  We report on investigations of phonons and lithium diffusion in LiAlO$_2$
based on inelastic neutron scattering (INS) measurements of the phonon density
of states (DOS) in {\gamma}-LiAlO$_2$ from 473 K to 1073 K, complemented with
ab-initio molecular dynamics (AIMD) simulations. We find that phonon modes
related to Li vibrations broaden on warming as reflected in the measured phonon
DOS and reproduced in simulations. Further, the AIMD simulations probe the
nature of lithium diffusion in the perfect crystalline phase
({\gamma}-LiAlO$_2$), as well as in a structure with lithium vacancies and a
related amorphous phase. Almost liquid-like super-ionic diffusion is observed
in AIMD simulations of the three structures at high temperatures; with
predicted onset temperatures of 1800 K, 1200 K, and 600 K in the perfect
structure, vacancy structure and the amorphous phase, respectively. In the
ideal structure, the Li atoms show correlated jumps; while simple and
correlated jumps are both seen in the vacancy structure, and a mix of jumps and
continuous diffusion occur in the amorphous structure. Further, we find that
the Li-diffusion is favored in all cases by a large librational amplitude of
the neighbouring AlO4 tetrahedra, and that the amorphous structure opens
additional diffusion pathways due to a broad distribution of AlO4 tetrahedra
orientations.
