The vibrational modes of three solid AlF3 phases (alpha, beta, and amorphous high surface area AlF3) are investigated. Calculations have been performed using hybrid exchange correlation functionals to determine the equilibrium geometries and Gamma-point phonon frequencies for the alpha-AlF3 and beta-AlF3 phases. The calculated optical modes are in excellent agreement with experiment. The IR absorption of the amorphous, glasslike high surface area (HS)-AlF3 is also discussed. Deconvolution of the broad envelope of IR stretches and bending vibrations identifies the components of the observed broad band. From the IR vibrational spectrum it has been shown that both short-range and medium-range disorder are present within HS-AlF3. Structural phase transitions are identified by their phase transition temperature T-c, measured by thermal analysis.