Theoretical Investigations of the Relaxation and Reconstruction of the

5228

J. Phys. Chem. C 2009, 113, 5228–5237

Theoretical Investigations of the Relaxation and Reconstruction of the γ-AlO(OH) Boehmite (101) Surface and Boehmite Nanorods Francesco Mercuri,*,†,‡ Dominique Costa,‡ and Philippe Marcus‡ ISTM-CNR c/o Department of Chemistry, UniVersity of Perugia, Italy, and Laboratoire de Physico-Chimie des Surfaces, CNRS-ENSCP (UMR 7045) Ecole Nationale Supe´rieure de Chimie de Paris, 11 rue Pierre et Marie Curie, 75005 Paris, France ReceiVed: July 29, 2008; ReVised Manuscript ReceiVed: January 8, 2009

Ab initio molecular dynamics calculations, combined with a simulated annealing approach, were undertaken to study reconstructions in boehmite surfaces and nanorods. Our calculations indicate significant reconstruction for the (101) boehmite surface, leading to dramatic changes on the surface geometry and to higher coordination numbers for Al atoms at the surface (from III for the unreconstructed surface to IV for the reconstructed surface). The energy of the reconstructed boehmite surface decreases by around 23%, and the electronic population is modified accordingly. Due to the recent interest in quasi-unidimensional aluminum oxyhydroxide structures, boehmite nanorods grown in the [100], [010], and [001] directions were also investigated. Whereas calculations suggest a relative stability for [001] and [100] and nanorods, with surface energies of 0.90 and 0.54 J/m2, respectively, and a majority of Al atoms coordinatively saturated at the surface, [010] nanorods undergo a significant reconstruction in vacuum with partial loss of the interlayer stacked structure. In particular, reconstructed [010] nanorods exhibit a significant amount of tetra- and tricoordinated Al atoms at the surface of the rod and a surface energy of 0.92 J/m2. At the interface with water, the Al coordination numbers of the [010] rod increase to IV and V, and accordingly, the surface energy decreases to 0.59 J/m2. Therefore, our calculations allow us to identify the [100] and [010] rods as the most stable structures. Most notably, [100] and [010] rods have indeed been observed and characterized experimentally. I. Introduction Alumina compounds are usually classified in trihydroxides, hydroxides, and oxides.1 Among them, oxyhydroxides as boehmite (AlOOH) are frequent constituents of soils and sediments due to their thermodynamic stability under hydrous conditions.2 Boehmite is also an important industrial mineral used as catalyst or catalyst support, and it is the precursor of the widely used catalyst γ-alumina.1,2 Recently, boehmite and γ-alumina pseudomonodimensional structures have also attracted great interest, and boehmite particles of controlled shape3 and nanorods have been synthesized to get samples of high surface area.4,5 In the past few years, experimental and theoretical works allowed us to assess the morphology of aluminum oxyhydroxide compounds.6-12 In particular, the crystal lattice of boehmite is organized in parallel (010) layers (basal plane) linked to each other by hydrogen bonds. Boehmite crystals expose usually (100), (010), (001), and (101) faces, in different ratios.3,12 The stability of the surface increases with the coordination numbers of Al and hydroxyl groups: the most stable is the basal (010) surface, which exhibits saturated 6-fold coordinated (AlVI) atoms and bridging OH groups and is characterized by low surface energy and low chemical reactivity. Accordingly, the surface energy has a low value of 0.45 J/m.3,12 The lateral (100) surface exhibits a steplike structure with alternating rows of 4and 6-fold coordinated Al atoms (AlIV and AlVI), as well as * Corresponding author. Address: Via Elce di Sotto 8, 06123 Perugia, Italy. Phone: +39 075 585 5526. Fax: +39 075 585 5606. E-mail: [email protected]. † University of Perugia. ‡ CNRS-ENSCP (UMR 7045) Ecole Nationale Supe´rieure de Chimie de Paris.

mono- and dicoordinated OH groups, with a surface energy estimated as 1.86 J/m.3,12 The (001) surface exhibits 5-fold coordinated Al atoms (AlV) and mono- and dicoordinated OH groups, with an estimated surface energy of 1.16 J/m.3,12 In contrast to these three cases, the lateral (101) surface has a high energy in vacuum (4.67 J/m2)12 as it presents highly unsaturated 3-fold coordinated (AlIII) atoms, when the surface is cleaved, as well as saturated AlV atoms, and mono- and dicoordinated OH groups. In controlled growth conditions, boehmite nanocrystals can be obtained with (101) surfaces amounting to 30-50% of the total surface exposed.3 Due to low coordination for surface Al atoms and to the aforementioned high energy, the (101) surface may reconstruct after cleavage, leading to saturation of surface Al atoms and changes in reactivity.12 However, many structural details of boehmite surfaces and related reconstruction processes remain, to a large extent, still unclear.7,13-19 In particular, boehmite is not stable under vacuum, and in situ dehydration is observed.3 For this reason, bare boehmite surfaces remain hypothetical and deserve further study of their stability. In this context, a theoretical approach represents a powerful investigation tool, allowing the study of surface reorganizations at an atomistic level of detail, the analysis of related energetic aspects, and the correlation with electronic and reactive properties. Indeed, the surface reactivity of Al oxides and hydroxides may be put in relation with the Al surface coordination number.12 In particular, it has been suggested that a combination of ab initio molecular dynamics (MD) and simulated annealing (SA) techniques can be successfully applied to resolve the structure of complex materials and elucidate surface reconstruction processes.21 In this work, we aim to surface relaxations and reconstructions occurring on the (101) surface of boehmite, as well as to clarify

