One-dimensional nanowires of pseudoboehmite(aluminum oxyhydroxide γ-AlOOH)Sumio Iijimaa,1, Takashi Yumurab, and Zheng Liuc,d,1

aGraduate School of Science and Technology, Meijo University, Nagoya 468-8502, Japan; bDepartment of Chemistry and Materials Technology, KyotoInstitute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan; cInorganic Functional Materials Research Institute, National Institute of AdvancedIndustrial Science and Technology, Nagoya 463-8560, Japan; and dNanomaterials Research Institute, National Institute of Advanced Industrial Science andTechnology, Tsukuba 305-8565, Japan

Contributed by Sumio Iijima, August 30, 2016 (sent for review June 14, 2016; reviewed by Darren W. Johnson and Alexandra Navrotsky)

We report the discovery of a 1D crystalline structure of aluminumoxyhydroxide. It was found in a commercial product of fibrouspseudoboehmite (PB), γ-AlOOH, synthesized easily with low cost.The thinnest fiber found was a ribbon-like structure of only twolayers of an Al–O octahedral double sheet having a submicrometerlength along its c axis and 0.68-nm thickness along its b axis. Thisthickness is only slightly larger than half of the lattice parameterof the b-axis unit cell of the boehmite crystal (b/2 = 0.61 nm).Moreover, interlayer splittings having an average width of 1 nminside the fibrous PB are found. These wider interlayer spaces mayhave intercalation of water, which is suggested by density func-tional theory (DFT) calculation. The fibers appear to grow as al-most isolated individual filaments in aqueous Al-hydroxide solsand the growth direction of fibrous PB is always along its c axis.

1D material | nanowire | TEM | aluminum oxyhydroxide | pseudoboehmite

Low-dimensional materials such as quantum dots (1), nanowires(2, 3), and nanosheets (4) have attracted interest in academia and

industry. Carbon nanotubes (5), a typical 1D inorganic material,have been investigated widely, but new 1D inorganic materials pre-pared by a simple and reliable method have rarely been reported.The aluminum ore bauxite primarily comprises aluminum hy-

droxide possessing different crystalline forms. The thermal de-hydration of aluminum hydroxide produces alumina Al2O3, oneof the most important materials in modern industries. γ-Boehmite(γ-AlOOH) (6) is a typical aluminum oxyhydroxide with a crystalstructure similar to that of lepidocrocite (γ-FeOOH) (7). Thesemetal oxyhydroxides, represented by γ-MO(OH), where M = Fe,Ni, Mn, Sc, Ti, etc., have attracted interest in fields from energyto medicine. In a nickel–hydrogen battery, the formation ofpoorly crystalline γ-NiOOH on the cathode has been shown tocause the memory effect of the battery (8). Titanate nanosheetshave recently attracted attention in the electronics communitybecause of their semiconducting properties (9). Hydrogen gen-eration by aluminum–water reactions for onboard vehicular hy-drogen storage (10) and the radiolytic generation of hydrogen inconjunction with metal corrosion in water in nuclear energy andwaste systems (11) both involve aluminum hydroxides as reactionproducts. Aluminum hydroxide has also been used as a vaccineadjuvant (12) and its biochemical mode of action in a recentmedical technology is being investigated (13).Boehmite is synthesized by aging noncrystalline aluminum hy-

droxide sol in an aqueous solution at a specific pH, and it has thebasic crystal structure of double sheet of a metal–oxygen octahe-dron layer piled up through hydrogen bonding, as illustrated inFig. S1. Poorly crystallized boehmite, often called pseudoboehmite(PB), forms in various crystal morphologies, such as thin films,thin platelets, and nanometer-sized rods or fibers. Importantly,the characteristics of alumina Al2O3 for industrial use preparedby thermal dehydration are influenced by the morphology of thestarting boehmite crystals.Fibrous PB has a particularly poor crystalline structure (14,

15), and its crystal structure and morphology have never been

clarified even by using the modern crystallography methods suchas radial distribution function analyses with synchrotron X-raydiffraction (16, 17) and NMR (18). To solve such a long-standingproblem with fibrous PB, we made full use of conventional trans-mission electron microscopy (TEM) methods, high-resolution TEM(HRTEM) imaging, and electron diffraction (ED), and successfullyrevealed the detailed morphologies and crystal structures, includingdetermination of the fiber axis, of fibrous PB.

