Three-Dimensional Tomographic Analyses of CeO2 Nanoparticles

Article pubs.acs.org/crystal

Three-Dimensional Tomographic Analyses of CeO2 Nanoparticles Ileana Florea,*,† Cédric Feral-Martin,‡ Jérome Majimel,‡ Dris Ihiawakrim,† Charles Hirlimann,† and Ovidiu Ersen† †

Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 CNRS-UdS, 23 rue du Loess, BP 43, F-67034 Strasbourg cedex 2, France ‡ Institut de Chimie de la Matière Condensée de Bordeaux, UPR9048, 87 Avenue du Docteur Schweitzer, 33608 Pessac cedex, France S Supporting Information *

ABSTRACT: A detailed morphological and structural analysis of CeO2 nanoparticles has been performed using electron tomography in scanning transmission mode in high angle annular dark field. The nanoparticles have been prepared through a solvothermal synthesis assisted by microwave heating. An adequate choice of the synthesis parameters leads to particles with various well-defined morphologies: cubes, octahedrons, and nanorods. In the case of cubic CeO2 nanoparticles, the three-dimensional analysis allowed us to precisely calculate the type and the proportion of the minor facets exposed at the nanoparticle surface. For the CeO2 nanoparticles with an octahedron shape, it has been demonstrated that the ambiguous interpretation of the objects giving triangular views in classical transmission electron microscopy can be prevented; furthermore, precise assignments of their external shape, surface crystallography, and type of minor facets were realized. In the case of nanorods, it was shown that the external shape and the transversal symmetry are strongly dependent on the nanorod sizes. The presence of a well-defined porosity inside the rods was also evidenced thanks to the ability of the electron tomography to solve the internal structure of a nano-object.

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INTRODUCTION During the last few decades, the synthesis of nanoparticles (NPs) with a controlled shape has received increasing attention due to their potential use in fields such as heterogeneous catalysis or optics. It is now well established that the subsequent properties of the nanocrystals depend on the type of their exposed facets and on the nature of atoms present at their surface. Thus, the key challenge is to precisely determine these parameters, which is an unavoidable step in establishing a correlation between the outstanding properties of the NPs and their structural and morphological characteristics. Such a complete analysis allows an optimal feedback toward the synthesis conditions that can be subsequently adjusted for obtaining the required properties. It is worth noting that, because of the three-dimensional (3D) character of the NPs, the use of techniques based on two-dimensional (2D) observations is not sufficient, as part of the characteristics of the object under study remains hidden. In addition, the interpretation of the corresponding images requires prior knowledge of the structure and external shape of the NPs. A great breakthrough in reaching volume information has been the development of electron tomography (ET), a technique allowing calculation of the volume of a nano-object using a series of 2D images recorded in transmission electron microscopy (TEM).1 With an almost exclusive application in the parallel TEM mode until 10 years ago, several imaging © 2013 American Chemical Society

modes existing in electron microscopy can nowadays be coupled with a tomographic approach, such as the scanning transmission mode (STEM) with acquisition in bright field (BF)2 and annular dark field (ADF),3,4 the energy filtered imaging mode (EFTEM),5,6 and the scanning mode (SEM) coupled with the focused ion beam technique (FIB).7 Among all these acquisition modes, the most appropriate for the study of crystalline materials is the STEM with the acquisition in high angle annular dark field (HAADF).4 Known as the Z-contrast mode, it satisfies in a first approximation the projection requirement for the tomography that stipulates that the intensity in the images of the tilt series must be proportional to the thickness-integrated signal of interest. In addition, the new TEM equipment and software make possible the simultaneous acquisition of several images in the STEM, by collecting the electrons scattered at various angles using multiple detectors. For instance, one of the possibilities is the recording of spatially correlated BF and ADF images that may contain complementary information on the characteristics of the object under study, which will be explained latter. Cerium oxide (CeO2) particles with nanometric size recently became interesting due to their potential applications in fields Received: October 3, 2012 Revised: December 20, 2012 Published: January 10, 2013 1110

dx.doi.org/10.1021/cg301445h | Cryst. Growth Des. 2013, 13, 1110−1121

Crystal Growth & Design

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is performed that allows us to obtain some crucial parameters, such as the relative amount of the exposed facets.