10.1021/jp810059w CCC: $40.75  2009 American Chemical Society Published on Web 03/10/2009

γ-AlO(OH) Boehmite Surface and Boehmite Nanorods electronic features of the reconstructed boehmite surface. Due to the recent interest attracted by quasi-unidimensional arrays of this material, we also apply the same method to the modeling of boehmite nanorods. Indeed, the atomic morphology of small size crystallites remains a difficult task to deal with microscopy and X-ray diffraction (XRD) techniques.3 To overcome this difficulty, a new method to fit the experimental XRD patterns has recently been proposed.3 However, as indicated by Chiche et al.3 in their work, the authors did not take into account relaxation and reconstruction effects. Thus, numerical simulations have the potential to investigate in detail eventual reconstruction effects, allowing the definition of new models to be used in XRD fitting. In particular, we investigated structural aspects and reconstruction processes of different boehmite nanorods in vacuum and at the interaface with water, thus obtaining a realistic picture of the system under study at experimental conditions. II. Computational Details Calculations were performed at the density functional theory (DFT) level, using a plane wave basis set. The gradient-corrected exchange/correlation functional of Perdew and Wang22 was adopted, and electronic states were described according to the projector augmented wave method,23 with an energy cutoff of 400 eV in all simulations and 500 eV for density of states (DOS) calculations. A converged regular 2D and 1D k-point mesh was adopted for calculations on surfaces and nanorods in vacuum, respectively, with an increased precision on the k-point mesh grid for DOS calculations. Geometry optimizations were carried out by applying a conjugated gradient algorithm until convergence of the energy to a threshold of 1 meV/cell was reached. Born-Oppenheimer MD simulations were performed in the microcanonical (NVE) ensemble and velocity rescaling, with a time step of 2.5 fs. The simulated annealing (SA) protocol was implemented by first heating the system to the target temperature and then equilibrating for around 1.5 ps. Subsequently, the system was gradually cooled by velocity rescaling, in a time-scale of around 1.5 ps, until negligible kinetic energies were obtained and a final geometry optimization was performed. Longer equilibration and cooling times were found to have no effect on the results. The convergence of the procedure was assessed by carrying out independent SA simulations on the same system, with different initial random velocities. For calculations on nanorods at the interface with water, constant energy (NVE) MD simulations were performed with an average kinetic energy for the nuclei corresponding to a temperature of 300 K. The time step was set at 1 fs with total simulation times of up to 5 ps, to have a reliable picture of equilibrium configurations for the solvated system. To ensure accurate integration of the dynamical trajectories, the mass of the hydrogen atom was set to 3 a.u. Such a procedure has been used successfully in past works on the boehmite/water12 interface. In all calculations, periodic boundary conditions in three dimensions were applied. For calculations on solvated nanorods, the simulation box was filled with water according to the experimental density of water at room temperature (33.3 molecule/nm3), corresponding to a total of 88 water molecules. Moreover, calculations in water were performed at the Γ point. Surface energies were computed from slab total energies as: Γ° ) [Eslab - nEbulk]/2A where Eslab and Ebulk are the total electronic energies of the slab considered and of the optimized Al2O3 or AlOOH bulk units, respectively; n is the number of Al2O3/AlOOH units in the slab; and A is the area of the surface

J. Phys. Chem. C, Vol. 113, No. 13, 2009 5229 of the slab. The factor 2 accounts for the two slabs created by cutting the bulk structure. In the case of nanorods, we considered the total outer surface A of the rod and the surface energy is given by the formula Γ° ) [Erod - nEbulk]/A, where Erod is the total energy of the optimized rod; n is the number of AlOOH units in the rod; and Ebulk the energy of one AlOOH unit of bulk boehmite. All calculations were performed with the VASP program package.24,25 III. Results and Discussion III.1. Models and Geometry Optimizations for Bulk and Surfaces of r-Al2O3, Boehmite and Boehmite Nanorods. R-Alumina is a stable and well-known material often taken as a reference in theoretical and experimental studies of alumina reactivity. Therefore, we first performed calibration calculations on the (0001) surface of R-alumina to assess the validity of our computational approach. The bulk structure of R-Al2O3, with 30 atoms in the unit cell, was first optimized in the hexagonal symmetry. From this, a four-layered slab (with each slab constituted of alternating aluminum and oxygen planes) was obtained by cleavage of the bulk along two parallel [0001] planes. The two cell vectors parallel to the cleavage planes are (4.765, 0.0) and (-2.383, 4.126) Å, respectively. Each of the three oxygen atoms of the lower surface was saturated with a hydrogen atom, in order to preserve charge neutrality. The cell length in the perpendicular direction was set to 23 Å, resulting in a distance between periodic images in the c direction of around 15 Å, thus obtaining negligible interactions between periodic images of the slab. In all simulations, atoms in the two lower layers were kept at fixed positions, and all other atoms were allowed to move. Because it represents a case study of polar surface relaxation, and for its numerous possible applications, the (0001) Al2O3 surface has been studied experimentally by X-ray diffraction29,30 and LEED.31,32 The experiment evidences an Al-terminated surface plane, with a significant inplane relaxation with respect to the bulk. First principles calculations have confirmed this trend as shown in refs33-38. The optimized geometry of the four-layered R-Al2O3 slab is shown in Figure 1a-b. Upon optimization, the plane of surface tricoordinated Al atoms undergoes an inward relaxation, leading to an overall decrease of the interplane distance of 87% with respect to the bulk, in agreement with previous calculations (see Table 1). A similar procedure was applied to boehmite. The orthorhombic cell of boehmite consists of eight AlO(OH) units. The bulk structure was first optimized, as described in the methods section, providing geometry in agreement with both experimental results39,40 and previous calculations.13 By cleavage of the optimized bulk structure along two parallel [101] planes, a four-layered slab with orthorhombic symmetry, exposing two parallel (101) surfaces, was obtained. Each sheet of the slab is polar, exposing either Al or OH terminated surfaces. However, the resulting surface charge is zero, due to charge compensation. Figure 1b shows the starting configuration at the surface, exhibiting alternating rows of AlIII atoms and AlVI-OH groups, respectively. For the resulting system, the two cell lengths parallel to the cleavage planes are 4.69 and 11.64 Å, respectively, whereas the cell length in the perpendicular direction was set to 23 Å. Similarly to the case of R-Al2O3, atoms of the two lower layers of the slab were kept fixed at the bulk positions, and all other atoms were allowed to move throughout all simulations. The system was allowed to relax to the closest energy minimum through geometry optimization (with the constraint of the two lowest layers kept fixed), leading to the

