Article pubs.acs.org/JPCC
Structure of δ‑Alumina: Toward the Atomic Level Understanding of Transition Alumina Phases Libor Kovarik,*,† Mark Bowden,† Arda Genc,§ János Szanyi,‡ Charles H. F. Peden,‡ and Ja Hun Kwak*,‡,∥ †
Environmental Molecular Sciences Laboratory and ‡Institute for Integrated Catalysis, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, United States § FEI Company, 5350 NE Dawson Creek Drive, Hillsboro, Oregon 97124, United States ∥ School of Nanobiotechnology & Chemical Engineering, UNIST, Ulsan 689-798, Korea S Supporting Information *
ABSTRACT: Transition Al2O3 derived from thermal decomposition of AlOOH Boehmite have complex structures and to a large extent remain poorly understood. Here, we report a detailed atomic level analysis of δ-Al2O3 for the first time using a combination of high-angle annular dark field electron microscopy imaging, X-ray diffraction refinement, and density functional theory calculations. We show that the structure of δ-Al2O3 represents a complex structural intergrowth from two main crystallographic variants, which are identified as δ1-Al2O3 and δ2-Al2O3. The two main variants are fully structurally described, and in addition, we also derive their energy of formation. On the basis of comparison with other relevant transition Al2O3 phases, it is shown how energetic degeneracy leads to the structural disorder and complex intergrowths among several transition Al2O3. The results of the work have important implications for understanding thermodynamic stability and transformation processes in transition alumina. At the basic structural level, the polymorphs of γ-Al2O3 and δ-Al2O3, as well as the known θ-Al2O3, share important similarities as they all have oxygen atoms located in a near close packed cubic arrangement.2,3,11 The differences then arise due to characteristic distribution of Al among the available octahedral and tetrahedral sites of the closely packed oxygen atoms. Generally, γ-Al2O3 can be represented as a defective cubic spinel structure,2 which provides a reasonable structural fit and very convenient way for indexing XRD peaks, labeling surfaces facets, and in general, referring to other crystallographic features.2,3 At a more quantitative level, there have been several specific defective spinel-based models considered for structural solution,12,13 but it is now becoming more accepted, based on XRD, neutron diffraction, and energy calculation, that much better fit and energy stability can be obtained when Al3+ ions are not only limited to spinel sites.2,14−16 It should be also noted that some earlier work suggested the presence of hydrogen in the structure, 17 but this view has been subsequently disputed.18,19 Importantly, more recent work utilizing a pair distribution function (PDF) from X-ray suggested that the closely packed oxygen sublattice may have a large density of faults that lead to formation of ∼1 nm domains and thus adding complexity to the structure. When heated in the temperature range 700−900 °C, γ-Al2O3 is known to gradually transform to a more stable form of δAl2O3.20 Although the δ-Al2O3 phase is thermodynamically
1. INTRODUCTION Transition Al2O3 represent an important group of materials with very attractive surface and structural properties, which make them a material of choice in a range of applications such as catalysts, catalytic supports, adsorbents, hard protective coatings, abrasives, or membrane.1 In an effort to advance the numerous technologies that exploit transition Al2O3, a significant research effort has been devoted in the past to develop basic understanding related to the structural nature,2,3 thermodynamic stabilities,4 and surface properties.5,6 While a substantial knowledge has been gained, many fundamental characteristics remain still elusive and actively studied. For transition Al2O3 derived from thermal decomposition of Boehmite, there are three main polymorphs of γ-Al2O3, δAl2O3, θ-Al2O3, where γ-Al2O3 represents the least thermodynamically stable form and δ-Al2O3 and θ-Al2O3 are each increasingly more stable.7 The polymorph of θ-Al2O3 is rather well understood as monoclinic (consistent with β-Ga2O3 structure) where 50% of Al3+ ions are in octahedral and 50% of Al3+ are in tetrahedral sites.2 However, for the other two polymorphs of γ-Al2O3 and δ-Al2O3, the situation is much more complex, and their structures are still actively studied. Because of their highly defective nature, small crystallite size, and coexistence in mutual intergrowth with each other, a reliable crystallographic analysis has proven extremely challenging.1,3,8 For example, X-ray diffraction (XRD) and neutron diffraction techniques lead to a rather strong background and broad peaks2,9 that are poorly suitable for conventional approaches in diffraction structural analysis.3,10,11 © 2014 American Chemical Society