such as heterogeneous catalysis, more particularly, in the oxygen storage process.8 Known also as ceria, this material presents in the bulk the properties of an insulating, nonmagnetic rare-earth oxide and crystallizes in the face-centered cubic (fcc) fluorite structure. Thus, the unit cell contains four cerium and eight oxygen atoms and has in the bulk a mean lattice parameter of 0.54 nm. From a general point of view, its applications are multiple, going from use as catalytic converters9−12 to potential use for the direct production of hydrogen from methanol.13 In this general framework, it is obvious that the catalytic activity of CeO2 material strongly depends on its specific surface area. Several synthesis paths such as precipitation,14 microemulsion,15 thermal decomposition,16 electrochemical synthesis,17 hydrothermal synthesis, and so forth18 have been developed in order to synthesize CeO2 nanoparticles with nanometer size. Very recently, a new preparation method based on green chemistry, that is, the solvothermal synthesis process assisted by microwave heating, was implemented. Adjusting accurately the synthesis parameters (for example, duration and heating temperature) allows the preparation of ceria nanoparticles with different morphologies and consequently adjustable properties in terms of reactivity and selectivity to a given reactant. More precisely, cubic and octahedral nanoparticles as well as nanorods can be obtained with various sizes. However, this recent progress in the synthesis methods must be completed by precise 3D analysis on the shape-control of the as-obtained nano-objects. In the quest for obtaining 3D information on the CeO2 nanoparticles with well-defined shapes, several works were published in the literature. Combining high-resolution TEM (HR-TEM) experimental images, simulations, and tomographic reconstructions, Kaneko et al.19 have characterized one of the typical CeO2 morphologies obtained by hydrothermal synthesis; a tetragonal shape was thus evidenced for NPs with a size of 8 nm, and the presence of some truncations at the edges and corners was directly illustrated. Xu et al.20 have examined by means of electron tomography a CeO2 particle with a size of 40 nm and evidenced its polyhedral shape, analysis which has also allowed the direct comparison of several tomographic modes. Tan et al.21 have analyzed CeO2 NPs prepared by hydrothermal synthesis with morphologies close to an ideal octahedron; in this case, a precise crystallographic analysis of the surface was carried out combining HR-TEM images and 3D tomographic reconstructions. In this context, the aim of the present paper is to solve the crystallographic structure of ceria cubes, octahedrons, and nanorods prepared by solvothermal synthesis assisted by microwave heating and to reveal their 3D surface characteristics by electron tomography combined with HR-TEM imaging. More precisely, using the electron tomography in STEMHAADF mode, a consistent three-dimensional characterization of these systems was achieved, allowing us to determine some crucial parameters such as crystallographic types of the exposed facets, their proportions, as well as the internal structure of the analyzed nano-objects. To the best of our knowledge, this is the first study dealing with ceria nanoparticles obtained by solvothermal synthesis assisted by microwave heating. In order to establish a direct correlation between the 3D characteristics of these nano-objects and their synthesis conditions, all the typical morphologies of CeO2 nanoparticles obtained by this method have been analyzed. More precisely, by combining both high-resolution and tomographic approaches for these systems, a quantitative analysis of their characteristics

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EXPERIMENTAL SECTION

Synthesis of CeO2 Nanoparticles. All reagents were analytical grade and used without further purification. To obtain CeO2 particles, 1.74 g of Ce(NO3)3 ([CeO2] = 496 g/L) was used as the cerium source and first dissolved into 50 mL of distilled water. This solution was added one drop at a time at room temperature under strong agitation in basic medium made of a mixture of 0.248 mol of aqueous NaOH (carbo erba reagent 35%) and 0.08 mol of NH4OH (B.T. baker 30%). This procedure led to the production of cubes. The obtained precipitate was then placed in a cubic poly(tetrafluoroethylene) container of 50 mL (XP-1500 plus) and was tightly sealed. After transfer, the synthesis was performed using a MARS-S microwave digestion system (CEM Corp.). The system was heated at 180 °C for 60 min for octahedrons and 45 min for cubes and then cooled at room temperature. The dispersion was finally centrifuged, washed three times with distilled water, and dried at 100 °C for 12 h. Table 1 summarizes all the information about the synthesis parameters used to obtain the desired morphologies.

