ASNT

original kinetic energy, E 0 , diminished by the binding energy of the inner shell election, E b . The remaining energy is less, so the wavelength is longer and the frequency is lower, by using

RADIATION EMERGING FROM THE TARGET Two processes affect the spectrum of the radiation emerging from a thick, dense target. One is the electron penetration into the target material before emitting X-radiation. The second is absorption of radiation by the target material as the X-rays make their way from the depth of X-ray emission to the target surface. This absorption is dependent upon the X-ray energy, the target material properties such as density, and Z , which is the identity of the material. Electron Penetration into the Target The depth of penetration of the electron into the target material, R in µm, can be parameterized as R = (4120 / ρ ) × E (1.265 - 0.0954 ln E ) , where ρ is the target density (g/cm 3 ), and E is in MeV, as shown in Figure 4 (Kaplan 1955). This means that there is a range of depths from which X-rays are emitted within the solid target. The generated X-rays must travel through the target material before reaching the surface to illuminate the object under inspection. Absorption of the X-rays by this material is said to "harden" the X-ray spectrum by preferentially removing lower-energy X-rays from the spectrum. ATTENUATION OF X-RADIATION BY MATTER The attenuation law of X-rays expresses the effect of three different X-ray photon energy loss mechanisms: photoelectric, compton scattering, and pair production. These act in overlapping energy ranges and produce different effects as illustrated in Figure 5 (Berger et al. 2010). As the energy of incident photons increases from a small value to a large value, absorption increases when the X-ray photon has sufficient energy to eject an atomic electron. As these energy absorption mechanisms

1000 1200 1400

200 400 600 800

Range (µm)

–200 0

0

1 3 Incident electron energy (MeV) 4 5 2

6

Figure 4 Range of electrons in solid pure tungsten at incident energies from 10 keV to 10 MeV. Incident electron energy range of interest is 50 keV to 450 keV for industrial tubes where the range varies from 3 µm to 75 µm.

M shell edge

1.E+04 1.E+03 1.E+02 1.E+01 1.E+00 1.E–01 1.E–02 1.E–03 1.E–04 1.E–05 1.E–06

L shell edge

K shell edge

Photon energy (MeV)

0.010 0.100 Total absorption cross section (cm 2 /g) 1.000

10.000

0.001

Legend Total absorption cross section in cm2/g vs photon energy (MeV) Photoelectric absorption Compton (incoherent) scattering Coherent scattering Pair production Figure 5 Contributions to total photon absorption cross section as a function of energy. Absorption coefficient µ/ ρ for tungsten as cm 2 /g over a range of X-ray energy 1 keV to 100 MeV. Discontinuities at approximately 2 keV, 10 keV and 70 keV reflect the M, L, and K-edges, respectively.

become possible, the observed absorption coefficient increases (Berger et al. 2010).

a. Photoelectric absorption refers to absorption of the photon’s energy by the electrons in the atom. The photon’s energy can eject an inner-shell electron and emerge from the atom with its

CHAPTER 2

44

Part 2