5230 J. Phys. Chem. C, Vol. 113, No. 13, 2009

Mercuri et al.

Figure 1. (a) Optimized geometry of the four-layer slab (0001) surface of R-Al2O3, (b) surface layers of the boehmite (101) surface, before geometry optimization, showing the layers alternance with Al coordination of VI (gray) and III (light blue), (c) four-layer-slab (101) surface of boehmite γ-AlO(OH) obtained after geometry optimization; (d) surface layers of the boehmite (101) surface, after geometry optimization. Red, O atoms; gray, AlVI atoms; blue, AlIII atoms; yellow, H atoms.

TABLE 1: Surface In-Plane Relaxations of the Al1-O2 (d12), O2-Al3 (d23), Al3-Al4 (d34), and Al4-O5 (d45) Planes, Computed with Respect to the Unrelaxed System, and Energy of the r-Al2O3 (0001) Surface Calculated Using Different Methods d12 GGA (geometry optimization)

-70%

d23

d34

10% -34%

d45 19%

Γ (J/m2)

SCHEME 1

ref 18

-85% 0% -35% 19% 16 -82% +7% -49% +25% 19 -84% +17% -58% 1.98 21 -87% +7% -48% +22% 1.66 this work -58% +4% -42% +24% 3.2 30 -81% -23% -33% +16% 29

MD (10 300 K) MD (500 K) (% bulk 500 K) Simulated annealing -83% (% bulk 0 K)

+6% -46% +22% 1.66 this work

structure already identified in ref 12 and depicted in Figure 1c-d. The Al atoms at the surface are still 3-fold coordinated, as before optimization, and the amount of inward relaxation is very limited (4%). The OH groups bridging two neighbor sheets relax also only by 7% in-depth. The only remarkable change in the bonding situation of surface atoms upon relaxation consists of the exchange of a hydrogen atom between two neighboring OH groups. In the case of either boehmite or R-alumina, we also performed geometry optimizations on the model systems described previously with only one of the layers kept fixed, thus allowing the three uppermost layers to be relaxed. However, for atoms at the surface we found essentially the same geometrical features as in the case of two relaxed layers. Therefore, we performed further simulations only on models with the two inner layers fixed, and only this case will be discussed hereafter. The bulk boehmite structure obtained as described above was also employed to build the models of boehmite nanorods. Boehmite nanofibers/rods are experimentally obtained by controlled crystal growth in one direction.4,41 Although the diameter of the fibers is usually between 3 and 5 nm,4 some studies report fiber diameters corresponding to 2-3 unit cells, i.e., 2-3 nm, exhibiting clear boehmite XRD patterns with increased reflections indicating the direction growth.5,42-45 To our knowledge, two direction growths were identified experimentally: HRTEM

data suggest that each fiber is composed of orthorhombic unit cells stacking along the fiber axis and grown along the [010] direction of boehmite.40 Chiche et al. suggested also evidence for the formation of [100] fibers.3 Therefore, for the definition of models of boehmite nanorods we started from the boehmite lattice and, as shown in Scheme 1, in order to explore the possible stable structures of boehmite nanorods, we carried out simulations on models of AlO(OH) nanorods resulting from cuts of bulk boehmite along [001], [100], and [010] directions. Calculations on nanorods were performed on periodic models along the nanorod axis, thus assuming models of infinite length along the growth direction (Scheme 1 and Figure 2). The cell lengths in directions perpendicular to the nanorod axes were set to 25 Å, to ensure negligible interactions among periodic images of the system. Rods with different widths were taken into account, from one to three unit cell size, corresponding to widths of around 5 Å and 10-12 Å, respectively. Although the chosen sizes, for computational cost reasons, are smaller than the experimentally observed ones, some trends may be driven from the results, as shown hereunder. The structures of [100], [001], and [010] rods in the starting configurations (as-cut from the bulk) are shown in Figure 2a-c. [100] and [001] rods are built from the (010) basal plane of boehmite and do not contain hydrogen bonds. One face of such rods has the (010) (basal plane) orientation (see

γ-AlO(OH) Boehmite Surface and Boehmite Nanorods

J. Phys. Chem. C, Vol. 113, No. 13, 2009 5231

Figure 2. Front (perpendicular to the rod’s growth direction) and side (perpendicular to the rod section) views of the boehmite nanorods (a) along the [001] direction (note the presence of monocoordinated OH groups and AlIV atoms); (b) along the [100] direction (here, all OH groups are bridging two Al atoms and the Al coordination is V or VI); and (c) along the [010] direction, with 40% of the Al atoms at the border of the rod under coordinated (IV (green) or III (light blue) fold coordinated) and monocoordinated OH groups located at the rod surface. Each rod is of infinite length in the growth direction.

