. The photoelectric interaction is the dominant process involved in photon-excited x-ray excitation. X-Ray Fluorescence 317 Kal Ka2 I Backscatter peak o 90 t Photon Energy (kev) Fig Kx-rayspectrum of uranium. Theexcitation source is S7Co. 150 I I I Backscatter Peak i-al! L P1 1-I%., c Photon Energy (kev) Fig Lx-ray spectrum of uranium. Theexcitation source islwcd. M. C. Miller 1.0 I I I 08 K 0,8 0.4 ~U,%.,0.5 o ZQ $ Atomic Number Z Fluorescence yield for K, L, and M x rays as a function of atomic number. Attenuation limits the sample size that can be analyzed by x-ray transmission techniques. Figure 10.7 shows tie mean free path of 400-, ~W-, id 20-keV photons in water and in a 50-gjL uranium solution. In general, transmission techniques are applicable for samples whose transmission path lengths are less than four or five mean free paths. Equation 10-2 is useful when comparing K XRF and L XRF. For L XRF, p is larger and more of the excitation flux interacts with the sample. For K XRF, Mis smaller and both the excitation photons and x rays are attenuated less (relative to L XRF). This attenuation difference implies that L XRF is more sensitive (more x rays produced pe runit excitation flux and cross-sectional area) than K XRF. On the other hand, K XRF allows greater flexibility with respect to the choice of sample container and intervening absorbers Measurement Geometry The choice of geometry is ve~ important in an XRF system. Although photoelectric interactions of the excitation photons with analyte atoms are of primary interest, other interactions, particularly Compton backscatter interactions, must be considered. The energy of a Compton-scattered gamma ray is (see Section of Chapter 2 and Ref. 5) Et = 511 (1 cos(#i+511/e) (lo-3) where E, E = scattered, incident photon energy in = angle between incident and scattered photons.. X-Ray Fluorescence I 1 I [ 1 I I 1 I 1 Ill 1 1 1, 1 1, r - Uranium ~ t I \ \/ Plutonium I s u) u) 10 s L 10- [ I 1 Ill I I!! 1 1Ill I I Photon Energy (kev) 103 Fig Mass attenuation coejjicient vs energy for uranium and plutonium. The energy E is a minimum 180, and photons that have scattered at or near this angle can produce a backscatter peak in the measured spectrum. For 122-keV photons from 57C0 (a suitable source for K XRF of uranium or plutonium), the backscatter peak is at 82.6 kev. If the scattering angle # is 90, E is 98.5 kev, which is in the middle of the K x-ray spectrum from uranium and plutonium. If 57C0 is used as an excitation source, the measurement geometry should be arranged such that # is close to 180 for most of the scattered gamma rays that reach the detector. This arrangement puts the backscatter peak and the Compton continuum of scattered photons below the characteristic x rays and minimizes the background under the x- ray photopeaks (see Figure 10.3). The annular source described later in the chapter provides this favorable geometry. For L x rays, the geometry is not as critical because E (180 ) is 20.3 kev for 22-keV silver x rays from 10gCd (a good L XRF source for uranium), and the backscatter peak is above the x-ray region of interest. Scattering 320 M. C. Miller 10 50gll Uranium H Water 8 - I I I Photon Energy (kev) Fig Mean free path of 400-, 100-, and 20-keV photons in water (p = 1 glc~) and in a 50-glL uranium solution. materials near the detector must be carefully controlled to minimize the magnitude of the backscatter peak. Some investigators (Ref. 6) use excitation sources with energies much higher than the binding energy of interest, thereby minimizing the scattering effects in the spectral region of the induced x rays. This approach requires higherintensity excitation sources (by an order of magnitude or more) in order to produce sufficient x-ray activity. The detector must be shielded from the excitation source and other background rdation to reduce deadtime and pileup losses. Detector collimation is usually necessary to limit the interference from unwanted sources. To stabilize the x-ray response, the relative positions of the source, sample, and detector must be fixed; often these components are physically connected. Figure 10.8 shows a possible geometry for a transmission-corrected XRF analysis TYPES OF SOURCES TWOtypes of sources are commonly used: discrete gamma-ray or x-ray sources and continuous sources such as x-ray generators. Each has advantages and disadvantages. The selection of a suitable source involves consideration of type, energy, and strength. It is most efficient to choose a source whose energy is above but as close as possible to the absorption edge of interest. As shown by the graph of # vs photon energy X-Ray Fluorescence 321 (To