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Cubic to monoclinic phase transformations in alumina
Acta mater. Vol. 45, No. 9, pp. 3659-3669, 1997 Inc. c~ 1997 Acta Metallurgica Published by Elsevier Science Ltd. All rights reserved
Pergamon
Printed in Great Britain 1359-6454/97 $17.00 + 0.00
PII: S1359-6454(97)00040-2
CUBIC TO MONOCLINIC
I. LEVIN’,
PHASE TRANSFORMATIONS ALUMINA
L. A. BENDERSKY:
D. G. BRANDON’
and M. RfJHLE3
‘Faculty of Materials Engineering, Technion, Haifa 32000, Israel; ‘Metallurgy MD 20899, U.S.A. and )Max-Planck Institut Fur Metallforschung, Institut Seestrasse 92, D-70 174 Stuttgart, Germany (Received 22 February
IN
Div., NIST, Gaithersbury, Fur Werkstoffwissenschaft,
1996; accepted IO January 1997)
Abstract-Cubic to monoclinic phase transformations in alumina were studied by high-resolution electron microscopy of anodic films annealed at 1200°C. In addition to the known monoclinic 0-Al~01 structure a new metastable alumina polymorph was identified also with apparent monoclinic symmetry. This new phase appears to evolve from y-alumina by cation ordering. The stoichiometric structure of this polymorph is consistent with the C2/m space group and unit cell containing 40 ions (8AhOj). Reasonably good fit between experimental and computer-simulated lattice images was obtained for the suggested structural model. The transformations of y-Al203 to both monoclinic alumina structures were assumed to be non-reconstructive and the possible transformation paths were analyzed in terms of symmetry group/subgroup relationships. c 1997 Acta Metallurgica Inc.
INTRODUCTION Alumina phases
has a large in addition
number to the
of metastable thermodynamically
crystalline stable
c!-AlZ03, or corundum phase. These metastable alumina polymorphs include y (cubic spinel), 6 (either tetragonal or orthorhombic), B (monoclinic), 1 ( a second cubic spinel), K (orthorhombic), x (cubic), p (hexagonal) and r-(?) [l]. These polymorphs are commonly obtained by dehydration of different alumina hydroxides, but can also be formed by rapid quenching from the melt, vapor deposition or crystallization of amorphous alumina. All the metastable aluminas (also termed “transition” aluminas) have reproducible crystal structures which are stable at room temperature. The most common metastable alumina polymorphs are y-, 6- and B-alumina. y-alumina has been described as a defect spine1 structure (space group Fd3m) [2]. This structure contains oxygen anions in 32e Wyckoff positions, which can be viewed approximately as a 2 x 2 x 2 array of f.c.c. unit cells [3]. The 64/3 Al cations (to satisfy Alz03 stoichiometry) are distributed over 16d (with occupancy 1) octahedrally-coordinated and 8a (occupancy 2/3) tetrahedrally-coordinated interstitial sites in the oxygen anion sublattice. In Y-alumina, the remaining S/3 vacant cation 8a sites are assumed to be randomly distributed. This structural model is closely related to the ideal spine1 structure AB204. In the Fd3m space group there are additional tetrahedral (48f and 8b) and octahedral sites (16~) which are empty in an ideal spinel, but may be partially occupied in defect alumina structures [3,4].
rhombohedral
8-A&O, has been shown to possess monoclinic symmetry with a space group C2/m. This structure contains 20 ions per unit cell with all the ions located at 4i Wyckoff positions (Table 1) [4, 51. The Al cations occupy four octahedrally and four tetrahedrally coordinated interstitial sites in the oxygen sublattice with an occupancy of 1. 6-A&O3 is viewed as a superstructure of y-AllOj. The unit cell contains 160 ions with eight ordered cation vacancies. Both tetragonal (a, = a:, c = 3a;.) and orthorhombic (a~ = a,, bs = 2u,, cg = 1.5u;,) unit cells have been reported for S-Al2O3 (a; is a lattice parameter of i;-A1203) [3, 6, 71. All the studies in which tetragonal 6-AlZ03 was observed started from boehmite (AlOOH), while the orthorhombic unit cell for &Al,O, was observed for the precursor phase obtained either by quenching the melt or by thermal oxidation. The atomic structure of either of the phases referred to as S-Al,O, remains unknown. Two possible space groups (P2,2,2 and P2,2,2,) have been proposed in the literature for the orthorhombic 6-A1203, based on convergent beam electron diffraction analysis [6]. Although extensive research over the past few decades has made progress in characterizing transition aluminas, little high-resolution transmission electron microscopy (HRTEM) has been reported. The present contribution is a part of a high-resolution TEM study of phase transformations which occur in alumina during the heating of amorphous alumina films formed by anodization. The paper is primarily concerned with cubic-to-monoclinic phase transition in alumina. In addition to the study of monoclinic &AlzO, structure, preliminary results are presented
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on a previously unknown metastable alumina polymorph. This polymorph also possesses monoclinic symmetry and is apparently formed directly from y-alumina. The experimental results were analyzed in terms of symmetry changes which occur during the phase transformation. A model structure for the observed new alumina phase (termed 19’) is proposed based on the assumption that the Al cations are ordered on interstitial sites of the oxygen sublattice of y-alumina. EXPERIMENTAL
PROCEDURE
Self-supported amorphous anodic alumina films were used as a precursor for the study of polymorphic phase transformations. The thin films of amorphous alumina were obtained by anodization of Al foil in a 0.01 M aqueous solution of ammonium tartrate at room temperature. Prior to anodization, the metal foil was electrochemically polished in perchloric acid/ethanol solution (1:4) with one side of the foil coated with an insulating lacquer to prevent the reaction. The thickness of the oxide film was slightly less than 20 nm. After anodization, the lacquer was dissolved in acetone and free-standing alumina films were released by dissolution of the remaining Al. The floating films were retrieved on a TEM ceramic support (diameter 3 mm) and dried in air. Films prepared and mounted by this route were placed in a pure alumina crucible and annealed in air at 1200°C. The ceramic TEM supports were produced from high-purity polycrystalline alumina as described in Ref. [8]. The use of these supports prevented film tearing as a result of thermal expansion mismatch between alumina and the metals used for commercially available grids (Ni, MO, Pt). High-resolution electron microscopes, a JEOL 3010UHR operated at 300 keV and a JEOL 4000EX operated at 400 keV, were used for structural lattice imaging. The samples were coated with a thin film of carbon to improve electrical conductivity. RESULTS The primary product after heat treatment was nanocrystalline (l&20 nm) y-alumina, confirmed by selected area electron diffraction (SAD) which yielded polycrystalline ring patterns and by occasional microdiffraction. In addition to the nanocrystalline y-alumina, larger grains (SO-ZOO nm in size) or conglomerates of slightly misoriented grains were observed. SAD patterns and lattice images taken Table 1. Atomc Atom Al AI 0 0 0
coordmates
Wyckoff position
x
4i 4i 4i 4i 4i
0.0843 0.3400 0.1614 0.4980 0.1674
for Q-ALO,
(space group CZ/m)
y
Ref. [S] i
x
0.0000 0.0000 0.0000 0.0000 0.0000
0.7929 0.6832 0.1071 0.2602 0.5596
0.0834 0.3405 0.1611 0.4950 0.8272
Fig. 1. Lattice image and selected area diffraction pattern attributed to Q-A1203in the [I 10]7//[010]~orientation.