Figure 2a and b). In particular, [001] rods with a width of 6 Å exhibit a majority of undercoordinated Al atoms at the surface (80% AlIV) with a surface energy of 0.90 J/m2. When the width of the rod increases to 10 Å, the ratio of undercoordinated Al ions at the surface decreases to 20%, corresponding to rows of AlIV atoms at the edge of the rod (see Figure 2a and Table 2). The surface energy (0.90 J/m2) is unchanged with respect to rods with smaller width. Inversely, [100] rods, even of very short widths (4-6 Å), exhibit only saturated Al ions at the surface and, consequently, low surface energy (0.54 J/m2), as less Al-O bonds are cut than for building the [100] nanorod. Structures grown

along the [010] direction differ strongly from the [100] and [001] ones: basic building blocks are stacked perpendicular to the growth direction, and the structure is maintained through hydrogen bonds. The lateral faces are oriented along the (100) and (001) directions, with alternate rows of 4-fold and 5-fold coordinated Al atoms (Figure 2c). Moreover, AlIII ions are also present at the edges of the rod. The ratio of the undercoordinated Al ions decreases when the diameter of the rod increases, from 75% (width 4.3 Å) to 60% (width 7 Å) and 38% (width 12 Å) with an amount of undercoordinated Al atoms significantly higher than on the [100] and [001] rods, within a comparable width range. Accordingly, the


Mercuri et al.

TABLE 2: Structural Parameters for Boehmite Nanorods before and after Simulated Annealing growth direction

unit cell width

AlOOH units/cell

rod diameter (Å)

[001]

2 cells along [100]

15

6

[100] [010]

2 2 1 2 1

cells along [100] cells along [010] cell along [001] cells along [001] ×1

36 12 20 9

10 4.4 6.5 4.3

2×2

20

7

3×3

36

12 14 14

surface energy is 2.60 J/m2, a value significantly higher than that of the [100] and [001] rods surfaces. III.2. Simulated Annealing and Surface Reconstruction of r-Al2O3 (0001) and Boehmite (101). As stated in the Introduction, the simulated annealing method allows one to search for the global (free) energy minimum of a crystal structure. When applied to a crystal slab with fixed internal layers, it can eventually lead to a relaxed structure where atomic rearrangements at the surface take place. In this case, the resulting system is a likely global free energy minimum for the surface cut considered. Reconstruction processes for the R-alumina (0001) surface at finite temperatures have been recently investigated by means of MD simulations based on empirical potentials.46-48 The relaxation phenomena were found to be practically independent from the equilibration temperature chosen in calculations. Therefore, to benchmark our calculations on boehmite, the behavior under annealing/cooling cycles of the (0001) surface of R-Al2O3 was analyzed. A first set of runs was performed by annealing the system up to a target temperature of 500 K, followed by cooling and geometry optimization. The surface structure after the SA cycle was found to be qualitatively not altered with respect to the starting state of Figure 1a. Accordingly, the surface energy is practically unchanged. However, the inward relaxation of the Al atom plane for the annealed surface amounts to 83% of the bulk interplane separation (instead of 87% for the optimized structure) and is therefore in slightly better agreement with the experiments. The known discrepancy between first principles calculations and experiments concerning the extent of the inward relaxation of Al2O3 (0001) (80% for GGA to be compared with 60% observed experimentally) is generally ascribed to the use of gradient-corrected exchange-correlation functionals,36 and the present results confirm this conclusion. We also checked the effect of a higher annealing target temperature, by setting it to 1000 K, finding again, after cooling and optimization, essentially the same structure. Hence, in agreement with previous studies,1 the (0001) surface of R-Al2O3 can be expected to be thermally stable after annealing in vacuum. Next, the SA technique was applied to study the effect of thermal relaxations on the structure of the boehmite (101)

reconstruction during SA

Γ (J/m2)

before SA 0/0.8/0.2 after SA 0/0.87/0.13

yes

0.90

0/0.20/0.80 (Figure 6) 0/0/100 0/0/100 before SA 0.5/0.25/0.25 after SA 0.38/0.62/0.00 before SA 0.3/0.3/0.4 after SA 0.12/0.88/0 before SA 0.125/0.25/0.625 after SA 0.20/0.80/0.00 after exposure to water 0.0/0.50/0.50

no no no yes

AlIII/AlIV/AlV-VI ratio

0.68 0.90 0.56 0.54 2.80 0.89 yes

2.75

yes

0.83 2.6 0.92 0.59

surface. MD simulations of annealing/cooling cycles with a target temperature of 500 K (a temperature lower than the typical temperature of boehmite transformation into R-alumina, 773 K) and subsequent geometry optimizations led to strong surface reorganizations, as shown in Figure 3. In particular, the two AlIII atoms in the first surface layer (see Figure 3a) strongly relax inward (by 100%, whereas the inward relaxation was only 4% after geometry optimization) and pull apart from each other, each Al atom translating around 1.63 Å along the (010) direction (perpendicular to the sheet) to bridge two boehmite sheets. The displacement of Al atoms leads to the formation of new Al-O bonds with oxygen atoms from the neighboring sheet and to the increase in the coordination number of surface Al atoms, passing from tricoordinated to tetracoordinated (AlIV) (Figure 3b). Moreover, reorganization of oxygen and hydrogen atoms leads to the formation of new OH groups, which completely saturate the surface, with the exceptions of two dicoordinated

Figure 3. (a) Geometry of the four-layer slab (101) surface of boehmite γ-AlO(OH) after simulated annealing at 500 K, cooling, and optimization. (b) The surface layers, showing the alternance of AlIV (green) and AlVI ions (gray); AlIII atoms on top of one layer have migrated between the two layers to increase their coordination number to IV.



