Alumina phases

Journal
J. Am. Ceram. Soc., 81 [8] 1995–2012 (1998)
Metastable Alumina Polymorphs: Crystal Structures and
Transition Sequences
Igor Levin*,† and David Brandon*
Faculty of Materials Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel
Because of their fine particle size, high surface area, and
catalytic activity of their surfaces, the transition aluminas (especially the ␥ form) find applications in industry as adsorbents,
catalysts or catalyst carriers, coatings, and soft abrasives. The
excellent stoichiometry and stability of Al2O3 help to make it
an important constituent of many protective oxide scales
formed on the surface of high-temperature metals and alloys.
The dominant (and stable) phase in these scales is ␣-Al2O3,
whose occurrence also dominates the adhesion and coherence
of the scale. Heat treatments designed to promote stable scale
formation depend on an understanding of the metastable intermediate polymorphic structures and the transformation mechanisms that result in the formation of ␣-Al2O3. An understanding of the mechanisms of polymorphic phase transformations
also is of major importance for the sintering of nanosized
Al2O3 powders, which are usually ␥-Al2O3 but transform during sintering to ␣-Al2O3. Both the sintering and the graingrowth behavior are related strongly to this phase transformation.
Extensive research has been reported over the past few decades characterizing the transition aluminas with respect to
dehydroxylation and the transformation mechanisms, porosity
and specific surface area, surface structure and chemical reactivity, and the defect crystal structure. However, poorly developed crystallinity and possible surface-energy stabilization
have made it difficult for advanced surface analytical techniques to probe such fine and irregular structures, and singlecrystal X-ray diffractometry (XRD) from such poorly ordered
structures is not feasible. The main tools used for the analysis
of the Al2O3 polymorphs were, therefore, powder XRD and
selected-area electron diffraction (SAD). Both methods suffer
from serious disadvantages when applied in isolation to such
complicated structures as the transition aluminas. These structures have very similar d-spacings, which makes difficult the
precise solution of the structure by XRD, especially because
the transformations appear to be continuous during heating,
with several phases coexisting in the samples. Moreover, the
phase transformations in Al2O3 are accompanied by changes in
symmetry that lead to a number of variants for both ␦- and
␪-Al2O3. It is impossible to include such detailed information
in polycrystal X-ray structure analysis, where the structure is
‘‘averaged’’ over many crystals. Conventional transmission
The available literature on the crystal structure of the
metastable alumina polymorphs and their associated transitions is critically reviewed and summarized. All the metastable alumina structures have been identified as ordered
or partially ordered cation arrays on the interstitial sites of
an approximately close-packed oxygen sublattice (either
face-centered cubic or hexagonal close packed). The analysis of the symmetry relations between reported alumina
polymorphs having an approximately face-centered cubic
packing of the oxygen anions allows for an exact interpretation of all the complex domain structures that have been
observed experimentally. Possible mechanisms for the
phase transitions between the different alumina polymorphs also are discussed.
I.
Introduction
A
LUMINUM OXIDE (alumina, Al2O3) exists in many metastable polymorphs besides the thermodynamically stable
␣-Al2O3 (corundum form). The metastable Al2O3 structures
can be divided into two broad categories: a face-centered cubic
(fcc) or a hexagonal close-packed (hcp) arrangement of oxygen
anions. It is the distribution of cations within each subgroup
that results in the different polymorphs.1 The Al2O3 structures
based on fcc packing of oxygen include ␥, ␩ (cubic), ␪ (monoclinic), and ␦ (either tetragonal or orthorhombic), whereas the
Al2O3 structures based on hcp packing are represented by the
␣ (trigonal), ␬ (orthorhombic), and ␹ (hexagonal) phases.
Some additional monoclinic Al2O3 phases have been identified
recently by the authors: ␪⬘, ␪⬙, and ␭.
D. E. Clarke—contributing editor
Manuscript No. 190604. Received October 28, 1997; approved April 16, 1998.
*Member, American Ceramic Society.
†
Present address: Ceramics Division, MSEL, NIST, Gaithersburg, MD 20889.
1995
1996
Table I.
Journal of the American Ceramic Society—Levin and Brandon
Vol. 81, No. 8
Common Processing Routes Resulting in Formation of Different Metastable Al2O3 Structures and the Sequences of
Phase Transformations toward the Stable ␣-Al2O3 Phase
Approximate packing of oxygen for the metastable Al2O3 structures
hcp
700°–800°C
␣-AlOOH (diaspore) → ␣-Al2O3
150°–300°C
650°–750°C
1000°C
␥-Al(OH)3(gibbsite) → ␹ → ␬ → ␣-Al2O3
700°–800°C
750°C
900°C
5Al2O3⭈H2O (tohdite) → ␬⬘ → ␬ → ␣-Al2O3
Vapor (CVD) → ␬ → ␣-Al2O3
fcc
300°–500°C
700°–800°C
900°–1000°C
1000°–1100°C
␥AlOOH (boehmite) → ␥ → ␦ → ␪ → ␣-Al2O3
200°–300°C
600°–800°C
1000°–1100°C
␣-Al(OH)3 (bayerite) → ␩ → ␪ → ␣-Al2O3
Amorphous (anodic film) → ␥ → ␦ → ␪ → ␣-Al2O3
Melt → ␥ → ␦,␪ → ␣-Al2O3
electron microscopy (TEM) can clarify some of these problems, but, unfortunately, electron diffraction contrast does not
provide information about the atomic positions in a crystal
structure. On the other hand, high-resolution electron microscopy (lattice imaging) can reveal the crystallographic relations
between the phases and allows the atomic structure to be determined through a comparison of the experimental images
with those calculated by computer simulation. Lattice imaging
of the interfaces between the Al2O3 polymorphs can provide
additional information about the transformation mechanisms.
However, until very recently, little high-resolution work on the
polymorphic phase transformations in Al2O3 has been reported,
and, as a result, the structure of most transition aluminas has
not been finally determined, nor are the mechanisms of the
polymorphic phase transformations understood.
The most comprehensive review of Al2O3 polymorphs is
that presented by Wefers and Misra1 in 1987. Since then, many
studies that have used modern experimental and theoretical
methods have reported on different aspects of polymorphism in
Al2O3. The goal of the present contribution is to provide an
updated review of the known metastable Al2O3 structures and
to summarize the current understanding of the mechanisms
involved in a number of the phase transformations.
II.
Common Processing Routes and Precursors for
Production of Transition Aluminas
Metastable Al2O3 phases commonly are obtained by one of
the processing routes summarized in Table I. Differences in the
phase transformation sequence usually are ascribed to differences in the precursor structure.2,3 The temperature ranges of
stability given for the transition aluminas are only approximate
and depend, among other things, upon the degree of crystallinity, the presence of impurities in the starting materials, and
the subsequent thermal history. All the phases observed in the
transition aluminas are reproducible and remain stable at room
temperature, but the sequence of transformations is not reversible when the temperature is decreased.1 The sequences of the
phase transformations reported in the literature on passing from
the metastable Al2O3 structures to the final stable ␣-Al2O3
phase also are approximate. For example, no direct experimental evidence has confirmed the existence of a direct ␦ → ␪
transformation or disproved a direct ␥ → ␣ transformation.
III. Structure of Al2O3 Polymorphs Based on
Face-Centered Cubic Packing of Oxygen Anions
Al2O3 polymorphs based on fcc packing of oxygen are represented by eight powder diffraction files,‡ based mainly on
X-ray analyses performed 30–40 years ago. These files describe structures denoted ␥, ␩, ␦, and ␪, with a few additional
files in which the same phase notation is used for similar but
not identical spectra.
Fig. 1. Three-dimensional view of the spinel structure. White balls
represent oxygen ions located at 32e Wyckoff positions. Larger dark
balls represent 16d, octahedrally coordinated sites, and the smaller
balls represent 8a, tetrahedrally coordinated Wyckoff positions. Presence of empty interstitial positions (16c, 48f, 8b) also can be observed.
(1) Cubic, Spinel-Type Aluminas: ␥- and ␩-Al2O3
␥- and ␩-Al2O3 have been described as defect spinel structures.1 The ideal spinel structure AB2O4 is represented by a
2 × 2 × 2 array of an fcc packed oxygen subcell, with the A and
B cations occupying the 8a (of the 64 available) tetrahedrally
and the 16d (of 32) octahedrally coordinated interstitial sites
(Fig. 1). The symmetry of the spinel structure is described by
‡
International Centre for Diffraction Data, Newtown Square, PA.
August 1998
Metastable Alumina Polymorphs: Crystal Structures and Transition Sequences
Fig. 2.
1997
Ideal spinel structure projected along the [110] direction.
the Fd3m space group, which is a maximal subgroup of the
Fm3m group.4 It is sometimes useful to describe the spinel as
a layered structure on the {111} planes (Fig. 2).5 The packing
of the {111} oxygen anion layers forms an ABCABC sequence, whereas the packing of the aluminum cations can be
described by two types of alternating layers: either (i) layers
containing only octahedrally coordinated cations or (ii)
‘‘mixed’’ layers containing both octahedrally and tetrahedrally
coordinated cations. There are two types of tetrahedrally coordinated sites in the mixed layers: (i) upward pointing or (ii)
inverted coordination tetrahedra.
The commonly accepted structural model of ␥-Al2O3 is
related to that of ideal spinel, and it is assumed to contain
oxygen ions in 32e Wyckoff positions, which are approximately
close packed, while 2131 aluminum cations (to satisfy Al2O3 stoichiometry) are distributed over 16d octahedral and 8a tetrahedral sites.4 In ␥-Al2O3, 8/3 aluminum vacancies have been
assumed randomly distributed over the tetrahedral sites,3 so
that the cation sublattice is partially disordered as compared to
an ideal spinel. Despite this disorder, the symmetry relations
between the equivalent cation positions remain those of the
Fd-3m space group. Formally, the cations in ␥-Al2O3 can partially occupy various combinations of symmetrically equiva-
lent positions in the Fd3m space group, namely 16d, 16c, 8a,
8b, and 48f. A spinel structure with the cations distributed over
16d (octahedral) and 8a (tetrahedral) sites should not allow
occupation of the nearest-neighbor octahedral–tetrahedral
pairs. Such pairs necessarily occur for any combination of cation-occupied Wyckoff positions other than 16c + 8b. In effect,
a strong repulsive interaction between the nearest-neighbor cations destabilizes the alternative structure with respect to ideal
spinel (16d + 8a).6 Nevertheless, some cation distributions that
involve combinations of different equivalent positions have
been suggested.7–10
Thus, Shirasuka et al.,7 based on powder XRD results, suggested that 62.5% of the aluminum ions occupy two 16-fold
(16c and 16d) octahedral sites and assumed the remaining aluminum ions to be distributed equally over the eightfold and the
48-fold tetrahedral sites. These results are in agreement with
those obtained by John et al.,8 who have deduced that 65% of
the aluminum ions are in the octahedral sites in ␩-Al2O3 from
the results of solid-state nuclear magnetic resonance (NMR)
with magic angle spinning (MAS). Ernst et al.,9 in their highresolution (HR) TEM study of the Cu–Al2O3 interface in an
internally oxidized Cu–Al alloy, have suggested that the Al2O3
precipitates possess a cubic disordered spinel-type structure
Crystal Structure of ␣-Al2O3
␣-Al2O3 possesses trigonal symmetry with rhombohedral
Bravais centering (space group R-3c (No. 167)) and has
10 atoms in the unit cell. The crystallography of ␣-Al2O3
has been discussed in detail by Kronberg,76 and more
recently by Bilde-Sørensen et al.77 The structure of ␣Al2O3 can be considered as an hcp sublattice of oxygen
anions, with 2/3 of the octahedral interstices filled
with aluminum cations in an ordered array. This simplified model describes the general nature of the ion packing,
but is somewhat misleading, because it does not reflect the
true trigonal symmetry of the crystal. One consequence of
the trigonal symmetry is the nonequivalence of cation layer
translations along the [1010] and [1010] directions (using
hexagonal indices), which has important implications
for both basal slip and basal twinning in ␣-Al2O3, as
discussed by Kaplan et al.78 and Pirouz et al.79 (In some
cases this nonequivalence has been attributed incorrectly
to the lack of an inversion center in ␣-Al2O3, which
would be inconsistent with a −3 centrosymmetric point
group.)
