Fig. 6

PDOS analysis showing the effect of Li vacancies on vibrational spectra in γ-LiAlO2 and LiAl5O8. (a–c) PDOS for Li, Al, and O atoms in γ-LiAlO2, respectively, comparing the pristine structure with the defected structure containing Li vacancies. The removal of Li causes a suppression in low-frequency vibrational modes, particularly in the Li and Al sublattices, indicating enhanced phonon scattering. (d–f) Corresponding PDOS for Li, Al, and O atoms in LiAl5O8. While Li vacancies reduce the vibrational contributions of Li atoms, the effect on Al and O PDOS is less pronounced than in γ-LiAlO2, suggesting stronger structural resilience in LiAl5O8.