First-Principles Study of Vacancies in Ti₃SiC₂ and Ti₃AlC₂

MAX phase materials have attracted increased attention due to their unique combination of ceramic and metallic properties. In this study, the properties of vacancies in Ti₃AlC₂ and Ti₃SiC₂, which are two of the most widely studied MAX phases, were investigated using first-principles calculations. Our calculations indicate that the stabilities of vacancies in Ti₃SiC₂ and Ti₃AlC₂ differ greatly from those previously reported for Cr₂AlC. The order of the formation energies of vacancies is V_Ti(a) > V_Ti(b) > V_C > V_A for both Ti₃SiC₂ and Ti₃AlC₂. Although the diffusion barriers for Ti₃SiC₂ and Ti₃AlC₂ are similar (~0.95 eV), the properties of their vacancies are significantly different. Our results show that the vacancy-vacancy interaction is attractive in Ti₃AlC₂ but repulsive in Ti₃SiC₂. The introduction of V_Ti and V_C vacancies results in the lattice constant c along the [0001] direction increasing for both Ti₃SiC₂ and Ti₃AlC₂. In contrast, the lattice constant c decreases significantly when V_A are introduced. The different effect of V_A on the lattice constants is explained by enhanced interactions of nearby Ti layers.