The oxygen anions in ␣-Al2O3 occupy 18c Wyckoff positions (in the hexagonal description) with coordinates
x,0,1/4 (x ⳱ 0.306), whereas the aluminum cations are located at 12c positions with coordinates 0,0,z (z ⳱ 0.347).75
Both the x and z values deviate from the ideal value of 1/3,
which would correspond to the atomic positions in the ideal
close-packed structure. The aluminum cations are displaced
along the [0001] direction toward the neighboring empty
octahedral sites, resulting in a ‘‘puckering’’ of the cation
layers. The cation displacements are accompanied by distortion of the oxygen sublattice. The hexagonal parameters
for ␣-Al2O3 are c ⳱ 1.297 nm and a ⳱ 0.475 nm, with
c/a ⳱ 2.73,74 and corresponds to six oxygen layers along
the c-axis of the unit cell. For the oxygen sublattice alone
(three oxygen layers), c/a ⳱ 1.58, slightly smaller than the
ideal value of 1.63 associated with a hard-sphere model.
1998
Journal of the American Ceramic Society—Levin and Brandon
(which they called ␩⬘) with 62.5% of the cations equally distributed over 16c and 16d octahedral sites and the remaining
aluminum ions located at the 8a (5.35%) and the 48f (32.15%)
tetrahedral sites. These results, derived from a qualitative comparison of the phase contrast in a computer-simulated image
with a single HRTEM micrograph, differ from those reported
by Shirasuka et al. for the ␩-Al2O3 only in the partition of the
aluminum cations between the tetrahedral 8a and 48f sites.
Recently, Zhou and Snyder10 have applied Rietveld analysis of
neutron diffraction spectra for the structure refinement of both
␥ and ␩ structures. They have suggested the presence of aluminum on abnormally coordinated 32e sites in the surface layers of both phases, but with no aluminum cations on the eightfold, tetrahedrally coordinated sites in ␩-Al2O3, in contradiction to
the results by Shirasuka et al. Nevertheless, the Zhou and Snyder
interpretation seems reasonable, because it is consistent with
molecular dynamic simulations of ␥-Al2O3 surfaces,11 but it is
not clear how these results associated with the influence of
surface ions should be related to the structure of the bulk.
Selected area diffraction (SAD) has revealed that ␩-Al2O3
formed from the hydroxides is tetragonally distorted, with a c:a
ratio between 0.985 and 0.993, whereas ␥-Al2O3 is even more
deformed, with a c:a ratio between 0.983 and 0.987.3 Moreover, the oxygen sublattice of ␥-Al2O3 is more ordered than
that of ␩-Al2O3. Lippens and De Boer3 have ascribed the morepronounced tetragonality of ␥-Al2O3 to strong shrinkage anisotropy in the a- and b-axes of boehmite, whereas Yamaguchi
et al.12 have related the tetragonal distortion to the distribution
of residual hydroxyl ions. In effect, the true symmetry of both
these tetragonally deformed structures (␥ and ␩) should be
described by one of the tetragonal space groups, which is expected to be a maximal subgroup of Fd3m, with a corresponding transformation of the lattice. On the other hand, the spinellike Al2O3 structure formed either upon quenching of the
Al2O3 melt or by thermal oxidation, and also commonly denoted as ␥-Al2O3, has been reported to be cubic.13–15 At present, there are no experimental data that would allow a comparison of the cation distribution in the spinellike structures
obtained by dehydration of hydroxides with those developed
from the melt.
␥-Al2O3 obtained by thermal oxidation of aluminumcontaining alloys, by annealing of amorphous anodic Al2O3
films, or by plasma spraying reproducibly shows preferred orientation (crystalline texture), with both ⟨100⟩␥ and ⟨110⟩␥ directions preferentially oriented parallel to the surface normal.16,17 Recent molecular dynamic simulations of the surface
structure of ␥-Al2O3, which have included the noninteger number of cations in the unit cell, result in the following relation
between the surface energies: ␥{001} < ␥{111} < ␥{110}.11 These
results are consistent with a {001} preferential orientation but
cannot explain a {110} texture. These calculations indicate that
the surface energies for ␥-Al2O3 are much lower than those for
␣-Al2O3, consistent with the high specific surface area typically observed for the ␥-Al2O3 phase.
␥-Al2O3, developed either by crystallization of anodic Al2O3
films or by thermal oxidation of aluminum and NiAl, contains
a high density of {111} growth twins. These twins have been
related to the platelike morphology of oxide scales18,19 developed at the surface of NiAl during the transient stages of thermal oxidation.20 The atomistic boundary structure of {111}
twins in ␥-Al2O3 remains to be determined.
(2) Al2O3 Structures with Tetragonal–Orthorhombic
Symmetry: ␦-Al2O3
␦-Al2O3 has been described as a superlattice of the spinel
structure with ordered cation vacancies.2,3 The ␦ supercell has
been confirmed to be a tripled unit cell of spinel with 160 ions
per unit cell. Two possible unit cells have been suggested based
on X-ray and SAD: either tetragonal with a␦ ⳱ b␦ ⳱ a␥, and
c␦ ⳱ 3a␥ (Refs. 2 and 3) or orthorhombic with a␦ ⳱ a␥, b␦ ⳱
1.5a␥, and c␦ ⳱ 2a␥ (Refs. 13, 16, 17, and 21–24).
In all reports of the tetragonal ␦ unit cell, the structure has
Vol. 81, No. 8
been derived from boehmite, whereas the orthorhombic ␦ unit
cell has been observed for precursors obtained either by
quenching of the melt or by thermal oxidation. It is not clear
whether both structures exist (in which case they should be
designated differently) or the tetragonal structure is a misinterpretation of the experimental data. The results available on the
orthorhombic ␦-Al2O3 structure provide convincing evidence
for the existence of this polymorph (Fig. 3), whereas the X-ray
data ascribed to the tetragonal unit cell also could have been
derived from an orthorhombic unit cell (apart from a few weak
reflections that perhaps should be overlooked in the early X-ray
studies, as discussed by Jayaram and Levi.13 The SAD patterns
attributed to tetragonal ␦-Al2O3 have been limited to a single
orientation, parallel to the ⟨110⟩␥ direction.2,3 The present authors have shown that similar electron diffraction patterns can
be obtained from coexisting crystallographic variants of orthorhombic ␦-Al2O3 and those of a newly identified phase,
monoclinic ␪⬙-Al2O3, which are discussed below (Fig. 4). A
Fig. 3. SAD patterns from orthorhombic ␦-Al2O3 in different orientations. ␦-Al2O3 was developed in a plasma-sprayed Al2O3 annealed at
1200°C in air.
August 1998
Metastable Alumina Polymorphs: Crystal Structures and Transition Sequences
1999
Fig. 4. SAD pattern from a single grain in both the [110]␥ and [001]␥ orientations obtained from plasma-sprayed Al2O3 annealed at 1100°C in
air. Domains of both ␦- (indicated by a rectangle) and ␪⬙-Al2O3 (indicated by a parallelogram) contribute to these patterns. In the [001]␥ orientation,
two 90° domains of ␦-Al2O3 that contribute to the pattern are in a [010]␦ orientation with [001]␦㛳[001]␥ and [001]␦㛳[100]␥ corresponding to the
domains I and II. Two other 90° domains of ␦-Al2O3 contributing to the pattern are in a [100]␦ orientation. Only variants I and II are indicated for
clarity. ␪⬙-Al2O3 is present with a [110]␪⬙㛳[010]␥ orientation. In the [110]␥ orientation, the domains I and II of the ␦-Al2O3 correspond to
[012]␦㛳[110]␥ and [210]␦㛳[110]␥. ␪⬙-Al2O3 is in the [010]␪⬙㛳[110][ orientation. Diffraction pattern in the [110]␥ orientation is similar to that given
in Ref. 3 and attributed there to tetragonal ␦-Al2O3.
reciprocal lattice section in the [001] orientation would confirm
or refute the presence of ␦-Al2O3 with the tetragonal unit cell,
and an additional electron diffraction study of the Al2O3 phases
developed by heating boehmite could resolve this question.
Repelin and Husson25 have applied a least-squares fitting
procedure to X-ray data from what they defined as ‘‘␦-Al2O3,’’
and which they have described by the P4m2 space group (with
lattice parameters a␦ ⳱ a␥√2/2 and c␦ ⳱ 3a␥). This unit cell
contains 80 ions with 4 cation vacancies randomly distributed
over octahedrally coordinated sites. No other results that would
support the existence of an Al2O3 structure with this unit cell
have been presented.
Jayaram and Levi13 have studied orthorhombic ␦-Al2O3 by
TEM. Convergent-beam electron diffraction (CBED) has been
used to determine the space group and P212121 tentatively has
been suggested. Bonevich and Marks24 also have applied
CBED to observe the symmetry of orthorhombic ␦-Al2O3 developed during sintering of nanosized particles and have proposed either P212121 or P21212 as the space group. No model
for the specific ionic positions in the framework of either of
these space groups has yet been suggested.
In the study performed by Levin et al.,26 ␦-Al2O3 with orthorhombic symmetry and lattice parameters a␦ ⳱ 2a␥, b␦ ⳱
a␥, and c␦ ⳱ 1.5a␥ has been identified in specimens obtained
by processing routes that included anodic Al2O3 films, thermally oxidized aluminum, and plasma-sprayed Al2O3. No ␦Al2O3 with a tetragonal unit cell has been observed in this
study. The extinction rules and periodicities in zero-order and
higher-order Laue zones (ZOLZ and HOLZ) (Fig. 3), with
tilting about all three ⟨100⟩␦ directions, have appeared consistent with a P212121 space group for ␦-Al2O3.
