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2008, 112, 1759-1763 Published on Web 01/23/2008
Determination of Nanocluster Sizes from Dark-Field Scanning Transmission Electron Microscopy Images Norihiko L. Okamoto,*,† Bryan W. Reed,‡ Shareghe Mehraeen,† Apoorva Kulkarni,† David Gene Morgan,† Bruce C. Gates,† and Nigel D. Browning†,‡ Department of Chemical Engineering and Materials Science, UniVersity of California, One Shields AVenue, DaVis, California, 95616, and Materials Science and Technology DiVision, Lawrence LiVermore National Laboratory, LiVermore, California 94550 ReceiVed: NoVember 16, 2007; In Final Form: January 6, 2008
A novel method of determining nanocluster sizes and size distributions using high-angle annular dark-field imaging in scanning transmission electron microscopy is described. This method is demonstrated for MgOsupported [Os10C(CO)24]2- clusters formed by treating Os3(CO)12 precursors in CO. The image analysis identified the presence of both Os3(CO)12 precursors and [Os10C(CO)24]2- clusters in the expected ratio (with the sizes matching those calculated on the basis of their crystallographically determined structures within 6%) and also larger clusters that can be readily identified as combinations of the former clusters.
Technologically important catalysts are typically metals, and the most useful of them are dispersed as nanoclusters on highsurface-area oxide supports.1,2 The properties of such catalysts depend on the sizes and shapes of the nanoclusters and their interactions with the support.1,3 It is therefore important to be able to determine the sizes and shapes of supported nanoclusters accurately to fully understand the catalytic properties. Extended X-ray absorption fine structure (EXAFS) spectroscopy is a standard method that provides detailed information about cluster sizes, but unfortunately, it is averaged over large areas of the sample through which the X-rays pass. Furthermore, the analysis is subject to interpretation and does not provide a direct image of the clusters. An alternative method to observe cluster sizes involves using the high-angle annular dark-field imaging (HAADF) technique in the scanning transmission electron microscope (STEM).4 HAADF-STEM has advantages over conventional TEM for the measurement of nanoclusters because (1) coherent contributions from the cluster and the oxide support are reduced and (2) heavy metal nanoclusters show a high contrast on the low background of a light oxide support because the image intensity is roughly proportional to the square of the atomic number. With this method, individual supported nanoclusters can be imaged directly and their sizes determined. The ability to quantify the size of individual nanostructures in the STEM is primarily determined by the size of the electron beam (probe) and the stability of the nanoclusters under the intense electron irradiation of the beam. The recent development of aberration correctors for STEM has vastly improved the spatial resolution possible with these instruments, taking the resolution to less than 0.1 nm. However, this advance does not automatically improve sensitivity/accuracy when the size measurement is limited by electron irradiation effects such as * To whom correspondence should be addressed. Tel: +1-530-754-8012. Fax: +1-530-752-9554. E-mail:
[email protected]. † University of California. ‡ Lawrence Livermore National Laboratory.
10.1021/jp710959x CCC: $40.75
chemical changes and the movement of the nanoclusters on the support surface.5 Reducing the electron dose mitigates beaminduced effects but only at the expense of the signal-to-noise ratio, partially negating the advantages of the finer probe in the aberration-corrected microscope. To maximize the resolution and sensitivity of the images, there is therefore a need for data analysis methods that can make the most of the information available in low-dose HAADF-STEM images. In this letter, we demonstrate a new approach that permits the quantitative determination of size distributions of supported nanoclusters only from the intensity profiles of the clusters in conventional STEM-HAADF images (low spatial resolution and signal levels). This approach is complementary to previous approaches6-8 that allow measurement of the masses of particles by integrating the HAADF signal over the area of each particle. Although the prior mass measurement approach is likely to be more sensitive to the differences between particles, it is more difficult to calibrate and hence more susceptible to variability between experiments. Furthermore, the intensity measurement requires large collection angles (∼100 mrad)6,7 to be used to minimize coherent effects, thereby resulting in either a reduction of the image intensity or requiring an increase in electron dose (leading to the issues discussed above). In contrast, the method described here requires only the probe size to be calibrated, after which the collection angle and dose can be reduced to levels at which beam irradiation effects are mitigated. The method described here produces accurate results even for the smallest clusters when the image has a low signal-to-noise ratio (S/N). Once all contributions to the images are accounted for, the method yields nanocluster sizes that agree with crystallographic data characterizing the clusters in the solid state, to within ∼15 pm or better, even when a nonaberration-corrected STEM with a 0.3 nm probe size is used. To begin the analysis of a low-dose HAADF image, we must first consider all of the contributions that give rise to the final © 2008 American Chemical Society
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Letters convenience of the rms width lies in its behavior under the convolution product. If the object function and experimental blurring effects are assumed to act as independent convolutions, the measured rms width of the particle, σmeas, is described by the following equation
σ2meas ) σ2obj + σ2probe + σ2vib + σ2focus + σ2gb
(2)
For a particle with anisotropic second moments, σobj will vary with the scan direction. However, by averaging σ2obj for a sufficiently large sample of randomly oriented particles, we can recover an orientation-independent measure of the rms radius of the particle (rrms). For comparison between theory and experiment, this quantity is defined via a weighted average that includes the electron-scattering factors
r2RMS )
Figure 1. (a) δ-Function-like intensity profile of an individual pixel in a STEM image. (b) Gaussian blurring function with a standard deviation of σgb. (c) Propagation of blurring in STEM; convolution of the object function with other blurring functions. (d) Schematic 2 illustration of σmeas plotted against σ2gb; the slope of the plot asymptotically approaches unity as σgb becomes large.
