γ-Ray, Charged Particle, and Neutron Attenuation Characteristics of Cadmium-Containing 211 MAX Phase Carbides, M ₂ CdC (M = Ti, Zr, and Hf)

This study examines the attenuation behavior of γ rays and both charged (proton, α, electron) and uncharged (neutron) particles in cadmium-containing Group 4 MAX phase carbides: Ti₂CdC, Zr₂CdC, and Hf₂CdC. Key parameters such as the linear attenuation coefficient (LAC), atomic cross section (ACS), electronic cross section (ECS), half-value layer (HVL), mean free path (MFP), effective atomic number (<i>Z</i> _eff), and energy absorption buildup factor (EABF) were evaluated for γ-ray interactions. Among the studied materials, Hf₂CdC, with a density of 12.67 g/cm³, exhibited superior γ-ray shielding performance, reflected in its high LAC and low HVL and MFP. Its effectiveness is comparable to that of conventional shielding materials such as lead (Pb). Notably, Hf₂CdC demonstrated an HVL of 0.968 cm at 1173 keV, outperforming Pb (0.990 cm) at the same energy. This enhanced performance at γ energies dominated by Compton scattering is primarily attributed to its high density. For charged particles, Ti₂CdC showed the highest mass stopping power for protons and α particles. However, due to its higher density, Hf₂CdC resulted in the shortest penetration depths; for example, 10 MeV protons had a penetration range of only 1.77 μm in Hf₂CdC. Additionally, Hf₂CdC exhibited a high fast neutron removal cross section (FNRCS) of 0.163 cm^-1, significantly outperforming common neutron shielding materials such as B₄C, graphite, and concrete. Furthermore, all three compounds demonstrated excellent thermal neutron absorption due to the presence of cadmium (Cd), with Hf₂CdC achieving the highest thermal neutron LAC of 43.38 cm^-1. These results identify Hf₂CdC as a strong candidate for integrated, multipurpose radiation shielding applications.