Table 1. Synthesis Parameters Used for the Preparation of the Three Types of Morphologies n (NaOH)

n (NH4OH)

n (Ce(NO3)3)

temp (°C)

time (min)

shape

− 0.248 0.248

0.02 0.08 0.08

0.0024 0.0019 0.0019

180 180 120

60 45 25

octahedron cube rod

Analyses by HR-TEM, STEM-HAADF, and STEM-EELS. For electron microscopy experiments, the powders containing the nanoparticles were dispersed on a holey carbon copper grid. The assembly was then treated during 5 s in a mixture of H2/Ar plasma gas in order to reduce the contamination, which is a typical problem for the observation in scanning mode. A drop of a solution containing calibrated gold nanoparticles with a size of about 0.8 nm was deposited on the grid supporting the samples. These gold nanoparticles were subsequently used as fiducial markers in the fine alignment process of the images of the recorded tomographic tilt series. HR-TEM images were recorded using a spherical aberration (Cs) corrected JEOL 2100F (FEG) TEM/STEM electron microscope, operating at 200 kV. The STEM-EELS measurements in line-profile mode and the HAADF images of the chosen areas were recorded using a 0.2 nm electron probe and an energy dispersion of 0.3 eV/channel, with an EELS acquisition time of 3 s/pixel. Electron Tomography Analysis. Electron tomography experiments were performed in the classical TEM mode and STEM. The acquisition of tilt series was done automatically using the tomography plug-in of the Digital Micrograph software, which controls the specimen tilt step by step, the defocusing, and the specimen drift. In the STEM, a projection image of the sample is obtained by scanning the sample with a focused probe in a raster pattern. For each tilt angle, two complementary BF and ADF images were simultaneously recorded. As detailed in one of our previous works,2 the two images do not contain the same information: a BF-STEM image is shapesensitive and is recommended for studying homogeneous objects, to obtain information on their borders and geometries; on the contrary, an ADF image is mass-sensitive, especially if the detector collects only the electrons scattered at high angles where the diffraction Bragg contrast can be considered negligible. The HAADF and BF tilt series in the STEM were generally acquired by using the ADF and BF detectors and tilting the specimen in the angular range of ±70° using an increment of 2.5° in the equal mode, giving thus a total number of images equal to 57 images in each series. The inner radius of the ADF detector was about 40 mrad, a relatively large value that allows us to consider that the intensity in the 1111



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Figure 1. Representative TEM images illustrating the three typical morphologies of CeO2 nanoparticles prepared by the solvothermal method: (A) cubes; (B) octahedrons; and (C) nanorods.