observed spatial resolution. Although noise in a low S/N image represents the primary difficulty for the size measurement (making a definition of the edges of the nanoparticles difficult), the size distribution of the intensity profile is also modified by standard blurring effects in STEM imagessinitial probe size, vibration, beam broadening, and so forth. However, as the HAADF image is incoherent in nature, each of these contributions can be considered to contribute to the final image independently. Hence, we can smooth the noise in an image by artificially broadening it with a Gaussian blur, whereby each image pixel (Figure 1a) is convoluted with a Gaussian distribution function having a standard deviation of σgb (Figure 1b). This artificial blurring function can then be considered as contributing with all the other experimental blurring effects, and the final image is a convolution of all of them with the object function, as shown in Figure 1c. It is mathematically convenient to treat all of these blurring effects, as well as the size of the object itself, in terms of their root-mean-square (rms) widths as measured in a one-dimensional projection. For example, the artificial Gaussian blurring involves a convolution with a two-dimensional kernel of the form
f(x,y) )
(
)
1 x 2 + y2 exp 2πσ2gb 2σ2gb
(1)
A one-dimensional projection of this is a Gaussian with a rms width σgb. Other blurring effects from the electron probe size, vibration, and off-focus effects are described by similar rms widths σprobe, σvib, and σfocus. The physical particle itself can be thought of as a three-dimensional distribution of scattering density which can be projected onto a specific axis (say, the x axis) corresponding to the scan direction, yielding a distribution which will have its own rms width σobj. The mathematical
∑i Sir2i /∑i Si
(3)
where ri stands for the distance between the center of gravity of the cluster and the ith constituting atom and Si represents the electron elastic-scattering cross section of the ith atom for the incident electron, which can be calculated by integrating the differential cross section over the solid angle of the STEM detector. The rms radius can be decomposed into three components, σobj-x, σ obj-y, and σ obj-z, when transformed to a Cartesian coordinate frame 2 2 2 + σobj-y + σobj-z r2RMS ) σobj-x
(4)
This follows from eq 3 when we recognize that r2i ) x2i + y2i + z2i . The quantity σobj-x is the value of σobj that would be obtained for a scan in direction x, and σobj-y and σobj-z are defined similarly. Next, we introduce the notion of an ensemble average, such that is defined as the expectation value (or mean) of some quantity f obtained from a large number of measurements of randomly oriented clusters. Because the expectation value of a sum is the sum of the expectation values, we have 2 2 2 〈r2RMS〉 ) 〈σobj-x 〉 + 〈σobj-y 〉 + 〈σobj-z 〉
(5)
Further, the isotropic expectation value as defined cannot be different for the x, y, and z directions, so that 2 2 2 〉 ) 〈σobj-y 〉 ) 〈σobj-z 〉 ≡ 〈σ2obj〉 〈σobj-x
(6)
which yields the equation
〈r2RMS〉 ) 3〈σ2obj〉
(7)
connecting an experimentally obtainable ensemble average to a theoretically derived orientation-independent measure of particle size. Measured σ values (σmeas: σmeas-x and σmeas-y for the two dimensions in the image) are obtained by fitting a twodimensional Gaussian distribution function to the intensity profile of the clusters in the STEM image. When the S/N is low (e.g., σgb is small), the noise still present in the image affects the σmeas-x and σmeas-y values, depending on the fitted area of the cluster, as indicated in the schematic illustration (Figure 1d). When the noise is smoothed out (e.g., σgb is large enough), however, its effect will be minimized. Furthermore, it is possible to estimate the σmeas value without the artificial blurring effect
Letters
J. Phys. Chem. C, Vol. 112, No. 6, 2008 1761
Figure 2. Structural models of (a) Os3(CO)12 and (b) [Os10C(CO)24]2clusters determined from crystallographic data characterizing the compounds in the solid state combined with EXAFS and infrared data characterizing these clusters supported on MgO;11-15 CO ligands are omitted for clarity.
