Anisotropy of elasticity and minimum thermal conductivity of monocrystal M₄AlC₃ (M=Ti, Zr, Hf)

The elastic constants, elastic anisotropy index, and anisotropic fractional ratios of Ti₄AlC₃, Zr₄AlC₃, and Hf₄AlC₃ are studied by using a plane wave method based on density functional theory. All compounds are characterized by the elastic anisotropy index. The bond length, population, and hardness of the three compounds are calculated. The degrees of hardness are then compared. The minimum thermal conductivity at high temperature limitation in the propagation direction of 0001 (0001) is calculated by the acoustic wave velocity, which indicates that the thermal conductivity is also anisotropic. Finally, the electronic structures of the compounds are analyzed numerically. We show that the bonding of the M₄AlC₃ lattice exhibits mixed properties of covalent bonding, ionic bonding, and metallic bonding. Moreover, no energy gap is observed at the Fermi level, indicating that various compounds exhibit metallic conductivity at the ground state.