eLearning

W. Y. Ching,
Lizhi Ouyang,
Paul Rulis,
and Hongzhi Yao1
Department of Physics, University of Missouri-Kansas City, Kansas City, Missouri 64110, USA

Department of Physics and Mathematics, Tennessee State University, Nashville, Tennessee 37211, USA

Based on the most recently determined noncubic structure for
-Al2O3 by Menendez-Proupin and Gutierrez,
a comprehensive list of physical properties is investigated theoretically. These include lattice dynamics and
phonon spectra, elastic constants and bulk structural parameters, electronic structure and interatomic bonding,
optical properties, and x-ray absorption near-edge structure
XANES spectra. Compared to similar calcula-
tions of -Al2O3, we find a smaller lowest zone-center vibrational mode at 97.6 cm−1
, a lower heat capacity,
a smaller bulk modulus, and a much larger thermal-expansion coefficient. The threefold bonded O ions intro-
duce highly localized vibrational modes near 751 cm−1
. The calculated thermal Grüneisen parameter indicates
a strong anharmonicity in
-Al2O3. The elastic tensor and the elastic wave velocities are also evaluated
showing the longitudinal wave to be nearly isotropic. For the electronic structure, we find that
-Al2O3 has a
smaller band gap but a refractive index similar to -Al2O3. Highly localized states at the top of the valence
band originating from threefold bonded O in the more covalently bonded AlO4 tetrahedra are identified. The
calculated Mulliken effective charges and bond order values indicate that the structural model for
-Al2O3 has
a high degree of disorder. The octahedral unit
AlO6 is a stronger polyhedron than the tetrahedral unit
AlO4
although the latter has stronger Al–O bonds. The calculated Al-K,Al-L3, and O-K edges for Al and O in

-Al2O3 show strong dependence on their local coordination and environments. These results are in good
agreement with available experimental data but the effect of the
-Al2O3 samples’ porosity should be properly
assessed. It is argued that the traditional view that stoichiometric
-Al2O3 is a defective spinel with cation
vacancies
or its variations should be modified.
-Al2O3 is better described as an amorphous networklike
structure such that the ratio of tetrahedrally coordinated Al to octahedrally coordinated Al is close to 0.6; and
the O ions are bonded to Al in either a threefold or fourfold configurations in about equal proportion.

I. INTRODUCTION
Alumina
Al2O3 is one of the most important structural
ceramics with vast applications in a variety of industrial sec-
tors ranging from pharmaceutical products and paint pig-
ments to thermobarrier coatings and microelectronic devices,
and much more.
1–4 Alumina exists in many different forms
with corundum
-Al2O3 being the most thermodynami-
cally stable phase. The process of reaching -Al2O3 involves
many intermediate phases or the so-called transition alumi-
nas
-,
-, -, -, -, -, etc..
5,6
Among these transition
alumina,
-Al2O3 is the most prominent and well studied
because of its important application as a catalyst or catalytic
support.
7–12
It also frequently occurs at ceramic interfaces or
as a minor component in multiphase Al-containing ceramics
such as in the Ca-Al-O and Al-Si-O systems.
In spite of many recent experimental
13–21
and
theoretical
22–36
studies of
-Al2O3, there are continuing de-
bates about its structure and properties.
-Al2O3 does not
exist in the pure single-crystal form. The samples obtained
are usually porous with large surface areas. The traditional
view of the structure of
-Al2O3 is that of a defective cubic
spinel with cation vacancies,
37 or the spinel lattice model. In
the spinel lattice AB2O4, where A is the tetrahedral cation
site and B the octahedral cation site, vacancies are required
at the cation sites in order to fit the exact stoichiometric
formula of Al2O3. There were then debates as to whether the
vacancy should occur at the A site or the B site or
both.
22–24,26
The issue of the presence of H in
-Al2O3 has
also been raised. However, it has been ruled out by extensive
simulation on spinel based models.
25
The spinel lattice model
has been challenged recently28,32,34,35
and models with
tetragonal
28 and monoclinc35 structures have been suggested.
Very recently, it is noted that the spinel model was still being
defended on the basis of x-ray powder-diffraction patterns,
36
but this argument was soundly refuted as due to problems
with the samples.
38,39
The common underlying message is
that Al occupies both the octahedral and tetrahedral sites in
the lattice. Recently, more rigorous theoretical simulations
suggest that that structure of
-Al2O3 is not a spinel with
cation vacancy, but is instead a low-symmetry crystal struc-
ture with a space group of I41/amd in which Al ions can have
both tetrahedral and octahedral coordination.
30
In this struc-
ture, the notion of ionic vacancy becomes less clear and an
alternative description in terms of local bonding is more ap-
propriate. Unlike -Al2O3 with a rhombohedral lattice,
where O ions are always fourfold bonded, the O ions in

-Al2O3 can be either threefold or fourfold bonded, a fact
shared by many other transition alumina such as -Al2O3 and
-Al2O3,
6,40
but seldom discussed. Thus, a proper descrip-
tion of the structure of
-Al2O3 should include the ratios of
Altet
/Aloct
and O3-fold /O4-fold. As a matter of fact, it is con-
ceivable that amorphous Al2O3
a-Al2O3 can be viewed as a
continuous random network with a variety of total Al and O
local bonding environments connected in a random
fashion.
41 The specific local cation/anion coordination pro-