Section 2.3.5.1. X-ray tubes

Modern X-ray generators have a high degree of electrical stability, of the order of 0.1 to 0.005%, which is sufficient for most applications. The current is continually monitored in the generator and used in feedback circuits to regulate the output. The high voltage is also monitored in some generators. Maximum long-time stability is obtained if the generator and X-ray tube are run continuously over long periods of time so that they reach stable operating conditions. Experienced technicians often advise that the X-ray tube life is shortened by frequent on–off use because the filament receives maximum stress when turned on. The tube may be left operating at low power, 20 kV, 5–10 mA, when not being used. It is inadvisable to operate at voltages below about 20 kV for long periods of time because space charge builds up, causing excessive heating of the filament and shorter life. The stability can be determined by measuring the intensity of a diffraction peak or fluorescence as a function of time. This is not an easy experiment to perform because the stability of the detector system must first be determined with a radioactive source and a sufficient number of counts recorded for the required statistical accuracy.

Alternatively, a monitor method can be used to correct for drifts and instabilities. The monitor is another detector with a separate set of electronics. It can be used in several ways: (1) as a dosimeter to control the count time at each step; (2) to measure the counts at each step and use the data to make corrections, i.e. counts from specimen divided by monitor counts. (It is usually advisable to average the monitor counts over a number of steps to obtain better statistical accuracy.) A thin Be foil or Mylar film inclined to the beam is ideal because they have little absorption and strong scattering. The monitor detector can be mounted out of the beam path and must be able to handle very high count rates and have an extended linear range to avoid introducing errors. In synchrotron-radiation EXAFS experiments, the beam passes through an ionization chamber placed in the beam to monitor the incident intensity.

Spikes in the data may arise from transients in the electrical supply and filtering at the source is required, although modern diffractometer control systems have provision for removing aberrant data.

Spectral contamination from metals inside the tube may occur and increase with tube use. This reduces the intensity by coating the anode and windows and may not be noticed when using an incident-beam or diffracted-beam monochromator. It can be measured by removing the monochromator or β filter, operating the tube at high kV, and recording the diffraction pattern of a simple powder (e.g. Si or W), a rolled metal foil, or a single-crystal plate (Ladell & Parrish, 1959). The contaminating elements can be identified from the extra peaks. It is advisable to check the spectral purity when the tube is new and periodically thereafter.

The intensity distribution of the focal line is usually not uniform. This has no apparent effect on the shapes of powder reflections but may cause difficulties with single crystals (Parrish, Mack & Taylor, 1966). The distribution can be measured with a small pinhole placed between the X-ray tube focal line and a dental or Polaroid film. The ratio of the distances between line-to-pinhole and pinhole-to-film determines the magnification of the image. The pinhole diameter should be small for good resolution. About 0.1 mm diameter is satisfactory and can be made with a special microdrill, spark erosion or other methods. The thickness of the metal must be minimal to avoid having the aperture formed by the length and diameter of the pinhole limit the length of focus photographed. Avoid overexposure which broadens the image. Also, the Polaroid film should be exposed outside the cassette to avoid broadening caused by the intensifying screen.

A more accurate method is to scan a slit and detector (mounted on the same arm) normal to the central ray from the focus as shown in Fig. 2.3.5.2(b) (Parrish, 1967). The slits are a pair of molybdenum rods (or other high-absorbing metal) with opening normal to the scan direction, and the slit width determines the resolution. This method gives a direct measurement of the intensity distribution from which the projected size can be determined.

Figure 2.3.5.2| top | pdf | (a) Transmission of Be, Al and air as a function of wavelength. (b) Method for measuring X-ray tube focus by scanning slit S2 and detector D. Slit S1 is fixed and the ratio of the distances d2/d1 gives the magnification. (c) Intensity of a copper target tube as a function of kV for various take-off angles. (d) Intensity and brightness as a function of take-off angle of a copper target tube operated at 50 kV. The intensity distributions for 1 and 4° entrance-slit apertures are shown at the top, and terms used to define ψ and αES are shown in the lower insert.

The actual size of the focus is foreshortened to by the small take-off angle ψ, . A typical 0.5 10 mm focus viewed at 6° appears to be a line 0.05 10 mm or a spot 0.05 1 mm [Fig. 2.3.1.9(a)]. The line focus is generally used for powder diffractometry and focusing cameras and the spot focus for powder cameras and single-crystal diffractometry.

