Assessment of a nanocrystal 3-D morphology by the analysis of single HAADF-HRSTEM images
© Stroppa et al.; licensee Springer. 2013
Received: 7 August 2013
Accepted: 6 October 2013
Published: 13 November 2013
This work presents the morphological characterization of CeO2 nanocrystals by the analysis of single unfiltered high-angle annular dark-field (HAADF)-high-resolution scanning transmission electron microscopy (HRSTEM) images. The thickness of each individual atomic column is estimated by the classification of its HAADF integrated intensity using a Gaussian mixture model. The resulting thickness maps obtained from two example nanocrystals with distinct morphology were analyzed with aid of the symmetry from the CeO2 crystallographic structure, providing an approximation for their 3-D morphology with high spatial resolution. A confidence level of ±1 atom per atomic column along the viewing direction on the thickness estimation is indicated by the use of multislice image simulation. The described characterization procedure stands out as a simple approach for retrieving morphological parameters of individual nanocrystals, such as volume and specific surface areas for different crystalline planes. The procedure is an alternative to the tilt-series tomography technique for a number of nanocrystalline systems, since its application does not require the acquisition of multiple images from the same nanocrystal along different zone axes.
Keywords3-D morphology HAADF HRSTEM Nanocrystal modeling
Elucidating the morphology of nanostructured materials with high resolution is essential for their optimization for specific applications. A remarkable example is the use of nanostructured materials in catalysis, as their performance often depends on the exposed facet crystallographic structure and surface areas [1, 2]. Even though significant efforts have been devoted to the three-dimensional (3-D) morphology characterization of individual nanocrystals [3, 4], a straightforward and undemanding method is still unavailable.
The high-angle annular dark-field (HAADF) imaging mode in high-resolution scanning transmission electron microscopy (HRSTEM) [5–7] is one of the most promising techniques for nanocrystal characterization. Besides allowing direct imaging of the atomic columns with a spatial resolution down to 50 pm , the high-angle scattered electron signal intensity can be directly correlated to the thickness of the atomic columns  and the atomic number of their constituent atoms [9–11].
Recent reports have shown the successful application of HAADF-HRSTEM for mapping the thickness of Au foils  and for reconstructing the 3-D morphology with atomic resolution of an Ag precipitate in an Al matrix after applying a tomographic reconstruction procedure . These studies benefit from the use of HRSTEM multislice image simulations [14, 15] and Gaussian mixture models (GMMs)  to relate the integrated signal of each atomic column to their thickness with high accuracy. However, the requirement of model samples and/or the acquisition of multiple images from the same nanocrystal along different zone axes may restrict the practical application of these methodologies, especially for those systems that cannot withstand a high electron dose. In addition, sample and microscope instabilities during sample tilting procedures may make the 3-D morphology characterization of nanocrystalline samples by tomography approaches very difficult or even impractical. Consequently, the determination of the 3-D structure from nanoparticles by the use of a single electron microscopy image is a current challenge, which has been accomplished so far only for very specific systems such as size-selected gold clusters  and thin layers of light-weight atoms .
This work presents an alternative approach for estimating the 3-D morphology of nanocrystalline samples by the analysis of single HAADF-HRSTEM images. The described methodology combines two steps, namely (1) the determination of the thickness of each atomic column by GMM classification and (2) the construction of a 3-D morphology model using crystallographic symmetry operations which define the atom positions in the unit cell of the examined sample.
We applied the method to faceted CeO2 nanocrystals displaying two different morphologies . The CeO2 nanocrystalline system was chosen for this study because of two characteristics. First, CeO2-based materials show outstanding catalytic properties depending on the exposed facets, their surface area, and crystallographic structure . Second, the highly regular faceting present on the studied CeO2 nanocrystals allows a quantitative comparison between experimental results and HRSTEM image simulations based on symmetric model structures, which in turn provides us with an evaluation of the accuracy of thickness determination. However, the method requires neither the presence of faceted nanocrystals nor the use of image simulation procedures.
CeO2 nanocrystals were synthesized following a previously reported two-phase approach . In this method, an aqueous solution of cerium(III) nitrate (30 mL, 0.085 mol/L) was transferred to a 100-mL Teflon-lined stainless steel autoclave, and then toluene (30 mL) and tert-butylamine (0.30 mL) were added under ambient conditions without stirring. CeO2 nanocrystals with distinctly differing morphologies could be generated by manipulating the oleic acid (OA) concentration employed in the preparation. Polyhedral (labeled type-A) and cube-like (labeled type-B) CeO2 nanocrystals were obtained by the use of low (3 mL) and high (6 mL) OA additions, respectively. A thermal treatment at 180°C for 24 h was carried out for both variants of the synthesis process. Finally the material was washed several times and re-dispersed in non-polar solvents (e.g., toluene, hexane, chloroform) after the reaction.
Samples for electron microscopy analysis were prepared by dropping the diluted colloidal solution onto copper grids covered with a thin (approximately 5 nm) continuous amorphous carbon film and allowing the solvent to evaporate. STEM characterization was carried out using a JEOL JEM-2200FS microscope (JEOL Ltd., Akishima, Tokyo, Japan) equipped with a probe corrector and a Schottky field-emission electron gun operating at 200 kV. The HRSTEM imaging experiments were carried out using an electron beam with a 25-mrad convergence angle, 0.09-nm spot size, and a 64 μs/pixel dwell time during scanning. The HAADF signal within the 110- to 330-mrad angular range was acquired simultaneously to the bright-field (BF) signal.