Received: January 3, 2014 Revised: June 30, 2014 Published: July 2, 2014 18051
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more stable than the γ polymorph, and inherently less defective, it is in fact a less understood polymorph with no structural models currently available.3 In XRD, the δ-Al2O3 formation is often recognized by subtle splitting of diffraction peaks and by developing characteristic shoulders. 21−23 The diffraction features can be very subtle and readily masked by γ-Al2O3, which may be one of the reasons why it has been sometimes neglected in the decomposition process.2 The current limited knowledge of the structure of δ-Al2O3 has been mainly derived from electron microscopy methods, and it has been summarized in a review article by Levin and Brandon.3 There has been several crystal symmetries and lattice parameters considered for δ-Al2O3. The proposed symmetry mostly include tetragonal7,24 and orthorhombic11,25 systems, with several different sets of lattice parameters reported. While some interpretations may be now ruled out, the strongest experimental evidence points to a structure with orthorhombic symmetry and the following lattice parameters: a = aγ, b = 2aγ, and c = 1.5aγ.3 The symmetry and lattice parameters of the unit cell were initially proposed by Jayram and Levi25 using selected area electron diffraction and convergent beam electron diffraction (CBED) and later independently supported by others.11,26 On the basis of the electron diffraction studies, it was also tentatively proposed that the crystal structure of δAl2O3 should possess a space group of P212121, which is in good agreement with the work of Bonevich and Marks26 who proposed P21212 or P212121 as possible space groups. Additionally, it has been reported that there exist additional and closely related structural variants of δ-Al2O3.25,27,28 However, it is not entirely clear how many of these variants do exist and how they are all related. In view of the limited knowledge regarding transition aluminas, the intent of this work is to focus on developing detail structural understanding of δ-Al2O3 by atomic level highangle annular dark field (HAADF) imaging. HAADF provides directly interpretable atomic level images, making this technique extremely useful for atomic level studies of nanoparticles, dopants, defects, interfaces, and surfaces,29,30 and this technique has been successfully applied for determination of highly defective, low-periodic crystallographic structures.31,32 As part of this study, we present a crystallographic approach based on real space interpretation of projected atomic potential that enabled us to unambiguously derive Al3+ coordination from a series of low-index atomic level HAADF images. In combination with XRD refinement and density functional theory (DFT) calculations, we then report full crystallographic information for the two structural variants of δ1-Al2O3 and δ2-Al2O3, which were identified as the main, highly intergrown components of δ-Al2O3.
on a HAADF detector with a detection angle that is approximately 3 times higher than the convergence angle. HAADF imaging enabled us to conclusively determine the position of Al3+ ions in tetrahedral/octahedral sites of δ-Al2O3, and then, crystallographic refinement of the structure was performed with DFT methods. We employed the Vienna Abinitio Simulation Package (VASP), which uses pseudopotentials and a plane wave basis set.35,36 All calculations reported in this work were done with projector augmented wave (PAW) potentials37 and the Generalized Gradient Approximation (GGA) of Perdew and Wang (PW91) for the exchange correlation potential.38 We used the Monkhorst−Pack scheme for k-point sampling of the Brillouin zone. The calculations were performed with k-point sampling that provided converged within ∼0.005 eV/formula unit. Plane-wave cutoff energy of 550 eV was used. The atomic positions were allowed to relax