Figure 4. DOS projected on oxygen (solid line) and aluminum (dashed line) atoms of the first layer of the (0001) surface of R-Al2O3: (a) optimized surface; (b) annealed surface.

Figure 5. DOS projected on oxygen (solid line) and aluminum (dashed line) atoms of the first layer of the (101) surface of boehmite: (a) optimized surface; (b) annealed surface.

oxygens, which are involved in bonds with the tetravalent aluminum atoms. In other words, surface reconstruction leads to a new configuration where aluminum atoms and OH groups bridge two different boehmite sheets. This effect was already indicated in ref 49 to explain the boehmite to γ-alumina phase transition. The bridging Al atoms are the most accessible metallic centers and are thus expected to play a major role in determining the reactive properties of the (101) boehmite surface toward nucleophilic agents. As a consequence of the structural reconstruction, the annealed structure exhibits also a dramatic rearrangement of hydrogen bonds at the surface (see Figure 3). Structural modifications affect consistently also the surface energy: the unrelaxed surface has an energy as high as 4.67 J/m2; after geometry optimization, the surface energy lowers to 3.88 J/m2 (17% reduction), with a significant additional energy gain upon surface reconstruction, leading to a surface energy of 2.97 J/m2 (36% lowering with respect to the unrelaxed surface). It is worth noting that simulations performed with different initial conditions led to similar final structures, with comparable surface energies, and differing mainly by the organization of the hydrogen bond network. III.3. Electronic Properties and Density of States for the r-Al2O3 (0001) and Boehmite (101) Surfaces. Surface reconstruction processes are expected to affect the electronic properties of the systems under study and, consequently, their chemical activity. To assess the effect of surface rearrangements on the

electronic properties, the DOS projected onto surface atoms was analyzed after geometry optimizations and after simulated annealing. As expected, the projected DOS for both aluminum and oxygen atoms for the (0001) surface of R-Al2O3 (Figure 4) is practically unaffected by the SA procedure. This confirms that there are no strong surface rearrangements. In contrast, the projection of the DOS on aluminum and oxygen atoms at the first layer of the (101) surface of boehmite is strongly affected by the surface reconstruction process discussed above, as evidenced in Figure 5. In particular, the localized DOS peaks around the Fermi level exhibited by atoms at the surface of the optimized slab (Figure 5a) disappear after the annealing/cooling cycle, thus indicating a strong modification of the electronic properties of the reconstructed surface. In particular, the reconstruction process induces a depletion of acceptor states for surface (three-coordinated) Al atoms observed for the unannealed structure, due to the change to higher coordination numbers. Such changes are expected to play a major role in the chemical properties of the (101) surface of boehmite, as suggested by Digne et al.,13 where the coordination number of surface Al atoms was related to the DOS. Moreover, the surface reconstruction process induces a larger dispersion of the conduction band, suggesting also an enhanced degree of covalence for the aluminum-oxygen bond, as expected for the AlIV-OIII configuration discussed above.


Mercuri et al.

Figure 6. Front (perpendicular to the rod’s growth direction) and side (perpendicular to the rod section) views of the final structure obtained after the simulated annealing (500 K) for the boehmite nanorods of (a) diameter 6 Å, grown along the [001] direction; (b) diameter 12 Å, grown along the [001] direction; (c) diameter 6.5 Å, grown along the [100] direction.

III.4. Simulated Annealing and Reconstruction of Boehmite Nanorods. The optimized structures of boehmite nanorods depicted in Figure 2 were subjected to the SA procedure described above (target temperature 500 K), thus obtaining likely minimum energy configurations. Table 2 reports structural information on the studied nanorods before and after simulated annealing. Our results indicate that the occurrence of reconstruction processes for boehmite nanorods depends on the growth direction: - Rods aligned along the [001] direction of very small width (6 Å), which exhibit a high amount of undercoordinated Al ions, strongly reconstruct upon SA, and the structure adopts a nanotube-like shape (Figure 6a). It is worth noting that the amount of undercoordinated Al is not significantly altered upon reconstruction. However, the surface energy lowers from 0.90 to 0.68 J/m2 due to a rearrangement of the bonds to achieve a tetrahedral symmetry of the AlIV atoms. In contrast, the [001] nanorod of larger width (10 Å, Figure 6b), which exhibits only 20% of undercoordinated Al ions, does not reconstruct upon SA and preserve its initial rodlike shape. In this case, Al atoms are 6- and 5-fold coordinated, and hydroxyl groups are di- and monocoordinated, with a surface energy of 0.90 J/m2. - Rods grown in the [100] direction exhibit faces with saturated Al ions and are remarkably stable as they exhibit no reconstruction, even when a rod with a single cell width is considered (Figure 6c). The surface energy (0.54 J/m2) is somewhat lower than that of [001] rods. This can be ascribed to the fact that all Al atoms are coordinatively saturated, with edge Al atoms bridged by hydroxyl groups, whereas monocoordinated OH groups and AlIV rows are still present at the [001] rod surface. - Rods grown in the [010] direction of widths from 6 to 12 Å undergo a significant reconstruction process upon SA (Figure 7). OH groups initially monocoordinated at the edges of the stacked layers now bridge the boehmite building blocks leading to a partial loss of the layered structure. The ratio of undercoordinated Al atoms at the surface increases to 100% after SA:

