4.2.5\ X-Ray Weights ofLines

Within these families, the relative abundances of the characteristic X-rays are not equal. For example, for sodium the ratio of the K-L2,3 to K-M is approximately 150:1, and this ratio is a strong function of the atomic number, as shown in

. Fig. 4.5a for the K-shell (Heinrich et al. 1979). For the L-shell and M-shell, the X-ray families have more members, and the relative abundances are complex functions of atomic number, as shown in . Fig. 4.5b, c.

4.2.6\ Characteristic X-Ray Intensity

Isolated Atoms

When isolated atoms are considered, the probability of an energetic electron with energy E (keV) ionizing an atom by ejecting an atomic electron bound with ionization energy Ec (keV) can be expressed as a cross section, QI:

QI (ionizations / e− (atom / cm2 ) )

where ns is the number of electrons in the shell or subshell

(e.g., nK = 2), and bs and cs are constants for a given shell (e.g., bK = 0.35 and cK = 1) (Powell 1976). The behavior of the ionization cross section for the silicon K-shell as a function of the energy of the energetic beam electron is shown in

. Fig. 4.6. Starting with a zero value at 1.838 keV, the K-shell ionization energy for silicon, the cross section rapidly increases to a peak value, and then slowly decreases with further increases in the beam energy.

The relationship of the energy of the exciting electron to the ionization energy of the atomic electron is an important parameter and is designated the “overvoltage,” U:

The overvoltage that corresponds to the incident beam energy, E0, which is the maximum value because the beam electrons subsequently lose energy due to inelastic scattering as they progress through the specimen, is designated as U0:

For ionization to occur followed by X-ray emission, U > 1. With this definition for U, Eq. (4.4) can be rewritten as

QI (ionizations / e− (atom / cm2 ) )

The critical excitation energy is a strong function of the atomic number of the element and of the particular shell, as shown in . Fig. 4.7. Thus, for a specimen that consists of several different elements, the initial overvoltage U0 will be different for each element, which will affect the relative generation intensities of the different elements.

X-Ray Production in Thin Foils

Thin foils may be defined as having a thickness such that most electrons pass through the foil without suffering elastic scattering out of the ideal beam cylinder (defined by the circular beam footprint on the entrance and exit surfaces and the foil thickness) and without suffering significant

4.2 · Characteristic X-Rays

. Fig. 4.5  a Relative abundance of the K-L2,3 to K-M (Kα to Kβ) (Heinrich et al. 1979). b Relative abundance of

the L-shell X-rays, L3-M4,5 (Lα1,2) = 1 (Crawford et al. 2011). c Relative abundance of the M-shell X-rays, M5-N6,7

(Mα) = 1 (Crawford et al. 2011)

4