Results and DiscussionStructure of Fibrous PB. Fig. 1A shows TEM images of fibrous PBforming a lacy network of randomly dispersed nanometer-sizedfibers prepared by drying a diluted sol of boehmite “F1000”(KAWAKEN Fine Chemical Co., Ltd.). The Debye–ScherrerED (DS-ED) ring patterns shown in Fig. S2 A and D demon-strate that the crystal structure of PB is γ-AlOOH, as reported inthe literature (17). However, the width of the DS-ED rings isgenerally broadened with some relatively sharper rings apparentas well, and the intensities of these rings differ slightly from thoseof the well-crystallized PB sample. The differences can be explainedby the crystallite size of the fibrous PB F1000 sample. Such dif-ferences in crystal size and morphology from the other two samples,provided by the KAWAKEN Fine Chemical Co., namely nanorod“10A” and platelet “Powder,” were confirmed as shown in Fig. S2 Band C, respectively. DS-ED patterns of the three samples (Fig. S2D–F) can be easily distinguished from each other in terms of thering width and intensity.A highly magnified image of a region enclosed by rectangle 1

in Fig. 1A clarifies the ribbon structure appearing as dark,

Significance

Pseudoboehmite (PB) is a poorly crystallized variant of boehm-ite, but its crystal structure and morphology have not beenclearly understood. In particular, PB gel crystals are formed in anaqueous solution, so the interface between the crystalline sur-face and water is of crucial importance for understanding itsproperties and growth mechanism. Here we report the detailedstructures of fibrous PB crystals obtained from high-resolutiontransmission electron microscopy and electron diffraction pat-terns. Some of the fibers consist of only two layers of an Al–Ooctahedral double-sheet ribbon structure, which is really a 1Dstructure. The findings will broaden the understandings in clas-sical but important fields of colloid science and clay mineralogy.

Author contributions: S.I. designed research; S.I. and Z.L. performed research; Z.L. con-tributed new reagents/analytic tools; S.I., T.Y., and Z.L. analyzed data; and S.I. wrotethe paper.

Reviewers: D.W.J., University of Oregon; and A.N., University of California, Davis.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.1To whom correspondence may be addressed. Email: iijimas@meijo-u.ac.jp or liu-z@aist.go.jp.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1614059113/-/DCSupplemental.

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parallel straight lines that can be seen in the upper portion of theimage (Fig. 1B), and a further enlarged image in Fig. 1C (forbetter visualization, this image has been rotated compared withFig. 1B). A model of γ-AlOOH projected on (100) (Fig. 1D)shows that the separation between the two layers of the Al–Ooctahedron double sheet is 0.61 nm. We refer to one Al–O oc-tahedron double sheet as “one layer” in this study for simplicity.By comparing the upper four dark lines in Fig. 1C with thosefrom the model shown in Fig. 1D, it can be seen that these darklines correspond to the (020) lattice image of the layers that are0.607 nm apart. Another ribbon was collected in an area sur-rounded by rectangle 2 located close to rectangle 1, and theenlarged image is reproduced in Fig. 1E. This particular ribbonsplits into two pieces with one piece having two layers on theleft side and three additional layers on the right side. Thecontrast of the two dark lines suddenly disappears and changesto a gray ribbon-like contrast, as shown by the arrow in Fig. 1B,indicating the twisting of the fibrous PB ribbon. Such a narrowribbon is expected to be inherently quite soft and flexible, aswill be discussed later.The anomalous white lines showing the splitting of the ribbons

indicated by the arrowheads in Figs. 1B and 1E can be foundfrequently in the present fibrous PB. The width of the white lines(separation between the two black lines) is roughly 1.0 nm, up to64% wider than the normal (020) lattice spacing (0.61 nm). Thewider layer spacing is likely associated with initiation of cleavageon the (020) planes, suggesting that some species like H2O areintercalated between the adjacent Al–O octahedral double sheet.The water intercalation will be discussed further below.