to their equilibrium positions using a conjugate-gradient algorithm with the symmetry constrains of considered space group. The current DFT calculations also enabled us to evaluate the thermodynamic stability and compare it with other transition and stable polymorphs of Al2O3. The simulation of the HAADF images was performed with a computer code developed by E. Kirkland.39 The calculations were performed with microscope parameters that closely correspond to the experimental conditions. (E = 300 kV; cs = 5 μm; convergence angle, 18 mrad; inner collection angle, 70 mrad; and outer collection angle, 240 mrad.) The samples were simulated along several low-index zone axes for thickness of approximately 15 nm. The simulated images were convoluted with a Gaussian of fwhm = 0.08 nm to account for spatial incoherence of the imaging system.40
3. RESULTS AND DISCUSSION 3.1. Complex Structural Intergrowth of Transition Al2O3. The electron microscope image in Figure 1a shows a typical example of the heat-treated particles of transition Al2O3 investigated in this work. In this laboratory synthesized system, the majority of Al2O3 particles have a rather well-defined morphology of thin platelets with a rhombus or truncated rhombus shape, which is a morphology fully inherited from Boehmite and γ-Al2O3 precursors.33 After calcination at a temperature range of 900−1100 °C for several hours, we find that the particles do not have a single crystal structure, but instead consist of a complex mosaic of crystallographic domains. As shown in Figure 1b, such domains can arise partly due to the presence of antiphase boundaries but also due to the structural intergrowth from a number of closely related crystallographic phases that evolve concurrently during the thermal treatment. At the basic structural level, the intergrowth can be rationalized in terms of δ-Al2O3 and θ-Al2O3 phases. At the detail crystallographic level, it is recognized that the δ-Al2O3 phase itself represents an intergrowth of several closely related crystallographic variants. The two main variants of δ-Al2O3 are identified in the text as δ1-Al2O3 and δ2-Al2O3. Both variants create a highly intergrown structure that lacks a long-range periodicity along one principal direction. In many projections, such as shown in Figure 1b, e, both δ1-Al2O3 and δ2-Al2O3 are superimposed on top of each other along the viewing direction and may not be distinguished. The combined structure is labeled under the term δ1,2-Al2O3. The characteristic features of δ1,2-Al2O3 in the HAADF images shown in Figure 1b, e are high-intensity atomic columns that create a network of oppositely distorted parallelograms, with a
2. EXPERIMENTAL SECTION The presently studied δ-Al2O3 was synthesized from aluminum isopropoxide by the hydrolysis method. The preparation involved synthesis of Boehmite, dehydration, and thermal decomposition to γ-Al2O3 and subsequent transformation to δAl2O3. Detailed description of the synthesis protocol of γ-Al2O3 can be found in our previous work.33 The final thermal decomposition of γ-Al2O3 to δ-Al2O3 was performed under in situ heating conditions inside the TEM with Aduro Protochips heating holder at 900−1100 °C.34 The TEM observations were performed with a probe corrected FEI Titan 80-300. The observations were performed in scanning mode with probe convergence angle of 18 mrad, and the images were recorded 18052
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Figure 1. (a) HAADF image of thermally treated particle of γ-Al2O3 (2 hours @ 900 °C). The particle consists of multiple crystallographic domains of δ-Al2O3 and θ-Al2O3. (b) Detailed depiction of the domains of δ-Al2O3 and θ-Al2O3. (c,d) Diffraction pattern from [010] and [210] orientations. (e,f,g) Individual representation from δ1/2-Al2O3, highly defected θ-Al2O3 and aperiodic Al2O3, as viewed along orientation.