The detection of peaks associated with atomic columns and their signal integration were performed for the 'as-obtained’ HAADF-HRSTEM images using circular masks with fixed radius. The size of the masks was selected to include approximately 80% of the peak intensities. A detailed description of these procedures can be found in Additional file 1.
The atomic column thickness estimation procedure was carried out separately for type-A and type-B nanocrystal images. The integrated intensities obtained for the individual atomic columns were classified as a histogram, and the data fitting procedure was performed by the use of multiple normal distributions according to the GMM . Multiple runs of the GMM algorithm were performed in order to optimize the model parameters, which were the number of Gaussian fitting distributions and their respective mean values, amplitudes, and standard deviations. The optimum GMM configuration was selected so that the absolute value of residual error between the model and the dataset was minimized.
After the GMM optimum parameter determination, each atomic column thickness was assigned to a Gaussian distribution. The correlation between the fitting distributions and the atomic column thicknesses was performed by taking into account (1) the monotonic increase of the mean value of the fitting curves and (2) the integrated intensity of the isolated Ce atoms. The integrated intensity analysis from isolated Ce atoms can be found in Additional file 1.
Finally, the spacing between Ce atoms along the imaging zone axes was evaluated for both type-A and type-B nanocrystals according to the allowed symmetry operations of the CeO2 unit cell. This approach led to the 3-D morphology models of the examined nanocrystals and to their geometrical parameter quantification. Atomic structure files of the 3-D morphology models are available in Additional files 2 and 3.
Results and discussion
Although the morphology of the nanocrystals can be roughly inferred from the integrated signal intensity of the columns and from the indexing of the projected crystallographic planes, a more accurate analysis can be achieved from a column-by-column thickness evaluation using the assumption that the number of Ce atoms in each column is an integer. Then, any unwanted contributions to the atomic column signal from other sources, such as the inherent (1) noise of the detection system, (2) electron channeling effects, and the (3) background HAADF signal from the oxygen atoms in the CeO2, the carbon support film, and the ligand molecules attached to the nanoparticles, are approximated to nearest value for the HAADF scattering of a discrete Ce atomic column.
The correlation between the distribution curves and the number of Ce atoms on the analyzed columns presented in Figure 3 was obtained from the analysis of two relevant aspects. The first is the monotonic increase of the mean values of the Gaussian distributions, as expected for an increasing number of atoms on the projected columns . The second parameter is the integrated intensity of the peripheral atomic positions in each HAADF image, which supports the intensity distribution assignment for a single Ce atom.
The standard deviation parameter from each GMM distribution curve is related to the overall noise contributions to the HAADF signal. However, the extent of such effects cannot be quantitatively analyzed from the fitting results due to the low occurrence of some atomic column lengths in the evaluated samples. Nevertheless, the thickness assignment precision can be conservatively estimated to be ±1 atom from the maximum overlap of the distribution curves, given the optimization of the Gaussian distribution standard deviations after the GMM fitting.
Calculated total surface areas of specific facets from the 3-D morphology models
Surface area (nm2)
The symmetry operations of the unit cell effectively apply to the morphology and also to the growth behavior general descriptions from several nanostructured systems . In such cases, the quantification of HAADF-HRSTEM images for the evaluation of the thickness of atomic columns and the use of symmetry operations to estimate the 3-D morphology is well founded. It may, however, be unrealistic for cases with element segregation that generates considerable Z contrast, such as core-shell structures and porous and/or non-convex structures, for example.
In order to further verify the adequacy of the models describing the CeO2 nanocrystalline systems evaluated here, HAADF-HRSTEM image simulations were carried out for symmetric model structures based on the 3-D morphology models presented in Figure 4, and the results were compared to the experimental images. The precise structures used in the image simulation , the simulation parameters, the corresponding simulated HAADF-HRSTEM images, and the qualitative comparisons between the simulated and experimental images are available in Additional files 1, 8 and 9.
It should be noted that the integrated peak intensity plot shown in Figure 5b includes error bars based on standard deviation measurements, which allow us to estimate the maximum error to be ±1 atom within a 90% confidence level.
We describe a practical procedure to extract the approximate 3-D morphology of nanocrystals from single HAADF-HRSTEM images using the GMM classification approach. The specific surface areas from different facets of CeO2 nanoparticles were estimated after reconstruction of the 3-D morphology. The method is based on a mapping of column thicknesses with a high level of precision from single unfiltered images, in conjunction with the utilization of symmetry information pertinent to the unit cell of the material under investigation. The procedure is an alternative to tomographic reconstruction approaches [4, 13, 24, 25] which tend to require a much greater experimental effort and may be prohibitive in practice due to electron beam sensitivity limitations of the nanocrystalline material under examination.
The authors would like to thank the STEM Group at Paris Sud Université, L. F. Zagonel, and J. Bettini for fruitful discussions. The authors also acknowledge the financial support of FAPESP and DAAD. WW and CJK gratefully acknowledge financial support from the NSF/EPSRC - Materials World Network Program (grant # DMR-0709887).
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