Figure 2. (A) Representative HR-TEM image of a CeO2 nanoparticle providing information on the crystallographic structure. Inset: (a) magnified area in the vicinity of a corner allowing the observation of its geometry; (b) the corresponding Fourier transform. (B) High-resolution HAADF image recorded in the STEM mode on the same nanoparticle, giving also access to its crystallographic structure; a direct observation of the {100} planes delimitating the particle was also possible. Inset: an intensity line profile corresponding to the area delimitated in green on the HAADF image and a magnified area zoom on the particle’s corner revealing its truncated geometry. corresponding images is proportional to the mean atomic number of the specimen in first approximation. The recorded images of the tilt series were spatially aligned using first a rough alignment by cross correlating consecutive images; a fine alignment was performed using gold particles as fiducial markers. Both alignment procedures are implemented in the IMOD software.22 For the volume calculation, we have used iterative methods that are more accurate than the one-step ones, providing high quality reconstruction volumes even from series with a quite limited number of projections. The algebraic reconstruction techniques (ART)23 implemented in the TomoJ plugin24 working in the ImageJ software25 were thus used to compute the reconstructed volumes. Finally, the visualization and the analysis of the final volumes were carried out using the displaying capabilities and the isosurface rendering method in the Slicer software.26 Ultramicrotomy. Ultramicrotome cutting was employed for allowing the TEM observation of the nanorods in cross section. A few milligrams of powder was dispersed and mixed in a soft resin, left for several hours to polymerize and solidify the resin, and then, cooled and sectioned with a diamond knife. Films of 50 nm thickness have been obtained and deposited afterward on a copper grid covered by a thin layer of carbone membrane.

cubes and octahedrons, leading to larger sizes when the duration increases. On the contrary, for the nanorods, a considerable difference in their external shape was observed between the small (20 nm) nanoparticles, especially close to the tips of the nanorods. CeO2 Nanoparticles with a Cubic Morphology. As pointed out in the introduction, up to now, only a few works have been devoted to the 3D analysis of CeO2 nanoparticles with a cubic shape. One can mention the work of Kaneko et al.19 in the context of a more general study that illustrated for the first time the usefulness of electron tomography in the STEM mode. A detailed analysis of the reconstructed volumes combined with high-resolution images and simulations has evidenced a rather tetragonal morphology of the analyzed NPs (8 nm size), as well as the presence of {200} crystallographic planes at the edges of the NPs and of truncated corners exposing the {111} crystallographic planes. However, in comparison to our work, this study deals with NPs prepared by the hydrothermal method. To obtain representative information on CeO2 NPs with a square symmetry in the 2D images, several single nanoparticle analyses were performed using electron tomography in the STEM-HAADF mode. Figure 2A presents a HR-TEM image taken on one of the analyzed NPs that was previously orientated along the [100] zone axis; its analysis suggests the existence of a cubic shape with {200} vertical facets and {110}

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RESULTS AND DISCUSSION Figure 1A−C presents the three typical morphologies of CeO2 nanoparticles that were obtained by the solvothermal method assisted by microwave heating. Note that the duration of the synthesis process does not influence the global shape of the 1112



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Figure 3. (A, B) Typical 2D images extracted from the spatially correlated BF and HAADF-STEM tilt series, for different tilt angles, used to reconstruct the volume of the analyzed CeO2 nanoparticle. (C) Its 3D representation obtained from the reconstruction using a data segmentation procedure and a surface-rendering method. (D) Illustration of the procedure used to estimate the angular position of the square-fold symmetry axis of the nanoparticle: it corresponds to the position for which the area of the perpendicular slice is minimum.

Figure 4. (A) Schematic representation of the CeO2 nanoparticle exhibiting a general shape. The green and red selected areas delimitate two series of orthogonal slices located in the middle of the NP, along the three highest symmetry axes of this geometrical shape. (B) xy (bottom) and xz (top) projections showing the shape in the middle of the NP; they were computed from the reconstruction by taking into account the slices contained in the green and red areas in panel A. The presence of the missing wedge in the xz plane leads to a poorer definition of the object along the z direction. (C) Various geometrical shapes that give a square symmetry in a classical TEM image: (a) cube; (b) cube with all the edges truncated; (c) cube with corners and edges truncated; and (d) cube-octahedron (d).

crystallographic planes at the edges of the cube parallel to the direction of observation (see inset). In STEM-HAADF, due to the direct dependence of the recorded signal on the thicknessintegrated atomic number, the analysis of the relative intensity across the image allows obtaining of the primary information on the external shape of the NPs. If the images are recorded using a high-resolution mode, such morphological information can be coupled with the crystallographic one, resulting thus in

precise information on the surface crystallography. Figure 2B presents a STEM-HAADF image acquired on the same NP as that studied by HR-TEM. The presence of {100} crystallographic planes parallel to the direction of the electron beam was once again revealed. The analysis of an intensity line profile between two edges of the NP (within the green area indicated in the figure) shows an almost constant thickness along the observation direction. As for HR-TEM images, a precise 1113



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Figure 6. Typical (A) BF and (B) HAADF images acquired simultaneously in the STEM mode on a collection of four CeO2 nanocrystals with a polyhedral shape, extracted from the corresponding tilt series at the angles −32°, 18°, 29°, 44° and used to calculate two spatially correlated volume reconstructions.