(3) Al2O3 Structures with Monoclinic Symmetry: ␪, ␪ⴖ, ␭,
and ␪ⴕ
The most studied Al2O3 polymorph with monoclinic symmetry is ␪-Al2O3, which is a structural isomorph of ␤Ga2O3.27–29 This structure has the space group C2/m and contains 20 ions, with the aluminum cations equally distributed
over octahedral and tetrahedral sites. In all studies, ␪-Al2O3 has
been reported to be multiple twinned, primarily on the (001)
plane.2,27 Although the true symmetry of ␪-Al2O3 has been
determined to be monoclinic, this phase also may appear orthorhombic as the result of polysynthetic twinning. The transformation matrix from the orthorhombic to monoclinic indexes
is2
冋 册
1 0 0
0 1 0
1Ⲑ2 0 1Ⲑ2
Rietveld analysis of neutron diffraction spectra performed by
Zhou and Snyder10 yields atomic positions similar to those
suggested earlier.28,29
Recently, the existence of three additional monoclinic Al2O3
structures—␪⬙-, ␪⬘-, and ␭-Al2O3— has been reported.16,17,26
␭-Al2O3 has been observed reproducibly in both plasma-
2000
Journal of the American Ceramic Society—Levin and Brandon
sprayed Al2O3 and thermally oxidized aluminum. ␪⬘ has been
found occasionally in annealed anodic Al2O3 films, and ␪⬙Al2O3 has been identified reproducibly in plasma-sprayed
Al2O3. Based on these results, all four monoclinic phases (␪⬘,
␪⬙, ␭, and ␪) are assumed to evolve from ␥-Al2O3 by cation
ordering on the interstitial sites of the oxygen subcell, which
remains approximately undisturbed by these transformations
(excluding small, homogeneous lattice distortions). The lattice
parameters and space groups of these four monoclinic Al2O3
phases, as well as their orientation relationship with respect to
␥-Al2O3, are summarized in Table II.
in the structural sequence from boehmite to ␪-Al2O3 were outlined: (i) a gradual decrease in occupancy of the tetrahedral
sites by aluminum cations, correlated with an increase in occupancy of the octahedral sites, and (ii) a gradual decrease in
the total number of cation vacancies. The relative occupancy of
the tetrahedral and octahedral sites was deduced from changes
in intensity of the {220} reflections, which, in the spinel structure, result only from the tetrahedrally coordinated cations.
Jayaram and Levi13 applied electron diffraction to study the
melt → ␦-Al2O3 and ␥-Al2O3 → ␦-Al2O3 phase transitions.
They realized that both ␥- and orthorhombic ␦-Al2O3 were
based on the fcc packing of oxygen anions but with a higher
degree of order for the interstitial cations in the ␦ phase. The
authors suggested that the ␥ → ␦ transformation begins with
the ordering of tetrahedral cations in small (1–2 nm) domains.
It was observed that this transformation is continuous, starting
from the diffraction spots characteristic of the disordered
spinel, through the development of diffuse scattering, until the
final appearance of the discrete superlattice reflections characteristic of orthorhombic ␦-Al2O3. No attempt was made to determine the distribution of the diffuse intensity in reciprocal space.
Dauger and co-workers22,23 suggested that the orthorhombic
␦-Al2O3 structure evolves from ␥-Al2O3 by the introduction of
periodic antiphase boundaries (APBs) on the {001}␥ planes, with
a shift vector of either 1/2⟨100⟩␥ or 1/4a␥⟨011⟩␥. They sketched
a model of cation jumps based on this hypothesis and assuming
preferential ordering of the cation vacancies at the APBs to
explain the transformation to the ␦-Al2O3 structure, but with no
clear description of the mechanism.
A further attempt to provide insight into the mechanisms of
phase transformation in metastable Al2O3 was undertaken by
Zhou and Snyder,10 who performed a Rietveld analysis of diffraction spectra from several Al2O3 polymorphs. Their results
suggested that the reduction of surface area and ordering of the
tetrahedral aluminum sublattice, which occurs during heating,
IV. Phase Transformations between Al2O3 Polymorphs
Based on Face-Centered Cubic Packing of Oxygen
A few studies of phase transformations between metastable
aluminas have been published and are discussed individually.
Wilson2 used conventional TEM to study the evolution of
the (porous) microstructure and the sequence of phase transformations on heating boehmite: boehmite → ␥ → ␦ → ␪. No
direct evidence for the ␦ → ␪ transformation was presented, but
it was observed that the structural transformation proceeded
topotactically to generate multiple twinned ␪-Al2O3. A welldeveloped pore structure was observed at all stages of the sequence, and it was characterized in terms of pore size and
morphology. The structural and morphological sequences were
closely related and determined by a combination of the original
boehmite structure and the dehydration mechanism. The orientation relationships observed during the transformation sequence were inherited from the original orthorhombic
boehmite precursor and were reflected in the morphology of
the pore structure. The ‘‘␦-Al2O3’’ reported in this work was a
supercell of the pseudocubic unit cell of ␥-Al2O3 with c␦ ⳱
3c␥, corresponding to a tripling of the ‘‘short’’ c-axis of the
␥-Al2O3 unit cell. Two important trends during cation ordering
Table II.
Vol. 81, No. 8
Metastable Al2O3 Structures Based on fcc Packing of Oxygen Anions
Phase
Lattice parameters
Space group
Cations/
unit cell
␥-Al2O3,
␩-Al2O3
a␥ ≈ 7.9 Å
Fd3m
64/3
␪-Al2O3
a ≈ 1.5a␥
C2/m
8
b ⳱ a␥√2/4
Orientation relationship
with respect to ␥-Al2O3
(100)␪㛳(001)␥
[010]␪㛳[110]␥
c ⳱ a␥√2/2
␤ ⳱ 104°
␪⬙-Al2O3
a ≈ 1.5a␥
A12/n1†
64
b ⳱ a␥√2
(100)␪⬙㛳(001)␥
[010]␪⬙㛳[110]␥
c = a␥√2
␤ ⳱ 104°
␪⬘-Al2O3
a ≈ a␥√3/2
C2/m
16
b ≈ a␥/√2
(010)␪⬘㛳(110)␥
[100]␪⬘㛳[112]␥
c ≈ a␥√3/2
␤ ≈ 94°
␭-Al2O3
a ≈ 3√2a␥/2
b ≈ 2a␥
c ≈ 1.5a␥
␤ ⳱ 115°
P21/c
64
[010]␭㛳[100]␥
(100)␭㛳(013)␥
␦-Al2O3
a ≈ a␥
b ≈ 2a␥
c ≈ 1.5a␥
P212121
64
[100]␦㛳[001]␥
(100)␦㛳(100)␥
␦⬘-Al2O3
a ≈ a␥
c ≈ 3a␥
P41
64
[001]␦㛳[001]␥
(100)␦㛳(100)␥
†
No. 15, cell choice 2.
August 1998
Metastable Alumina Polymorphs: Crystal Structures and Transition Sequences
2001
Fig. 5. (a)–(c) SAD patterns from monoclinic ordered Al2O3 phases in an orientation along the unique monoclinic axis: (a) ␪,␪⬙; (b) ␪⬘; and (c)
␭. ␪ and ␪⬙ are indistinguishable when the orientation is parallel to the unique monoclinic axis. Two twin-related variants I and II contribute to the
diffraction pattern of ␪⬘-Al2O3. (d) SAD pattern from orthorhombic ␦-Al2O3 in [210]␦㛳[110]␥ orientation. Diffraction patterns were obtained from
a plasma-sprayed Al2O3 annealed at 900°, 1100°, and 1200°C in air, corresonding to the ␭-, ␪⬙-, and ␦-Al2O3 phases. Diffraction patterns for both
␪- and ␪⬘-Al2O3 phases were obtained from self-supported anodic Al2O3 films annealed at 1200°C in air. Detailed preparation procedure for the
anodic Al2O3 films is described in Ref. 16.
cause a gradual collapse of the cubic spinel framework, so that,
in the early stages of transformation, the structure exhibits
tetragonal character, then settles displacively into the monoclinic ␪-Al2O3 configuration before transforming reconstructively to rhombohedral corundum.
All published experimental results demonstrate that reflec-
tions that result mainly from the oxygen subcell remain
approximately unchanged during these phase transformations.
Indeed, a comparison of the SAD patterns from ␥-, ␦-, ␪-, ␪⬘-,
and ␭-Al2O3 shows that the principal reflections that result
from both the anion (oxygen) and the cation sublattices of
␥-Al2O3 ({400}, {440}, and {222}) are preserved in all the
2002
Journal of the American Ceramic Society—Levin and Brandon
phases (Fig. 5). Changes occur only in those specific ␥-Al2O3
reflections ({hhl}, h,l ⳱ 2n + 1, and {hh0}, h ⳱ 2n) that result
only from the cation sublattices. Streaks that are associated
with the presence of planar defects in the observed diffraction
patterns pass through no reflections primarily associated with
the oxygen anions. This implies that the oxygen subcell
is practically unaffected by the transformations from ␥-Al2O3
to the other transition Al2O3 phases. On the other hand,
the {111}␥ growth twins in ␥-Al2O3, which affect both the
oxygen and the cation sublattices, are retained up to the
␥ → ␣ transformation, whereas the transformations from
␥-Al2O3 to other metastable polymorphs do not remove these
twins, which would require reconstruction of the oxygen
sublattice (Fig. 6).
Levin et al.,16,17 based on the above evidence, have proposed
that all the major changes occur only by cation redistribution
and that the transformations from ␥ to ␦, ␪, ␪⬘, and ␭ phases can
be assumed to proceed by cation ordering on the interstitial
sites of the fcc oxygen-anion subcell. Symmetry changes that
accompany transitions of this type can be treated formally using a chain of maximal symmetry group/subgroup relations that
connects the crystal structures of the parent and product
phases.30 The advantage of this approach in the analysis of
phase transformations has been discussed extensively.31,32 The
unit cell and space groups of the transition phases and the
orientation relationships between them have been established
experimentally by electron diffraction in recent studies by the
Vol. 81, No. 8
present authors.16,17,26 A formal sequence of symmetry maximal group/subgroup relations connecting parent and product
structures has been proposed to rationalize each mechanism of
phase transformation (Fig. 7). The type and hierarchy of the
ordering domains and the interdomain interfaces expected from
each minimal formal symmetry reduction have been compared
to lattice images of the transition Al2O3 structures observed by
high-resolution electron microscopy, and the details of the observed domain structure have been related to the predicted
symmetry changes (Fig. 8).
It has been shown that all Al2O3 structures based on fcc
packing of oxygen anions can be derived formally from the
(hypothetical) disordered fcc structure either by a combination
of both displacive (changes in occupancy accompanied by
atomic displacements) and chemical (change in occupancy)
ordering of the aluminum cations on the interstitial sites of the
oxygen sublattice or by purely chemical ordering. The packing
of the oxygen anions remains approximately unaffected by
these transformations in all cases. Purely chemical ordering of
the cations in the fcc anion structure results in either a spinel
phase ␥-Al2O3 or a ␩-Al2O3 with a partially disordered cation
sublattice. A combination of both displacive and chemical ordering can produce fully ordered structures, of which four
monoclinic (␪, ␪⬘, ␪⬙, and ␭) and one orthorhombic (␦) structures have been confirmed.
A common feature of all the fully ordered transition Al2O3
phases (except for the questionable identification of tetragonal
Fig. 6. Lattice image of a single grain in an anodic Al2O3 film annealed at 1200°C in air. Growth twins on the {111}␥ planes can be observed.
Ordering of aluminum cations, corresponding to the formation of ␦-Al2O3, occurs on both sides of the twin boundaries, as deduced from a fast
Fourier transform (FFT) of these regions in the image. {111}␥ twins are preserved through the ␥ → ␦ transformation.
August 1998
Metastable Alumina Polymorphs: Crystal Structures and Transition Sequences
Fig. 7. Maximal subgroup/supergroup symmetry relations between
the Fd3m and C2/m space groups for the ␥ → ␪ transformation. Arrows pointed upward and downward indicate an increase or decrease
in symmetry, respectively. Inclined arrows corresponds to a change in
point group (rotational symmetry) due to atomic displacements and a
change in occupancy (displacive ordering). Vertical arrows corresponds to changes in translational symmetry due to a change in occupancy (chemical ordering). Numbers in brackets indicate the number
of crystallographic variants expected to accompany a symmetry reduction (from Ref. 16).