for the three rod diameters studied, only 4- and 3-fold coordinated Al atoms are present at the surfaces of the rods upon reconstruction. The snapshot in Figure 7 illustrates rows of 4-fold coordinated Al ions. Rows of alternating AlIV and AlIII atoms are also identified. The surface energy decreases dramatically upon SA, from 2.60 to 0.92 J/m2. After reconstruction, the [010] has a surface energy as low as the [001] nanorod. Therefore, we observe that [001] and [100] nanorods around 1 nm width do not reconstruct. This result suggests that rods of larger diameter do not reconstruct either. This behavior can be explained by the fact that [001] and [100] rods are cut from the very stable (010) basal plane of boehmite and, consequently, exhibit low surface energies of 0.54 and 0.90 J/m2 for the [100] and [001] nanorods, respectively. In particular, the [100] rods exhibit the lowest surface energy, due to higher coordination numbers (5 or 6) for surface Al atoms. Our results suggest a [100] fiber to be remarkably stable and to exhibit no surface reconstruction. The [010] nanorod, in contrast to the rods grown in the [100] and [001] directions, contains a significant amount of surface undercoordinated AlIII and AlIV atoms. In consequence, a significant reconstruction is observed for the [010] nanorods. The reconstruction process is very similar to that observed for the boehmite (101) surface, with the formation of hydroxyls bridging two adjacent building blocks. However, even after reconstruction, the surface energy does not reach the low value observed for [100] or [010] rods. Indeed, the Al atoms at the surface are all undercoordinated, mostly as AlIV. Again, the presence of a significant amount of undercoordinated Al ions suggests a corresponding surface reactivity that cannot take place on bulk boehmite surfaces. As the boehmite nanorods are synthesized under hydrothermal conditions, it is interesting to study the nanorod-water interface and particularly to investigate whether the coordination number of the surface Al ions changes in the presence of water molecules. We focused on the [010] grown nanorods, which are observed experimentally, taking into account models obtained from either the unreconstructed (ascut from the bulk) and the reconstructed nanorods. As explained



Figure 7. (a) Front (perpendicular to the rod’s growth direction) and (b) side (perpendicular to the rod section) views of the final structure obtained after the simulated annealing (500 K) for the boehmite nanorods of diameter 12 Å, grown along the [010] direction. Note the partial loss of the stacked structure. In the rod section (where atoms are shown in sticks), the Al’s of different coordination numbers are evidenced: tricoordinated (light blue), tetracoordinated (green), and pentacoordinated (violet) surface Al ions. (c) Snapshot on a portion of the rod with AlIV ions. (d) Snapshot on a portion with AlIII ions. Compared to the (101) surface, many more AlIV atoms are present.

in the Computational Details section, the models were inserted in a box of equilibrated water molecules, on which a cavity was created to host the boehmite nanorod (Figure 8a). After an equilibration time of 500 fs, the resulting structures were analyzed. At equilibrium, the surface energy of the reconstructed rod in water is 0.59 J/m2, whereas that of the rod at the initial configuration, after MD in contact with water, is slightly higher, 0.63 J/m2. This is likely due to the fact that heating at 300 K does not allow reaching the global minimum of the energy surface. In the subsequent 5 ps of simulation, both nanorods are stable and no dissolution of Al atoms is observed. Although ab initio MD allows following the evolution of the system only on relatively short timescales, the stability of boehmite rods in water can be expected, as boehmite is known to be the stable alumina phase in the presence of water, like in natural hydrous conditions.1 On the contrary, boehmite is known to be unstable in vacuum and to dehydrate.3 A snapshot of the solvated nanorod after equilibration (section view) is shown in Figure 8b. The structure is similar in shape with that of the nanorod reconstructed in vacuum. The Al surface coordination numbers for the nanorod in water at equilibrium

increase with respect to the nanorod reconstructed in vacuum. Indeed, water is adsorbed on 3-fold and part of the 4-fold coordinated Al atoms at the surface, becoming 5- and 4-fold coordinated, respectively, as shown in Figure 8b. Moreover, rows of 4-fold coordinated Al atoms are still present on the hydrated surface. Finally, the structure of the solvated nanorod was reoptimized after elimination of the water molecules, conserving the Al saturated coordination numbers shown in Figure 8b. The geometry of the rod does not vary significantly. The surface energy decreases significantly from 0.92 for the structure in vacuum to 0.59 J/m2. It finally appears that the saturation of the coordination of Al ions allows the surface energy of the [010]-rod to decrease to a value (0.59 J/m2) as low as that of the [100]-rod (0.54 J/m2), a value very close to that of the bulk boehmite basal plane (010) (0.45 J/m2). Such rods have been observed and characterized experimentally. As for the [001]-rod, the surface energy could also decrease at the interface with water, but the decrease in energy can be expected to be small, due to the low amount (20%) of undercoordinated Al atoms at the rod edge after reconstruction in vacuum.


Mercuri et al. 30-33% Al undercoordinated could be the criteria to take into account to predict whether surface reconstruction occurs on nanorods. As stated in ref 3, “one possibility to correct surface relaxation effects is to compute, using molecular modeling techniques, the relaxed nanoparticle geometry and the corresponding diffraction pattern”. Indeed, from the obtained nanorods atomic topologies, the simulation of XRD patterns as recently developed by Chiche et al.3 could be of interest to compare the obtained data to the experimental ones on nanorods, to get a precise idea of the local arrangement of atoms at the rod surfaces and bring insight into the characterization of nano-objects, which remain a technical challenge using the experimental tools. IV. Conclusions

Figure 8. [010] nanorod after MD simulation at the water interface. (a) Cell showing the water molecules in the cell; (b) rod section showing the Al coordination numbers obtained at the thermal equilibrium; water molecules are not shown, for clarity.

