2.5.3.6. Line Intensities

Line intensities are a function of transition probabilities and the rate at which the appropriate atomic shell is ionized by the incident electrons. The probability of ionization is a function of the effective target-atom ionization "cross-section," Q. The ionization cross-section is small (0.01 Å) compared with the typical atomic diameter (1 Å) and decreases with increasing atomic number. Thus, only a small proportion of atoms in the target material are ionized. Line intensities may be described by an empirical relationship:

Thus, the intensity of a line depends on the amount to which E_o exceeds E_c (Figure 2.5.3.6). The ratio E_o/E_c is termed the overvoltage. Optimal overvoltages may be calculated using the expression for the capture cross-section (Q) for a given shell. For example, for the K-shell this is:

Recommended values for the K-shell are b_s = 0.9 and C_s = 0.65. Typical capture cross-sections for the K shell are on the order of 10^-20 cm², about a hundredth of the atomic diameter. Clearly, K-shell ionization has a very low probability! This function peaks at E_o of about 2.5 times E_c, thus this overvoltage for K-lines is optimal. With higher E_o and higher overvoltages, there is a greater chance of decreasing X-ray intensities through the production of satellite peaks.

Figure 2.5.3.6. Spectra of pure copper taken at accelerating voltages of 10 keV (above) and 20 keV (below). At 10 keV, only the L lines are efficiently excited (Kab = 8.98 keV) (after Kevex Corporation 1983).