‘‘␦-Al2O3’’) is that one of their lattice parameters is a noninteger expansion of the lattice parameter of ␥-Al2O3 by 3/2.
Such an expansion cannot be derived by direct ordering of
␥-Al2O3, which would require an integer multiplication of a␥
rather than by a factor of 3/2. It follows that any continuous
transformation from ␥ phase to a completely ordered structure
(␪⬘, ␪⬙, ␭, ␪, and ␦) must proceed through disordering of the ␥
phase to the simple fcc structure.16 All the octahedral (d and c)
and tetrahedral (a, b, and f ) cation sites should become equivalent for this disordering transformation to occur, giving 4c
octahedrally and 8d tetrahedrally coordinated sites in the Fm3m
space group of the fcc-packed oxygen anions. Such a requirement does not imply the existence of a disordered fcc phase
(even as a transition state) but, rather, some filling, in the
product phase, of both occupied and unoccupied interstitial
positions in the parent, spinel structure.26 The equilibrium order–disorder transformation temperature for the formation of a
disordered, fcc phase, in practice, could be above the melting
point of Al2O3, which would be consistent with the reported
structure of liquid Al2O3.33
Each form of displacive ordering for the aluminum cations
produces a lattice distortion of corresponding symmetry, with a
fixed orientation relationship between the parent phase and the
product phase.17 All three possible symmetry distortions of the
cubic structure—tetragonal, orthorhombic, or rhombohedral—
have been found to occur, each resulting in a different transition Al2O3 characterized by a different array of ordering domains and interdomain boundaries. As a result of the
predominantly ionic nature of Al2O3, the filling of the interstitial positions by the aluminum cations in each structure must be
highly correlated, leading to the formation of cation clusters in
the transient stages of the ordering reactions.26 Analysis of the
diffuse intensity contours developed in reciprocal space has
suggested that, in particular, both the ␥ → ␦ and the ␥ → ␭
2003
transformations proceed through a planar ordering of the aluminum cations on the (001) planes, equivalent to the convolution of two- and four-point cation-vacancy clusters.26 This ordering results in a doubling of one of the edges of the fcc anion
structure. The stacking of (001) planes in the normal direction
then can be described as derived from the parent structure by
introducing nonconservative APBs with a shear vector R ⳱
1/4⟨011⟩␥ every three (004)␥ planes. Periodic APBs with alternating shear vectors of R1 ⳱ 1/4[011]␥ and R2 ⳱ 1/4[011]␥
for the two successive planar defects then result in the orthorhombic unit cell of ␦-Al2O3. Conversely, APBs with the same
shear vector for successive shears result in a monoclinic structure that corresponds to a transition state for the ␥ → ␭ transformation (Figs. 9 and 10).
Thermal analysis has detected no measurable effect for
transformations from ␥-Al2O3 to the ordered Al2O3 polymorphs,1 which might indicate that these transformations are
second order. However, the experimental TEM results have
demonstrated that transformations from ␥-Al2O3 to the other
metastable polymorphs occur by the nucleation and growth of
ordered domains in the ␥-Al2O3 matrix (Fig. 11), indicating a
first-order transformation. The energy barrier for the nucleation
of any of these ordered polymorphs is expected to be determined by a combination of the energy required to disorder the
cations of the ␥-Al2O3 structure and the strain energy associated with lattice mismatch between the parent and product
phases.
V.
Common Metastable Al2O3 Polymorphs Based on
Hexagonal Close Packing of Oxygen
The common metastable Al2O3 crystal structures based on
an hcp packing of the oxygen anions are ␬- and ␹-Al2O3,
although the existence of a transient ␬⬘ phase, formed by dehydrating tohdite, also has been reported.
Three different unit cells have been suggested for ␹-Al2O3.
Stumpth et al.34 have indexed XRD patterns of ␹-Al2O3 by assuming a cubic (not spinel) unit cell of lattice parameter 7.95
Å, whereas two hexagonal unit cells also have been suggested
for ␹-Al2O3 with lattice parameters either a ⳱ 5.56 Å and c ⳱
13.44 Å (space group P6/mm or P63/mcm)1 or a ⳱ 5.57 Å
and c ⳱ 8.64 Å.35 Hexagonal ␹-Al2O3 has been suggested to
possess a layer structure, the arrangement of anions being inherited from gibbsite, whereas the aluminum cations occupy
octahedral interstitial sites within the hexagonal oxygen layers.
The stacking of the layers has been shown to be strongly disordered in the c-direction. It is not yet clear whether all three of
the above ␹ structures exist, or whether the differences between
them are merely a matter of interpretation.
␬⬘-Al2O3 has been described in terms of an hcp packing of
oxygen anions (inherited from tohdite), with a random distribution of cations over both tetrahedrally and octahedrally coordinated positions.36 This polymorph is considered to be a
transient phase in the transformation from tohdite to ␬-Al2O3.
The structure of ␬-Al2O3, which is of considerable importance in chemical vapor deposition (CVD) technology, had
been believed for many years to be hexagonal.35,36 However, a
recent lattice-image study of ␬-Al2O3 by Liu and Skogsmo,37
combined with CBED, shows that the true symmetry for this
structure is orthorhombic. The pseudohexagonal symmetry
then results from the coexistence of three twin-related orthorhombic variants rotated by 120° with respect to one another.
The space group for ␬-Al2O3 is Pna21, and the lattice parameters are a ⳱ 4.69 Å, b ⳱ 8.18 Å, and c ⳱ 8.87 Å. The
proposed unit cell contains 16 cations that are ordered on both
tetrahedrally and octahedrally coordinated sites, but the exact
atomic positions in this structure have yet to be determined.
VI.
Transformations from a Transition Al2O3 to ␣-Al2O3
The influence of various CVD processing parameters on the
rate of the ␬ → ␣ transformation has been studied extensively,
2004
Journal of the American Ceramic Society—Levin and Brandon
Vol. 81, No. 8
1
Fig. 8. Ordering domains observed in ␪-Al2O3. Both (a) rotational and (b) and (c) translational interfaces with the displacement vector R1 ⳱ 3 a ␪ and
1
R2 ⳱ 2c␪ can be observed. Rotational interface is attributed to the symmetry reduction Immm → I2/m (Fig. 7). This interface lies on the (001)␥㛳(100)␪
plane, which is strain free for the orthorhombic → monoclinic transformation. Translational interface corresponding to R1 has been ascribed to a
tripling of the lattice parameter in the I/mmm space group and that with R2 probably corresponds to a doubling of the lattice parameter in the C2/m
space group (Fig. 7) (from Ref. 16). Image shown in (b) has been compressed in the vertical direction to improve recognition of the antiphase shift.
August 1998
Metastable Alumina Polymorphs: Crystal Structures and Transition Sequences
Fig. 9. Lattice image corresponding to a transient stage of the transformation from ␥- to either ␭- (monoclinic) or ␦-Al2O3 (orthorhombic)
obtained from a single grain in a plasma-sprayed Al2O3 annealed at
900°C in air. Contrast can be explained by the stacking of lamellae
having monoclinic symmetry and a thickness of 3xd{004}␥, as indicated in the image. Regions with stacking of alternating, twin-related
lamellae result in an apparent orthorhombic symmetry (indicated by
‘O’), and stacking of the lamellae without alternation (indicated by
‘M’) results in monoclinic symmetry (from Ref. 26).
but no attempt at structural analysis of this transition appears to
have been published.38–40 On the other hand, the mechanism of
the ␥ → ␣ transformation has been the subject of several published studies.
Chou and Nieh41 have reported the nucleation of polycrystalline ␣ phase from a highly textured ␥-Al2O3 matrix in reactive, radio-frequency (rf) sputter-deposited, nanocrystalline
Al2O3 thin films. TEM analysis indicates that the as-deposited
films contain both an amorphous phase and metastable ␥ phase.
In the films annealed at 1200°C for 2 h, nucleation and concurrent anomalous grain growth of ␣-Al2O3 are observed in the
fine-grained, polycrystalline ␥-Al2O3 matrix.
The following orientation relationships between ␥- and ␣Al2O3 have been determined from electron diffraction: ⟨001⟩␥//
⟨0001⟩␣, {440}␥//{3030}␣, and {310}␥//{2110}␣. However,
these orientation relationships differ from those based upon
precipitation of corundum from MgAl2O4–Al2O3 solutions,
which have been characterized by (0001)␣//{111}spinel and
⟨0110⟩␣//⟨110⟩spinel, consistent with a classical fcc–hcp transformation. This difference was not discussed by Chou and
Nieh,41 although their diffraction analysis, obtained from a
polycrystalline region, is ambiguous. Furthermore, these authors have ignored some important features in the diffraction
patterns that they analyzed. The pattern that they have ascribed
to polycrystalline ␥-Al2O3 in a ⟨001⟩ orientation clearly shows
the superlattice diffraction spots characteristic of a tripled
spinel unit cell, which contradicts the interpretation presented
in their work. Most probably, the layered structure observed by
these authors results from either ␦ or ␪ phases.
The only atomistic model for ␥ → ␣ phase transformations
is that of synchro-shear, first propose in 1963 by Kachi et al.42
for Fe2O3, and widely referenced in the literature for the ␥ →
␣ transformation in Al2O3. This model describes ␥-Al2O3 as a
layered structure (Fig. 2). The ␣-Al2O3 structure corresponds to
hcp packing of oxygen anions, in which the metallic cations
occupy octahedral interstices. The stacking sequence of the
close-packed oxygen layers is interrupted by the intervening
cation layers to form a ‘‘honeycomb’’ lattice (see below).
The change of stacking of the oxygen layers from fcc to hcp
2005
packing proposed in the model is illustrated in Fig. 12(a). Open
circles indicate the arrangement of oxygen ions on a {110}
plane of ␥-Al2O3, and the hatched circles show the stacking of
oxygen ions for ␣-Al2O3 formed by the shear displacement of
oxygen layers. Each set of oxygen layers shears by a√3 with
respect to the set above and below it, where a is the nearest
interatomic distance of oxygen, corresponding to (1/12)a␥⟨112⟩␥.
The aluminum ions located at the shear interface between the
neighboring oxygen layers then rearrange (Fig. 12(b)). Aluminum ions in octahedral sites in the ␥-Al2O3 lattice jump in
either the [121]␥ or the [21̄1̄]␥ direction, whereas tetrahedral
aluminum ions must also shift with the displacement of their
coordinating oxygen ions, breaking one of the four bonds
around the aluminum. Figure 12(c) illustrates this short-range
diffusion of an aluminum ion within one set of oxygen layers,
according to the model of Kachi et al.42 The circles represent
the positions of octahedrally coordinated aluminum ions within
one set of oxygen layers of ␥-Al2O3. If one-ninth of the cation
lattice sites are occupied by vacancies, as shown in Fig. 12, a
‘‘honey-comb’’ lattice of aluminum ions (represented by the
black circle) can be constructed by short-range diffusion to
form ␣-Al2O3. The shear of the oxygen layers has been suggested to occur by sweeping partial dislocation.