maintainrigidgeometfy) -Annular Excitation CO source Esl Aluminum N Lead Fig. 10,8 Cross-sectional view of geometry for a transmission-corrected assay using an annular excitation source. in Figure 10.6, the value of the mass attenuation coefficient is greatest just above an absorption edge. Cobalt-57 emits a gamma ray at 122 kev, an efficient energy for K-shell ionization ofeither uranium or plutonium. X-ray generators are available for KXRFof uranium and plutonium, but they are too bulky for portable applications. A good discrete source for L XRF of uranium and plutonium is 09Cd, which emits silver K x rays (Kal energy = 22 kev). X-ray generators are available that are small enough for portable applications that require photons in the 25-keV energy range. Discrete line sources are small, extremely stable, and operationally simple, making them attractive for many XRF applications. Their major dkadvantage is that they decay with time and require periodic replacement. (Two commonly used sources, 57C0 and 1 gcd, have half-lives of 272 days and 453 days, respectively.) Another disadvantage is that discrete sources cannot be turned off, causing transportation and handling difficulties. Because the source strength is often 1 mci or greater, both personnel and detector must be carefully shielded. Table 10-2 lists some radioisotopes that can be used for XRF analysis of uranium and plutonium. The geometry of the annular source shown in Figure 10.9 is commonly used because it shields the detector from the excitation source and minimizes backscatter interference. 322 M. C. Miller Table Excitation sources suitable for uranium and plutonium assay Useful Emissions Radionuclide Half-Life Decay Mode Type Energy (kev) 57C0 270 d electron gamma rays 122 Iogcd capture gamma rays d electron Ag K x rays 22 capture 75se 120 d electron gamma rays 121 capture gamma rays ce 285 d beta decay Pr K x rays gamma rays d electron Te K x rays 27 capture gamma rays 35 latpm-al 2.6 y beta decay continuum 12-45a End point of bremsstrahlung spectrum. I Sample I Fig Annular excitation source. I Pb X-ray generators produce bremsstrahlung by boiling electrons off a filament and accelerating them into a target. Because they require a high-voltage supply and a means of dissipating the heat produced in the target, x-ray generators can be bulky, especially for higher operating potentials. Small generators are available that operate below 70 kev, and portable generators, with power ratings up to 50 W, are available that do not require elaborate cooling systems. For a given power rating, higher maximum operating voltage is achieved at the expense of lower available cument. The spectrum from an x-ray generator spans the energy range from the accelerating potential of the generator to the transmission cutoff of the x-ray window. The shape I(E) and total intensity (I) of this distribution is given by (Ref. 4) I(E) w iz(v E)E I IX izv2 (lo-4) X-Ray Fluorescence 323 where i = tube current V = operating voltage Z = atomic number of target. Figure shows the output spectrum from an x-ray generator. In addition to the continuous spectrum, the characteristic x rays of the target material are produced. These x rays may cause an interference, which can be removed with filters. The filter chosen should have an absorption edge just below the energy to be attenuated. X-ray generators can be switched on and off, and their energy distribution and intensity can be varied as desired. They typically provide a more intense source of photons than radioisotopic sources (N 1012photons/s or greater). However, their flexibility is possible only at the expense of simplicity and compactness. Because an x-ray generator is an electrical device, system failures and maintenance problems are possible concerns. The assay precision is dictated by the stability of the x-ray tube. Modem generators exhibit less than 0.1% fluctuation for short-term stability and 0.2 to 0.3% for Iong-term stability. Figure shows two different portable x-ray generators. ~ : ~ mo - g 450- Fig Typical x-ray generator spectrum. g u m - Z The generator target is tungsten ~ ~ _ and the operating potential is z 20.4 kv, o PhotonEnerw WV) Fig Portable x-ray generators. 