# Electromagnetic Radiation Shielding Using Carbon Nanotube and Nanoparticle Composites
## 6 Example: Design of a CNT-Nanoparticle Material for Photon Attenuation  
This section presents an example of designing a material for photon attenuation at energy levels in the X-ray and higher frequency range. The number of photons in a beam that interact in an absorber per unit time is called the intensity, \(I\) (e.g., gamma rays/sec). If the initial intensity is designated as \(I_{o}\), the reduction in intensity is related to the likelihood of photon interaction per unit pathlength, where  
\[I=I_{o}e^{-\mu x} \tag{1}\]  
and \(x\) (cm) is the thickness of the absorber and \(\mu\) (cm\({}^{-1}\)) is the linear attenuation coefficient. Values of \(\mu\) depend upon the photon energy and the absorber material. If the absorber is fabricated as a mixture of atoms, values of \(\mu\) are calculated as the weighted percentage content of each element in the mixture. The attenuation of photons in an n-layer composite is thus given by the ratio of the transmitted to the incident photons:  
\[I/I_{o}=e^{-\sum_{i=1}^{n}\mu_{i}x_{i}} \tag{2}\]  
where \(\mu_{i}\) is the attenuation coefficient for the _ith_ component material and \(x_{i}\) is the thickness of the _ith_ layer. This model of attenuation is based on the type and thickness of material. It does not depend on the configuration of the material. The National Institute for Standards and Technology (NIST) offers tables of values for \(\mu/\rho\) (cm\({}^{2}\)/g) which is called the mass attenuation coefficient. The mass attenuation coefficient is related to the photon interaction cross-section, \(\sigma\), that is described in [85]. Consider an absorber fabricated from a pure carbon material, \({}_{6}\)C [12]. Figure 3a illustrates how the mass attenuation coefficient, \(\mu/\rho\), decreases with an increasing photon energy in the energy range from 10 keV up to 10\({}^{4}\) MeV. The mass attenuation coefficient represents the interaction probability and decreases with increasing photon energy. Thus, the likelihood of the photon being absorbed or scattered by the target decreases significantly as photon energy increases. Data for the C (100%) material are as follows. The Atomic Number and Fraction by Weight are: carbon \(Z=6\): 1.0. Density of C = 2.26 g/cc. Table 2 gives attenuation coefficients for C material in the lower energy range. Using the data in Table 2, Figure 3b was produced and shows the relative intensity, \(I/I_{o}\), of photons with energies between 0.010 MeV and 1 MeV as they penetrate increasingly thick carbon-only targets, where _Io_ is the initial intensity of the photon beam, and \(I\) is the intensity after penetrating the carbon target having a thickness \(x\) cm. It is apparent that mainly low-energy photons are attenuated by carbon targets. \begin{table}
\begin{tabular}{l l l l l l} \hline Energy (MeV) & 0.01 & 0.05 & 0.08 & 0.5 & 1.0 \\ \hline Mass attenuation coefficient (cm\({}^{2}\)/g) & 2.37 & 0.187 & 0.161 & 0.0872 & 0.064 \\ \hline Linear attenuation coefficient (1/m) & 5.363 & 0.423 & 0.364 & 0.197 & 0.144 \\ \hline \end{tabular}
\end{table} 
Table 2: Attenuation coefficients for solid C material. The above analysis demonstrates that carbon does not significantly attenuate photons with energy greater than 1 MeV. Thus, particles or fibers must be added to CNT fabric to attenuate high-energy photons. As an example, W particles can be added to CNT fabric during the CNT synthesis process. Fe is also present in the CNT fabric from the residual catalyst. Figure 4a shows the mass attenuation coefficient for a C-Fe-W composite mixture material. This material represents a solid C-Fe-W material. The objective of using CNT hybrid fabric is to achieve significant attenuation using a lightweight material. CNTs are not solid materials and thus may behave differently than solid C analyzed in XCOM [85]. Integrating nanoparticles into a CNT fabric provides a large surface area to scatter photon radiation. The Fe and W greatly increase the linear attenuation coefficient compared to C, but the mass attenuation coefficient is similar at high energies.