Lattice dynamics of Al-containing MAX-phase carbides: A first-principle study

A systematic study on lattice dynamics of M_{n + 1}AlC_n (n = 1-3) phases using first-principle calculations is reported, where the Raman-active and infrared-active (IR) modes are emphasized. The highest phonon wavenumber is related to the vibration of C atoms. The 'imaginary wavenumber' in the phonon spectrum of Nb₃AlC₂ contributes to the composition gap in Nb-Al-C system (Nb₂AlC and Nb₄AlC₃ do appear in experiments, but there are no experimental reports on Nb₃AlC₂). The full set of Raman-active and IR-active modes in the 211, 312, and 413 M_{n + 1}AX_n phases is identified, with the corresponding Raman and IR wavenumbers. The 211, 312, and 413 M_{n + 1}AX_n phases have 4, 6, and 8 IR-active modes, respectively. There is no distinct difference among the wavenumber ranges of IR-active modes for 211, 312, and 413 phases, with the highest wavenumber of 780 cm^-1 in Ta₄AlC₃. The Raman wavenumbers of M₂AlC phases all decrease with increasing the d-electron shell number of transition metal M. However, this case is valid only for the Raman-active modes with low wavenumbers of M₃AlC₂ and M₄AlC₃.