[4, 51
Ref. [4] Y 2 0.0000 0.0000 0.0000 0.0000 0.0000
(b)
0.7927 0.6835 0.0984 0.2526 0.4273
from these grains proved that they are either 6 (orthorhombic) or f3polymorphs. All the phases show preferred orientation corresponding to either the (loo), or (1 lo), directions perpendicular to the film surface.
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Absence of Kikuchi and high-order Laue zone (HOLZ) lines (due to the small foil thickness), together with the fine spatial scale and the lack of distinct morphology for the metastable alumina phases (when observed in diffraction contrast) made controlled tilting of the specimens to align specific zone axes parallel to the beam direction extremely difficult. Therefore, lattice imaging of metastable aluminas was limited to the direction of preferred orientation.
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Since the present paper is primarily concerned with the cubic-to-monoclinic phase transition in alumina, further analysis is limited to the monoclinic B-Al,O, phase. Figure 1 shows a SAD pattern and lattice image taken from a single grain. Fundamental spots in the pattern correspond to the (110) pole of cubic y-A1203 while additional spots can be attributed both to the 6 (orthorhombic) and the 0 phase in [210]~ and [OIO]s orientations, respectively. Optical diffraction from
Fig. 2(a) and (b)-Caption
overleaf.
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Fig. 2. Lattice images of B-A1203showing interfaces between crystallographic variants of 0-Alz0,. (a) and (b) Translational (APB type) interfaces with translational vectors RI= fanand R2= ~CO, respectively; (c) rotational (twin type) interface with a twinning plane corresponding to (100)~.
the lattice image is consistent only with monoclinic f3-A1203 in [OlO] orientation. The { 11 l)? and {113}, reflections present on the SAD pattern are not expected for 8-Alz0, [only one of the (111); reflections is preserved, being transformed to (zOl)O]. This suggests that both y- and B-Al,Os coexist in the area from which the SAD is obtained. Diffuse streaks which pass through the { 1111 and { 113) reflections in the [OOl],* (the asterisk * indicates reciprocal space) direction can also be attributed to an incomplete y + 8 transformation in the area of the SAD aperture. Lack of information about precise zone axis orientation with respect to the electron beam direction precludes quantitative matching of the phase contrast simulated by computer to that obtained experimentally. However, the main features of the contrast observed can be reproduced by image simulations assuming a structural model for Q-A1203 suggested in the literature [4]. Based on this analysis the observed region [Fig. l(a)] was attributed to 8-AlzO,. All the recorded lattice images of Q-A&O3 shown an orientation relationship between y- and Q-A&O, phases corresponding to [010]0//( 1 lo), Lattice images obtained from B-Al,O, (Fig. 2) revealed the presence of two types of domain boundaries: a translation (APB type) with the vectors of translation RI = $zo and RZ = fcs; and a rotational (twin type) with the interface plane corresponding to (001); = (100)s. In addition to the y, 6 and B-A&O, phases identified in the present specimens, some regions result in
diffraction which could not be assigned to any previously reported alumina phase. One such region is seen in Fig. 3(a) as a conglomerate of slightly misoriented grains. The SAD pattern taken from one of the grains (which appears dark in the image) is shown in Fig. 3(b). The pattern does not match any of the known alumina polymorphs, although the strong fundamental spots can be ascribed to the reflections of cubic y-alumina in the (li0) zone axis, with the exception of the absence of { 11 l}? and { 113}: reflections and the small lattice distortion (the angle between k = [l 111: and k = [223],* is 94” instead of 90”). At this stage of the analysis, the distortion is ignored and the structure is treated as a derivative of the ideal cubic y-Al,O, structure. The corresponding lattice image [Fig. 3(c)] clearly shows the presence of a lamellar structure with two different orientations of this phase. The lamellae are lenticular, with interfaces approximately normal to [l lo], An optical diffraction pattern taken from one lamella showed superlattice spots at l/3 and 2/3[222],, indicating ordering of the (222}, planes with an ordering vector k = 1/3[222],?. Two variants of this ordering, k = 1/3[222]* and k = 1/3[22?.]* are present in the image, as alternating lamellae. The streaks passing through the superlattice reflections in the [110]: direction apparently result from near-planar domain boundaries, while the curvature of the streaks can be ascribed to the lamellae edges. Based on this observation of a single orientation, we infer that the lamellar phase (denoted 0’) can be described by
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ordering of (22 2ji planes of the y-alumina. It is not clear if the lan nellar structure is a product of the decomposition (by ordering) of an individual y-alumina grair I, or if a y-alumina grain acted as a precursor to th le ordered phase, which then grows discontinuously in a twin-coupled mode. DISCUSSION
The comparis ion of the SAD patterns
from y, 0 and
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newly observed 0’ aluminas shows that all the reflections which arise from both the anion (oxyg Len) the cation and 20, in Obfoth :A1 and ({400}, {440],{222}) ares$~~~~~ 0’-AlzO,. The changes occur to those y-A; 20) reflections ({ 11 l), {113}) which arise solely from the cation sublattices. Hence the absence of the { 1 II l)? and { 113},. reflections in the diffraction patterns fr ‘om 8- and B’-ALO, [Figs l(b) and 3(b)] suggests than lges
(4
Fig. 3(a) and (b)-Caption
overleaf.
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(4
. ds
092 . . 0
??
.
?20 ??
??
.
0
.
.
.
Fig. 3. (a) Bright field image showing a two-dimensional aggregation of misoriented grains. (b) and (c) The SAD and lattice image taken from one of these grains. The dominant spots correspond to y-Al203 in a [l lo] zone axis orientation. Two crystallographic variants rotated by 72” are indicated on the lattice image. (d) A computer simulated SAD.
in the cation sublattice of y-alumina which lead to 1/6[004]: (kinematically forbidden for &A1203) or 1/3[222]* ordering for 0- and 0’-A1203, respectively. In addition, the streaks in the diffraction patterns from 8- and 0’-AlzO, phases do not pass through the reflections which are associated primarily with the anion sublattice. This implies that the oxygen sublattice is practically uneffected by both the y --t 6 and y + 0’ transformations. In the case of 0’-A1203,
the oxygen sublattice remains continuous through the whole lamellar structure. That is, the primary changes occur by cation re-distribution. The y + Q transformations may therefore be and y--+8’ assumed to occur by ordering on interstitial sites in the f.c.c.-packed oxygen anion sublattice and can be treated in terms of the Landau theory of continuous phase transitions, using maximal subgroup relations [9,
101.
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y + 8-AlzO~ TRANSITION
The lattice parameters of @-A&O3 are a = 11.8 1 A, h = 2.9 8, and c = 5.61 A and can be related to that of y-A1203, a; as follows a z ia: ,
b = a: j2J2,
c = a;/,/2.