X-rays emerge from three or four Be windows spaced 90° apart around the circumference. Their diameter and position with respect to the plane of the target determine the usable ψ-angle range. The length of line focus that can pass through the window can be seen with a flat fluorescent screen in the specimen holder using the largest entrance slit. The Be window thickness often used is 300 μm and the transmission as a function of wavelength is shown in Fig. 2.3.5.2(a).

The absorption of X-rays in air is also wavelength-dependent and increases rapidly with increasing wavelength, Fig. 2.3.5.2(a). The air absorption was calculated using a density of 0.001205 g cm⁻³ at 760 mm Hg pressure (1 mm Hg = 133 Pa), 293 K, and 0% humidity. Changes in the humidity and barometric pressure can cause small changes in the intensity. Baker, George, Bellamy & Causer (1968) measured the intensity of the Cu Kα and barometric pressure over a 5 d period and found the counts increased 2.67% as the barometric pressure decreased 3.7%. However, they used an Xe proportional counter whose sensitivity is also pressure-dependent and a large amount of the change may have been due to changes in the detector efficiency.

Air scattering increases rapidly at small 2θ's, increasing the background. It is advisable to use a vacuum or helium path to avoid problems in this region.

The intensity of the characteristic line spectrum emerging from the tube depends on the anode element, voltage, and take-off angle ψ. The depth of penetration of the electrons in the anode is approximately proportional to kV²/ρ, where ρ is the density of the anode metal. The path length L of the X-rays to reach the surface depends on the depth D at which they are generated and the take-off angle, . Self-absorption in the anode causes a loss of intensity that increases with D and decreasing ψ. The intensity of Cu Kα radiation at 50 kV as a function of take-off angle is shown in Fig. 2.3.5.2(d). This effect has been described in a number of publications: Green (1964), Brown & Ogilvie (1964), Birks, Seebold, Grant & Grosso (1965), Parrish (1968), and Phillips (1985). Because of the self-absorption, the wavelength distribution varies slightly with take-off angle (Wilson, 1963, pp. 61–63).

The optimum kV and mA operating conditions are not sharply defined and the range can be determined with a powder reflection or by using small apertures in the direct beam with balanced filters and pulse-amplitude discrimination. The intensity is measured at various voltages, keeping the current constant and converting the data to constant power. Typical experimental curves relating Cu Kα intensity to kV for various ψ's are given in Fig. 2.3.5.2(c). At 50 kV, the intensity doubles by increasing ψ from 3 to 12° (although the projected width of the focal spot also increases). The effect is much larger for Cr Kα and W Lα because of their higher absorptions. The linear region of I versus V is relatively short and increases with ψ. At small ψ's, I is virtually independent of V and could decrease with increasing voltages; increasing the current would give a greater increase using the same power. For a tube with maximum power values of 60 kV, 55 mA and 2200 W, the relative intensities of Cu Kα are about 100 for 40 kV/55 mA, 88 for 50 kV/44 mA and 74 for 60 kV/37 mA. However, the filament life decreases with increasing current and most manufacturers specify a maximum allowable current.

The intensity distribution reaching the specimen is not uniform over the entire illuminated area. In the direction normal to the specimen axis of rotation, one end of the specimen views the X-ray tube focus at an angle ψ − (α/2) and the other at ψ + (α/2), where α is the angular aperture of the entrance slit [Fig. 2.3.5.2(d)]. The intensity differences are determined by ψ and α_ES so that the centre of gravity does not coincide with the geometrical centre. The dependence of the diffracted-beam intensity on the aperture of the entrance slit α_ES, therefore, may also be nonlinear. For example, at ψ = 6°, the intensity difference at the ends of the specimen is 9% for α_ES = 1°, and 44% for α_ES = 4°; the corresponding numbers for ψ = 12° are 2 and 10% respectively.

Although increasing ψ increases the intensity, it also increases the projected width and may increase the widths of the reflections (§2.3.1.1.5). The brightness expressed as also decreases rapidly. When one is working with small apertures, as in grazing incidence and the analysis of small samples, the brightness becomes a very important factor in obtaining the maximum number of counts. For example, the intensity at ψ = 12° is twice that at 3° but the brightness is one half [Fig. 2.3.5.2(d)]. However, it should be noted that the smaller the take-off angle the greater the possibility of intensity losses due to target roughening.