LAUSR

We present a combined study based on experimental measurements of infrared (IR) dielectric function and first-principles calculations of IR spectra and vibrational density of states (VDOS) of amorphous alumina (am-Al$_2$O$_3$). In particular, we show that the main features of the imaginary part of the dielectric function $\epsilon_2(\omega)$ at $\sim$380 and 630 cm$^{-1}$ are related to the motions of threefold coordinated oxygen atoms, which are the vast majority of oxygen atoms in am-Al$_2$O$_3$. Our analysis provides an alternative point of view with respect to an earlier suggested assignment of the vibrational modes, which relates them to the stretching and bending vibrational modes of AlO$_{n}$ ($n=$ 4, 5, and 6) polyhedra. Our assignment is based on the additive decomposition of the VDOS and $\epsilon_2(\omega)$ spectra, which shows that: (i) the band at $\sim$380 cm$^{-1}$ features oxygen motions occurring in a direction normal to the plane defined by the three nearest-neighbor aluminum atoms, i.e. out-of-plane motions of oxygen atoms; (ii) Al--O stretching vibrations (i.e. in-plane motions of oxygen atoms) appear at frequencies above $\sim$500 cm$^{-1}$, which characterize the vibrational modes underlying the band at $\sim$630 cm$^{-1}$. Aluminum and fourfold coordinated oxygen atoms contribute uniformly to the VDOS and $\epsilon_2(\omega)$ spectra in the frequency region $\sim$350--650 cm$^{-1}$ without causing specific features. Our numerical results are in good agreement with the previous and presently obtained experimental data on the IR dielectric function of am-Al$_2$O$_3$ films. Finally, we show that the IR spectrum can be modeled by assuming isotropic Born charges for aluminum atoms and fourfold coordinated oxygen atoms, while requiring the use of three parameters, defined in a local reference frame, for the anisotropic Born charges of threefold coordinated oxygen atoms.