![]() Anderson: Calculated strain energy of hexagonal epitaxial thin films. Cohen: Relaxation of crystals with the quasi-newton method. Pack: Special points for Brillouin-zone integrations. Fiolhais: Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Vanderbilt: Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Payne: First-principles simulation: Ideas, illustrations and the CASTEP code. Li: Raman active phonon modes and heat capacities of Ti 2AlC and Cr 2AlC ceramics: First-principles and experimental investigations. Zhou: Dependence of elastic stiffness on electronic band structure of nanolaminate M 2AlC (M=Ti, V, Nb, and Cr) ceramics. Barsoum: The M N+1AX N phases: A new class of solid. Wang: Atomic-scale microstructures of Zr 2Al 3C 4 and Zr 3Al 3C 5 ceramics. He: First-principles prediction of mechanical properties and electronic structure of ternary aluminum carbide Zr 3Al 3C 5. Vaccaro: The ternary systems: Cr-Al-C, V-Al-C, and Ti-Al-C and the behavior of H-phases (M 2AlC). Hashimoto: Crystal structure of Zr 2Al 3C 4. Nowotny: Investigations of the ternary systems (Zr, H, Nb, Ta)-Al-C and studies on complex carbides. Jeitschko: The crystal structures of Zr 3Al 3C 5, ScAl 3C 3, and UAl 3C 3 and their relation to the structures of U 2Al 3C 4and Al 4C 3. 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. We also present close relationships between the atomic radii of transition metal and lattice mismatch, as well as the strain energy. Moreover, the discrepancy between crystal structures of T nAl 3C n+2 and T n +1AlC n is interpreted by lattice mismatch and the produced strain energy for the ternary T-Al-C ceramics. ![]() Ternary carbides following the T nAl 3C n+2 formula experience small lattice mismatches and strain energies. In the present study, we suggest that the ability of forming the T nAl 3C n+2 carbide could be traced back to the structure mismatches between the TC, Al 4C 3 and T nAl 3C n+2 compounds. ![]() Ternary T nAl 3C n+2 ceramics are structurally characterized by NaCl-type TC slabs being separated by Al 4C 3-type AlC layers. Layered ternary T-Al-C ceramics containing early transition metal Sc, Zr, and Hf, crystallize with the T nAl 3C n+2 formula, while others containing neighbor elements Ti, V, Cr, Nb, Mo, W, and Ta yield the T n +1AlC n formula. ![]()
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