Atomic Structure of Two-Layered Double Sheet of Fibrous PB.One ofthe most important results in the present study is the finding ofthe thinnest fibrous PB ribbon with 1D crystalline structure in a

synthetic aluminum oxyhydroxide. The ribbon consists of a pairof Al–O octahedral double-sheet layers (imaged as two darkparallel lines), as shown in Fig. 2A. By measuring the interlayerspacing between two layers of double sheet (i.e., the distancesbetween the two dark parallel lines in Fig. 2A), it is noted that theaverage distance is about 0.68 nm, as shown in Fig. 2A, which is12% wider than the normal (020) lattice spacing (b/2 = 0.607 nm)of the boehmite crystal. A similar expansion was observed ondouble layers of graphene (19). One plausible explanation is thesurface effect in nanoscale crystalline systems as demonstrated bydensity functional theory (DFT) calculation. Another possibleexplanation is the intercalation of small molecules, such as H2O,between the layers.The long double-sheet nanoribbon is bent and twisted, which

is highlighted by a dotted line in Fig. 2B. The winding ribbonproves its softness and flexibility. A rectangular area in Fig. 2Bexhibits a clear image of the double-sheet nanoribbon (Fig. 2A).Schematic models of the straight, bent, and twisted double-sheetnanoribbon are illustrated in Fig. 2C. The thinnest fiber isa freestanding ribbon structure consisting of only two layers ofAl–O octahedral double sheet terminated with (100) and (010)surfaces, extending in the [001] direction, as shown in Fig. S1.The atomic structure of the fibrous PB nanoribbon can be ob-served in HRTEM images at atomic resolution (Fig. 2D). It re-veals directly the arrangement of Al and O atoms (Al atomsshow darker contrast in this image). Differences in the detailedcontrast of the two magnified HRTEM images indicated by tworectangles on the right side of Fig. 2D are caused by the bendingand twisting along this nanoribbon. The corresponding bendingand twisting models are schematically illustrated in Fig. 2E. Themodel in the upper part is rotated by 5° around both the b and caxes relative to the model in the lower part. This HRTEM image

Fig. 1. TEM images of fibrous PB. (A) An electron micrograph shows a thin lacy film of fibrous boehmite samples F1000 from KAWAKEN Fine Chemical Co.(B) An enlarged image of a rectangular region 1 in A shows a ribbon-like crystalline structure. The contrast of the two dark lines suddenly disappeared andchanged to a gray ribbon-like contrast, as shown by the arrow, indicating the twisting of the fibrous PB nanoribbon. (C) The dark lines in an enlarged imageof the upper rectangle part in B are the (020) lattice image. (D) The corresponding Al–O hydroxides double sheet of crystal model of γ-AlOOH. (E) Anotherribbon-like image of a rectangular region 2 in A. The wider separation indicated by the arrowheads in B and E suggests some species like H2O are intercalatedbetween the adjacent Al–O octahedral double sheet.

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with atomic resolution further reveals the local distortion of suchthin PB nanoribbons and proves its flexibility.The mean thickness of the PB nanoribbon was measured from

large numbers of TEM images. A typical TEM image is shown inFig. S3A. The arrows indicate occurrence of two-layered double-sheet nanoribbons that happen to be imaged due to their edge oncondition. The histogram of fiber thickness shown in Fig. S3B iscentered at 1.8 nm, which corresponds to the width of 3–4 layersof the Al–O double sheet. The frequency of the discernible two-layered double-sheet nanoribbons is estimated to be more than5%. It is noteworthy that, despite frequent appearances of themultilayered double sheets, a single-layered double sheet has neverbeen observed in the present fibrous PB. The lack of a single Al–Ooctahedral double-sheet nanoribbon structure may be related tothe instability or growth of the double sheet itself in aqueous alu-minum hydroxides sols, whereas the two-layered nanoribbons arespeculated to be nucleated more stably due to the interactionsbetween their two layers. Further investigation is necessary.