Figure 7. (A) Orthogonal slices through the reconstructed volume obtained for an assembly of four CeO2 nanoparticles with a polyhedral shape. The volume was calculated by using a tomographic approach from a series of BF images recorded in STEM mode. (B) Individual 3D representations of the four nanoparticles oriented to present the same global appearance; they have been obtained by applying a classical data segmentation process to the subvolumes extracted from the computed reconstruction. (C) Idealized representation of an octahedral crystal: eight facets of {111} type are visible, with a (100) basal plane; the angle between the facets and the basal plane is 55°.

measurement of the (100) interatomic distance was possible, which has provided a mean value of about 0.28 nm, in good agreement with the bulk CeO2. Last, the analysis of the STEMHAADF image revealed the presence of {110} truncations at the edges of the NP and allowed us to precisely measure their depth, which was about 2.5 nm. Although the 2D analyses in high-resolution mode give crucial information on the crystallographic structure of the nanoparticle, they have some limitations that underline the need of electron tomography for the complete study of such 3D nanosystems: (i) the impossibility to physically orient the NPs within the microscope along the other equivalent symmetry axis, making the realization of a completely reliable analysis on a unique object difficult; (ii) the existence of different sizes of NPs that makes the transport of the results obtained from one NP to the others impossible; (iii) the characteristics of all the minor facets and especially their spatial extensions have to be precisely evaluated, in order to provide a precise determination of the external shape and surface crystallography.

Figure 8. (A) TEM image of a CeO2 nanoparticle with polyhedral shape oriented in order to present a square global appearance. (B) Zoom (HR-TEM image) on one of the four corners and the corresponding Fourier transform, allowing assigning the plane perpendicular to the observation axis to {100}. A simple visualization of the crystallographic structure at the corner suggests the presence of truncations of {011} type.

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Figure 9. (A) Slice extracted from the reconstruction of one of the four analyzed CeO2 octahedral nanoparticles (left) and the borders of the NP within this slice obtained by a simple “edge-detection” procedure. (B) The same as panel A, but here, the corresponding slice is perpendicular to the basal plane and crosses four corners, with two located at the apex of the bipyramids and the two others in the basal plane.

projections calculated from the reconstruction volume along the high symmetry axis, that is, the three orthogonal axes with approximate square-fold symmetry. It is obvious that, using this method, one can benefit from all the information contained in the reconstruction, and not only the one relative to its surface as in the case of a surface modeling. To precisely determine the orientation of the high symmetry axes for the studied NP, we used a geometrical method that was applied to its 3D representation deduced by data segmentation. This method consists of rotating step by step in three dimensions the subvolume that defines the NP and then computing the areas that contain the intersection between the object and the horizontal plane (Figure 3D). The spatial orientation for which a local minimum is obtained provides one of the square-fold symmetry axis chosen to be the [001] crystallographic axis. The same procedure applied to the directions orthogonal to the as-determined [001] one provides the set of the [100] crystallographic axes. This procedure allowed us to assign a 3D crystallographic referential to our system (Oz along [001], Ox along [100], and Oy along [010]). Once the NP is orientated, its projections can be computed along any crystallographic axis, by considering the whole NP or only a fragment with chosen width and position. More specifically, considering only series of xy, xz, and yz slices surrounding the center of the nanoparticle (see the schematic representation in Figure 4A), one obtains projections that are not really representative of the full NP but present reduced reconstruction artifacts. Figure 4B shows two xy and xz

Figure 10. Typical TEM images for two nanorods with different diameters (10 and 18 nm).

