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tion. The partial DOS
PDOS for the two types of Al and
two types of O are shown in Fig. 8. It can be seen that there
are enormous differences between the PDOS of Altet
and
Aloct
, and also between O3-fold and O4-fold. For Al, the main
differences are in the CB whereas for O, the differences are
mostly in the VB region. Altet
has a huge peak at 7.3 eV in
the lower CB region and another peak at 13.7 eV. From
orbital-resolved PDOS
not shown, it is revealed that the
lower peak involves strong hybridization of Al-p and Al-3d
orbitals whereas the higher peak predominately originates
from the 3d orbitals. The Aloct
has a completely different CB
DOS, featuring two main peaks at 11.5 and 13.7 eV. The
orbital origins of these peaks are states dominated by Al-3d
and Al-4p orbitals, respectively. These different features in
the CB DOS are also reflected in the different XANES/
ELNES spectra to be discussed in Sec. V.
The PDOS for the O can be clearly divided into two seg-
ments, the upper 2p band
0 to −8.8 eV and the lower 2s
band
−16.4 to −20.4 eV. The spectral weights of the O3-fold
and O4-fold in these two regions and their peak positions are
different. By having one more bond, O4-fold has peaks in the
PDOS at a lower binding energy than does O3-fold, so, the
O-2s peaks are centered at −18.5 and −17.1 eV, respec-
tively. The top of the VB is derived mostly from the 2p states
of O3-fold. The peak structures and their binding energies can
be easily revealed by x-ray photoelectron
XPS or soft x-ray
emission spectroscopy. However, it takes theoretical results
to resolve them into partial components of atoms with differ-
ent local coordination. The VB DOS is in good agreement
with the XPS data of Ealet et al.
19 Our calculated DOS and
PDOS have minor deviations from that of Digne et al.
35
which can be attributed to the difference in the structural
models used for
-Al2O3.
Figure 9 shows the localization index Ln of each electron
state n across the energy range according to:

where Ci are the eigenvector coefficients for the n state
with orbital and atomic specifications of i and . Each data
point is the average of the states over all k points in the BZ.
Ln is used mostly to characterize electron states of amor-
phous systems using large structural models.
74–76
For a non-
crystalline solid, the states near the band edges are usually
more localized. It is interesting to note that even with only
40 atoms in the cell, the Ln shows the states at the top of the
VB to be highly localized, indicating that
-Al2O3 resembles
more of an amorphous glass than an inorganic crystal. In-
spection of the wave functions
also from the PDOS of Fig.
8 reveals that the two highly localized states at the top of the
VB originate from two of the 12 O3-fold atoms
labeled with
atom number 19 and 21. What makes these two O3-fold at-
oms different from the others such that they are responsible
for the highly localized electron states at the top of the VB?
We found that these two atoms experience the least signifi-
cant charge transfer from Al, or that they have a more cova-
lent character to their bonding
see Fig. 10. These two atoms
are also the only O3-fold atoms in the tetrahedral units that
contain only one O3-fold ion, and they have a total bond order