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Vibrational spectra of am-Al 2 O 3 : tuning a parametric model. : Written report: in fulfillment of Diploma Seminar 1FAF29 requirementsKurtović Jasmin, 2021, research project (high school)

**Abstract:** The present diploma seminar work has been dedicated first to the implementation of a procedure
to calculate the vibrational density of states of two structural models of vitreous SiO 2 (v-
SiO 2 ) and amorphous Al 2 O 3 (am-Al 2 O 3 ) models, and next to tune a parametric model for the
calculation of the infrared (IR) spectra of am-Al 2 O 3 , in particular of the imaginary part of
the dielectric function. The ground state of both structural models is obtained by relaxing
the atomic structure by using the conjugate gradient method as implemented in the LAMMPS
code. Vibrational frequencies and modes are obtained, in the harmonic approximation, by
diagonalizing the dynamical matrices calculated for the given v-SiO 2 and am-Al 2 O 3 structural
models. Dynamical matrices are obtained through a finite differences approach and vibrational
density of states are plotted by applying Gaussian broadening. The calculation of the dielectric
function requires the knowledge of the vibrational frequencies as well as the knowledge of the
dynamical (or Born) charge tensors related to the atoms of the am-Al 2 O 3 structural model.
For the latter model, a parametrization of the ab-initio Born charge tensors has been carried
out with the purpose to allow for the fast calculation of the IR spectrum of any other am-
Al 2 O 3 model without the need to calculate for it the Born charge tensors using expensive ab-
initio methods. The parametrization of Born charge tensors takes into account, for aluminium
atoms, only of the isotropic charge which depends on coordination number and average Al-
O bond length of aluminium atoms, while for oxygen atoms coordinated to three Al atoms
(75%), dynamical charges are parametrized also by the area bounded by aluminium atoms
nearest neighbours of the 3-coordinated oxygen atom. Moreover for analyzing the dynamical
charge tensors of 3-coordinated oxygen atoms a decomposition in terms of the representations
of the spatial rotations was used. The IR spectrum obtained by means of the above described
parametrization provides a good approximation to the IR spectrum obtained by using the ab-
initio calculated dynamical charges, as it differs from it, on average, by around 5.1% which
is much better (12%) than using a average isotropic charge model (i.e. diagonal Born charge
tensors where each diagonal element is one third of the average isotropic charge).

**Keywords:** Vibrational spectra, am-Al 2 O 3, parametric model

**Published in RUNG:** 15.09.2021; **Views:** 2634; **Downloads:** 0

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