In this framework, to obtain a full 3D characterization of these NPs, electron tomography experiments were performed in the STEM mode. Figure 3A, B presents some typical 2D images recorded on a CeO2 nanoparticle and extracted from the two spatially correlated BF and HAADF tilt series that were simultaneously recorded. Figure 3C shows two different views of the 3D representation of the NP obtained by modeling the reconstructed volumes that allow the visualization of the whole nanoparticle. As observed on this figure, due to the unavoidable approximations induced by the data segmentation process, the edges of the NPs seem to be rather rounded than faceted. As a consequence, such analysis is not accurate enough to definitely conclude on the exact geometry of the NP, especially at its edges and corners. For this purpose, we have analyzed the

Figure 11. (left) STEM-HAADF image recorded on a CeO2 nanorod with a diameter of 20 nm. (right) Dependences of the HAADF intensity and Ce elemental signal, deduced from a series of EELS spectra recorded in line-scan mode along the white line drawn on the HAADF image. Inset: a typical EELS spectrum recorded at the Ce M-edge, after background removal. 1115



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Figure 12. (top) Three pairs of typical HAADF and BF images, extracted from the corresponding tilt series recorded in the tomographic STEM mode and used to calculate HAADF and BF reconstructions. (bottom, left) Examples of longitudinal (up) and transversal (bottom) slices through the spatially correlated shape- and mass-sensitive volumes. (bottom, right) 3D modeling of the nanorod obtained from tomographic reconstruction using a classical data segmentation procedure.

projections computed by considering 75 slices surrounding the central part of the NPs. It is worth noting that the total number of slices defining the whole nanoparticle is about 200 in all the three orthogonal directions. One can easily observe the presence of the missing wedge in the z direction due to an incomplete sampling of the angular range. The consequence is a poor definition of the volume of the NP at the borders perpendicular to its direction as well as an artificial elongation effect. These undesirable effects are not present in the plane xy, allowing a precise determination of the Lx and Ly lengths of the NP along the [100] and [010] directions, 20 and 21 nm. A second parameter deduced by analyzing the xy projection is the depth of the truncations in the xy plane (Figure 4B). By analyzing the four corners of the NP, we observed that the truncations are similar and made of facets of the {110} type.

Finally, a mean value of 2.5 nm was obtained for the depth of the truncation gxy in the corresponding (001) plane. However, a complete analysis of the NP crystallography and morphology requires the determination of the other equivalent parameters, namely, Lz, gxz, and gyz. Indeed, the NP does not necessarily exhibit a cubic shape (which would imply equivalent values of Lx, Ly, and Lz), as suggested by a direct comparison of Lx and Ly as well as by a more global analysis of their typical dimensions performed by X-ray diffraction.27 As pointed out previously, the presence of the missing wedge in this region makes it difficult to quantitatively analyze the reconstruction along the z direction. Consequently, we implemented a customized analysis procedure based on a data segmentation method using shape constraints. More precisely, we took advantage of a prior knowledge of the type of major facets that define the external surface of the NP; these are the six facets of 1116



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Figure 13. (top) Dependence of the nanorod morphology in cross section on the external diameter. For illustration, several transversal sections extracted from the reconstructed volumes are shown for each type of nanorod. (bottom) Typical cross-sectional TEM images of several nanorods obtained using an ultramicrotome.