Although this model might be plausible for the direct ␥ → ␣
transformation during sintering under high pressure,43,46,47 no
specific experimental evidence has been presented to support
this model for the ␥ → ␣ transformation at atmospheric pressure. Moreover, it remains uncertain whether ␥-Al2O3 transforms directly to ␣-Al2O3 on heating at atmospheric pressure or
whether there are intermediate phases in a transformation sequence. The published experimental results suggest that the
␥ → ␣ transformation is not direct. Even in the original work
of Kachi et al.,42 additional reflections have been reported in
the SAD pattern of ␥-Fe2O3, and these reflections appear to
correspond to a supercell of spinel with c ⳱ 3a␥, that is, the
tetragonal ‘‘␦-Fe2O3’’ phase.
All studies have reported an ␣-Al2O3 grain size at least an
order of magnitude larger than that of the parent transition
Al2O3 and no ␣-Al2O3 nuclei have been noted, suggesting that
the growth of ␣-Al2O3 into a transition Al2O3 matrix is ‘‘explosive,’’ once a ‘‘critical’’ nucleus size is formed. No simple
orientation relationship between metastable Al2O3 structures
and ␣-Al2O3 has been identified in the advanced stages of the
transformation.
The transformation from fcc-based transition aluminas to
␣-Al2O3 in precursors derived by calcination of various salts
and hydroxides often proceeds by nucleation and growth of
individual single crystals of ␣-Al2O3, with an internal porous
vermicular-like microstructure, characterized by the coexistence of contiguous solid and pore phases44–47 and associated
with the comparatively large volume change accompanying the
transformation, as suggested by Dynys and Halloran.44 Alternatively, Badkar et al.45 have related the pores in a vermicular
structure to those previously present in a highly porous transition Al2O3 precursor, suggesting that these are ‘‘swept-up’’ by
the migrating transition Al2O3–␣-Al2O3 interface. A vermicular microstructure is not observed for the fcc-based transition
Al2O3 → ␣-Al2O3 transformation in all precursors, for example, anodic Al2O3 films, Al2O3 films developed on the surface of thermally oxidized alloys, and plasma-sprayed Al2O3
coatings—a fact that should be considered when attempting to
explain the formation of a vermicular structure.
The internal pores are retained inside the ␣-Al2O3 crystals,
although grain coarsening occurs to reduce the specific surface
area. The development of a vermicular microstructure during
the transition Al2O3 → ␣-Al2O3 transformation has been found
to be a major obstacle inhibiting the pressureless sintering of
nanosized transition Al2O3 powders at low temperatures
(<1300°C).
A mechanical pretreatment (compaction or dry ball-milling)
of transition Al2O3 powders significantly affects the kinetics of
the transformation, and very high compaction pressures (>2.5
2006
Journal of the American Ceramic Society—Levin and Brandon
Vol. 81, No. 8
Fig. 10. Model representing (a) the monoclinic unit cell developed at the transient stage of the ␥ → ␭ (monoclinic) transformation and (b)
the orthorhombic unit cell corresponding to ␦-Al2O3. Both models are derived from the parent ␥ unit cell by introducing periodic crystallo1
graphic shears on the (001) plane with a shear vector R ⳱ 4[011]␥ (from Ref. 26). Open and filled circles correspond to the occupied cation positions
in the fcc lattice before and after introducing the shears, respectively.
GPa) can prevent the formation of a vermicular microstructure.43,46,47 The mechanical pretreatment apparently increases
the rate of nucleation frequency of ␣-Al2O3, but the mechanism
remains uncertain. Nucleation of ␣-Al2O3 in a ␥-Al2O3 precursor at a high compaction pressure may occur by shear of the
atomic planes in the ␥-Al2O3, as suggested by Kachi et al.43
Seeding of a transition Al2O3 with ␣-Al2O3 particles also accelerates the kinetics of transformation and prevents formation
of a vermicular structure.48 Both seed concentration and seed
size are critical for the successful control of the transformation.
The characterization of vermicular microstructures has received little attention, and no detailed attempt to analyze the
morphology and crystallography of this structure has been
found in the literature.
A common, although indirect, approach to determining the
kinetics of phase transformations is based on measurements of
the volume fraction of a product phase as a function of temperature and time. Empirical fitting of a theoretical model,
August 1998
Metastable Alumina Polymorphs: Crystal Structures and Transition Sequences
2007
Fig. 11. Lattice image showing a single grain of ␥-Al2O3 in the ⟨110⟩ orientation. Image is from a self-supported anodic Al2O3 film annealed at
1200°C in air. Growth twin on the {111} plane can be observed. Contrast in the region marked by the arrows has been attributed to Moiré effects.
Optical diffraction from the region outlined is consistent with the presence of orthorhombic ␦-Al2O3 in the [210]␦㛳⟨110⟩␥ orientation.
developed for any specific transformation mechanism, therefore allows qualitative confirmation of the mechanism of transformation and permits the thermal activation energy associated
with any particular transformation to be determined. Several
studies that have applied this approach to phase transformations in Al2O3 have been reported.49–52 Powder XRD has been
used to determine the volume fraction of a product phase. In
most cases, heating of ␥-Al2O3 has resulted in the development
of ordered phases prior to, or in parallel with, the formation of
␣-Al2O3.2,3 The similar values of the lattice d-spacings for the
transition Al2O3 phases, with uncertainty concerning the atomistic structure of some phases, precludes an exact determination
of the phase composition by powder XRD, and, in practice, all
the experimental data based on either powder XRD or thermal
analysis can be interpreted only in terms of a global transformation: transition Al2O3 → ␣-Al2O3.
Recently, the kinetics of the ␥ → ␣ transformation have been
determined for Al2O3 films deposited on sapphire singlecrystal substrates in various orientations.53 The as-received deposited film always has been amorphous and has transformed
on annealing, first to an epitaxial layer of ␥-Al2O3 and then to
␣-Al2O3. The activation energies of the amorphous → ␥ and
the ␥ → ␣ transformations are 4.5 and 5.2 eV, respectively.
This difference in the activation energies suggests that the
atomic rearrangements that control the rates of these transformations are different. It has been proposed that the activation
energy for the ␥ → ␣ transformation is related primarily to
rearrangement of the oxygen sublattice. This is consistent with
the observation that the activation energy of transformation for
similar specimens is unaffected by the presence of Fe3+ and
Cr3+ cation dopants, which, nevertheless, significantly affects
the transformation rate.54 The electron energy loss near-edge
structures (ELNESs) of both the O–K and Al–L2,3 edges, when
measured for amorphous- and ␥-Al2O3, are similar, but both
differ significantly from the ELNES for ␣-Al2O3. Theoretical
calculations suggest that the ELNES in Al2O3 is determined
primarily by the local ionic-packing geometry of the anions
surrounding the absorbing atom, suggesting that the ionicpacking arrangements for oxygen in both amorphous- and ␥Al2O3 are similar, but differ from corundum.55 A detailed
analysis of the atomistic structure of the ␥–␣ interface in these
specimens should provide some insight into the mechanism of
the ␥ → ␣ transformation, but it is not clear how the results
obtained for the ␥ epilayer on a sapphire (␣) template in the
above experiments can be related to the nucleation of ␣ phase
in bulk specimens, where no such ‘‘seed’’ template is present.
VII.
Energy Stability of Al2O3 Phases
Theoretical calculations based on shell models, which use an
empirical potential and account for the oxygen-ion dipole polarization, falsely predict a C-type lanthanum oxide (bixbyite)
structure as the stable crystal structure for Al2O3. Although the
bixbyite structure has been identified for systems with other
2008
Journal of the American Ceramic Society—Levin and Brandon
Vol. 81, No. 8
with a local-density approximation for exchange and correlation effects. The energy differences between ␣-Al2O3, ␪-Al2O3,
and bixbyite have been calculated ab initio and compared with
ground-state energies obtained from four different empirical
models. The first of these is a simple shell model that accounts
for the dipole polarization of oxygen ions. The second, socalled compressive-ion model (CIM), does not include dipole
polarizability, but does include the compressibility of the oxygen ions. Finally, the addition of dipole, and then both dipole
and quadrupole polarizabilities to the compressive ion model
characterizes the third and fourth models, designated CIM-D
and CIM-DQ, respectively. Formal ionic charges for both the
oxygen anions and the aluminum cations are used in these
calculations, and the results, as reported by Wilson et al., are
summarized in Table III. As stated above, the corundum structure is predicted to be stable with respect to bixbyite by the ab
initio calculations, and the addition of anion quadrupoles to the
compressive ion model has been shown to be crucial in stabilizing corundum as opposed to the bixbyite structure. The
−0.57 eV ab initio ground-state energy difference between the
structures of ␣- and ␪-Al2O3, derived by Wilson et al., is consistent with the −0.44 eV energy difference previously reported
from Hartree–Fock calculations.57
␪-Al2O3 possesses an ordered structure with 20 ions per unit
cell, and, therefore, its energy can be estimated unambiguously
from ab initio calculations within a reasonable computing time.
However, a first-principles energy calculation for ␥-Al2O3
(containing 64/3 cations per unit cell) would require an expanded supercell with 160 ions (64 aluminum and 96 oxygen).
Recently, the results of energy calculations based on an empirical pair potential model have been reported for ␥-Al2O3.58
In this work, the energy difference is compared for two models
that assume that the cation vacancies are randomly distributed
over either (model A) 16d octahedrally or (model B) 8a tetrahedrally coordinated sites. The calculations rely on empirical
pair potentials derived for ␣-Al2O3 and use formal ionic
charges for both the aluminum and oxygen ions. These calculations show an energy preference of ∼3.7 eV for the vacancy
to occupy an octahedral site. The available experimental data
are controversial but are commonly interpreted in terms of
preferential filling of the octahedral interstices, which would
contradict the results of these energy calculations. Although the
interpretation of the experimental ␥-Al2O3 data in terms of the
cation occupancy is somewhat ambiguous,2,3 the application of
a simple empirical model to the energy calculations for these
Al2O3 phases is clearly unreliable.56 It would seem that, to
determine with any confidence the relative stability of Al2O3
spinel structures having different occupancies of octahedrally
and tetrahedrally coordinated cation sites, ab initio calculations
need to be performed.
No other theoretical data on the ground-state energy difference between the ␥- and ␪-Al2O3 structures or the other metastable aluminas have been found in the literature.
VIII.
Fig. 12. (a) Change of stacking of {111} spinel oxygen layers from
fcc to hcp. (b) Shear of an oxygen layer having aluminum cations in
the interstices. (c) Cooperative migration of the cations around regularly distributed vacancies, resulting in a ‘‘honey comb’’ lattice for
␣-Al2O3 (modified from Ref. 42).
cations (lanthanum and manganese), it never has been observed
experimentally for Al2O3. A theoretical explanation for the
stability of the corundum structure has had to await the 1996
results of ab initio calculations by Wilson et al.,56 who, in their
energy calculations, have combined density functional theory
Influence of Residual Hydroxyl Groups on
Structure of Metastable Aluminas
␩- and ␥-Al2O3 obtained by dehydroxylation of aluminum
hydroxides contain residual hydroxyl ions, and De Boer and
Houben59 believe these phases to be hydrogen spinels, analogous to lithium spinel. Soled60 has postulated that the hydroxyl
ions are a necessary component of the defect structure of ␩and ␥-Al2O3, their number being equal to the number of cation
vacancies. Zhou and Snyder10 have measured the content of
residual hydroxyl-ion groups in these phases by weight loss,
and they have found it to be about 1 group per unit cell, an
order of magnitude less than the results reported by Tsuchida
and Takahashi61 from XPS analysis. It subsequently has been
proposed that ordering of the tetrahedrally coordinated cation
sublattice, rather than the residual water, is responsible for the
tetragonality of ␥-Al2O3, although, it can be argued that even
one hydroxyl-ion group per unit cell should be quite signifi-
August 1998
Metastable Alumina Polymorphs: Crystal Structures and Transition Sequences
2009
Precursors for Metastable Aluminas
Aluminum Hydroxides
Aluminum trihydroxide (Al(OH)3) and monohydroxide
(AlOOH) exhibit polymorphism and exist in many structural forms. The structures of all aluminum hydroxides consist of the stacking of double oxygen layers with the aluminum cations located in octahedrally coordinated interstices.