DFT Calculations. To obtain a better understanding of the struc-tural features of the 1D PB structure observed by HRTEM, spin-polarized DFT calculations were performed under periodicboundary conditions. Two types of bonding patterns of oxygenatom termination were considered: the presence (Fig. 3 A and B)and absence (Fig. 3C) of H-atom saturation. Fig. 3 displays op-timized structures for the PB nanoribbons, whose interlayerspacings, corresponding to half the lattice parameter of the b-axisunit cell of the boehmite crystal (blue lines), are given. First, theinterlayer spacing of PB nanoribbons without water moleculeswas calculated to be 0.66 nm (Fig. 3A), which is 8% larger thanthe normal (020) spacing. Such an expansion fits very well withthe TEM observations (0.68 nm for two layers of the Al–Odouble sheet), demonstrating the interlayer spacing in nanoscale2D crystalline structure is slightly wider than in the bulkstructure. Second, a model including the presence of water inwhich the adjacent Al–O octahedral double-sheet layers are

bound with a monolayer of water molecules was considered.Different interlayer spacings of PB nanoribbons with and withoutintercalation of a monolayer of water molecules can be found bycomparing Fig. 3A and Fig. 3B. The intercalation of only a singlelayer of water molecules strikingly expands the interlayer spacingof PB nanoribbons from 0.66 to 0.90 nm. In addition, the in-terlayer spacing is slightly affected by whether H-atom saturationis involved or not: 0.90 nm (Fig. 3B) and 0.89 nm (Fig. 3C) forthe presence and absence of H-atom saturation, respectively.Within the inner space of the PB nanoribbon containing amonolayer of water molecules, the H atoms in water are sepa-rated by 0.17 nm from the O atoms in the Al–O octahedral sheetof the PB nanoribbon, and at the same time the O atoms in waterare separated by 0.17 nm from the H atoms terminating theO atoms in the Al–O octahedral sheet of the PB nanoribbon.These interatomic separation ranges are suitable for attractivehydrogen-bonding interactions connecting water molecules andthe Al–O octahedral sheet in the PB nanoribbon. The watermolecules can act as adhesive agents for connecting Al–O oc-tahedral double-sheet layers of the PB nanoribbon as shown inFig. 1 B and E. Similar adhesion effects of water molecules be-tween a γ-alumina surface and an epoxy resin were also found(20). The DFT results clearly indicate the influence of interca-lated water molecules in enhancing interlayer spacings of PBnanoribbons, which provide a hint to understand the splittingobserved in the TEM results. The calculated value of the sepa-ration, 0.9 nm, seems to support the observation on the largeseparation of splitting ribbons (∼1.0 nm, indicated by white ar-rowheads in Fig. 1 B and E) due to water intercalation. Althoughour calculation model containing three water molecules per unitcell gives rise to an interlayer spacing of 0.9 nm in the b axis,decreasing or increasing the number of water molecules withinthe Al–O octahedral double-sheet layers would diminish or ex-pand interlayer spacing from 0.9 nm. Actually, the splitting widthobserved in this study has a distribution from 0.83 to 1.5 nm withan average value of 1.0 nm. However, in this study the occurrence

Fig. 2. Two-layered double sheet of fibrous PB. (A) HRTEM images of nanoribbons consisting of two-layered Al–O hydroxide double sheet. The two layers areseparated by 0.68 nm. (B) TEM image of a flexible and lengthy double-sheet nanoribbon, highlighted by a dotted line. (C) Schematic models of straight, bent,and twisted double-sheet nanoribbon. (D) HRTEM image with atomic resolution shows local distortion of a two-layered double sheet. The enlarged images ofenclosed regions are shown in the right side inserted with the corresponding simulated images (labeled by ”S”) and Al and O atoms overlaid in the lowersimulated image. (E) The corresponding models used for simulation in D. The model in the upper part is rotated by 5° along both the b and c axes relative tothe model in the lower part.