{100} type. Then, a preliminary surface modeling was deduced through a simple data threshold as a function of the gray level of the voxels in the reconstructed volume. By considering this modeling as a data input, a fitting procedure was applied to the external surface of the NP, to determine the six surfaces that at best define the boundaries of the NP. It allowed a precise determination of the Lz length of the NP in the z direction, that is, 22 nm. The difference with respect to Lx and Ly lengths (20 and 21 nm) allowed us to conclude that the external shape of the NP is rather parallelepipedic than cubic, as presumed. Finally, comparing Lz to the length of the nontruncated area of the NP in the z direction (determined by measuring the cornerto-corner distance in the xz and yz slices) allowed a precise determination of the truncation depths in the corresponding planes (gxz, gyz). The as-obtained values are similar (about 2.5 nm) and close to that of the truncation depth in the xy plane, gxy. This result, which is in agreement with the previous hypothesis that stipulates similarity, proves that the apparition of the {111} facets at the corners of the tetragonal NP originates from the truncation of the edges between two neighboring facets of {100} type. A schematic representation of this geometrical shape is illustrated in Figure 4C, together with the other possible shapes agreeing with a square symmetry in a 2D image. The last step of the analysis has consisted in the determination of the relative amount of the different surface facets (with {100} defined as major facets and {110} and {111} as minor ones), by using the geometrical parameters deduced

previously: we obtain 86%, 10%, and 4% for the {100}, {110}, and {111} planes, respectively. Note that the high contribution of the {100} facets to the total surface represents a notable difference with respect to the other cubic morphologies of CeO2 NPs obtained using other preparation methods. This result is of fundamental interest regarding the potential use of these nanoparticles in some catalytic applications, in particular, for the reactions that take advantage of the high reactivity of these crystallographic planes with respect to the other ones.28−30 CeO2 Nanoparticles with an Octahedral Morphology. Among the published studies devoted to 3D analyses of CeO2 NPs with a triangular view in a simple TEM image, one can mention the work by Xu et al.20 In a more general study devoted to a comparative presentation of different TEM tomographic modes, several CeO2 NPs have been analyzed, and their polyhedral shape systematically have been revealed. Alternately, Midgley et al. have investigated by STEMHAADF tomography the morphology of CeO2 NPs doped with Zr31 and observed that these NPs present the same octahedron morphology. In another study, Tan et al.21 have analyzed polyhedral CeO2 nanoparticles synthesized by the hydrothermal method and determined the type of exposed facets, their relative amount, and the presence and type of truncations. However, to our knowledge, no work published until now refers to polyhedral NPs deposited by solvothermal synthesis assisted by microwave heating. As explained in the Introduction, one of the peculiarities of this synthesis method is 1117



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Figure 14. (top) Global view of a typical nanorod and HR-TEM image taken on its central part (left), Fourier transform pattern corresponding to this area (middle), and the corresponding electron diffraction pattern (right). (bottom) FFT pattern measured by Bugayeva32 on a similar nanorod, its crystallographic indexation, as well as the corresponding structural model.

reconstruction in order to obtain the 3D representation of the assembly. Figure 7A presents three orthogonal sections through the reconstructed volume that cross four nanoparticles. The other way consists in extracting subvolumes from the reconstruction containing a unique object, followed by an individual analysis. Note that once each subvolume has been extracted, it can be individually rotated until similar orientations for all the nanoparticles are obtained. Figure 7B illustrates the modeling of the assembly and the individual modeling obtained for the four nanoparticles once their subvolumes have been oriented, using the isosurface rendering method. Surprisingly, the four nanoparticles have similar sizes, and that is a rather unexpected result given their relative appearance in simple BF or HAADF images. From a quantitative point of view, by decomposing the external surface of each NP in several planes, we have showed that it can be described by eight identical triangles. In addition, the relative angles between two adjacent triangles were systematically found, and values close to that between {111} planes in a crystal were generally found. To confirm the as-obtained crystallographic type of the facets, additional characterizations were performed by HR-TEM. The HR-TEM image on one of the four nanoparticles, oriented along a high symmetry axis is shown in Figure 8. Note that the crystallographic distances calculated by a Fourier analysis are in complete agreement with the expected values for the CeO2 system. It has been observed that, if the particle presents a square global appearance in a TEM image, it is observed along a [100] zone axis, which corresponds to a {100} basal plane. As the angles between the basal plane and the lateral facets

