Trend in crystal structure of layered ternary T-Al-C carbides (T = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, W, and Ta)

Layered ternary T-Al-C ceramics containing early transition metal Sc, Zr, and Hf, crystallize with the T_nAl₃C_n+2 formula, while others containing neighbor elements Ti, V, Cr, Nb, Mo, W, and Ta yield the T_n+1AlC_n formula. Ternary T_nAl₃C_n+2 ceramics are structurally characterized by NaCl-type TC slabs being separated by Al₄C₃-type AlC layers. In the present study, we suggest that the ability of forming the T_nAl₃C_n+2 carbide could be traced back to the structure mismatches between the TC, Al₄C₃ and T_nAl₃C_n+2 compounds. Ternary carbides following the T_nAl₃C_n+2 formula experience small lattice mismatches and strain energies. Moreover, the discrepancy between crystal structures of T_nAl₃C_n+2 and T_n+1AlC_n is interpreted by lattice mismatch and the produced strain energy for the ternary T-Al-C ceramics. We also present close relationships between the atomic radii of transition metal and lattice mismatch, as well as the strain energy. The proposed method is not only helpful to explain the trend in crystal structure of T-Al-C based ceramics, but may be also general to predict the crystal structure of layered compounds constructed by alternatively stacked structural units.