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of such kinds of splitting is not so frequent that the intercalatedwater content does not obviously affect the total amount ofabsorbed water in the present PB. Moreover, the slight expansionof the interlayer spacing from 0.61 to 0.68 nm could be associatedwith intercalation of small amount of water. The conclusion pre-sented here suggests that the thicker PB nanoribbons showing thenormal interlayer spacing of boehmite (b/2 = 0.61 nm) containalmost no water in their interlayer spaces.

Growth Direction of Fibrous PB. To determine the fiber axial di-rection of the fibrous PB, we systematically examined the DS-EDpatterns of the fibrous PB crystals that tend to agglomerate todifferent degrees from completely randomly dispersed fibers to

well-bundled ones. Two typical DS-ED patterns from thesecrystals are shown in Fig. 4 A and B. It is noted here that the 020reflections were not observed in most of the DS-ED patterns.The absence of the 020 reflections was understood as a diffrac-tion phenomenon for an extremely narrow ribbon structure offibrous PB. Compared with the DS-ED ring pattern from ran-domly dispersed fibers (Fig. 4A), the pattern for the well-bundledfibers showed characteristic intensity maxima on each DS-EDring (Fig. 4B). Regardless of which bundled fibers are observed,these maxima always appear at the same positions and canbe indexed as labeled in Fig. 4B. The position of the intensitymaxima of the 002 reflection always lies on the direction parallelto the bundle axis. This means that the individual fibrous PBcrystals grow along the c axis, namely the [001] direction; 200, 002,and 202 reflections appear to belong to h0l reflections from a singlecrystal of γ-AlOOH, but 120 and 031 reflections do not. In addi-tion, 120 reflections always appear in the same direction as the 200reflection in the ED pattern, which should not be observed in asingle crystal of γ-AlOOH. Such kinds of contradictions can beexplained as long as the incident electron beam is perpendicular tothe c axis of the fibrous PB crystal. This situation is illustrated in across-sectional view of a bundle of fibrous PB in Fig. 4C. Thisconclusion could explain many other experimental observationsregarding the fiber morphology proposed here. An importantconclusion is that the appearance of the intensity maxima in theDS-ED pattern (Fig. 4B) is a summation of diffraction intensitiesfrom every individual fiber in a bundle.Although a bulk boehmite crystal is an electrical insulator,

1D nanoribbon PB crystals could have different physical prop-erties when intercalated with some ion species, as is known forfunctionalized carbon nanotubes (21, 22) and 2D materials(23). The electronic structure of intercalated 1D PB nano-ribbon is of interest in theoretical and experimental investiga-tions, in terms of the nanoribbon size, layer distance betweenadjacent Al–O octahedral double sheet, and a sol state wherethe structure is immersed in an aqueous ionic solution.One of the differences between bulk boehmite and PB is that

the latter contains more water. In general, the specific surface areaof a crystal is increased with a decrease in crystal size. Therefore,the fibrous PB crystals, which have a larger specific surface areathan the bulk boehmite crystals, could adsorb more water on theirsurfaces (24). The present study could specify the site for the waterthat goes preferentially into the interlayer spaces of the fibrous PBnanoribbons having splitting or cleavage on the (010) plane. Asimilar interlayer structure for water intercalation will be takingplace in the bundle of the fibrous PB nanoribbons.Synthesis of several different types of morphologies of boehmite