These parameters are fully compatible with the orientation relationship between ‘J- and 0-Al,Oi [llO]j//[OIO]O, (OO1).,.//(lOO)n suggested by Wilson [ll] and confirmed by the present SAD analysis. a of 8-AlzOi cannot be The lattice parameters derived solely by ordering of >l-AlzOi, which would require integer multiplication of a7 but not by a factor of 3/2. To account for the extension of a, by 3/2 it is necessary to assume that the y-AIZ03 lattice is either first disordered, with a,, reduced by 2, and then ordered with a threefold increase of the lattice parameter (resulting in aB= 3/2a,.), or vice versa, that is first ordered and then disordered with the corresponding changes in the lattice parameter. The maximal group/subgroup sequence was sought, which connects the space groups of y-A&O, (FdTm) and 0-A1203 (monoclinic C2/m), is consistent with the experimentally observed lattice parameters and atomic positions for 0-A1203, and gives the correct orientation relationship between y- and 0-A1,03. The sequence found is represented by the diagram shown in Fig. 4, where an increase or decrease in symmetry is indicated by a rising or descending arrow, respectively. These arrows connect the allowed maximal group/subor supergroups, while the numbers in brackets (subgroup index)
/ PnBm
/ f=Om
2a’=a 2b’=b 2c’=c (r)
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indicate the number of crystallographic variants corresponding to a particular symmetry reduction. The intermediate structures in the Fd3m + C2/m space group sequence should be regarded as transitory states of the transformation, which may not necessarily occur. The increase in symmetry from FdJm to Fm?m space groups does -not produce new variants but requires disordering of the cation sublattice. For this disordering transition to occur, all the octahedral (d and c) and tetrahedral (a, b and f) cation sites should become equivalent, giving 4a octahedrally and 8c tetrahedrally coordinates sites in the FmSm space group of f.c.c. packed oxygen ions (Table 2). The interfaces which have been observed (two translational and one rotational) in 0-A1203 are all consistent with the suggested ordering path. Translational interface with R, = fao could be formed by tripling of the c lattice parameter in the tetragonal space group 14/mmm, while a rotational interface on (OOl).,.planes is consistent with monoclinic distortion of the orthorhombic structure (I/mmm + C2/m). This generates two twin related monoclinic variants. Translational interfaces with Rz = fco can be formed by ordering which doubles the c lattice parameter in the C2/m space group. The lattice parameters of 0-Al2O3 and its orientation relationship with y-A1203 can be exactly reproduced by the suggested transformation sequence (Table 2). Transformation of Wyckoff sites according to this sequence results in atomic coordinates (underlined in Table 2) reproducing the final structure reported for 0-A1203 (neglecting small relaxations).
Fm3m
[61
‘\‘\14/mmm (c’=3c)
4 [3]
IWmmm
r21 \ Ymmm
r21
\ 112/ml
C12/ml (c’=2c) B C2/m Fig. 4. Subgroup/supergroup
symmetry relations between the Fdlm ~-A1203 -+ 0-AlzO, transformation.
and CZ/m space
(CZ/m)
(C2/m)
[21 (0) groups
for the
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Superlattice ordering with k = l/3(222),* suggests a rhombohedral distortion of the cubic y-alumina in one of the (111); directions. Similar to the 11+ Q transition, the spine1 unit cell was decomposed into eight f.c.c. latices by disordering (to FmJm), then followed by a cubic-to-rhombohedral symmetry reduction. There is only one rhombohedral group which is a maximal subgroup of Fm3m, and this is Rgrn [3]. To obtain l/3(222)* superlattice reflections, a further reduction in symmetry, from the RJm to the trigonal P5ml (version # 1) space group, is required. The reciprocal lattice vector 1/3[222],* corresponds to the rhombohedral vector [OOl]*, with c = a,,,/312 (in the hexagonal unit cell). This is just one half of the (111); diagonal of cubic y-AlzOi. The path of symmetry change, from the spine1 symmetry to the primitive trigonal unit cell is represented by the diagram shown in Fig. 5. The ideal lattice parameters of the trigonal (# 1) unit cell (ignoring lattice distortion) are a = a,/(2,/2) and c = a; J3/2. The Pgml space group has Wyckoff positions which can accommodate AlzOz stoichiometry without any need for partial cation site occupancy. Oxygen occupies the 1b and 2d Wyckoff positions, with z = 5/6 of the 2d position. Aluminium ions can fill either the 2d octahedral site (z = l/3) or one of the three pairs of tetrahedral sites (Table 3). For aluminum cations, the filling of the 2c positions corresponds to a structure which is isomorphous with LazOj [12]. The proposed structure accounts for the 1/6[224]* superlattice reflections [Fig. 3(b)], if double diffraction is invoked. However, for double diffraction to make a significant contribution to scattering of electrons, adjacent domains would have to overlap significantly in the beam direction. Such an overlap is unlikely for the observed morphology of interfaces [Fig. 3(c)]. The experimental diffraction pattern could also be explained without double diffraction, by
Fm3m
/ Pn3m Za’- a, Zb’=b, Zc’-c
\
R3m 4 P3ml
P3ml
FdStiy)
PI [#l)
[#2]
131 1 CZ/m
Fig. 5. Subgroup/supergroup summery relations between the Fdgm and C2/m space groups for the y-AlsOi --* f3’A1203 transformation.
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Table 3. Wyckoff sites transformation for the Fdjm Z. CZ/m space group sequence through rhombohedral
Fdjm, u = a;
FmTm, a = a,/2
I6c, l/8, l/8, l/8 16d 5/8, 5/8, 5/8
4a; 0, 0, 0
R%n, a = a: l(2J2) a = 60” la; 0, 0. 0
8a. 0, 0, 0
8b.
8~ l/4, 114, 114
2c; X, X, X z= 114
48f, X, 0, 0 .Y= l/4
P3m1, a = a,l(2J2) c = a, J3/2 y= 120
4b; l/2, l/2, l/2
lb; 112%112. 112
distortion
b = y$&&2
i fiI 94”’
Octahedral sites la; 0, 0, 0 la; 0, 0, 0 3d; l/3, 213, z 3e; l/2, 0, 0 z= l/3 2d; l/3, 213, z 6i; 5/6, l/6, z z= l/3
2a 0, 0, 0 2b 0, l/2, 0, 4e 114, 114, 0 4i x = l/6, z = l/3 4i x = 213, z = l/3 8j, x = 5/12, y = l/4, 2 = l/3
Tetrahedral sites 2c; 0, 0, z 2c; 0, 0, z *= l/4 6i, X, --x, z X = 112, z = l/4 2d; l/3, 2/3, z 2d; l/3, 213, 2 z= l/4 6i, I, --I, z x=S/6,z=1/4 2d; 113, 2/3, z 2d; l/3, 213, z z = 314 6i; X, --x, z x = 516, z = 314
4i 8j 4i 4i 8j 4i 4i 8j 4i
Oxygen sites lb, 0, 0, l/2 32e 318, 318, 318
P5ml, a=a;/ 2 c = a.,/ 312 y = 120”
2d, l/3, 213, z z = 516,
invoking a structure with the same P3ml space group but with a’ = 2a [Fig. 3(d)]. This space group (#2) is an isomorphous maximal subgroup of P3ml. In such a space group, the trigonal phase would have a unit cell with a = ailJ2 and c = a,J3/2, and would contain 20 ions (12 0 and eight Al for the ALO, stoichiometry). As in the first trigonal structure (# l), the oxygen remains in the f.c.c. positions when placed in the lb, 3f, 2d and 6i sites with the ideal value of z = 5/6 (Table 3). The Al cations can now fill both the octahedral and tetrahedral positions, with multiplicities of two and six, and still preserve stoichiometry at full occupancy. Alternatively, the cations could occupy four octahedral sites (la and 3e) with a value of z = 0, leaving six possibilities for the other four cations to fill other octahedral and tetrahedral sites (which have a multiplicity of 2).