The packing of oxygen ions inside the layer can be either
hexagonal or cubic, whereas the symmetry of the overall
structure for each hydroxide is determined by the distribution of hydrogen. The relative distances between hydroxyl
groups, both within and between the layers, have been suggested to control the mechanism of dehydration for the particular hydroxide. The structures of the most common aluminum hydroxides are briefly summarized below.
ferred to as pseudoboehmite or gelatinous boehmite.1 A
pseudoboehmite typically contains >15 wt% excess water,
as compared to the stoichiometric composition AlOOH.
Controversy continues concerning the exact location of the
excess water in this structure. Heating pseudoboehmite results in the formation of transition aluminas in a sequence
similar to that associated with bayerite.1
Diaspore—␣-AlOOH: Diaspore occurs in nature. The
structure consists of hexagonal layers of oxygen, which,
however, are significantly distorted. Aluminum cations are
located in octahedrally coordinated interstices between the
adjacent oxygen layers. Diaspore possesses orthorhombic
symmetry with the Pbnm space group and lattice parameters of a ⳱ 4.4 Å, b ⳱ 9.43 Å, and c ⳱ 2.84 Å. The
structure has four formula units per unit cell.67
Aluminum Trihydroxides
Tohdite—5Al2O3ⴢH2O
Gibbsite (hydrargillite)—␥-Al(OH)3: Gibbsite is a
naturally occurring mineral, but it also can be produced by
the Bayer process. The oxygen ions in the gibbsite structure
form close-packed layers with aluminum cations sandwiched in octahedrally coordinated interstices between the
layers, with an occupancy of 2/3.67 There are two such
double layers in the gibbsite unit cell, which contains eight
Al(OH)3 formula units. Each oxygen has one hydrogen
atom attached to it to form a hydroxyl ion, and the number
of O–O bonds in the gibbsite structure is less than the number of hydrogen atoms to be accommodated. The resulting
distribution of O–H bonds distorts the structure, yielding a
monoclinic symmetry described by the space group P21/n
(No. 14). The lattice parameters are a ⳱ 8.62 Å, b ⳱ 5.06 Å,
c ⳱ 9.7 Å, and ␤ ≈ 94°, and the stacking of the O–H layers
can be described as AB-BA. Complete details on the crystallography of gibbsite and the atomic positions can be
found in Ref. 67.
Bayerite—␣-Al(OH)3: Bayerite rarely is found in nature, but it can be prepared in the laboratory by many processing routes.1 The oxygen coordination in the bayerite
structure is similar to that in gibbsite, but the distribution of
hydrogen atoms is different, resulting in an AB-AB stacking
sequence of the O–H layers. There is some controversy in
the literature concerning the true symmetry of bayerite. Although both hexagonal and orthorhombic symmetry have
been proposed for bayerite, based on powder XRD spectra,3
a later refinement of neutron powder diffraction spectra has
resulted in an unambiguous monoclinic symmetry described
by the space group P21/n.68 Three of the six symmetrically
independent hydrogen atoms in the unit cell are located
within a single oxygen layer, and the remaining three form
bonds between adjacent layers.
The crystal structure of tohdite, as determined by
Yamaguchi et al.,70,71 consists of close-packed layers of
oxygen with an approximately ABACABAC stacking. The
hexagonal unit cell of tohdite has lattice parameters of a ⳱
5.576 Å and c ⳱ 8.768 Å, and it contains ten aluminum
cations, eight of which are in octahedrally coordinated and
two in tetrahedrally coordinated interstices. The symmetry
of this structure has been described by the hexagonal P63mc
space group. The refined positions of oxygen and aluminum
for this structure are given in Ref. 71, but the exact distribution of hydrogen atoms in the tohdite structure remains
uncertain.
Aluminum Monohydroxides
Boehmite—␥-AlOOH: Boehmite is the major constituent of many bauxite minerals, and it also can be produced in
the laboratory, for example, either by neutralizing aluminum salts at temperatures close to the boiling point of water
or by treating activated aluminum with boiling water. The
boehmite crystal structure consists of cubic-packed layers of
oxygen ions with aluminum cations sandwiched between
adjacent layers. The distribution of hydrogen atoms results
in an orthorhombic unit cell that has been described by the
Cmcm space group. The lattice parameters of boehmite are
a ⳱ 2.861 Å, b ⳱ 3.696 Å, and c ⳱ 12.233 Å.69
In addition to the stoichiometric crystal structure described above, the name boehmite has been used to describe
the product of aging aluminum hydroxide gel, better re-
Amorphous Anodic Al2O3 Films
Amorphous Al2O3 films can be formed by anodization of
aluminum in acid solution. Nonporous (‘‘barrier’’) amorphous Al2O3 films are formed in solutions that do not dissolve Al2O3, whereas porous Al2O3 films are developed in
acid solutions, where partial solubility is possible.72
The structure of amorphous Al2O3 formed by anodization
has been studied by both extended X-ray absorbtion fine
structure (EXAFS)73 and electron extended energy loss fine
structure (EXELFS)74 techniques. Amorphous Al2O3 films
commonly have been assumed to contain a mixture of tetragonally and octahedrally coordinated aluminum, and
both EXAFS and EXELFS have confirmed that dense
Al2O3 films contain 80% of aluminum cations in octahedral
sites and 20% in tetrahedral sites. The aluminum cations in
the porous Al2O3 films predominantly have tetrahedral or
even lower coordination.
Alumina Melt
The radial distribution function for an Al2O3 melt recently has been measured by Ansell et al.32 in the temperature range 2200–2700 K using X-ray synchrotron radiation.
Al2O3 undergoes a structural rearrangement on melting,
with a change of the aluminum cation coordination from
octahedral, in ␣-Al2O3, to predominantly tetrahedral in the
Al2O3 melt. These results contradict those reported earlier
by Waseda et al.,75 who found octahedrally coordinated
aluminum as the fundamental cluster configuration in the
melt. No explanation that might account for this discrepancy
has been given by Ansell et al.; however, quenching experiments do support the proposed tetrahedral coordination
above the melting point, because high cooling rates (>105
K/s) from the melt result in crystallization of either ␥-Al2O3
or various ordered transition Al2O3 phases, all containing
tetrahedrally coordinated aluminum.
2010
Journal of the American Ceramic Society—Levin and Brandon
Table III.
Vol. 81, No. 8
Energy Differences for the Shell and CIM Models and Local Density
Approximation Calculations†
Energy difference (kJ⭈mol−1)
Structure
Shell model
CIM model
CIM-D model
CIM-DQ model
LDA
␣–␪
␣-Bixbyite
−27.7
38.8
−156
50
−139.8
65
−74
−86
−55
−70.4
†
Reference 56.
Table IV.
Density of Common Al2O3 Precursors and
Metastable Al2O3 Structures†
Density (g/cm3)
Structure
Precursors
Gibbsite
Bayerite
Boehmite
Diaspore
Anodic alumina
Melt
␥, ␩
␦, ␪, ␪⬘, ␪⬙, ␥
␬
␣
2.45
2.5
3.08
3.38
3–3.1
2.97‡
Al2O3polymorphs
3.65–3.67
3.6–3.65
3.98
3.99
†
Reference 80. All densities except for those of anodic Al2O372 and melt80 were
calculated from the lattice parameters of the crystal structure. ‡T ⳱ 2100°C.
cant, because only 22⁄3 cation vacancies are present per unit
cell in the ‘‘spinel’’-type Al2O3 structures. No published work
has been found that addresses the influence of hydroxyl-ion
groups on the structural stability of the Al2O3 polymorphs in any
depth.
IX.
Influence of Dopants on Phase
Transformations in Al2O3
The transformations between the Al2O3 polymorphs are influenced, among other factors, by the presence of additives and
impurities.
Pijolat et al.62 have studied the influence of zirconium and
magnesium dopants on the transformation from the transition
aluminas to ␣-Al2O3. The addition of magnesium cations enhances the rate of transformation from ␥ or ␦ aluminas into the
␣ form, whereas the addition of zirconium cations inhibits the
transformation. The influence of water vapor on the ␥ → ␣
phase transformation in pure Al2O3 also has been investigated,
and it has been demonstrated that the presence of water vapor
enhances the rate of transformation, in agreement with the
conclusions of Hrabe et al.63
In other work,50 the influence of different additives on
the kinetics of the phase transformation has been studied.
Less than 1 wt% of additive does not change the sequence
of the polymorphic transformations during dehydroxylation
of Al(OH)3, but it has been observed that the promotion of
␣-Al2O3 formation is accompanied by destabilization of ␪Al2O3. The influence of the additives on the transformation has
been related to the respective radii and charge of the specific
cations. The additives promote ␣-Al2O3 formation for differences in ionic radii between host and foreign cations of <33%,
whereas a difference in the radii of >33% stabilize the lessdense ␦- or ␪-Al2O3 forms. However, deviations from this dependence also have been observed, thus Sc3+, Y3+, and La3+
stabilize ␣-Al2O3, even though the cations differ in radius by
>33%.
The effect of chromium and iron in solid solution on the rate
of conversion of ␥-Al2O3 to ␣-Al2O3 has been investigated by
Bye and Simpkin64 using reflectance spectra and magnetic susceptibilities. They have shown that chromium exists as Cr6+ in
␥-Al2O3 but as Cr3+ in ␣-Al2O3, with ␪-Al2O3 as an intermediate phase. The intermediate phases form rapidly, and their
rates of conversion to ␣-Al2O3 are increased by 2 and 5 wt%
additions of iron, but decrease by 2 and 4 wt% of chromium.
Moroz et al.65 have analyzed the phase composition of aluminas with chromium, copper, and nickel additions using hightemperature XRD. An interesting peculiarity has been observed
in the sequence of the ␥ → ␣ phase transformation. For
samples with Cr3+ cations, the conversion occurs through a
␦-Al2O3 containing Cr3+ in its structure, whereas, in those
samples with Cu2+ and Ni2+ cations, no ␦-Al2O3 is observed
during the transformation. The authors have suggested that the
divalent cations are localized in tetrahedral sites, whereas the
aluminum cations occupy only octahedral positions, inhibiting
structure rearrangement.
A study of oxide additives that form a liquid phase at
relatively low concentrations shows that ZrO2 strongly retards
the ␥ → ␣ transformation, whereas B2O3 and SiO2 have less
effect. No plausible explanation has been given.66 Many metal
oxides (Zn, Ti + Cu, Ti + Mn, Cu, V, and Li) have been
observed to enhance the transformation, at least to some extent.67 This has been attributed to the formation of a liquid
phase below the ␥ → ␣ transformation temperature. ZnF2 has
the largest effect.