crystals has been established in the sol–gel reaction of Al-hydroxidesolution by controlling the pH, temperature, and reaction time. Incontrast with the rod PB and platelet PB, the fibrous PB crystalsextend preferentially in the c-axis direction. Such an extremelyanisotropic linear growth of the fibrous PB-like carbon nanotubes(5) may be caused by a reactive site on the tip of the nanoribbon,where Al-hydroxide ionic species could be attracted. The amountof surface negative charge was counted to be slightly higher on the(001) surface than on the (100) and (010) surfaces. Therefore,positive Al-hydroxide ion clusters will be continuously attractedmore on the (001) plane that accelerates the growth of c-axis di-rection. The TEM image shown in Fig. 5A and an amplified area(white rectangle area in Fig. 5A) showing one of the terminatedfibers (Fig. 5B) will serve to clarify more specifically the growthmechanism of the fibrous PB. The tip shapes of the terminatedfibers (indicated by an arrow in Fig. 5B) show a geometrical fea-ture and its possible model is illustrated in Fig. 5C. The knife-edgeshape of the tip appears to fit well with the (101) crystal surfaceand therefore this surface is considered to be a growth front of thefiber. By comparing the (101) surface (Fig. 5C) with the (001)surface (Fig. 5D), it is known that the total amount of charge of

Fig. 3. Spin-polarized DFT optimized geometries for PB nanoribbons in theabsence (A) and presence (B) of a monolayer of water molecules intercalated.Some terminated oxygen atoms are bound with H atoms. Interspace betweenAl–O octahedral double sheet with intercalated water molecules, surroundedby purple lines, was magnified (B). (C) Terminated oxygen atoms on PB nano-ribbons are not bound with H atoms. Interspace between Al–O octahedraldouble sheet with intercalated water molecules, surrounded by purple lines,was magnified. Note that the separation of a water H atom to an end O atomon a PB nanoribbon (0.19 nm) is slightly longer than those to a normal O atomon a PB nanoribbon (0.16 and 0.17 nm). The unit of interlayer spacing betweenadjacent Al–O octahedral double sheet, corresponding to the half-lattice pa-rameter of b-axis unit cell of the boehmite crystal (blue lines), and the length ofhydrogen bonds (dotted lines in the inserted images), is given in nanometers.

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the wedge tip ending with the (101) surface is slightly larger thanthat of the flat (001) surface on the assumption that the alu-minum ions are fully saturated with O−2 or OH−1 when countingthe amount of the local net charges near the tips. It is reason-able therefore that positively charged Al–O clusters can beattracted and deposited onto the tip surface, and fibrous PBgrows along its c axis. The growth should be influenced by thestability of the positively charged multivalent octahedral clusters[Al–O]n, (n = 0 ∼ +3) (25–27). The absence of the monolayeredAl–O octahedral double sheet is demonstrated by DFT energycalculation shown in Fig. S4, in which two-layered Al–O octahedraldouble sheet is 0.8 eV (per unit cell) and 1.5 eV (per unit cell) moreenergetically favorable than monolayered Al–O octahedral doublesheet without and with water intercalation, respectively. This maybe a tie into the Al Keggin cluster intermediates and their assembly(25). It could be interesting to explore further in the future.We conclude that a “genuine 1D” nanoribbon of fibrous boehm-

ite has been found in commercial products of PB. Although 1Dnanoribbons of two-layered Al–O octahedral double sheet are aminor structure in the present product (more than 5%), it could besynthesized to be a major structure by fully controlling growth pro-cesses. It is challenging to form the nanoribbons in other similarmetal oxyhydroxides γ-MO(OH). Moreover, the growth mechanismof fibrous PB will broaden deeper understandings in classical butimportant fields such as nucleation and growth in sol–gel processes,polymorphic transformations, and related aluminum aqueous clusters.

