X-Ray Inspection of Lead and Lead-Free Solder Joints

Estimated reading time: 13 minutes

where I is the intensity of the X-rays transmitted through the subject, I₀ is the original intensity of the X-rays incident on the object, μ is the linear attenuation coefficient of the object, and x is the thickness of the object, as seen also in Figure 3.

Figure 3: X-ray photons passing through a homogeneous attenuating (μ) material of constant thickness (x).

Therefore, absorption of X-rays by a material is dependent on the thickness of the material and on the material-dependent attenuation coefficient. Diagnostic X-rays can be absorbed by a material via two primary mechanisms: Compton scattering and the photoelectric effect.

Compton scattering occurs when an X-ray photon collides with an outer shell electron within the subject. Upon collision, the electron absorbs a portion of the X-ray energy and is ejected from the atom. The X-ray photon is deflected from its original direction and loses some energy. This scattering can occur in all directions and can lead to noise at the detector. The amount of Compton scattering that occurs within an object depends primarily on the energy of the incident X-ray photon and the density of the object. Compton scattering decreases slightly with increasing photon energy, so higher energy X-rays are better able to pass through a sample without attenuation. The density of outer shell electrons increases with the mass density of a material, so denser materials tend to have more Compton scattering and therefore more X-ray attenuation.

The photoelectric effect occurs when an X-ray photon transfers all of its energy to an inner shell electron within the subject. This electron is ejected from the atom and its vacancy is subsequently filled by an outer-shell electron, which leads to the release of a secondary photon. The photoelectric effect is highly dependent on both the energy of the incident X-ray and the atomic weight of the object. The photoelectric effect is strongest when the X-ray energy matches the binding energy of the inner-shell electrons. As X-ray energy increases, the likelihood of the photoelectric effect drops rapidly, proportional to the inverse cube of the X-ray energy (1/E3). If the X-ray energy is below the energy of a particular electron shell, then none of those electrons can participate in the photoelectric effect because the X-ray does not have enough energy to overcome the electron binding energy. This leads to the K-edge effect, where the probability of absorption due to the photoelectric effect jumps abruptly as the X-ray energy increases above the K shell electron binding energy. The photoelectric effect is also proportional to the cube of a material’s atomic number (Z3), so high atomic weight materials exhibit a much stronger photoelectric effect than low atomic weight materials. This is why contrast agents for CT traditionally include high atomic weight elements (e.g., iodine, barium). The K-edge effect is shown in Figure 4, which demonstrates the relative probability of X-ray photon attenuation at different X-ray energies for several high Z materials commonly found in lead and lead-free solder compounds.

Figure 4: Mass attenuation coefficients for various elements as a function of X-ray photon energy. Note the dominance of the photoelectric cross-section, followed by the Rayleigh and Compton cross-sections.

Many factors affect the attenuation of X-rays as they pass through a material. These “factors” are summarized in terms of a number of parameters known as scattering cross-sections, which may be loosely thought of as an effective capture area over which an X-ray photon experiences some type of scattering event. X-ray photons experience a variety of scattering interactions, including photoelectric, Compton, pair production, Rayleigh, and photonuclear^[2]. For the energy range in which the X-ray machine used in these experiments operates, photoelectric interactions are predominant, followed by Rayleigh and Compton. The parameter that provides all the information necessary to predict bulk attenuation properties is known as the attenuation coefficient. Scattering cross sections and attenuation coefficients have been measured for the elements and are readily available^[3,4].

Lead, for example, has a linear attenuation coefficient μ = 26.43 cm-1 for 80keV X-rays. (80keV is the middle of the energy spectrum in the TruView FUSION 150kV.) Thus, 1mm of lead reduces transmitted intensity to 7.1% of the incident intensity. The ability of a material to attenuate the X-rays produced by the X-ray machine depends primarily on three factors: 1) its atomic number, 2) its density, and 3) the frequency of the radiation. The photoelectric cross-section depends on these three factors approximately as

for hν below 100keV, where τ is the photoelectric cross-section, ρ is the density, Z is the atomic number, ν is the radiation frequency, and h is Planck’s constant. This expression indicates why lead and other high Z materials are such good attenuators of lower energy X-rays. Rayleigh scattering behaves as

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