The published results demonstrate that additives can influence both the temperature and the rate of the ␥ → ␣ phase
transformation, and they can change the sequence of intermediate phases during the transformation. Although some suggestions have been made to rationalize the influence of different
additives on the mechanism of the ␥ → ␣ phase transformations in Al2O3, no consistent atomistic model as yet exists in
the literature.
X.
Conclusions
Significant progress has been made over the past decade in
developing an understanding of polymorphism in Al2O3. The
metastable Al2O3 structures can be described consistently in
terms of ordered cation arrangements on the interstitial sites of
the oxygen anion sublattice, which remains approximately
close packed (either cubic or hexagonal). The Al2O3 polymorphs commonly observed include six structures based on the
fcc and three structures based on the hcp packing of oxygen
anions. A combined use of CBED, electron microdiffraction,
and lattice-imaging in HRTEM has made possible a reasonable
determination of the lattice parameters and the true symmetry
for most of these structures. A formal analysis of the symmetry
changes that accompany the phase transformations between the
Al2O3 polymorphs has permitted a rational interpretation of the
complex domain structure typically developed in the metastable Al2O3 phases.
Despite the progress that has been made, there remain some
fundamental unanswered questions. In particular, the exact distribution of the aluminum cations in all the metastable Al2O3
structures, other than ␪-Al2O3, remains unknown, as do the
precise conditions that determine the formation of one or another polymorph. Another issue concerns the transformation
from a metastable polymorph to the stable corundum structure
of ␣-Al2O3. An experiment is needed that would allow the
observation of ␣-Al2O3 at the (apparently very unstable) nucleation stage. The analysis of the growth–transformation front
between ␣- and ␥-Al2O3 using sapphire substrates on which an
epitaxial layer of ␥-Al2O3 has been grown could be a starting
point toward some understanding of this transformation.
August 1998
Metastable Alumina Polymorphs: Crystal Structures and Transition Sequences
Acknowledgments:
This research was supported by the German–Israel
Foundation for Scientific Research and Development under Contract No. 040551. I.L. is grateful to the Israel Ministry of Science for financial support.
References
1
K. Wefers and C. Misra, ‘‘Oxides and Hydroxides of Aluminum,’’ Alcoa
Technical Paper No. 19, Alcoa Laboratories, Pittsburgh, PA, 1987.
2
S. J. Wilson, ‘‘Phase Transformations and Development of Microstructure
in Boehmite-Derived Transition Aluminas,’’ Proc. Br. Ceram. Soc., 28, 281–94
(1979).
3
B. C. Lippens and J. H. De Boer, ‘‘Study of Phase Transformations during
Calcination of Aluminum Hydroxides by Selected Area Electron Diffraction,’’
Acta Crystallogr., 17, 1312 (1964).
4
T. Hahn (Ed.), International Tables of Crystallography, Vol. A. Kluwer,
London, U.K. 1995.
5
J. Hornstra, ‘‘Dislocations, Stacking Faults, and Twins in the Spinel Structure,’’ J. Phys. Chem. Solids, 15, 311–23 (1960).
6
A. G. Khachaturyan and B. I. Pokrovsky, ‘‘Concentration Wave Approach
in Structural and Thermodynamic Characterization of Ceramic Crystals,’’ Prog.
Mater. Sci., 29, 1–138 (1985).
7
K. Shirasuka, H. Yanagida, and G. Yamaguchi, ‘‘The Preparation of ␩Alumina and Its Structure,’’ Yogyo Kyokai-shi, 84 [12] 610–13 (1976).
8
C. S. John, V. C. M. Alma, and G. R. Hays, ‘‘Characterization of Transition
Alumina by Solid-State Magic Angle Spinning Aluminum NMR,’’ Appl. Catal.,
6, 341–46 (1983).
9
F. Ernst, P. Pirouz, and A. H. Heuer, ‘‘HRTEM Study of a Cu–Al2O3 Interface,’’ Philos. Mag. A, 63 [2] 259–77 (1991).
10
R. S. Zhou and R. L. Snyder, ‘‘Structures and Transformation Mechanisms
of the ␩, ␥, and ␪ Transition Aluminas,’’ Acta Crystallogr., Sect. B: Struct. Sci.,
47, 617–30 (1991).
11
S. Blonski and S. H. Garofalini, ‘‘Molecular Dynamics Simulations of ␣Alumina and ␥-Alumina Surfaces,’’ Surf. Sci., 295, 263–74 (1993).
12
G. Yamaguchi and H. Yanagida, ‘‘Thermal Effects on the Lattices of ␩ and
␥ Aluminum Oxide,’’ Bull. Chem. Soc. Jpn., 37, 1229–31 (1964).
13
V. Jayaram and C. G. Levi, ‘‘The Structure of ␦-Alumina Evolved from the
Melt and the ␥ → ␦ Transformation,’’ Acta Metall., 37 [2] 569–78 (1989).
14
A. L. Dragoo and J. J. Diamond, ‘‘Transitions in Vapor-Deposited Alumina
from 300° to 1200°C,’’ J. Am. Ceram. Soc., 50, 568 (1967).
15
K. J. Morrisey, K. K. Czanderna, R. P. Merrill, and C. B. Carter, ‘‘Transition
Alumina Structures Studied Using HREM,’’ Ultramicroscopy, 18, 379–86 (1985).
16
I. Levin, L. A. Bendersky, D. G. Brandon, and M. Rühle, ‘‘Cubic to Monoclinic Phase Transformations in Alumina,’’ Acta Metall. Mater., 45 [9] 3659–69
(1997).
17
I. Levin and D. G. Brandon, ‘‘A New Alumina Polymorph with Monoclinic
Symmetry,’’ Philos. Mag. Lett., 77 [2] 117–24 (1998).
18
J. Doychak, J. L. Smialek, and T. E. Mitchell, ‘‘Transient Oxidation of
Single-Crystal Nickel–Aluminum (␤-NiAl),’’ Metall. Trans. A, 20, 499 (1989).
19
K. Prüssner, J. Bruley, U. Salzberger, H. Zweygart, E. Schumann, and M.
Rühle, ‘‘SEM and TEM Observations on the Development of the Oxide Scale
on Y-Implanted Single Crystalline ␤-NiAl under Low Oxygen Partial Pressure’’; p. 435 in Microscopy of Oxidation—2, Proceedings of 2nd International
Conference. Edited by S. Newcomb and M. Bennett. Cambridge University
Press, Cambridge, U.K., 1993.
20
J. Yang, E. Schumann, I. Levin, and M. Rühle, ‘‘Transient Oxidation of
NiAl,’’ Acta Mater., 46 [6] 2195–201 (1998).
21
H. P. Rooksby and C. J. M. Rooymans, ‘‘The Formation and Structure of
Delta Alumina,’’ Clay Miner. Bull., 4, 234 (1961).
22
A. Dauger, D. Fargeot, and P. Lortholary, ‘‘Transformations de Phase Dans
Al2O3 et (Al2O3)n–MgO Projetes au Chalumeau a Plasma. I. Phases Metastables
Dans l’Alumine Pure’’; pp. 157–63 in Science of Ceramics, Vol. 11. Edited by
R. Carlsson and S. Karlsson. Swedish Ceramic Society, 1981.
23
A. Dauger, D. Fargeot, and J. P. Laval, ‘‘Metastable Phases of Alumina,’’
Mater. Res. Soc. Symp. Proc., 21, 207 (1984).
24
J. E. Bonevich and L. D. Marks, ‘‘The Sintering Behavior of Ultrafine
Alumina Particles,’’ J. Mater. Res., 7 [6] 1489–500 (1992).
25
Y. Repelin and E. Husson, ‘‘Etudes Structurales d’Aluminides de Transition. I—Alumines Gamma et Delta,’’ Mater. Res. Bull., 25, 611–21 (1990).
26
I. Levin, T. Gemming, and D. G. Brandon, ‘‘Some Metastable Phases and
Transient Stages of Transformation in Alumina,’’ Phys. Status Solidi, A, 166 [1]
197–218 (1998).
27
J. A. Kohn, G. Katz, and J. D. Broder, ‘‘Characterization of ␤-Ga2O3 and
its Alumina Isomorph, ␪-Al2O3,’’ Am. Mineral., 42, 398–407 (1957).
28
S. Geller, ‘‘Crystal Structure of ␤-Ga2O3,’’ J. Chem. Phys., 33, 676
(1960).
29
G. Yamaguchi, I. Yasui, and W.-C. Chiu, ‘‘A New Method of Preparing
␪-Alumina and the Interpretation of Its X-ray Powder Diffraction Pattern and
Electron Diffraction Pattern,’’ Bull. Chem. Soc. Jpn., 43, 2487–91 (1970).
30
L. D. Landau and E. M. Lifshitz, Statistical Physics. Pergamon Press, Oxford, U.K., 1970.
31
L. A. Bendersky, W. J. Boettinger, B. P. Burton, F. S. Bianconniello, and
C. B. Shoemaker, ‘‘The Formation of Ordered ␻-Related Phases in Alloys of
Composition Titanium, Aluminum, Niobium (Ti4Al3Nb),’’ Acta Metall., 38 [6]
931–43 (1990).
32
L. A. Bendersky, A. Roytburd, and W. J. Boettinger, ‘‘Phase Transformations in the (Ti,Al)3Nb Section of the Ti-Al-Nb System—I. Microstructural
Predictions Based on a Subgroup Relation Between Phases,’’ Acta Metall., 42
[7] 2323 (1994).
33
S. Ansell, S. Krisshnan, J. K. R. Weber, J. Felten, P. C. Nordine, M. A.
2011
Beno, D. L. Price, and M.-L. Saboungi, ‘‘Structure of Liquid Aluminum Oxide,’’ Phys. Rev. Lett., 78 [3] 464–66 (1997).
34
H. C. Stumpf, A. S. Russel, J. W. Newsome, and C. M. Tucker, Ind. Eng.
Chem., 42, 1398 (1950).
35
G. W. Brindley and J. O. Choe, ‘‘The Reaction Series, Gibbsite → ␹Alumina → ␬-Alumina → Corundum. I,’’ Am. Mineral., 46, 771–85 (1961).
36
M. Okumiya, G. Yamaguchi, O. Yamada, and S. Ono, ‘‘The Formation of
␬- and ␬⬘-Al2O3 from the Dehydration of Tohdite 5Al2O3⭈H2O,’’ Bull. Chem.
Soc. Jpn., 44, 418–23 (1971).
37
P. Liu and J. Skogsmo, ‘‘Space-Group Determination and Structure Model
for ␬-Al2O3 by Convergent-Beam Electron Diffraction (CBED),’’ Acta Crystallogr., Sect. B: Struct. Sci., 47, 425–33 (1991).
38
E. Fredriksson and J. O. Carlsson, ‘‘Factors Influencing the ␬-Al2O3 →
␣-Al2O3 Transformation during CVD Growth,’’ Surf. Coat. Technol., 56 [2]
165–77 (1993).
39
N. Lidulf, M. Halvarsson, H. Norden, and S. Vuorinen, ‘‘Microstructural
Investigation on the ␬-Al2O3 → ␣-Al2O3 Transformation in Multilayer Coatings
of Chemically Vapor Deposited ␬-Al2O3,’’ Thin Solid Films, 253 [1–2] 311–17
(1994).