neighboring columns creating a “Z-like pattern”, with either left- or right-handed orientation. For the structure denoted as δ1-Al2O3, the unit cell is defined by a sequence of an alternating left- and right-handed Z-like pattern stacked along the [010] direction. The left- and right-handed patterns are not mirror images but are offset along [100] by 1/2a with respect to each other as evidenced in Figure 2a, c. For δ2-Al2O3, the unit cell is defined by only one pattern, which is either right-handed or left-handed. The patterns are stacked directly on top of each other, and thus, the detected periodicity of δ2-Al2O3 is half the size of δ1-Al2O3. In the structural intergrowth, both variants of δ1-Al2O3 and δ2-Al2O3 can be as short as one unit cell, but in some cases, each variant can extend over several units cells. To relate the orientation of these two structures with respect to each other, Figure 2b includes a schematic depiction of the morphology and the crystallographic relationship with respect to the δ1 and δ2 phases. 3.2. Crystallographic Analysis of δ 1 -Al 2 O3 . The following text focuses on crystallographic analysis of δ1-Al2O3, which is the most prominent variant of the intergrowth structure of δ-Al2O3. To address the crystallographic nature of δ1-Al2O3, we have obtained a series of HAADF images from a number of low-indexed zones. Figure 2c−e depicts a detailed atomic representation from three cube orientations of [001], [010], and [100]. On the basis of the observed symmetry and periodicity in the presented HAADF images, the δ1-Al2O3 unit cell has an orthorhombic symmetry, with lattice parameters assessed as aδ = aγ; bδ = 2aγ; and cδ = 1.5aγ. The lattice parameters are inscribed in the individual images and are fully consistent with previous reports.11,25,26 In addition to the revealed symmetry and periodicity, the directly interpretable HAADF images provide a wealth of information regarding the projected atomic potential and thus important information for the derivation of Al3+ positions in the structure. Under general consideration, the HAADF intensity variation can be interpreted as either due to occupancy variation, or from differences in the atomic numbers, such that the intensity scales
projected periodic pattern that is defined by lattice vectors √2[1 1̅0]γ and 1.5[001]γ (referenced in γ-Al2O3 spinel structure). (Note that the projection of the particle is consistent with ⟨110⟩γ of the cubic γ-Al2O3 structure and in terms of δ1Al2O3 it is [210]δ1 and δ2-Al2O3 it is [110]δ1, as it will become evident in the later part of the text.) A confirmation regarding the interpretation of these domains in terms of the phase that has been previously considered as δ-Al2O3 can be obtained from selected area electron diffraction (SAED).25 Examples from [010] and [210] of the δ-Al2O3 phase are shown in Figure 1c, d, both of which images show a diffraction symmetry and spacing that are characteristics for the δ-Al2O3 phase. In addition to the intergrowth structure of δ1,2-Al2O3, one can also readily identify θ-Al2O3 as an important component of the overall micostructure, as shown in Figure 1b, f. As evidenced in a more detailed view in Figure 1f, θ-Al2O3 is often found to be highly defected and twinned on (100)θ. In this [010]θ projection, which is consistent with ⟨110⟩γ, a twinfree θ-Al2O3 would exhibit pairs of high-intensity columns inclined in the same direction rather than alternating directions as indicative of twins. In addition to δ1,2-Al2O3 and θ-Al2O3, there are also other less prevalent transition Al2O3 polymorphs that could be identified in the microstructure. Perhaps the most intriguing is the aperiodic type shown in Figure 1g. This structure lacks a long-range periodicity along two principal directions but maintains full periodicity along [110]γ. The periodicity along the viewing direction is expected on the basis of intensity of the brighter Al columns, which is consistent with that of δ1,2-Al2O3 and θ-Al2O3. The detailed representation of δ1-Al2O3 and δ2-Al2O3 intergrowth is shown in Figure 2. As evidenced in these images, the intergrowth proceeds along the [010] direction, and thus, any perpendicular direction, such as [001] or [100], represents a suitable orientation for the atomic scale analysis (both structures are independently projected). From the [001] direction shown in Figure 2a, c, the two variants of δ1-Al2O3 and δ2-Al2O3 can be readily distinguished from the symmetry of the most intense atomic columns, which are grouped as four 18053
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Figure 2. (a) HAADF image of the intergrowth of δ1-Al2O3 and δ2-Al2O3 as observed along the [001] orientation. (b) Schematic depiction of the morphology and the crystallographic relationship with respect to δ1- and δ2-phases. (c−e) Detail atomic level depictions of the structure δ1-Al2O3 along [001], [100] and [010] zone axes.
