Section 2.3.5.2. X-ray spectra

The X-ray tube spectrum consists of sharp characteristic lines superposed on broad continuous radiation as shown in Fig. 2.3.5.3 . The continuous spectrum begins at a wavelength determined by the voltage on the X-ray tube, λmin 12.4/kV. It reaches a maximum at about 1.5 to 2λmin and gradually falls off with increasing λ [Fig. 2.3.5.4(a) ]. The intensity increases with voltage and current, and also with the atomic number of the target element. The integrated intensity is greater than that of the spectral lines. It is used for Laue patterns, fluorescence analysis, and energy-dispersive diffraction. It is troublesome in powder diffraction because it contributes to the background by scattering and by causing specimen fluorescence.

Figure 2.3.5.3| top | pdf | X-ray spectrum of copper target tube with Be window, 50 kV constant potential, 12° take-off angle. (a) Unfiltered, (b) with Ni filter, (c) unfiltered with pulse-height discrimination (PHD), (d) Ni filter + PHD. (1) λmin = 0.246 Å (4.5°2θ), (2) I K-absorption edge (from NaI scintillation crystal), (3) peak of continuous radiation (about 19% of Cu Kα peak), (4) W Lγ contaminant, (5) W Lβ, (6) Cu K-absorption edge, (7) Cu Kβ, (8) W Lα, (9) Cu Kα1 + Kα2, (10) Co Kα, (11) Fe Kα, (12) Mn Kα, (13) Ni K-absorption edge, (14) escape peak. Experimental conditions: Si(111) single-crystal analyser, vacuum path, Ni filter 0.18 mm, scintillation counter with 45% resolution for Cu Kα, lower-level discrimination only against circuit noise. ES 0.25 × 1.5 mm, AS 1.4 mm, no RS, Δ2θ 0.05°, FWHM 0.3°2θ.

Figure 2.3.5.4| top | pdf | (a) Continuous X-ray spectrum of tungsten target X-ray tube as a function of voltage and constant current. Full-wave rectification, silicon (111) crystal analyser, scintillation counter. (b) Plot of Moseley's law for four characteristic X-ray spectral lines.

The wavelengths of the spectral lines decrease with increasing atomic number Z of the target element [Moseley's law, Fig. 2.3.5.4(b)]. All the lines in a series appear when the critical excitation voltage is exceeded. For a Cu target, this is 9 kV and the approximate relative intensities are Cu Kα₂ 50, Kα₁ 100 and Kβ 20. The peak intensities of Cu Kα₁ and Cu Kα₂ in diffractometer patterns may not be exactly 2:1 but closer to 2.1:1 in resolved doublets because of the different profile widths. The profile widths of the spectral lines vary among the different elements used for X-ray tube targets (Compton & Allison, 1935), as does the Kβ/Kα ratio (Smith, Reed & Ware, 1974). The observed ratio varies with the degree of overlap. The rate of increase with voltage and other factors is described above.

A broad weak group of satellite peaks, Kα₃, occurs near the bottom of the short-wavelength tail of the Kα₁ peak (see Fig. 2.3.3.3). The intensity varies with the target element and is about 0.5% for the Cu K spectrum. The satellites appear as a small, broad, ill defined peak in powder diffraction patterns (Parratt, 1936; Parrish, Mack & Taylor, 1963; Edwards & Langford, 1971).

The spectral lines have an approximately Lorentzian shape when measured with a two-crystal diffractometer. They usually have a small asymmetry and their widths vary among the elements and also in the same series of lines. Bearden (1964) defined the wavelength as the peak determined by extrapolation of the centres of chords near the top of the peak. The corresponding energy levels have been compiled by Bearden & Burr (1965). The centroid of the , peaks of Cu and Fe has been calculated from the Bearden experimental two-crystal data (Mack, Parrish & Taylor, 1964). X-ray wavelengths are discussed in Chapter 4.2 . The standard targets provide the K spectra of Ag, Mo, Cu, Co, Fe and Cr, and the W L spectrum. Other targets may be obtained on special order. The K spectra of the elements of high atomic number require a radiographic tube and power supply that can operate continuously at about 150 kV or higher. (Caution: The radiation-shielding problems multiply exponentially at high voltages.)

2.3.5.2.1. Wavelength selection

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The selection of the X-ray tube anode is determined by several factors such as intensity, specimen fluorescence, and dispersion. The intensity of the characteristic line radiation varies among the target elements depending on the voltage and if a vacuum or He path is used. The recorded intensities also change abruptly at the absorption edges of the elements in the specimen. If a diffracted-beam monochromator or solid-state detector with narrow window centred on the characteristic line energy is used, the specimen fluorescence is eliminated (except for the element that is the same as the anode), and one tube can be used for all compositions. If the pattern has severe overlapping, the separation of the peaks can be increased with longer wavelengths, which increase the dispersion expressed as °θ Å⁻¹ of d. Fig. 2.3.5.5 shows portions of diffractometer patterns of topaz in which the same d ranges were recorded with Cu Kα (a) and Cr Kα (b). The greater separation of the peaks is clearly advantageous in analysing the patterns.

Figure 2.3.5.5| top | pdf | Portion of diffractometer pattern of topaz showing effect of increasing dispersion on separation of peaks. (a) Cu Kα, (b) Cr Kα.

Copper-anode tubes are most frequently used for powder work because of their high intensity and good dispersion. Chromium tubes are often used for specimens containing iron and other transition elements to avoid fluorescence, and for larger dispersion, but require a vacuum or helium path and the intensity is usually one-half or less than that of copper. Molybdenum tubes are often used for single-crystal analysis, but not often for powders because of the low dispersion.