40
S. Vuorinen and J. Skogsmo, ‘‘Characterization of Aluminum Oxide ␣Al2O3, ␬-Al2O3, and ␣–␬ Multioxide Coatings on Cemented Carbides,’’ Thin
Solid Films, 193–194, 536–46 (1990).
41
T. C. Chou and T. G. Nieh, ‘‘Nucleation and Concurrent Anomalous Grain
Growth of ␣-Al2O3 during ␥ → ␣ Phase Transformation,’’ J. Am. Ceram. Soc.,
74, 2270 (1991).
42
S. Kachi, K. Momiyama, and S. Shimuzu, ‘‘An Electron Diffraction Study
and a Theory of the Transformation from ␥-Fe2O3 to ␣-Fe2O3,’’ J. Phys. Soc.
Jpn., 18 [1] 106–16 (1963).
43
Y. Ishitobi, M. Shimada, and M. Koizumi, ‘‘Sintering of Dense Alumina by
Direct Transformation from Eta to Alpha Al2O3 under High Pressure’’; pp.
113–32 in Proceedings of Round Table Meeting on Special Ceramic Electronics
and Electrical Engineering (1979).
44
F. W. Dynys and J. W. Halloran, ‘‘Alpha Alumina Formation in AlumDerived Gamma Alumina,’’ J. Am. Ceram. Soc., 65 [9] 442–48 (1982).
45
P. A. Badkar, J. E. Biley, and H. A. Barker, ‘‘Sintering Behaviour of
Boehmite Gel’’; pp. 311–22 in Sintering and Related Phenomena, Materials
Science Research, Vol. 6. Plenum, New York, 1973.
46
Y. Ishitobi, M. Shimada, and M. Koizumi, ‘‘Reactive Pressure Sintering of
Alumina,’’ Am. Ceram. Soc. Bull., 59 [12] 1208–11 (1980).
47
E. J. Gonzalez, B. Hockey, and G. J. Piermarini, ‘‘High Pressure and Sintering
of Nano-Size ␥-Al2O3 Powder,’’ Mater. Manuf. Processes, 11 [6] 951–67 (1996).
48
M. Kumagai and G. L. Messing, ‘‘Controlled Transformation and Sintering
of a Boehmite Sol–Gel by ␣-Alumina Seeding,’’ J. Am. Ceram. Soc., 68 [9]
500–505 (1985).
49
C. J.-P. Steiner, D. P. H. Hasselman, and R. M. Spriggs, ‘‘Kinetics of the
Gamma-to-Alpha Alumina Phase Transformation,’’ J. Am. Ceram. Soc., 54 [8]
412 (1971).
50
V. J. Vereshagin, V. Yu Zelinskii, T. A. Khabas, and N. N. Kolova, ‘‘Kinetics and Mechanism of Transformations of Low-Temperature Forms of Alumina in ␣-Aluminum Oxide in the Presence of Additives,’’ Zh. Prikl. Khim., 55,
1946–51 (1982).
51
N. N. Sirota and G. N. Shokhina, ‘‘Kinetics of Polymorphous Transformations of Anodic Alumina,’’ Krist. Tech., 9 [8] 913–19 (1974).
52
J. R. Wynnyckyj and C. G. Morris, ‘‘A Shear-Type Allotropic Transformation in Alumina,’’ Metall. Trans. B., 16B, 345–53 (1985).
53
T. W. Simpson, Q. Wen, N. Yu, and D. R. Clarke, ‘‘Kinetics of the Amorphous → Gamma → Alpha Transformations in Aluminum Oxide: Effect of
Crystallographic Orientation,’’ J. Am. Ceram. Soc., 81 [1] 61–66 (1998).
54
N. Yu, T. W. Simpson, P. C. McIntyre, M. Nastasi, and I. V. Mitchell,
‘‘Doping Effects on the Kinetics of Solid-Phase Epitaxial Growth of Amorphous Alumina Thin Films on Sapphire,’’ Appl. Phys. Lett., 67 [7] 924
(1995).
55
R. Brydson, ‘‘Multiple Scattering Theory Applied to ELNES of Interfaces,’’ J. Phys. D: Appl. Phys., 29, 1699–708 (1996).
56
M. Wilson, M. Exner, Y.-M. Huang, and M. Finnis, ‘‘Transferable Model
for the Atomistic Simulation of Al2O3,’’ Phys. Rev. B: Condens. Matter, 54 [22]
15683 (1996).
57
A. P. Borosy, B. Silvi, M. Allavena, and P. Nortier, ‘‘Structure and Bonding of Bulk and Surface ␪-Alumina from Periodic Hartree–Fock Calculations,’’
J. Phys. Chem., 98, 12189–3194 (1994).
58
S.-D. Mo, Y.-N. Xu, and W. Y. Ching, ‘‘Electronic and Structural Properties of Bulk ␥-Al2O3,’’ J. Am. Ceram. Soc., 80 [5] 1193–97 (1997).
59
J. H. De Boer and G. M. Houben, ‘‘Binding of Water in and on Al2O3’’; pp.
237–44 in Proceedings of the International Symposium on the Reactivity of
Solids, Part I (1952).
60
S. Soled, ‘‘␥-Alumina Viewed as a Defect Oxyhydroxide,’’ J. Catal., 81,
252–57 (1983).
61
T. Tsuchida and H. Takahashi, ‘‘X-ray Photoelectron Spectroscopic Study
of Hydrated Aluminas and Aluminas,’’ J. Mater. Res., 9 [11] 2919–24 (1994).
62
M. Pijolat, M. Dauzat, and M. Soustelle, ‘‘Influence of Additives and
Water Vapour on the Transformation of Transition Aluminas into Alpha Alumina,’’ Thermochim. Acta, 122, 71–77 (1987).
63
Z. Hrabe, S. Komarneni, L. Pach, and R. Roy, ‘‘The Influence of Water
Vapor on Thermal Transformations of Boehmite,’’ J. Mater. Res. 7 [2] 444–49
(1992).
64
G. C. Bye and G. T. Simpkin, ‘‘Influence of Cr and Fe on Formation of
␣-Al2O3 from ␥-Al2O3,’’ J. Am. Ceram. Soc., 57 [8] 367–71 (1974).
65
E. M. Moroz, O. A. Kirichenko, A. V. Ushakov, and E. A. Levitski, ‘‘Phase
Composition of Aluminum Oxides Promoted by Cr, Cu, and Ni Additives,’’
React. Kinet. Catal. Lett., 28 [9] 9–15 (1985).
2012
Journal of the American Ceramic Society—Levin and Brandon
66
L. A. Xue and I-W. Chen, ‘‘Influence of Additives on the ␥-to-␣ Transformation of Alumina,’’ J. Mater. Sci. Lett., 11, 443–45 (1992).
67
H. D. Megaw, Crystal Structures: A Working Approach. Saunders, Philadelphia, London, Toronto, 1973.
68
F. Zigan, W. Joswig, and N. Burger, ‘‘Die Wasserstoffpositionen in
Bayerit, Al(OH)3,’’ Z. Kristallogr., 148, 255–73 (1978).
69
C. E. Corbato, R. T. Tettenhorst, and G. G. Christoph, ‘‘Structure
Refinement of Deuterated Boehmite,’’ Clays Clay Miner., 33 [1] 71–75
(1985).
70
G. Yamaguchi, H. Yanagida, and S. Ono, ‘‘New Alumina Hydrate, ‘Tohdite’ (5Al2O3⭈H2O),’’ Bull. Chem. Soc. Jpn., 37, 1555–57 (1964).
71
G. Yamaguchi and M. Okumiya, ‘‘Refinement of the Structure of Tohdite
5Al2O3⭈H2O,’’ Bull. Chem. Soc. Jpn., 42, 2247–49 (1969).
72
L. Young, Anodic Alumina Films. Academic Press, New York, 1961.
73
S. M. El-Mashri, R. G. Jones, and A. J. Forty, ‘‘An Electron-Yield EXAFS
Study of Anodic Oxide and Hydrated Oxide Films on Pure Aluminum,’’ Philos.
Mag. A, 48, 665 (1983).
74
A. J. Bourdillon, S. M. El-Mashri, and A. J. Forty, ‘‘Application of TEM
Vol. 81, No. 8
Extended Electron Energy Loss Fine Structure to the Study of Aluminum Oxide
Films,’’ Philos. Mag. A, 49 [3] 341 (1984).
75
Y. Waseda, K. Sugiyama, and J. M. Toguri, ‘‘Direct Determination of the
Local Structure in Molten Alumina by High-Temperature X-ray Diffraction,’’
Z. Naturforsch., A: Phys. Sci., 50 [8] 770–74 (1995).
76
M. L. Kronberg, ‘‘Plastic Deformation of Single Crystals of Sapphire—
Basal Slip and Twinning,’’ Acta Metall., 5, 507–24 (1957).
77
J. B. Bilde-Sørensen, B. F. Lawlor, T. Geipel, P. Pirouz, A. H. Heuer, and
K. P. D. Lagerlöf, ‘‘On Basal Slip and Basal Twinning in Sapphire (␣-Al2O3)—
I. Basal Slip Revisited,’’ Acta Metall. Mater., 44 [5] 2145–52 (1996).
78
W. D. Kaplan, P. R. Kenway, and D. G. Brandon, ‘‘Polymorphic Basal
Twin Boundaries and Anisotropic Growth in ␣-Al2O3,’’ Acta Metall. Mater.,
43, 835–48 (1995).
79
P. Pirouz, B. F. Lawlor, T. Geipel, J. B. Bilde-Sørensen, A. H. Heuer,
and K. P. D. Lagerlöf, ‘‘On Basal Slip and Basal Twinning in Sapphire (␣Al2O3)—II. A New Model of Basal Twinning,’’ Acta Metall. Mater., 44 [5] 2153–
64 (1996).
80
Slag Atlas, 317–18. Verlag Stahleisen, 1995.
䊐
Igor Levin is a Guest Researcher at the Ceramics Division of the National Institute
of Standards and Technology (NIST), Gaithersburg, MD. He received his degree
(honors) in physical metallurgy from the St. Petersburg (Leningrad) Polytechnical
Institute in 1987, a M.Sc. in 1994 and a D.Sc. in 1997 in materials science and
engineering from the Technion-Israel Institute of Technology. He was a visiting
scientist at the Max-Planck Institute für Metallforschung, Stuttgart, Germany. Dr.
Levin’s current research focuses on crystal structures and phase transitions in complex ceramic oxides for use in microwave wireless communications.
On receiving his Ph.D. in 1959 from Cambridge University (U.K.), David Brandon
joined that university’s Department of Metallurgy, where he was in charge of the
development of field ion microscopy. In 1963 he moved to the Battelle Memorial
Institute, Geneva, Switzerland, and, in 1966, he joined the Technion-Israel Institute
of Technology. Dr. Brandon was a Senior SRC Fellow at the University of Cambridge and a Visiting Senior Scientist at the Ecole National Superieure des Mines,
Paris. He was a Visiting Fellow of Wolfson College at the University of Oxford and
a Visiting Scholar at Lehigh University. Dr. Brandon is a Fellow of the Institute of
Physics (U.K.), of the Institute of Metals (U.K.), and of ASM International. He holds
the Arturo Gruenebaum Chair in Mining and Metallurgy and is currently Technion
Coordinator for International Student Exchange and a member of the Board of Directors of Acta Metallurgica Inc.