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tice, or equivalently, cation vacancies should be at the octa-
hedral site if the spinel lattice model for
-Al2O3 is adopted.
This is consistent with an earlier investigation22
and with a
number of other studies.
24,26
In the spinel lattice, all O are
fourfold bonded. The creation of cation vacancies naturally
leads to threefold bonded O. The distribution of O coordina-
tion in
-Al2O3 has not been discussed in the past. In most
oxides, the likely O coordination is either twofold
bridging
such as in quartz, or fourfold as in -Al2O3. It may assume
sixfold coordination in some high-pressure phases such as in
stishovite. The threefold coordinated O is a special feature in
most transition alumina. The electronic structure and spec-
troscopic properties of crystals with threefold coordinated O
can be very different from those with twofold or fourfold
coordination.
40,44,45
Our calculations of the physical properties of
-Al2O3
using the above structure includes lattice dynamics and pho-
non spectra, temperature-dependent thermodynamic func-
tions, vibrational contribution to the free energy, bulk elastic
parameters and elastic wave velocities, electronic structure
and bonding, interband optical properties, and x-ray absorp-
tion near-edge structure
XANES spectra for Al and O with
different local coordinations. In principle, the XANES spec-
tra are similar to the electron energy-loss near-edge spectros-
copy
ELNES spectra and there are some limited experi-
mental XANES/ELNES measurements for
-Al2O3.
15–17
We
are not aware of any previous calculations of the phonon
spectrum of
-Al2O3 using a fully ab initio method. Lodiana
and Parlinski did the phonon calculations for -Al2O3 and
-Al2O3
Ref. 46 but not
-Al2O3. Very recently, Lee et al.
33
carried out electronic structure and dielectric properties cal-
culations of four alumina polymorphs including
-Al2O3.
They have also calculated the zone-center phonons in these
polymorphs. However, the structure they used for
-Al2O3 is
an earlier model structure,
26
different from the one we used
in the present calculation. Our results will be compared with
available experimental data and other existing calculations
whenever possible.
The paper is organized as follows. In Sec II, we describe
our calculations of the vibrational properties and present our
results on the thermodynamic functions of
-Al2O3.InSec
III, we present the elastic properties and bulk structural pa-
rameters for
-Al2O3 and compare them to -Al2O3.InSec
IV, we discuss the results of the electronic structure and
bonding calculated using the orthogonalized linear combina-
tion of atomic orbitals method
OLCAO.
47
The spectro-
scopic properties which include the valence-band optical
properties and the Al-K, Al-L3 and O-K edges of the XANES
are presented and discussed in Sec V. We further discuss
these results and their implications in Sec VI together with a
brief summary.

II. LATTICE DYNAMICS AND THERMO PROPERTIES
In recent years, it has become possible to calculate the
attice dynamic properties of crystals based on fundamental
ab initio electronic structures.
48 The lattice dynamics of

-Al2O3 were studied within the qausiharmonic approxima-
ion
QHA by calculating the phonon spectrum using a first-