Physical properties of the recently discovered Zr₂(Al_1−x Bi _x )C MAX phases

In this study we investigate the structural, electronic and optical properties of the recently synthesized bismuth based Zr₂(Al_1−x Bi _x )C MAX phases. It is revealed that the inclusion of Bi in the A site causes an increase of lattice constant a, whereas the lattice constant c decreases with increasing Bi content x up to 0.58. The c values are more influenced than the a values while Al is substituted by Bi, which implies that the c value is more dependent on the M–A bonds than the M–X bonds. The calculated band structures imply that the electrical conductivity along the c direction should be small enough compared to that in the ab plane. The low density of states (DOS) around the Fermi level indicate that Zr₂(Al_1−x Bi _x )C should be stable in view of the electronic structure. The total DOS at the Fermi level increases almost linearly with the increase of the Bi content x between 0.25 and 0.75. The Mulliken atomic population calculations indicate that the Zr–C bonds are more covalent in Zr₂BiC than that of Zr₂AlC. The calculated Vickers hardness of Zr₂AlC and Zr₂BiC are calculated to be 5.96 and 1.94 GPa, respectively, implying that Zr₂BiC is relatively soft and easily machinable compared to Zr₂AlC. The calculated optical functions (dielectric constants, refractive index, extinction coefficient, absorption coefficient, loss function, reflectivity, and optical conductivity) show the dependence on the polarization directions.