lb, 0, 0, l/2 3f, l/2, 0, l/2 2d; 113. 213, z 6i; x - X, z I = 516, z = 516
x= x= x= l/3, .X= x= l/3, x= x=
0, z = 114 5/12, y = l/4, I = l/4 213, z = l/4 0, z (2 = l/4) 5/12, y = l/4, z = l/4 213, z = l/4 0, z (2 = 3/4) S/12, y = 114, z = 3/4 213, z = 314
2c, 0, 0, 112 2d 0, l/2, l/2 4i l/3, 0, z (z 8j x, Y, 2 x = 5112, y = 4i x, 0, z x =
4f l/4, l/4, l/2 = 5/6) l/4, z = S/6 213. z = 516
The only remaining difference between the experimental diffraction pattern and that calculated for the trigonal (# 2) structure is the angle of 94” between k = [OOOl]* and k = [liOO]* instead of 90” required for the trigonal lattice. This angular difference corresponds to a homogeneous distortion of the trigonal lattice and further reduces the symmetry to the monoclinic C2/m space group, which is a maximal subgroup of the P3ml space group. The monoclinic unit cell with a = n,J(3/2), b = a,/J2, c = ajJ3/2, 0 = 94” (b is a unique axis) contains 40 ions. The Wyckoff positions available for the ions can be obtained easily from those in P3ml space group by applying the appropriate hexagonal-to-orthorhombic unit cell transformation matrix and adding a [$ f 0] centering translation.
Fig. 6. Experimental and calculated lattice images for &“-Ah03 in [OlO],,, orientation. The experimental image was obtained using a JEOL-3010 microscope. The calculations were performed for a monoclinic structure with the C2/m space group. Ideal values of lattice parameters (see text) were assumed. The oxygen anions were located in the 2c, 2d, 4i (x = l/3, z = 5/6), 4i (x = 2/3, z = 5/6) and Sj Wyckoff positions, while the aluminum cations were placed in 2a,4e, 2b, 4i (x = 0, z = l/4) and 4i (x = l/3, z = l/4) sites (Table 3). The thickness of the crystal and defocus value for the calculated image are 17 nm and 36.9 nm (Scherzer defocus for JEOL-3010), respectively.
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Fig. 7. A lattice image of the translational interface between two crystallographic variants in 0’-A120,. The translational vector R is l/3 [OOOl]. While this proposed structure possesses the same space group as the O-AlzOz structure, its unit cell parameters are significantly different from those obtained for the f3-A120, structure. The number of ions per unit cell in the new 0’ monoclinic phase is twice that in 0-ALO,. Comparison of the experimental high-resolution images with those simulated for models with different cation distributions confirms that the main features of the experimentally observed lattice image can be reproduced for only a limited number of combinations of Wyckoff positions which are available for Al cations. Figure 6 shows a comparison of the experimental lattice image with that computer-simulated for a structural model with Al in 2a,4e, 2b, 4i (x = 0, z = l/4) and 4i (x = l/3, z = l/4) positions of the C2/m space group. Nevertheless, it is not possible to select a unique set of Wyckoff positions, or to refine the position parameters from high-resolution structural imaging alone. Crystal lattice energy calculations are now in progress in order to evaluate which of a specific cation distribution is energetically favorable. The Fm?!m to R?m transition (index [4]) generates four crystallographic rotational variants with their c-axes oriented in the (11 l), directions. Two of these twin related variants are observed in the lattice images [Fig. 3(c)]. Additional symmetry reduction to the trigonal P?ml (index [3]) space group could result in three translational variants, with a displacement vector equal to ic. Interfaces consistent with such translational variants were also observed (Fig. 7), in
agreement with the suggested ordering path. All the domain intervariant boundaries present in the images lie on the (110) twinning planes. These interfaces are stress-free for the cubic + trigonal lattice transformation [13], and are responsible for the lamellar morphology of the final, monoclinic phase. The diffraction pattern shown in Fig. 3(b) does resemble those obtained for the w-phase in alloys based on certain b.c.c. metals. Moreover, the symmetry group/subgroup sequence suggested for the y -8’ transformation is the same (up to Pm31 + C2/m transition) as that proposed for the /I --f o-transition [14], although the morphologies of the w-phase and 0-A1203 are completely different. The /3 + w transformation has been described in terms of longitudinal atomic displacements in the [ll 1] directions (with corresponding real planes of intensity) leading to the collapse of the { Ill} planes in the parent b-phase. However, such cation displacements in an ionic alumina structure would result in significant polarization which would seem to be energetically unfavorable. We believe that the mechanisms operating in the /I + w transition in metal alloys and the y + 8’ transition in alumina have to be different, even though the symmetry changes accompanying these transformations are similar. SUMMARY AND CONCLUSIONS Formally, there are two transformation paths which generate monoclinic structures from the cubic
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Fdgm space group and follow the maximal subgroup relationships [3]. The first one proceeds through tetragonallorthorhombic distortion of the cubic structure to give the cubic/monoclinic relationship reported for the y- and Q-aluminas, with [ 1TO],./[OOl], and (llO):.//(OIO)o [ll]. The second path requires a rhombohedral distortion of the cubic structure and yields the cubic/monoclinic relationship observed between y- and 8’-Alz03 with [ll 1],,//[001]0, and (1 lo)i//(olo), The present analysis demonstrates that both these possibilities occur in the case of cubic + monoclinic phase transformation in alumina. It is suggested, that the transformations proceed by first disordering the spine1 to a sample f.c.c. unit cell of oxygen, a transition state with higher configurational entropy than of y-Al,O,. The nature of the lattice distortion (either along (loo), or (11 l),) in the f.c.c. structure then determines the subsequent cation ordering path and the final ordered structure. In both cases the subgroup relation between the cubic and monoclinic structures is not maximal and involves a chain of intermediate structures between the parent and product space groups. These intermediate structures can be viewed as forma1 transitory states of transformation which do not necessarily occur. The new O/-alumina polymorph was identified by high-resolution electron microscopy of heat-treated anodic alumina films. This polymorph appears to be formed from y-alumina by cation ordering and has monoclinic symmetry corresponding to the C2/m space group, with a unit cell containing 40 ions. The idea1 values of the lattice parameters are a = a.,,J(3/2), b = a,/J2, c = a;J3/2, /I = 94’, where a; is the lattice parameter of y-alumina. There are a limited number of structural models which
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satisfy Al203 stoichiometry and are consistent with the phase contrast obtained by high-resolution imaging. research was supported by the German-Israel Foundation under contrast # 040-55 1. The authors would like to acknowledge the use of the facilities of the Israel National Facility for High Resolution Electron Microscopy. I.L. is grateful to the Minerva Foundation for allowing him to work at MPI (Stuttgart), where some of the Acknowledgements-This
experimental results were obtained. L.A.B. is grateful to the Technion Foundation which allowed him to collaborate in this work.
REFERENCES 1. Wefer, K. and Misra, C., Alcoa Technical Paper No. 19,
Alcoa Laboratories,
1987.