corresponding to Z1.7−1.9.41 In the specific case of δ-Al2O3 variants, which are well established to have oxygen atoms distributed on face centered cubic (fcc) lattice, the image intensity reflects variations in Al occupation in the atomic columns. For the cube orientations of [100], [010], or [001], the occupation of octahedral Al(Oh) and tetrahedral Al(Td) sites can be independently evaluated. The octahedrally coordinated Al ions Al(Oh) align with the oxygen sublattice while the tetrahedrally coordinated Al ions Al(Td) are projected in the center of the squares obtained from Al(Oh)/oxygen columns. Overall, the contrast in the HAADF images in Figure 2c−e is mostly dominated by intensities at octahedral Al(Oh) sites. This is partly due to the fact that Al(Oh) are aligned with the oxygen sublattice, which adds additional image intensity, but also due to the fact that Al(Oh) are present in the structure in higher quantities than Al(Td). In the case of the [001] projection, the square lattice of the octahedral sites can be well distinguished in the images, and importantly, it can be shown that the atomic columns from the Al(Oh) display two types of image intensities. The more intense Al(Oh) columns, which indicate higher occupation of Al on these octahedral sites, are grouped as four neighboring columns creating a Z-like pattern as previously discussed. There are eight high-intensity Al(Oh) columns per unit cell. From imaging on complementary [100], we have consistently obtained images that are less readily interpretable, and the individual columns may not be clearly resolved. This is indicative of the fact that both octahedral and tetrahedral sites do contribute to the overall image contrast. The dominant features in the recorded images are dark streaks tilted 45°, which have either short or long characteristic length. Along the horizontal direction, the dark streaks create a sequence of short
and long dark streaks. In one row, all dark streaks are tilted 45° to the right, and in the subsequent row, they are tilted 45° to the left. Although the resolution in the as-acquired images does not allow us to clearly distinguish the individual tetrahedral/ octahedral atomic columns, the dark streaks can be associated with neighboring octahedral/tetrahedral columns that are either vacant or at a very low Al occupancy. Supplementary imaging along [010] is again dominated by well-distinguished octahedral sites. The images show a complex pattern with a high- and low-intensity atomic columns of octahedral sites. In addition to the cube orientations, the previously presented ⟨210⟩ orientation, as shown in Figure 1b, e, provides important information and further constraints regarding the distribution of Al in the lattice. Please note that [010] and [210] correspond to directions where δ1-Al2O3 and δ2-Al2O3 are superimposed on top of each other. Derivation of the crystal structure of δ1-Al2O3 can be formulated as identification of octahedral and tetrahedral Al sites within the oxygen framework, and the constraints from the series of low-index HAADF images enable us to directly seek the reconstruction of Al positions in octahedral sites Al(Oh). In the orthorhombic cell (aδ = aγ, bδ = 2aγ, cδ = 1.5aγ), it is expected that there is a total of 96 oxygen atoms distributed on fcc lattice and a total of 64 Al atoms distributed among octahedral and tetrahedral sites. Finding positions of octahedral sites was then accomplished by detailed analysis of the projected potentials and by building structural models that satisfied the relative distribution of intensities in the low-index HAADF images. In our comprehensive search, we found that, to fully reproduce the experimental HAADF image intensities, the solution can be only obtained when considering 40 Al in octahedral positions (40Al(Oh)/cell), which represents 62.5% of total Al atoms. 18054
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Figure 3. (a) Schematic representation of δ1-Al2O3. Octahedral coordinated Al is in blue, tetrahedral Al in yellow, and oxygen atoms are in red circles. (b−e) HAADF simulation of δ1-Al2O3 along several low-indexed zones with inset experimental images. The δ1-Al2O3 can be independently resolved along [001] and [100], and thus, the experimental and simulated images can be directly compared. Along [010] and [210], the experiment images consist of superposition of δ1-Al2O3 and δ2-Al2O3 along the viewing direction. Because of structural similarities of δ1-Al2O3 and δ2-Al2O3, the simulation provides a match with the experimental images.
