# Electromagnetic Radiation Shielding Using Carbon Nanotube and Nanoparticle Composites
## 6 Example: Design of a CNT-Nanoparticle Material for Photon Attenuation
### Material Design Based on Compton Scattering  
Compton scattering is a reaction that involves the partial absorption of X-rays or gamma rays that are in the middle energy range. The X-rays or gamma rays give up some of their energy as they strike an outer-shell electron in an absorbing material. Nanoparticles, particularly those made from high-atomic-number elements with a high electron density, like lead, bismuth, and tungsten, can attenuate X-ray and gamma radiation. These nanoparticles can be incorporated into composites for radiation shielding. A CNT fabric with nanoparticles inside potentially offers better protection on a per weight basis than traditional shielding materials like lead alone. However, the effectiveness of CNT composites depends on the specific nanoparticle composition, size, shape, and concentration within the material. The energy of a Compton scattered photon depends upon the energy of the incident photon and the angle of scatter, where the energy is given as  
\[E=\frac{E_{o}}{\frac{E_{o}}{0.511}(1-cos\theta)-1} \tag{3}\]  
where \(E_{o}\) is the energy of the incident photon, and \(\theta\) is the scattering angle of the photon. Thus, the photon scattering angle following a Compton interaction is determined only by the difference in energy between the incident and scattered photons. The probability of an interaction is dependent upon the incident photon energy and the type of absorber material. In Compton scattering, the photon interacts with a single electron, and the scattering angle is calculated based on the electron's mass and the incident photon's energy, not the properties of the atom or material to which it is bound. The photon primarily interacts with loosely bound electrons in the outer shells of atoms. This means that the Compton wavelength shift (the change in wavelength after scattering) is the same for all materials, as it only depends on the scattering angle and the electron's properties. The probability of Compton scattering occurring within a material does depend on the bulk  
Figure 4: Radiation attenuation characteristics of C-Fe-W material based on total coherent scattering. (**a**) Mass attenuation coefficient (cm\({}^{2}\)/g) versus photon energy (MeV) for C-Fe-W material. Here, C is 24%, Fe is 6%, and W is 70% of the material weight. Figure generated using XCOM. (**b**) Photon attenuation versus material thickness for different photon energy levels. A ratio of 1 means there is no attenuation. The green curve in Figure (**b**) is an overlay of three curves that represents attenuation due to lower energy photons, viz, 0.01 MeV, 0.05 MeV, and 0.08 MeV. material properties. The higher the electron density in a material, the more likely it is for a Compton scattering event to occur. While not directly affecting the scattering angle, the atomic number of the material can influence the probability of Compton scattering due to its correlation with electron density. During the collision, the photon transfers some of its energy to the electron, causing the electron to recoil. The scattered photon has a longer wavelength (lower energy) compared to the original photon. The angle at which the photon is scattered depends on the energy transfer and is described by the equation  
\[\lambda_{2}-\lambda_{1}=2\pi\text{h}(1-\text{cos}\theta)/(\text{mc}) \tag{4}\]  
where \(\lambda_{2}-\lambda_{1}\) are the wavelength of the photon after and before the collision, respectively, h is [PERSON]'s constant, m is the mass of an electron, c is the speed of light, and \(\theta\) is the photon scattering angle. Note that the angle \(\theta\) is not a direct function of the material properties. The angle is modeled using the Klein-Nishina formula [88]. These formulas are not very useful to optimize the atomic cross-sections of materials to control Compton scattering and to block radiation. The equations that define gamma ray cross-sections are given in Wikipedia. The cross-sections can be computed using NIST XCOM software, version 1.5, November 2010.