It is interesting to investigate whether reconstruction occurs on the [010]-rod surface for rods of larger diameter than the one shown here. Therefore, one may count the Al-undercoordinated atoms ratio at the rod surface. The equations used for such calculations are reported in the Supporting Information. With increasing diameter, the ratio of Al undercoordinated from the edges and corners compared to Al at the (100) and (001) planes decreases. We found that the Al-undercoordinated/total Al ratio at the rod surface tends to the value of 0.33 for the [010]-rod by increasing the rod diameter, a value close to that of 0.38 (before SA) for the rod of smaller diameter (12 Å). This result suggests that reconstruction still occurs at the rod surface. A test performed on a 4 × 4 cell (diameter 15 Å) gives an Al undercoordinated ratio of 0.36, and reconstruction is also found to occur (result not shown). The same ratio calculated for the [001]-rod gives 0.25 for the Al undercoordinated/Al total ratio at the surface. It is interesting to notice that for rods of smaller diameters we have shown that reconstruction does not occur. Therefore, we may conclude that a value of 0.25 for the Al undercoordinated ratio is too low to induce surface reconstruction. Finally, it seems possible that a threshold value of

First principles MD and SA calculations were applied to investigations of surface reconstruction and relaxed structures of the (101) boehmite surface and boehmite nanorods. For the (101) surface of boehmite, a marked reconstruction is observed, which induces a change in the coordination number for Al atoms at the surface, with Al and O atoms bridging two surface sheets. The reconstruction process leads to a decrease of 23% of the surface energy, and accordingly, the DOS at the surface is substantially altered with respect to the as-cleaved and optimized structures. The stability of the (0001) R-Al2O3 surface is confirmed, and the application of SA does not alter its geometric, energetic, and electronic features. Our results also suggest that [100] and [001] boehmite nanorods are not subjected to reconstruction even when rods of very small widths are taken into account. [100]-rods have the lowest surface energy. The surface of the rod exhibits planes of saturated AlV ions which present a high homogeneity and likely a low acid reactivity. In contrast, [010]-rods undergo a structural reconstruction giving rise to bridging oxygens and Al ions between layers and a variety of low-coordinated Al ions which account for the acid character and a distribution of sites of different acid-base character, as observed on γ-alumina surfaces.13 In the presence of water, the Al coordination numbers at the surface of the [010]-rod increase to coordination IV and V. The nature and repartition of the low-coordinated Al ions at the surface of the [010]-rods, which are significantly different from those of bulk boehmite surfaces, suggest that γ-alumina rods obtained by topotactic transformation will conserve a variety of undercoordinated Al surface ions. Acknowledgment. This work has been performed under the HPC-EUROPA Project (RII3-CT-2003-506079), with the support of the European Community - Research Infrastructure Action under the FP6 “Structuring the European Research Area” Programme. The computing centre of Paris 6 (CCRE) is also acknowledged. F.M. thanks the Laboratoire de Physico-Chimie des Surfaces at the Ećole Nationale Supe´rieure de Chimie de Paris, France, for support. Boubakar Diawara is acknowledged for the use of Modelview software. Supporting Information Available: Figure of the final structure obtained after the simulated annealing (500 K) for the boehmite nanorods of diameter 12 Å, grown along the [010] direction, and formulas for the determination of the amount of undercoordinated Al atoms at the [010], [100], and [001] rod surface. This material is available free of charge via the Internet at http://pubs.acs.org.

γ-AlO(OH) Boehmite Surface and Boehmite Nanorods References and Notes (1) Euzen, P.; Raybaud, P.; Krokidis, X.; Toulhoat, H.; le Loarer, J.L.; Jolivet, J.-P.; Froidefond, C. Handbook of Porous Solids; Shu¨th, F., Sing, K. S. W., Weitkamp, J., Eds.; Wiley: New York, 2002; Vol. 3, pp 1591-1677. (2) Majzlan, J.; Navrotsky, A.; Casey, W. H. Clays Clay Miner. 2000, 48, 699. (3) Chiche, D.; Digne, M.; Revel, R.; Chaneác, C.; Jolivet, J.-P. J. Phys. Chem. C 2008, 112, 8524. (4) Mathieu, Y.; Lebeau, B.; Valtchev, V. Langmuir 2007, 23, 9435. (5) Zhu, H. Y.; Gao, X. P.; Song, D. Y.; Bai, Y. Q.; Ringer, S. P.; Gao, Z.; Xi, Y. X.; Martens, W.; Riches, J. D.; Frost, R. L. J. Phys. Chem. B 2004, 108, 4245. (6) Maurice, V.; Marcus, P. Structure of thin anodic films formed on single crystals metal surfaces, Interfacial Electrochemistry: Theory, Experiment and Applications; Wieckowski, 1999; pp 541-558. (7) van den Brandt, J.; Sloof, W. G.; Terryn, H.; de Wit, J. H. W. Surf. Interface Anal. 2004, 36, 81. (8) van den Brandt, J.; Snijders, P. C.; Sloof, W. G.; Terryn, H.; de Wit, J. H. W. J. Phys. Chem. B 2004, 108, 6017. (9) Alexander, M. R.; Beamson, G.; Bailey, P.; Noakes, T. C. Q.; Sekldon, P.; Thompson, G. E. Surf. Interface Anal. 2003, 35, 649. (10) Wefers, K.; Misra, C. Oxides and Hydroxides of Aluminium, Alcoa Technical Paper N. 19, Alcoa Technical Center: Alcoa, PA, 1981. (11) Hart, R. K. Trans. Faraday Soc. 1954, 50, 269. (12) Raybaud, P.; Digne, M.; Iftimie, R.; Wellens, W.; Euzen, P.; Toulhoat, H. J. Catal. 2001, 201, 236. (13) Digne, M.; Sautet, P.; Raybaud, P.; Euzen, P.; Toulhoat, H. J. Catal. 2004, 226, 54. (14) Lewis, D. G.; Farmer, V. C. Clay Miner. 1986, 21, 93. (15) Ruan, H. D.; Frost, R. L.; Kloprogge, J. T. Appl. Spectrosc. 2001, 55, 190. (16) Morterra, C.; Emanuel, C.; Cerrato, G.; Magnacca, G. J. Chem. Soc., Faraday Trans. 1992, 88, 339. (17) Ruan, H. D.; Frost, R. L.; Kloprogge, J. T. J. Raman Spectrosc. 2001, 32, 745. (18) Walter, T. H.; Oldfield, E. J. Phys. Chem. 1989, 93, 6744. (19) Kloprogge, J. T.; Duong, L. V.; Wood, B. J.; Frost, R. L. J. Colloid Interface Sci. 2006, 296, 572. (20) Banfield, J. F.; Zhang, H. ReV. Miner. Geochem. 2001, 44, 1. (21) Kresse, G.; Bergermayer, W.; Podloucky, R.; Lundgren, E.; Koller, R.; Schmid, M.; Varga, P. Appl. Phys. A: Mater. Sci. Process. 2003, 76, 701. (22) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (23) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758.