the rapid growth speed of the NPs. Combined with a specific stabilization rate for the different crystallographic facets, one can expect a relative amount different from that obtained for the NPs prepared by others methods. To obtain reliable information for the assembly, the tomographic analysis was performed on a collection of NPs. Figure 6A,B illustrates typical images extracted from the tilt series acquired simultaneously in BF and HAADF modes. Their simple aspect suggests that the NPs are not identical from a morphological point of view but that it depends on their relative orientations with respect to the observation axis. By comparing them to projections of a model crystal, one can associate them to octahedrons or other close geometrical shapes, but their exact 3D representation is required in order to definitely conclude on their global shape. From a general point of view, this requirement points out one of the benefits of the electron tomography that furnishes collective information on a set of nano-objects randomly oriented with respect to the observation direction. Once the spatially correlated BF and HAADF volumes are computed, they can be visualized and analyzed in a similar manner. As pointed out in the experimental part, even if they do not contain the same information, both can be used for the morphological analysis of homogeneous nano-objects,20 even crystalline ones, with a first preference for the BF volume where the SNR ratio is higher. The analysis of the shape of the nanoobjects can be performed first by considering the whole reconstruction and extracting slices orientated at will or by modeling simultaneously all the objects contained in the 1118



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Figure 15. (left) Four typical transversal slices and a longitudinal one extracted from the BF reconstruction obtained for a 15 nm sized nanorod, as well as a longitudinal section through its 3D modeling. (right) Examples of transversal and longitudinal slices extracted from the HAADF reconstruction corresponding to a 20 nm nanorod. The red arrows indicate the positions of some well-defined pores within the two nanorods, whereas the blue ones show their accessibility from the outside. Lamellar pores seem to be preferentially present in the small nanorod, whereas cylindrical ones are visible in the bigger nanorod.

deduced from the reconstruction are about 55°, one can definitely conclude that the NPs have an octahedral shape and their external surface is essentially made of {111} crystallographic planes. The question that arises at this stage of the analysis remains the geometrical characteristics of the truncations at the corners, knowing that their presence was clearly revealed by the analysis of HR-TEM images (Figure 8). With this aim in view, a detailed analysis of the reconstruction was performed (Figure 9). It presents two orthogonal slices extracted from the reconstruction: one corresponding to the basal plane and the other perpendicular to that plane crossing two opposite corners located in the basal plane. For a better visualization, the borders of the analyzed nanoparticle deduced by a simple edgesdetection procedure are also represented. We have thus observed that the apexes of the bypiramids are rather rounded, as well as two corners contained in the basal place (shown as 1 and 3 on Figure 9). On the contrary, the two opposite corners (shown as 2 and 4) are well faceted and thus introduce two minor facets {110} in nature. With all the geometrical parameters quantitatively determined from the corresponding slice, we were able to precisely determine the relative amount of the major and minor facets, that is, 98% for the {111} planes and 2% for the {110} ones. As a conclusion, we have presented in this section a 3D analysis of the polyhedral NPs obtained by solvothermal synthesis assisted by microwave heating, using electron tomography combined with high-resolution imaging. It has been possible to assign an octahedral shape to all the analyzed NPs and to reveal the presence and the characteristics of the truncations at the corners. The relative amount of the crystallographic planes present at the surface has been

estimated, illustrating that, for such NPs, the contribution of the minor facets (assigned to be {110} planes) is quite insignificant. CeO2 Nanorods. The third morphology of CeO2 NPs obtained by the solvothermal synthesis assisted by microwave heating corresponds to nanorods. This morphology remains relatively unknown, as no detailed 3D study has been published in the literature until now. As illustrated in Figure 10, the analysis of classical 2D TEM or STEM images shows that these nanoparticles seem to be relatively complex from structural and morphological points of view. In addition, we can observe that the nanorod tips present geometrical characteristics that are strongly dependent on their diameter: the larger nanorods (with size >15 nm) have short tips that seem to be faceted, whereas the shorter ones (with size

Three-Dimensional Tomographic Analyses of CeO2 Nanoparticles

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