can lead to loss of resolution. The additional images in Figure 3d, e are from [010] and [210], where δ1 and δ2 are expected to be intergrown, and thus, a direct comparison cannot be made. Nevertheless, due to the close structural similarities of the two structures, the simulation of δ1-Al2O3 also provides a very good match with the experimental images. In support of the proposed structure of δ1-Al2O3, it is important to point out that it belongs to the P212121 space group, which is fully consistent with one of the previously proposed space groups for δ-Al2O3 from electron diffraction measurement.25,26 Importantly, it is also relevant to point out that there are 37.5% (AlTd) tetrahedral and 62.5% (AlOh) octahedral sites, which is consistent with previous NMR studies that indicated δ-Al2O3 to be intermediary between γ-Al2O3, which is normally reported to contain 25−30% (AlTd), and θAl2O3, which contains 50% (AlTd) .42,43 While the HAADF analyses enabled us determine the location of octahedral and tetrahedral sites for Al in the oxygen fcc lattice, this structural analysis approach does not allow to assess a fine relaxation on these sites, and thus, the HAADFderived model represents only a first approximation of the structure. A further refinement of the atomic positions and lattice parameters was done using DFT methods, which have now become well established for structural refinement. Small errors in the lattice parameters may be expected depending on the choice of exchange correlation approximation. In the current calculation, we use the GGA PW91 approximation, which may overestimate the lattice parameters by as much as 1% in transition Al2O3.19 The results of the DFT calculations show the relaxed lattice parameters are aδ = 7.99, bδ = 16.101, and cδ = 11.80. The structure has orthorhombic symmetry and belongs to the space group P212121. Full crystallographic description of the δ1-Al2O3 structure, including the initial and refined condition, is reported in the Supporting Information in Table S1. Table S2 (Supporting Information) contains a full structural description
Because of the limited contrast, the tetrahedral sites could not be determined from the HAADF images directly, and their determination required a different approach. Specifically, we analyzed the bonding environment for all possible tetrahedral sites in the unit cell that are populated by octahedral Al atoms, and then, we assessed the viability of each individual tetrahedral site in the context of established bonds with octahedral Al. In the orthorhombic cell of δ1-Al2O3, there is a total of 192 available tetrahedral sites, which are either corner-, edge-, or face-shared with the octahedral sites. From all of these tetrahedral sites, however, only the corner-shared tetrahedral sites can be considered as viable because the edge- or faceshared tetrahedral sites have an unfavorable proximity to the Al atoms in octahedral positions. Using a computer search algorithm developed as a part of this analysis, we find that there are 24 corner-shared tetrahedral sites (37.5% of total Al atoms), which is the exact number required to complete the stoichiometry of δ1-Al2O3 and thus provide a complete determination of all Al sites in the structure. Importantly, the locations of the tetrahedral sites are fully consistent with the [100] projection where the tetrahedral sites also give rise to the image contrast. The derived crystal structure of δ1-Al2O3 is depicted in Figure 3a, and the consistency of this structure with the experimental observations can be demonstrated by performing HAADF images simulation along a series of low-indexed projection. The results from the simulation, with added experimental images as insets, are depicted in Figure 3(b−e). For images from [001] and [100], where the structure of δ1Al2O3 is independently projected, the simulations provide a full match with the experiment. Please note that the resolution and the contrast in the experimental images is lower than in the simulations, which is associated with experimental difficulties to obtain high-resolution HAADF images of transition Al2O3. For small, highly defected flakes of transitional alumina, it is often very difficult to ensure that the crystal stays perfectly still and oriented on the zone during the course of acquisition, which 18055
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for δ2-Al2O3, which has been derived using an analogous approach as for determination of the δ1 phase. 3.3. Enthalpy of Formation. In addition to the structural refinement, DFT calculations also enable us to derive the equilibrium enthalpy of formation, which can be used as a basis for a comparison of thermodynamic stability. To compare the stability of the derived δ1-Al2O3 and δ2-Al2O3 phases, we have also calculated the enthalpy of formation for γ-Al2O3 and θAl2O3 and the thermodynamically stable α-Al2O3. Because of the controversy surrounding the structure of γ-Al2O3, two models are used in the current study for comparison purposes: one of which has Al constrained to spinel sites,13 and the other has also some Al on nonspinel sites.16 As reported in Figure 4, the results of the calculations indicate that δ1-Al2O3 and δ2-Al2O3 have a very favorable
show the gradual appearance of new features corresponding to the higher temperature (and lower symmetry) phases.20 The work presented here helps to explain this, since a particular sample is likely to contain a mixture of nearly degenerate polymorphs. The structural intergrowth prevented us from carrying out a complete refinement based on the powder pattern. Nevertheless, the powder pattern calculated from DFT-derived δ1Al2O3 showed good general agreement with the experimental pattern, as shown in Figure 5. All of the observed peaks are
Figure 5. XRD data showing the characteristic peaks of a Boehmite sample thermally treated at 1000 °C for 6 h. The calculated pattern represents a linear combination of δ1-Al2O3, δ2-Al2O3, and θ-Al2O3.
