Scanning Electron Microscopy and X-Ray Microanalysis

44

4

4.2.5 X-Ray Weights of Lines

Within these families, the relative abundances of the charac-

teristic 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:

Qe

nb EE

I

2

20

ss c

ionizations atom cm

6.51 l

//

/

−

=×

() ()

() 

10 − oog

es()cE/Ec (4.4)

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 ion-

ization 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 fur-
ther 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:

UE= /Ec (4.5a)

The overvoltage that corresponds to the incident beam

energy, E 0 , 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 U 0 :

UE 00 = /Ec (4.5b)

For ionization to occur followed by X-ray emission, U > 1.

With this definition for U, Eq. (4.4) can be rewritten as

Qe

nb UE

I

2

20

ss c

2

ionizations atom cm

6.51 10

//

/

−

× −

() ()

= () lloges()cU

(4.6)

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 sev-

eral different elements, the initial overvoltage U 0 will be dif-

ferent 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 elas-

tic 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

. Table 4.1 Correspondence between the Siegbahn and IUPAC nomenclature protocols (restricted to characteristic X-rays observed
with energy dispersive X-ray spectrometry and photon energies from 100 eV to 25 keV)

Siegbahn IUPAC Siegbahn IUPAC Siegbahn IUPAC

Kα 1 K-L 3 Lα 1 L 3 -M 5 Mα 1 M 5 -N 7

Kα 2 K-L 2 Lα 2 L 3 -M 4 Mα 2 M 5 -N 6

Kβ 1 K-M 3 Lβ 1 L 2 -M 4 Mβ M 4 -N 6

Kβ 2 K-N2,3 Lβ 2 L 3 -N 5 Mγ M 3 -N 5

Lβ 3 L 1 -M 3 Mζ M4,5-N2,3

Lβ 4 L 1 -M 2 M 3 -N 1

Lγ 1 L 2 -N 4 M 2 -N 1

Lγ 2 L 1 -N 2 M 3 -N4,5

Lγ 3 L 1 -N 3 M 3 -O 1

Lγ 4 L 1 -O 4 M 3 -O4,5

Lη L 2 -M 1 M 2 -N 4

Ll L 3 -M 1

Chapter 4 · X-Rays