2. Lippens, B. C. and De Boer, J. H., Acta Cryst., 1964, 17, 1312. 3. Hahn, T. (Ed.), Internationul Tables of Crystallography, Vol. A. Luwer Academic Publishers, London, 1995. 4. Zhou, R. S. and Snyder, R. L., Acta Cryst., 1991, 847, 617. G., Yanagida, H. and Ono, S., Bull. Chem. 5. Yamaguchi, Sot. Jpn, 1964, 37, 752. 6. Jayaram, V. and Levi, C. G., Acta metall., 1989, 37(2), 569. 7. Bonevich, J. E. and Marks, L. D., Maf. Res. Sot. Symp. Proc., 1993, 286, 3. 8. Kaplan, W. D., D.Sc. Thesis, Technion, 1994. 9. Landau, L. D. and Lifshitz, E. M., Statistical Physics. Pergamon Press, Oxford, 1970. 10. Bendersky, L. A., Roytburd, A. and Boettinger, W. J., Acta metall. mater., 1994, 42(7), 2323. 11. Wilson. S. J., Proc. Br. Ceram. Sot., 1967, 50, 568. 12. Villers, P. and Calvert, L. D. (Ed.), Pearson’s Handbook qf Crystallographic Data .for Intermetallic Phases. American Society for Metals, 1986. 13. Sapriel, J., Phys. Rev. B., 1975. 12(11), 5128. 14. Bendersky, L. A., Boettinger, W. J., Burton, P. B., Bianconniello, F. S. and Shoemaker, C. B., Arta metall. mater., 1990, 38(6), 931.
Pergamon
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PII: S1359-6454(97)00040-2
CUBIC TO MONOCLINIC
I. LEVIN’,
PHASE TRANSFORMATIONS ALUMINA
L. A. BENDERSKY:
D. G. BRANDON’
and M. RfJHLE3
‘Faculty of Materials Engineering, Technion, Haifa 32000, Israel; ‘Metallurgy MD 20899, U.S.A. and )Max-Planck Institut Fur Metallforschung, Institut Seestrasse 92, D-70 174 Stuttgart, Germany (Received 22 February
IN
Div., NIST, Gaithersbury, Fur Werkstoffwissenschaft,
1996; accepted IO January 1997)
Abstract-Cubic to monoclinic phase transformations in alumina were studied by high-resolution electron microscopy of anodic films annealed at 1200°C. In addition to the known monoclinic 0-Al~01 structure a new metastable alumina polymorph was identified also with apparent monoclinic symmetry. This new phase appears to evolve from y-alumina by cation ordering. The stoichiometric structure of this polymorph is consistent with the C2/m space group and unit cell containing 40 ions (8AhOj). Reasonably good fit between experimental and computer-simulated lattice images was obtained for the suggested structural model. The transformations of y-Al203 to both monoclinic alumina structures were assumed to be non-reconstructive and the possible transformation paths were analyzed in terms of symmetry group/subgroup relationships. c 1997 Acta Metallurgica Inc.
INTRODUCTION Alumina phases
has a large in addition
number to the
of metastable thermodynamically
crystalline stable
c!-AlZ03, or corundum phase. These metastable alumina polymorphs include y (cubic spinel), 6 (either tetragonal or orthorhombic), B (monoclinic), 1 ( a second cubic spinel), K (orthorhombic), x (cubic), p (hexagonal) and r-(?) [l]. These polymorphs are commonly obtained by dehydration of different alumina hydroxides, but can also be formed by rapid quenching from the melt, vapor deposition or crystallization of amorphous alumina. All the metastable aluminas (also termed “transition” aluminas) have reproducible crystal structures which are stable at room temperature. The most common metastable alumina polymorphs are y-, 6- and B-alumina. y-alumina has been described as a defect spine1 structure (space group Fd3m) [2]. This structure contains oxygen anions in 32e Wyckoff positions, which can be viewed approximately as a 2 x 2 x 2 array of f.c.c. unit cells [3]. The 64/3 Al cations (to satisfy Alz03 stoichiometry) are distributed over 16d (with occupancy 1) octahedrally-coordinated and 8a (occupancy 2/3) tetrahedrally-coordinated interstitial sites in the oxygen anion sublattice. In Y-alumina, the remaining S/3 vacant cation 8a sites are assumed to be randomly distributed. This structural model is closely related to the ideal spine1 structure AB204. In the Fd3m space group there are additional tetrahedral (48f and 8b) and octahedral sites (16~) which are empty in an ideal spinel, but may be partially occupied in defect alumina structures [3,4].
rhombohedral
8-A&O, has been shown to possess monoclinic symmetry with a space group C2/m. This structure contains 20 ions per unit cell with all the ions located at 4i Wyckoff positions (Table 1) [4, 51. The Al cations occupy four octahedrally and four tetrahedrally coordinated interstitial sites in the oxygen sublattice with an occupancy of 1. 6-A&O3 is viewed as a superstructure of y-AllOj. The unit cell contains 160 ions with eight ordered cation vacancies. Both tetragonal (a, = a:, c = 3a;.) and orthorhombic (a~ = a,, bs = 2u,, cg = 1.5u;,) unit cells have been reported for S-Al2O3 (a; is a lattice parameter of i;-A1203) [3, 6, 71. All the studies in which tetragonal 6-AlZ03 was observed started from boehmite (AlOOH), while the orthorhombic unit cell for &Al,O, was observed for the precursor phase obtained either by quenching the melt or by thermal oxidation. The atomic structure of either of the phases referred to as S-Al,O, remains unknown. Two possible space groups (P2,2,2 and P2,2,2,) have been proposed in the literature for the orthorhombic 6-A1203, based on convergent beam electron diffraction analysis [6]. Although extensive research over the past few decades has made progress in characterizing transition aluminas, little high-resolution transmission electron microscopy (HRTEM) has been reported. The present contribution is a part of a high-resolution TEM study of phase transformations which occur in alumina during the heating of amorphous alumina films formed by anodization. The paper is primarily concerned with cubic-to-monoclinic phase transition in alumina. In addition to the study of monoclinic &AlzO, structure, preliminary results are presented
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on a previously unknown metastable alumina polymorph. This polymorph also possesses monoclinic symmetry and is apparently formed directly from y-alumina. The experimental results were analyzed in terms of symmetry changes which occur during the phase transformation. A model structure for the observed new alumina phase (termed 19’) is proposed based on the assumption that the Al cations are ordered on interstitial sites of the oxygen sublattice of y-alumina. EXPERIMENTAL
PROCEDURE
Self-supported amorphous anodic alumina films were used as a precursor for the study of polymorphic phase transformations. The thin films of amorphous alumina were obtained by anodization of Al foil in a 0.01 M aqueous solution of ammonium tartrate at room temperature. Prior to anodization, the metal foil was electrochemically polished in perchloric acid/ethanol solution (1:4) with one side of the foil coated with an insulating lacquer to prevent the reaction. The thickness of the oxide film was slightly less than 20 nm. After anodization, the lacquer was dissolved in acetone and free-standing alumina films were released by dissolution of the remaining Al. The floating films were retrieved on a TEM ceramic support (diameter 3 mm) and dried in air. Films prepared and mounted by this route were placed in a pure alumina crucible and annealed in air at 1200°C. The ceramic TEM supports were produced from high-purity polycrystalline alumina as described in Ref. [8]. The use of these supports prevented film tearing as a result of thermal expansion mismatch between alumina and the metals used for commercially available grids (Ni, MO, Pt). High-resolution electron microscopes, a JEOL 3010UHR operated at 300 keV and a JEOL 4000EX operated at 400 keV, were used for structural lattice imaging. The samples were coated with a thin film of carbon to improve electrical conductivity. RESULTS The primary product after heat treatment was nanocrystalline (l&20 nm) y-alumina, confirmed by selected area electron diffraction (SAD) which yielded polycrystalline ring patterns and by occasional microdiffraction. In addition to the nanocrystalline y-alumina, larger grains (SO-ZOO nm in size) or conglomerates of slightly misoriented grains were observed. SAD patterns and lattice images taken Table 1. Atomc Atom Al AI 0 0 0
coordmates
Wyckoff position
x
4i 4i 4i 4i 4i
0.0843 0.3400 0.1614 0.4980 0.1674
for Q-ALO,
(space group CZ/m)
y
Ref. [S] i
x
0.0000 0.0000 0.0000 0.0000 0.0000
0.7929 0.6832 0.1071 0.2602 0.5596
0.0834 0.3405 0.1611 0.4950 0.8272
Fig. 1. Lattice image and selected area diffraction pattern attributed to Q-A1203in the [I 10]7//[010]~orientation.