present in the calculated pattern, and the intensities match approximately but not exactly. When we included approximately 20% δ2-Al2O3 and 28% θ-Al2O3 in the Rietveld refinement shown in Figure 5, the overall match is better, but there remains significant diffracted intensity near 45° and 65° 2θ, which correspond to (400) and (440) when indexing in terms of cubic γ-Al2O3. This can be attributed to several factors, such as the use of simple linear combination for the highly intergrown microstructure, disregarding the fact that θ-Al2O3 is heavily twinned, and also due to exclusion of other less prevalent phases such as the aperiodic Al2O3 shown in Figure 1g. For example, it is expected that the aperiodic structure should have relatively strong intensity for the (004) planes. While the crystal is aperiodic, the high-intensity columns are all aligned with (004) (which is perpendicular to the image and intersecting the horizontal lines in Figure 1g), and consequently, the diffracted (004) intensity should remain high while that from oblique planes will be reduced by the aperiodicity. Similar arguments apply to the (440) planes. The lattice parameters of δ1-Al2O3 were relaxed during the XRD refinements to values of a = 7.937(5), b = 15.900(10), and c = 11.679(3) Å. These are consistently lower than the DFT-derived values by approximately 1%. Given the known tendency of the GGA PW91 approximation to overestimate the lattice parameters, the XRD values are considered to be the more accurate.
Figure 4. Comparison of the enthalpies of formation for the newly derived crystals of δ-Al2O3 and several other reported polymorphs of γ-Al2O3, θ-Al2O3, and α-Al2O3.
enthalpy of formation (ca. −0.1 eV/Al2O3) compared with the reported γ-Al2O3 structures. On the other hand, the enthalpies of formation for θ-Al2O3, δ1-Al2O3, and δ2-Al2O3 are almost identical (within the estimated accuracy of the current calculations). Because of the similarity in the enthalpies of formation and also a high degree of structural compatibility, it can now be easily understood why the structures of δ1-Al2O3, δ2-Al2O3, and θ-Al2O3 can readily intergrow during the thermal decomposition of γ-Al2O3. By similar reasoning, we expect additional structures, such as the aperiodic region seen in Figure 1e, to have similar formation enthalpies, leading to additional intergrowths. Lastly, the current calculations include a comparison with the stable polymorph of α-Al2O3, which has an enthalpy of formation lower by −0.05 eV/unit, thus completing the energetic sequence for structural evolution from γ-Al2O3. The calculated value for α-Al2O3 is consistent with previous reports in the literature.19 3.4. X-ray Diffraction Refinement. The identification of transition phase aluminas is traditionally made using powder XRD. As samples change from γ-Al2O3 through δ-Al2O3 and on to θ-Al2O3, the XRD patterns do not exhibit abrupt changes but
4. CONCLUSIONS The current work has focused on the structural analysis of δAl2O3. It has been shown that δ-Al2O3 is a phase that should be understood as a structural intergrowth from two main 18056
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crystallographic variants. The two variants are identified as δ1Al2O3 and δ2-Al2O3, and it is shown that they can create a highly intergrown structure that lacks a long-range periodicity along one principal direction. As a part of this study, we present a crystallographic approach that enabled us to unambiguously derive the Al coordination in these structures from a series of low-index zone atomic level HAADF images. In combination with XRD refinement and DFT calculations, we then report full crystallographic information for both δ1-Al2O3 and δ2-Al2O3 crystallographic variants. The new crystallographic knowledge allowed us to examine the enthalpy of formation and compare it with enthalpy of formation of other transition phases and αAl2O3. The results suggest that δ1-Al2O3, δ2-Al2O3, and θ-Al2O3 have very similar enthalpies of formation, which explains the frequently observed intergrowth of these structures. Overall the current findings provide important new information in the overall effort to rationalize the transformation processes in transition Al2O3.
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ASSOCIATED CONTENT
S Supporting Information *
Full crystallographic information on δ1-Al2O3 and δ2-Al2O3 are presented in Tables S1 and S2 and in CIF format. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*(L.K.) Phone: (509) 375-4377; e-mail: libor.kovarik@pnnl. gov. *(J.H.K.) E-mail:
[email protected]. Notes
The authors declare no competing financial interests.
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ACKNOWLEDGMENTS The research described in this paper is part of the Chemical Imaging Initiative at Pacific Northwest National Laboratory (PNNL). It was conducted under the Laboratory Directed Research and Development Program at PNNL, a multiprogram national laboratory operated by Battelle Memorial Institute for the U.S. Department of Energy under contract no. DE-AC0576RLO1830. C.H.F.P., J.S., and J.H.K. were supported by the U.S. DOE, Office of Basic Energy Sciences, Division of Chemical Sciences, Biosciences and Geosciences. The work was conducted in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the DOE’s Office of Biological and Environmental Research and located at PNNL.
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