MethodsThree PB samples examined in the present study are F1000: fibers of 0.7–3-nmthickness, 10A: nanometer-sized rod-like crystallites of 1.2–6-nm thicknessand 4–5-nm length, and Powder: platelet crystallites with diameters of 20–30-nm and 5–10-nm thickness. All are commercial products (KAWAKEN FineChemical Co.) prepared by hydrolysis and peptization of aluminum iso-propoxide and their morphologies are controlled by reaction processes. TheF1000 is synthesized at the reaction temperature of 150 °C and aged for 6 hwith stabilizer of acetic acid (pH 3.4–4.2) (28). The first two samples areaqueous hydroxide sols, and the last one is a dried powder. For the TEM ob-servation, the samples were diluted in water and collected on a TEM gridcovered with a holey carbon film. The TEM specimens were examined by a JEM2010F electron microscope with a Corrected Electron Optical Systems GmbH(CEOS) spherical aberration corrector operated at 120 keV. Many clay mineralsthat contain hydroxyl groups or water are unstable under electron beam ir-radiation (29). In this study, the electron beam damage to the specimen was

minimized as much as possible [the beam density during the observationsranged from 50 to 150 electrons/(nm2·s)]. A sequence of HRTEM images (up to20 frames) was recorded with an exposure time of 0.5–1 s for each frame, andafter drift compensation, some frames can be superimposed to increase thesignal-to-noise ratio for better visualization.

DFT calculations were performed by using the projected augmented wavemethod, implemented in the Vienna ab initio Simulation Package (VASP 4.6)(30). In the VASP calculations, the Perdew, Burke, and Ernzerhof (PBE)functional was used to describe electronic exchange and correlation (31).Previous studies confirmed that the PBE functional is suitable for describinghydrogen-bond interactions (32–35), together with metal–oxygen bond in-teractions. All calculations for optimizing PB nanoribbon structures werespin polarized. Kinetic energy cutoff of the plane-wave basis is 400 eV. Forthe calculations of two Al–O octahedral double-sheet layers with a mono-layer of water molecules, we used a square supercell, containing 77 and 68atoms for the H-atom saturated and unsaturated models, respectively.We allowed full geometry relaxation of PB nanoribbons directed in thec direction, where the lattice parameters in the a- and b directions werefixed at 3 nm to avoid significant interactions of the two Al–O octahedral

Fig. 4. Bundles of fibrous PB. (A) DS-ED pattern recorded from a randomly dispersed thin film of fibrous PB crystals. (B) DS-ED pattern from bundled fibrousPB crystals, where the bundle axis is shown by the double-headed arrow. Both patterns are indexed as those from a bulk crystal of γ-AlOOH. The (002)reflections, however, are relatively strong in both DS-ED patterns in A and B, suggesting the long ribbon-like structure of PB. Broadening of the (200) re-flection is caused by an extremely narrow width of the PB ribbon. The intensity maxima, which look like a single crystal, can be explained by a model in whichindividual fibers form in a bundle, and align parallel to the [001] direction (i.e., c axis) but randomly rotated around this axis. (C) A cross-sectional view of abundle is illustrated. Some of the fibers aligned in low-index zone axes are indicated by the index numbers shown in C.

Fig. 5. Tip shapes of the fibrous boehmite – F1000. (A) An electron micro-scope image showing some terminated fibers enclosed by a rectangle; theirenlarged image is reproduced in B. (C) A possible structure of the tip of thefibers terminated with the (101) facet of the boehmite crystal. The tip regionhas a slight excess positive charge comparing to a tip terminated with the(001) facet shown in D. The excess charge would promote an anisotropiccrystal growth of the fibrous PB.

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double-sheet layers with those located on the neighboring unit cells. AΓ-centered 1 × 1 × 2 k-point mesh was used for the geometry optimization.The optimization processes were stopped when the forces on all of themobile atoms were smaller than 0.01 eV/0.1 nm.

ACKNOWLEDGMENTS. We thank Dr. F. Mizukami (National Institute ofAdvanced Industrial Science and Technology) and Dr. N. Nagai (KawakenFine Chemicals Co.) for discussions. Z.L. acknowledges Japan Society for thePromotion of Science KAKENHI Grant JP 25107003.

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