[4, 51
Ref. [4] Y 2 0.0000 0.0000 0.0000 0.0000 0.0000
(b)
0.7927 0.6835 0.0984 0.2526 0.4273
from these grains proved that they are either 6 (orthorhombic) or f3polymorphs. All the phases show preferred orientation corresponding to either the (loo), or (1 lo), directions perpendicular to the film surface.
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Absence of Kikuchi and high-order Laue zone (HOLZ) lines (due to the small foil thickness), together with the fine spatial scale and the lack of distinct morphology for the metastable alumina phases (when observed in diffraction contrast) made controlled tilting of the specimens to align specific zone axes parallel to the beam direction extremely difficult. Therefore, lattice imaging of metastable aluminas was limited to the direction of preferred orientation.
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Since the present paper is primarily concerned with the cubic-to-monoclinic phase transition in alumina, further analysis is limited to the monoclinic B-Al,O, phase. Figure 1 shows a SAD pattern and lattice image taken from a single grain. Fundamental spots in the pattern correspond to the (110) pole of cubic y-A1203 while additional spots can be attributed both to the 6 (orthorhombic) and the 0 phase in [210]~ and [OIO]s orientations, respectively. Optical diffraction from
Fig. 2(a) and (b)-Caption
overleaf.
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Fig. 2. Lattice images of B-A1203showing interfaces between crystallographic variants of 0-Alz0,. (a) and (b) Translational (APB type) interfaces with translational vectors RI= fanand R2= ~CO, respectively; (c) rotational (twin type) interface with a twinning plane corresponding to (100)~.
the lattice image is consistent only with monoclinic f3-A1203 in [OlO] orientation. The { 11 l)? and {113}, reflections present on the SAD pattern are not expected for 8-Alz0, [only one of the (111); reflections is preserved, being transformed to (zOl)O]. This suggests that both y- and B-Al,Os coexist in the area from which the SAD is obtained. Diffuse streaks which pass through the { 1111 and { 113) reflections in the [OOl],* (the asterisk * indicates reciprocal space) direction can also be attributed to an incomplete y + 8 transformation in the area of the SAD aperture. Lack of information about precise zone axis orientation with respect to the electron beam direction precludes quantitative matching of the phase contrast simulated by computer to that obtained experimentally. However, the main features of the contrast observed can be reproduced by image simulations assuming a structural model for Q-A1203 suggested in the literature [4]. Based on this analysis the observed region [Fig. l(a)] was attributed to 8-AlzO,. All the recorded lattice images of Q-A&O3 shown an orientation relationship between y- and Q-A&O, phases corresponding to [010]0//( 1 lo), Lattice images obtained from B-Al,O, (Fig. 2) revealed the presence of two types of domain boundaries: a translation (APB type) with the vectors of translation RI = $zo and RZ = fcs; and a rotational (twin type) with the interface plane corresponding to (001); = (100)s. In addition to the y, 6 and B-A&O, phases identified in the present specimens, some regions result in
diffraction which could not be assigned to any previously reported alumina phase. One such region is seen in Fig. 3(a) as a conglomerate of slightly misoriented grains. The SAD pattern taken from one of the grains (which appears dark in the image) is shown in Fig. 3(b). The pattern does not match any of the known alumina polymorphs, although the strong fundamental spots can be ascribed to the reflections of cubic y-alumina in the (li0) zone axis, with the exception of the absence of { 11 l}? and { 113}: reflections and the small lattice distortion (the angle between k = [l 111: and k = [223],* is 94” instead of 90”). At this stage of the analysis, the distortion is ignored and the structure is treated as a derivative of the ideal cubic y-Al,O, structure. The corresponding lattice image [Fig. 3(c)] clearly shows the presence of a lamellar structure with two different orientations of this phase. The lamellae are lenticular, with interfaces approximately normal to [l lo], An optical diffraction pattern taken from one lamella showed superlattice spots at l/3 and 2/3[222],, indicating ordering of the (222}, planes with an ordering vector k = 1/3[222],?. Two variants of this ordering, k = 1/3[222]* and k = 1/3[22?.]* are present in the image, as alternating lamellae. The streaks passing through the superlattice reflections in the [110]: direction apparently result from near-planar domain boundaries, while the curvature of the streaks can be ascribed to the lamellae edges. Based on this observation of a single orientation, we infer that the lamellar phase (denoted 0’) can be described by
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ordering of (22 2ji planes of the y-alumina. It is not clear if the lan nellar structure is a product of the decomposition (by ordering) of an individual y-alumina grair I, or if a y-alumina grain acted as a precursor to th le ordered phase, which then grows discontinuously in a twin-coupled mode. DISCUSSION
The comparis ion of the SAD patterns
from y, 0 and
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newly observed 0’ aluminas shows that all the reflections which arise from both the anion (oxyg Len) the cation and 20, in Obfoth :A1 and ({400}, {440],{222}) ares$~~~~~ 0’-AlzO,. The changes occur to those y-A; 20) reflections ({ 11 l), {113}) which arise solely from the cation sublattices. Hence the absence of the { 1 II l)? and { 113},. reflections in the diffraction patterns fr ‘om 8- and B’-ALO, [Figs l(b) and 3(b)] suggests than lges
(4
Fig. 3(a) and (b)-Caption
overleaf.
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PHASE TRANSFORMATIONS
IN ALUMINA
(4
. ds
092 . . 0
??
.
?20 ??
??
.
0
.
.
.
Fig. 3. (a) Bright field image showing a two-dimensional aggregation of misoriented grains. (b) and (c) The SAD and lattice image taken from one of these grains. The dominant spots correspond to y-Al203 in a [l lo] zone axis orientation. Two crystallographic variants rotated by 72” are indicated on the lattice image. (d) A computer simulated SAD.
in the cation sublattice of y-alumina which lead to 1/6[004]: (kinematically forbidden for &A1203) or 1/3[222]* ordering for 0- and 0’-A1203, respectively. In addition, the streaks in the diffraction patterns from 8- and 0’-AlzO, phases do not pass through the reflections which are associated primarily with the anion sublattice. This implies that the oxygen sublattice is practically uneffected by both the y --t 6 and y + 0’ transformations. In the case of 0’-A1203,
the oxygen sublattice remains continuous through the whole lamellar structure. That is, the primary changes occur by cation re-distribution. The y + Q transformations may therefore be and y--+8’ assumed to occur by ordering on interstitial sites in the f.c.c.-packed oxygen anion sublattice and can be treated in terms of the Landau theory of continuous phase transitions, using maximal subgroup relations [9,
101.
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y + 8-AlzO~ TRANSITION
The lattice parameters of @-A&O3 are a = 11.8 1 A, h = 2.9 8, and c = 5.61 A and can be related to that of y-A1203, a; as follows a z ia: ,
b = a: j2J2,
c = a;/,/2.
