Structural inheritance and difference between Ti₂AlC, Ti₃AlC₂ and Ti₅Al₂C₃ under pressure from first principles

The structural inheritance and difference between Ti2AlC, Ti3AlC2 and Ti5Al2C3 under pressure from first principles are studied. The results indicate that the lattice parameter a are almost the same within Ti2AlC, Ti3AlC2 and Ti5Al2C3, and the value of c in Ti5Al2C3 is the sum of Ti2AlC and Ti3AlC2 which is revealed by the covalently bonded chain in the electron density difference: Al–Ti–C–Ti–Al for Ti2AlC, Al–Ti2–C–Ti1–C–Ti2–Al for Ti3AlC2 and Al–Ti3–C2–Ti3–Al–Ti2–C1–Ti1–C1–Ti2–Al for Ti5Al2C3. The calculated axial compressibilities, volumetric shrinkage, elastic constant [Formula: see text], [Formula: see text] ratio, bulk modulus, shear modulus, and Young’s modulus of Ti5Al2C3 are within the range of the end members (Ti2AlC and Ti3AlC2) in a wide pressure range of 0–100 GPa. Only Ti2AlC is isotropic crystal at about 50 GPa within the Ti–Al–C compounds. All of the Ti 3d density of states curves of the three compounds move from lower energy to higher energy level with pressure increasing. The similarities of respective bond length, bond overlap population (Ti–C, Ti–Al and Ti–Ti), atom Mulliken charges under pressure as well as the electron density difference for the three compounds are discovered. Among the Ti–Al–C ternary compounds, Ti–Ti bond behaves least compressibility, whereas the Ti–Al bond is softer than that of Ti–C bonds, which can also been confirmed by the density of states and electron density difference. Bond overlap populations of Ti–Ti, Ti–C and Ti–Al indicate that the ionicity interaction becomes more and more stronger in the three structures as the pressure increasing. Mulliken charges of Ti1, Ti2, Ti3, C and Al are 0.65, 0.42, 0.39, −0.73, −0.04 at 0 GPa, respectively, which are consistent with the Pauling scale.