International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 4.2, pp. 191-192
|
The efficiency of the production of characteristic radiation has been calculated by a number of authors (see, for example, Dyson, 1973, Chap. 3). For a particular line, it depends on the fluorescence yield, that is the probability that the decay of an excited state leads to the emission of a photon, on the statistical weights of the X-ray levels involved, on the effects of the penetration and slowing down of the bombarding electrons in the target, on the fraction of electrons back-scattered out of the target, and on the contribution caused by fluorescent X-rays produced indirectly by the continuous spectrum. The emerging X-ray intensity is further affected by the partial absorption of the generated X-rays in the target.
Dyson (1973) has also reviewed calculations and measurements made of the relative intensities of different lines in the K spectrum. The ratio of the
to
intensities is very close to 0.5 for Z between 23 and 48. The ratio of
to
rises fairly linearly with Z from 0.2 at Z = 20 to 0.4 at Z = 80 and that of
to
is near zero at Z = 29 and rises linearly with Z to about 0.1 at Z = 80. Relative intensities of lines in the L spectrum are given by Goldberg (1961
).
Green & Cosslett (1968) have made extensive measurements of the efficiency of the production of characteristic radiation for a number of targets and for a range of electron accelerating voltages. Their results can be expressed empirically in the form
where
is the generated number of Kα photons per steradian per incident electron, N0 is a function of the atomic number of the target, E0 is the electron energy in keV and
is the excitation potential in keV. It should be noted that
decreases with increasing Z.
For a copper target, this expression becomes or
where
is the number of Kα photons per steradian per second per milliampere of tube current.
These expressions are probably accurate to within a factor of 2 up to values of of about 10. Guo & Wu (1985
) found a linear relationship for the emerging number of photons with electron energy in the range
.
To obtain the number of photons that emerge from the target, the above expressions have to be corrected for absorption of the generated radiation in the target. The number of photons emerging at an angle to the surface, for normal electron incidence, is usually written
where
(Castaing & Descamps, 1955
). Green (1963
) gives experimental values of the correction factor f(χ) for a series of targets over a range of electron energies. His curves for a copper target are given in Fig. 4.2.1.1
. It will be noticed that the correction factor increases with increasing electron energy since the effective depth of X-ray generation increases with voltage. As a result, curves of
as a function of
have a broad maximum that is displaced towards lower voltages as
decreases, as shown in the experimental curves for copper K radiation due to Metchnik & Tomlin (1963
) (Fig. 4.2.1.2
). For very small take-off angles, therefore, X-ray tubes should be operated at lower than customary voltages. Note that the values in Fig. 4.2.1.2
agree to within ∼40% with those of Green & Cosslett. f(χ) at constant
increases with increasing Z, thus partly compensating for the decrease in
, especially at small values of
. A recent re-examination of the characteristic X-ray flux from Cr, Cu, Mo, Ag and W targets has been carried out by Honkimaki, Sleight & Suortti (1990
).
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