These parameters are fully compatible with the orientation relationship between ‘J- and 0-Al,Oi [llO]j//[OIO]O, (OO1).,.//(lOO)n suggested by Wilson [ll] and confirmed by the present SAD analysis. a of 8-AlzOi cannot be The lattice parameters derived solely by ordering of >l-AlzOi, which would require integer multiplication of a7 but not by a factor of 3/2. To account for the extension of a, by 3/2 it is necessary to assume that the y-AIZ03 lattice is either first disordered, with a,, reduced by 2, and then ordered with a threefold increase of the lattice parameter (resulting in aB= 3/2a,.), or vice versa, that is first ordered and then disordered with the corresponding changes in the lattice parameter. The maximal group/subgroup sequence was sought, which connects the space groups of y-A&O, (FdTm) and 0-A1203 (monoclinic C2/m), is consistent with the experimentally observed lattice parameters and atomic positions for 0-A1203, and gives the correct orientation relationship between y- and 0-A1,03. The sequence found is represented by the diagram shown in Fig. 4, where an increase or decrease in symmetry is indicated by a rising or descending arrow, respectively. These arrows connect the allowed maximal group/subor supergroups, while the numbers in brackets (subgroup index)
/ PnBm
/ f=Om
2a’=a 2b’=b 2c’=c (r)
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indicate the number of crystallographic variants corresponding to a particular symmetry reduction. The intermediate structures in the Fd3m + C2/m space group sequence should be regarded as transitory states of the transformation, which may not necessarily occur. The increase in symmetry from FdJm to Fm?m space groups does -not produce new variants but requires disordering of the cation sublattice. For this disordering transition to occur, all the octahedral (d and c) and tetrahedral (a, b and f) cation sites should become equivalent, giving 4a octahedrally and 8c tetrahedrally coordinates sites in the FmSm space group of f.c.c. packed oxygen ions (Table 2). The interfaces which have been observed (two translational and one rotational) in 0-A1203 are all consistent with the suggested ordering path. Translational interface with R, = fao could be formed by tripling of the c lattice parameter in the tetragonal space group 14/mmm, while a rotational interface on (OOl).,.planes is consistent with monoclinic distortion of the orthorhombic structure (I/mmm + C2/m). This generates two twin related monoclinic variants. Translational interfaces with Rz = fco can be formed by ordering which doubles the c lattice parameter in the C2/m space group. The lattice parameters of 0-Al2O3 and its orientation relationship with y-A1203 can be exactly reproduced by the suggested transformation sequence (Table 2). Transformation of Wyckoff sites according to this sequence results in atomic coordinates (underlined in Table 2) reproducing the final structure reported for 0-A1203 (neglecting small relaxations).
Fm3m
[61
‘\‘\14/mmm (c’=3c)
4 [3]
IWmmm
r21 \ Ymmm
r21
\ 112/ml
C12/ml (c’=2c) B C2/m Fig. 4. Subgroup/supergroup
symmetry relations between the Fdlm ~-A1203 -+ 0-AlzO, transformation.
and CZ/m space
(CZ/m)
(C2/m)
[21 (0) groups
for the
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Superlattice ordering with k = l/3(222),* suggests a rhombohedral distortion of the cubic y-alumina in one of the (111); directions. Similar to the 11+ Q transition, the spine1 unit cell was decomposed into eight f.c.c. latices by disordering (to FmJm), then followed by a cubic-to-rhombohedral symmetry reduction. There is only one rhombohedral group which is a maximal subgroup of Fm3m, and this is Rgrn [3]. To obtain l/3(222)* superlattice reflections, a further reduction in symmetry, from the RJm to the trigonal P5ml (version # 1) space group, is required. The reciprocal lattice vector 1/3[222],* corresponds to the rhombohedral vector [OOl]*, with c = a,,,/312 (in the hexagonal unit cell). This is just one half of the (111); diagonal of cubic y-AlzOi. The path of symmetry change, from the spine1 symmetry to the primitive trigonal unit cell is represented by the diagram shown in Fig. 5. The ideal lattice parameters of the trigonal (# 1) unit cell (ignoring lattice distortion) are a = a,/(2,/2) and c = a; J3/2. The Pgml space group has Wyckoff positions which can accommodate AlzOz stoichiometry without any need for partial cation site occupancy. Oxygen occupies the 1b and 2d Wyckoff positions, with z = 5/6 of the 2d position. Aluminium ions can fill either the 2d octahedral site (z = l/3) or one of the three pairs of tetrahedral sites (Table 3). For aluminum cations, the filling of the 2c positions corresponds to a structure which is isomorphous with LazOj [12]. The proposed structure accounts for the 1/6[224]* superlattice reflections [Fig. 3(b)], if double diffraction is invoked. However, for double diffraction to make a significant contribution to scattering of electrons, adjacent domains would have to overlap significantly in the beam direction. Such an overlap is unlikely for the observed morphology of interfaces [Fig. 3(c)]. The experimental diffraction pattern could also be explained without double diffraction, by
Fm3m
/ Pn3m Za’- a, Zb’=b, Zc’-c
\
R3m 4 P3ml
P3ml
FdStiy)
PI [#l)
[#2]
131 1 CZ/m
Fig. 5. Subgroup/supergroup summery relations between the Fdgm and C2/m space groups for the y-AlsOi --* f3’A1203 transformation.
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Table 3. Wyckoff sites transformation for the Fdjm Z. CZ/m space group sequence through rhombohedral
Fdjm, u = a;
FmTm, a = a,/2
I6c, l/8, l/8, l/8 16d 5/8, 5/8, 5/8
4a; 0, 0, 0
R%n, a = a: l(2J2) a = 60” la; 0, 0. 0
8a. 0, 0, 0
8b.
8~ l/4, 114, 114
2c; X, X, X z= 114
48f, X, 0, 0 .Y= l/4
P3m1, a = a,l(2J2) c = a, J3/2 y= 120
4b; l/2, l/2, l/2
lb; 112%112. 112
distortion
b = y$&&2
i fiI 94”’
Octahedral sites la; 0, 0, 0 la; 0, 0, 0 3d; l/3, 213, z 3e; l/2, 0, 0 z= l/3 2d; l/3, 213, z 6i; 5/6, l/6, z z= l/3
2a 0, 0, 0 2b 0, l/2, 0, 4e 114, 114, 0 4i x = l/6, z = l/3 4i x = 213, z = l/3 8j, x = 5/12, y = l/4, 2 = l/3
Tetrahedral sites 2c; 0, 0, z 2c; 0, 0, z *= l/4 6i, X, --x, z X = 112, z = l/4 2d; l/3, 2/3, z 2d; l/3, 213, 2 z= l/4 6i, I, --I, z x=S/6,z=1/4 2d; 113, 2/3, z 2d; l/3, 213, z z = 314 6i; X, --x, z x = 516, z = 314
4i 8j 4i 4i 8j 4i 4i 8j 4i
Oxygen sites lb, 0, 0, l/2 32e 318, 318, 318
P5ml, a=a;/ 2 c = a.,/ 312 y = 120”
2d, l/3, 213, z z = 516,
invoking a structure with the same P3ml space group but with a’ = 2a [Fig. 3(d)]. This space group (#2) is an isomorphous maximal subgroup of P3ml. In such a space group, the trigonal phase would have a unit cell with a = ailJ2 and c = a,J3/2, and would contain 20 ions (12 0 and eight Al for the ALO, stoichiometry). As in the first trigonal structure (# l), the oxygen remains in the f.c.c. positions when placed in the lb, 3f, 2d and 6i sites with the ideal value of z = 5/6 (Table 3). The Al cations can now fill both the octahedral and tetrahedral positions, with multiplicities of two and six, and still preserve stoichiometry at full occupancy. Alternatively, the cations could occupy four octahedral sites (la and 3e) with a value of z = 0, leaving six possibilities for the other four cations to fill other octahedral and tetrahedral sites (which have a multiplicity of 2).
