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1. Generation and Properties of X-rays

X-rays are electromagnetic waves whose wavelengths range from about 0.1 to 100 $\times$ 10-10 m. They are produced when rapidly moving electrons strike a solid target and their kinetic energy is converted into radiation. The wavelength of the emitted radiation depends on the energy of the electrons.

Figure 1
\includegraphics {fig1.ps}

Figure 1 shows schematically a simple X-ray tube. A very high voltage is placed across the electrodes in the two ends of the tube and the tube is evacuated to a low pressure, about 1/1 000 mm of mercury. The current flows between the two electrodes and the electrons carrying this strike the metal target. This causes the emission of X-rays. If one plots a graph of the wavelength of the X-rays emitted against their intensity for varying applied accelerating voltages one obtains results of the kind in Fig. 2. The target for Fig. 2 would be tungsten.

Figure 2
\includegraphics {fig2.ps}

The curves are typical of black body radiation. What is interesting is the very sharp cut-off at short wavelength. This minimum wavelength, lambda minimum, corresponds to the maximum efficiency of conversion of the kinetic energy to electromagnetic radiation; in other words if we use Planck's equation, $E=h\nu=hc/\lambda$, we can calculate lambda minimum. If the accelerating voltage is V, then this minimum is 1.240 $\times$ 10-6 m. If we now change the target to a metal of a smaller atomic number such as copper or molybdenum, then we observe very sharp spikes appearing above this smooth background radiation--Fig. 3.

Figure 3
\includegraphics {fig3.ps}

These very sharp spikes are called characteristic lines and the X-radiation is termed characteristic radiation. These sharp lines are caused by electrons being knocked out of the K shell of an atom and then the electrons from the L shell cascading down into the vacancies in this K shell. The energy emitted in this process corresponds to the so-called K alpha and K beta lines. If several metals are present in the target, each will emit its characteristic radiation independently. This property can be used to determine qualitatively which elements are present in an alloy by making it the target in an X-ray tube and then scanning all wavelengths emitted by the target. Typical targets and their related constants are given in Table 1.

Table 1: Target materials and associated constants
  Cr Fe Cu Mo
Z 24 26 29 42
$\alpha_1$, Å 2.2896 1.9360 1.5405 0.70926
$\alpha_2$, Å 2.2935 1.9399 1.5443 0.71354
$\bar\alpha*$, Å 2.2909 1.9373 1.5418 0.71069
$\beta_1$, Å 2.0848 1.7565 1.3922 0.63225
$\beta$, filt. V, 0.4mil$
$ Mn, 0.4mil Ni, 0.6 mil Nb, 3mils
$\alpha$, filt. Ti Cr Co Y
Resolution, Å 1.15 0.95 0.75 0.35
Critical potential, kV 5.99 7.11 8.98 20.0
Operating conditions, kV: 30-40 35-45 35-45 50-55
  half- or full-wave-rectified, mA 10 10 20 20
  constant potential, mA 7 7 14 14

*$\bar\alpha$ is the intensity-weighted average of $\alpha_1$ and $\alpha_2$ and is the figure usually used for the wavelength when the two lines are not resolved.

$1 mil =0.001 inch = 0.025 mm.

It is fairly obvious that X-rays can be absorbed by solids, and this absorption phenomenon can be described by a very simple equation. The observed intensity I is given by: $I=I_0 \exp(\mu t)$ where $\mu$ is a linear absorption coefficient and t is the path length through which the X-rays are moving. The value of this absorption coefficient increases as the atomic number of the element concerned increases. Also, if we plot $\mu$against wavelength of the X-rays being absorbed for any one given element, we find a rather unusual curve (see Fig. 4). A smooth curve in this plot is followed by very sharp jumps. These discontinuities are called absorption edges and they occur at the wavelength corresponding to the energy needed to knock an electron out of an atomic orbital in the material that is doing the absorbing. In particular, the K absorption edge of an element lies very slightly to the short wavelength side of the K beta lines for that element. Like the characteristic lines, the absorption edge shifts to longer wavelength with decrease in atomic number. If you look now at Fig. 5, you will see that the absorption curve for the element zirconium when superimposed on the X-ray emission curve for the element molybdenum is such that the absorption edge of zirconium comes directly between the K beta and K alpha lines of molybdenum. In other words, if we pass Mo radiation through a sheet of Zr metal, the Zr metal will absorb the beta Mo radiation far more strongly than the alpha radiation. Figure 5 also shows schematically what the resulting distribution of radiation intensities will look like after filtering.

Figure 4
\includegraphics {fig4.ps}

In most X-ray work only one well-defined wavelength of radiation is needed and so the X-rays are filtered. Filtering is probably the cheapest and simplest way of obtaining approximately monochromatic X-rays. One can achieve far `cleaner' radiation by using a so-called monochromator, however, the cost of the monochromator could be 10,000 times the cost of a thin sliver of metal of the correct thickness. Table 2 shows suitable filters for various radiations.

Figure 5
\includegraphics {fig5.ps}

Table 2: $\beta$ filters to reduce integrated intensity ratios to K$\beta_1$/K$\alpha_1$=1/500
Target material $\beta$ filter Thickness, mm Thickness, in. g per cm2 Per cent loss, $K\alpha_1$
Ag Pd 0.092 0.0036 0.110 74
  Rh 0.092 0.0036 0.114 73
Mo Zr 0.120 0.0047 0.078 71
Cu Ni 0.023 0.0049 0.020 60
Ni Co 0.020 0.0008 0.017 57
Co Fe 0.019 0.0007 0.015 54
Fe Mn 0.018 0.0007 0.013 53
  Mn2O3 0.042 0.0017 0.019 59
  MnO2 0.042 0.0016 0.021 61
Cr V 0.017 0.0007 0.010 51
  V2O5 0.056 0.0022 0.019 64

Generally speaking the source of X-rays used will be a commercial generator. Typical X-ray tubes fitted to these generators will have life times of 5000 to l0,000 h, but incorrect handling can reduce the life time very severely. The two most commonly used targets are copper and molybdenum but certain problems may require other wavelengths. For example, if an element two to five places left of copper in the periodic table is being studied, fluorescent radiation is emitted and will completely blacken the film. Cobalt $K\alpha$ radiation can be used for samples containing iron without causing fluorescence as would be the case with Cu $K\alpha$radiation. Of course the emission of this fluorescent radiation is itself an important phenomenon which can be used for analysis as will be described later.

Nowadays X-ray generators are available with highly stabilised power supplies, though of course such apparatus is very expensive. It is necessary when Geiger counters or solid state detectors are being used to measure X-ray intensities, but for photographic work a high degree of stability is not so necessary.

The actual window through which the X-rays emerge is usually made of beryllium--which has an atomic number of only 4 and therefore very low absorption. The windows are delicate and should not be touched.

Figure 6
\includegraphics {fig6.ps}

X-ray tubes are sometimes constructed so that two of the windows will provide a line focus while the other two provide what is called a point focus. This is shown diagrammatically in Fig. 6. The line focus is most suitable for powder work but the point focus should always be used for single crystal studies. The tube is clearly marked so there can be no mistaking which of the windows corresponds to either the line or the point focus.

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Next: Safety and other Practical Considerations Up: An Introduction to the Scope, Potential Previous: An Introduction to the Scope, Potential

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