324 M. C. Miller Other sources may be used for XRF. A secondary fluorescent source uses a primary photon source to excite the characteristic x rays of a target, and the target x rays are used to excite the sample to be analyzed. The primary excitation source can be discrete or continuous. This scheme can produce a great variety of monoenergetic excitation photons, depending on the target material. The major drawback is the need for a high-intensity primary source. If the primary source is a radioisotope, radiation safety may be an important concern. It is possible to make a bremsstrahlung source using a radioisotope tiher than an x-ray generator. Such a source consists of a beta-decaying isotope mixed with a target material (for example, 147Prn-Al, with aluminum being the target material) CORRECTION FOR SAMPLE A ltenua~on Effects of Sample Attqmatlon As in passive gamma-ray assays, sample attenuation is a fundamental limitation to the accuracy of XRF analysis. Attenuation corrections are required for the x rays leaving the sample and also for the gamma rays or x rays from the excitation source. X-ray fluorescence analysis is unsuitable for large, solid samples, because the attenuation is too large to be accurately treated with any correction procedure. For example, the mean free path of 122-keV gamma rays in uranium metal is approximately cm. The low penetrability of ibis radiation means that XRF cambe accurately used only if the sample is smooth and homogeneous. This limitation is even more true for L XRF using 22-keV photons. X-ray fluorescence can be used to accurately assay dilute uranium solutions because the mean free path of photons in water is approximately 6.4 cm at 122 kev and 1.7 cm at 22 kev. Because the excitation source energy is above the absorption edge and the energies of the characteristic x rays are just below the absorption edge, the attenuation of the excitation radiation is higher and determines the range of sample thickness that can be accurately assayed. Figure plots the mean free path of 122-keV gamma rays as a function of uranium concentration (urtiyl nitrate in 4-M nitric acid). Attenuation considerations also affect the choice of sample containers. Because the K x rays of ~ium and plutonium are in the 100-keV range, metal containers can K ~! can be applied measurements. L x rays, however, are attenutied t$ even tidn metal containers and can only be measured in low-z co~~e$, such as plastic or glass. ;!:!!,,~ ~~ ~a~ : j:! For quantitative $e x-ray emission ~ate must be related to the element concentration. The desired Te.lation,as presented in Section of Chapter 5, is X-Ray Fluorescence I I I I g s 5 i t c g =2 6 o I I I I o Uranium Concentration (g/l) Fig The 122-keVphoton mean fieepath vs uranium concentration (uranyl nitrate in 4-M nitric acid). RR x CF(RL) X CF(AT) p= (lo-5) K where p = element concentration RR = raw rate of x-ray detection CF(RL) = correction factor for rate-related losses CF(AT) = correction factor for attenuation K = calibration constant. CF(RL) can be determined using either pulser or radioisotope normalization (see Section 5.4 of Chapter 5). The attenuation correction has two parts, one for excitation radiation and one for fluoresced x rays. Consider a far-field measurement geometry where the sample is approximated by a slab and the excitation source is monoenergetic (see 10.13). The flux F7 of excitation photons at a depth x in the sample is given by FT = 17exp( p~x/cos#). (10-6) 326 M. C. Miller * 17 1 L~ $ e Fluorescence Site Fig General XRF slab geometry. The variables in Equation 10-6 through are defined in Table The number of excitation photons that interact in the volume dx and create a K~l x ray is dx F. dx = FTTPWB. (lo-7) cos# The fluoresced x rays are attenuated in the sample according to F.(out) = Faexp(-pzX/cosf3). (10-8) Combining and integrating Equations 10-6 through 10-8 yields the following expression for the x-ray rate at the detector surface: 1.= 17r/wBf2 + #u ] { -exp[-(%+a l} (lo-9) The factor (L /47r)cos#/cosO has been added for normalization. If an x-ray generator is used as the excitation source, Equation 10-9 must be integrated from the absorption edge to the maximum energy of the generator. When the sample is infinitely thick for the radiation of interest, Equation 10-9 becomes 17 ~pwbf2 1.= + p ] (lo-lo) This equation is similar to that of the enrichment meter (see Chapter 7). The result is very important for XRF analysis because it implies that the x-ray rate is directly proportional to the concentration of the fluoresced element.. - X-Ray Fluorescence 327 In plutonium and highly enriched uranium materials, theself-excitationof x rays bythepassive gamma rays cancomplicate the assay. Formixed uranium/plutonium materials, the dominant signals are passive x rays from the alpha decay of plutonium. When the excitation source can fluoresce both plutonium and uranium (as can 57C0 and 1 gcd), additional uranium fluorescence is caused by the plutonium x rays. A separate passive count is usually required to correct for this interference. Table Variables in Equations 10-6 through e
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