J. Phys. Chem. C, Vol. 113, No. 13, 2009 5237 (24) (a) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558. (b) Kresse, G.; Furthmuller, J. Phys. ReV. B 1996, 54, 11169. (c) Kresse, G.; Hafner, J. J. Phys.: Condens. Matter 1994, 6, 8245. (25) Kresse, G.; Hafner, J. J. Phys. ReV. B 1994, 49, 14251. (26) Bergerhoff, G.; Berndt, M.; Brandenburg, K. J. Res. Natl. Inst. Stand. 1996, 101, 221. (27) Pennington, W. T. J. Appl. Crystallogr. 1999, 32, 1028. (28) http://www.crystalimpact.de/diamond/download.htm. (29) Gueńard, P.; Renaud, P.; Gautier-Soyer, M. Applications of Synchrotron Radiation to Material Science III In MRS Symposia Proceedings, No 437; Terminello, L., Ed.; Materials Research Society: Pittsburgh, 1996; p 15. (30) Gueńard, P.; Renaud, G.; Barbier, A.; Gautier-Soyer, M. Surf. ReV. Lett. 1997, 5, 321. (31) Walters, C. F.; McCarthy, K. F.; Soares, E. A.; Van Hove, M. A. Surf. Sci. 2000, 464, L372. (32) Ahn, J.; Rabalais, J. W. Surf. Sci. 1997, 388, 121. (33) Gomes, J. R. B.; Moreira, I. de P. R.; Reinhardt, P.; Wander, A.; Searle, B. G.; Harrison, N. M.; Illas, F. Chem. Phys. Lett. 2001, 341, 412. (34) Rouberto, C.; Tourdashahyan, Y.; Lundqvist, B. I. Phys. ReV. B 2003, 67, 195421C. (35) Batirev, I. G.; Alavi, A.; Finnis, M. W.; Deutsch, T. Phys. ReV. Lett. 1999, 82, 1510. (36) Hass, K. C.; Schneider, W. F.; Curioni, A.; Andreoni, W. J. Phys. Chem. B 2000, 104, 5527. (37) Goniakowski, J.; Finocchi, F.; Noguera, C. Rep. Prog. Phys. 2008, 71, 016501. (38) Marmier, A.; Parker, S. C. Phys. ReV. B 2004, 69, 115409. (39) Farkas, L.; Gado, P.; Werner, E. Mater. Res. Bull. 1977, 12, 1213. (40) Christoph, G. G.; Corbato, D.; Hofmann, A.; Tettenhorst, T. T. Clays Clay Miner. 1979, 27, 81. (41) Cao, H.; Zhang, L.; Xiangwen, L.; Zhang, S.; Liang, Y.; Zhang, X. Appl. Phys. Lett. 2007, 90, 193105, and references therein. (42) Alphonse, P.; Courty, M. Thermochim. Acta 2005, 425, 75. (43) Webster, T. J.; Hellenmeyer, E. L.; Price, R. L. Biomaterials 2005, 26, 953. (44) Lee, H. C.; Kim, H. J.; Chung, S. H.; Lee, K. H.; Lee, H. C.; Lee, J. S. J. Am. Chem. Soc. 2003, 125, 2882. (45) Zhu, H. Y.; Riches, J. D.; Barry, J. C. Chem. Mater. 2002, 14, 2086. (46) Sun, J.; Stirner, T.; Matthews, A. Surf. Sci. 2007, 601, 1358. (47) Baudin, M.; Hermansson, K. Surf. Sci. 2001, 474, 107. (48) Marmier, A.; Finnis, M. W. J. Phys.: Condens. Matter 2002, 14, 7797. (49) Kuiry, S. C.; Megen, E.; Patil, S. D.; Deshpande, S. A.; Seal, S. J. Phys. Chem. B 2005, 109, 3868.

JP810059W

Theoretical Investigations of the Relaxation and Reconstruction of the

Recommend Documents