lb, 0, 0, l/2 3f, l/2, 0, l/2 2d; 113. 213, z 6i; x - X, z I = 516, z = 516
x= x= x= l/3, .X= x= l/3, x= x=
0, z = 114 5/12, y = l/4, I = l/4 213, z = l/4 0, z (2 = l/4) 5/12, y = l/4, z = l/4 213, z = l/4 0, z (2 = 3/4) S/12, y = 114, z = 3/4 213, z = 314
2c, 0, 0, 112 2d 0, l/2, l/2 4i l/3, 0, z (z 8j x, Y, 2 x = 5112, y = 4i x, 0, z x =
4f l/4, l/4, l/2 = 5/6) l/4, z = S/6 213. z = 516
The only remaining difference between the experimental diffraction pattern and that calculated for the trigonal (# 2) structure is the angle of 94” between k = [OOOl]* and k = [liOO]* instead of 90” required for the trigonal lattice. This angular difference corresponds to a homogeneous distortion of the trigonal lattice and further reduces the symmetry to the monoclinic C2/m space group, which is a maximal subgroup of the P3ml space group. The monoclinic unit cell with a = n,J(3/2), b = a,/J2, c = ajJ3/2, 0 = 94” (b is a unique axis) contains 40 ions. The Wyckoff positions available for the ions can be obtained easily from those in P3ml space group by applying the appropriate hexagonal-to-orthorhombic unit cell transformation matrix and adding a [$ f 0] centering translation.
Fig. 6. Experimental and calculated lattice images for &“-Ah03 in [OlO],,, orientation. The experimental image was obtained using a JEOL-3010 microscope. The calculations were performed for a monoclinic structure with the C2/m space group. Ideal values of lattice parameters (see text) were assumed. The oxygen anions were located in the 2c, 2d, 4i (x = l/3, z = 5/6), 4i (x = 2/3, z = 5/6) and Sj Wyckoff positions, while the aluminum cations were placed in 2a,4e, 2b, 4i (x = 0, z = l/4) and 4i (x = l/3, z = l/4) sites (Table 3). The thickness of the crystal and defocus value for the calculated image are 17 nm and 36.9 nm (Scherzer defocus for JEOL-3010), respectively.
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Fig. 7. A lattice image of the translational interface between two crystallographic variants in 0’-A120,. The translational vector R is l/3 [OOOl]. While this proposed structure possesses the same space group as the O-AlzOz structure, its unit cell parameters are significantly different from those obtained for the f3-A120, structure. The number of ions per unit cell in the new 0’ monoclinic phase is twice that in 0-ALO,. Comparison of the experimental high-resolution images with those simulated for models with different cation distributions confirms that the main features of the experimentally observed lattice image can be reproduced for only a limited number of combinations of Wyckoff positions which are available for Al cations. Figure 6 shows a comparison of the experimental lattice image with that computer-simulated for a structural model with Al in 2a,4e, 2b, 4i (x = 0, z = l/4) and 4i (x = l/3, z = l/4) positions of the C2/m space group. Nevertheless, it is not possible to select a unique set of Wyckoff positions, or to refine the position parameters from high-resolution structural imaging alone. Crystal lattice energy calculations are now in progress in order to evaluate which of a specific cation distribution is energetically favorable. The Fm?!m to R?m transition (index [4]) generates four crystallographic rotational variants with their c-axes oriented in the (11 l), directions. Two of these twin related variants are observed in the lattice images [Fig. 3(c)]. Additional symmetry reduction to the trigonal P?ml (index [3]) space group could result in three translational variants, with a displacement vector equal to ic. Interfaces consistent with such translational variants were also observed (Fig. 7), in
agreement with the suggested ordering path. All the domain intervariant boundaries present in the images lie on the (110) twinning planes. These interfaces are stress-free for the cubic + trigonal lattice transformation [13], and are responsible for the lamellar morphology of the final, monoclinic phase. The diffraction pattern shown in Fig. 3(b) does resemble those obtained for the w-phase in alloys based on certain b.c.c. metals. Moreover, the symmetry group/subgroup sequence suggested for the y -8’ transformation is the same (up to Pm31 + C2/m transition) as that proposed for the /I --f o-transition [14], although the morphologies of the w-phase and 0-A1203 are completely different. The /3 + w transformation has been described in terms of longitudinal atomic displacements in the [ll 1] directions (with corresponding real planes of intensity) leading to the collapse of the { Ill} planes in the parent b-phase. However, such cation displacements in an ionic alumina structure would result in significant polarization which would seem to be energetically unfavorable. We believe that the mechanisms operating in the /I + w transition in metal alloys and the y + 8’ transition in alumina have to be different, even though the symmetry changes accompanying these transformations are similar. SUMMARY AND CONCLUSIONS Formally, there are two transformation paths which generate monoclinic structures from the cubic
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et al.:
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Fdgm space group and follow the maximal subgroup relationships [3]. The first one proceeds through tetragonallorthorhombic distortion of the cubic structure to give the cubic/monoclinic relationship reported for the y- and Q-aluminas, with [ 1TO],./[OOl], and (llO):.//(OIO)o [ll]. The second path requires a rhombohedral distortion of the cubic structure and yields the cubic/monoclinic relationship observed between y- and 8’-Alz03 with [ll 1],,//[001]0, and (1 lo)i//(olo), The present analysis demonstrates that both these possibilities occur in the case of cubic + monoclinic phase transformation in alumina. It is suggested, that the transformations proceed by first disordering the spine1 to a sample f.c.c. unit cell of oxygen, a transition state with higher configurational entropy than of y-Al,O,. The nature of the lattice distortion (either along (loo), or (11 l),) in the f.c.c. structure then determines the subsequent cation ordering path and the final ordered structure. In both cases the subgroup relation between the cubic and monoclinic structures is not maximal and involves a chain of intermediate structures between the parent and product space groups. These intermediate structures can be viewed as forma1 transitory states of transformation which do not necessarily occur. The new O/-alumina polymorph was identified by high-resolution electron microscopy of heat-treated anodic alumina films. This polymorph appears to be formed from y-alumina by cation ordering and has monoclinic symmetry corresponding to the C2/m space group, with a unit cell containing 40 ions. The idea1 values of the lattice parameters are a = a.,,J(3/2), b = a,/J2, c = a;J3/2, /I = 94’, where a; is the lattice parameter of y-alumina. There are a limited number of structural models which
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satisfy Al203 stoichiometry and are consistent with the phase contrast obtained by high-resolution imaging. research was supported by the German-Israel Foundation under contrast # 040-55 1. The authors would like to acknowledge the use of the facilities of the Israel National Facility for High Resolution Electron Microscopy. I.L. is grateful to the Minerva Foundation for allowing him to work at MPI (Stuttgart), where some of the Acknowledgements-This
experimental results were obtained. L.A.B. is grateful to the Technion Foundation which allowed him to collaborate in this work.
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