Title:  Vibrational spectra of amAl 2 O 3 : tuning a parametric model. : Written report: in fulfillment of Diploma Seminar 1FAF29 requirements 

Authors:  Jasmin, Kurtović (Author) Luigi, Giacomazzi (Mentor) More about this mentor... 

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Language:  Slovenian 

Work type:  Research project (high school) (p5) 

Organization:  FN  School of Science 

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 (amAl 2 O 3 ) models, and next to tune a parametric model for the
calculation of the infrared (IR) spectra of amAl 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 vSiO 2 and amAl 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 amAl 2 O 3 structural model.
For the latter model, a parametrization of the abinitio 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 3coordinated oxygen atom. Moreover for analyzing the dynamical
charge tensors of 3coordinated 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, amAl 2 O 3, parametric model 

Year of publishing:  2021 

Number of pages:  36 str 

COBISS_ID:  76519427 

URN:  URN:SI:UNG:REP:YGKTMCYZ 

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