(σmeas_gb)0) by extrapolating the σ2meas values for various σ2gb values to the vertical axis, as shown Figure 1d. Under the best observation conditions (i.e., the microscope environment is sufficiently isolated, and the microscope is optimally aligned), the vibration and off-focus effects (σvib and σfocus) can be neglected. Then, eq 2 can be rewritten as follows 2 σmeas_gb)0 ) σ2obj + σ2probe
(8)
Because the value of σprobe is known from a direct measurement of the electron probe, the σobj value and rms radius can be calculated by using eqs 7 and 8. We found that the more direct method of simply applying eq 8 without going through the blurring-and-fitting procedure was far too sensitive to random noise and could not produce a reliable measurement. We used the method described here to analyze images of MgO-supported decaosmium carbidocarbonyl clusters, [Os10C(CO)24]2-, formed by the reaction of triosmium carbonyl precursors, Os3(CO)12, in the presence of CO. Osmium in various forms is a catalyst for various conversions of hydrocarbons, including alkene hydrogenation.9-10 MgO-supported osmium carbonyl clusters were chosen because (1) osmium clusters of various nuclearities (such as 3, 5, and 10 atoms) can be synthesized uniformly and selectively on MgO support surfaces,11-13 (2) the structures of [Os10C(CO)24]2- and Os3(CO)12 are well-characterized (in the solid state by X-ray diffraction crystallography14,15 and on MgO surfaces by EXAFS spectroscopy and infrared spectroscopy11-13), and (3) the heavy Os atoms show high contrast relative to the light MgO support in HAADF imaging. The core structural models of the [Os10C(CO)24]2- and Os3(CO)12 clusters determined from the crystallographic data are illustrated in Figure 2; EXAFS data characterizing these clusters on MgO are consistent with the crystallographic dimensions.13-15 MgO-supported [Os10C(CO)24]2- was prepared by slurrying Os3(CO)12 in dried deoxygenated n-pentane with calcined MgO powder, followed by evacuation at room temperature. The powder samples contained 2 wt % Os. The sample was further subjected to treatment in flowing He at 548 K for 2 h followed by treatment in flowing CO at 548 K for 4 h.13 The STEM sample was prepared by dipping a 200 mesh copper grid supporting a holey carbon film into the powder samples in a nitrogen-filled glovebox. To protect the air-sensitive sample from exposure to the atmosphere, the grid was loaded on a Fischione vacuum transfer holder (Model 2020) that allowed transfer from the glovebox into a JEOL JEM-2500SE (S)TEM with the sample under a nitrogen atmosphere. The MgO-supported clusters were examined by using the STEM at 200 kV with a probe size of 0.30 nm at full-width-halfmaximum (fwhm), a convergence semiangle of 12 mrad, and a collection semiangle of 35-90 mrad. The probe fwhm was obtained by taking a probe image in the TEM mode with a Gatan
Figure 3. (a) HAADF-STEM image of osmium carbonyl clusters on a MgO support. (b) Raw image of the cluster indicated by the arrow in (a) and intensity profile along the line X-Y. (c-g) Gaussian blurred images of (b) and intensity profiles. The σgb values are indicated on the top right of each profile.
imaging filter at a magnification of 800 000× after manually changing the probe-forming lens conditions to those in the STEM mode. If the probe intensity is assumed to have a normal distribution, the probe fwhm is larger than the σprobe value by a factor of (8ln2)0.5. We have used this relation to calculate the σprobe value from the obtained fwhm value because the probe intensity can be appropriately approximated by a normal distribution under the best probe-forming conditions. The scan resolution and field size were 0.042-0.063 and 21-32 nm, respectively. The rms radii of Os3(CO)12 and [Os10C(CO)24]2- were calculated from the crystal structures, eq 2, and the electron elastic-scattering cross section database distributed by the National Institute of Standards and Technology (NIST).16 The resultant theoretical rms radii of Os3(CO)12 and [Os10C(CO)24]2are 0.202 and 0.295 nm, respectively. Note that the CO ligands (not shown in the figure) are significant contributors to the overall rms radii. Figure 3a shows a raw HAADF-STEM image of the MgOsupported clusters. It is very difficult to measure the cluster size from the raw image because of the noisy intensity profile, as shown in Figure 3b. Figure 3c-g shows Gaussian blurred images and intensity profiles of the cluster indicated by the arrow in Figure 3a. Although the noise is not completely smoothed out with small σgb values (Figure 3c and d), it is smoothed out with larger σgb values (Figure 3e-g). Square regions, each including an individual cluster, were cut from the STEM images that were blurred with different σgb values. The largest clusters visible in the image were clearly too large to be single Os3(CO)12 or [Os10C(CO)24]2- units and were not included in the analysis. The presence of such clusters is not surprising; these materials tend to agglomerate at the high treatment temperatures that were used in the preparations.17 The threshold maximum size for accepting a cluster for analysis was deliberately set fairly high in order to ensure that all of the clearly visible, isolated Os3(CO)12 and [Os10C(CO)24]2- units were included. A two-dimensional Gaussian function with a planar background was fitted to the intensity profiles of the square regions to obtain standard deviations of the fitted function (σmeas-x and σmeas-y). The window size for the fit was about four times as large as the resultant σmeas values because neighboring clusters interfered when the window size was too large, and the background fit was not accurate when the window size was too small. Thus, using either larger or smaller windows failed to produce significant σmeas values.
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Letters
2 Figure 4. Values of σmeas characterizing 30 clusters plotted as a 2 function of σgb. Lines are the best-fit straight lines for each cluster.
The mean square value of σmeas-x and σmeas-y (i.e., σ2meas ) 2 + σmeas-y )/2) for each cluster is plotted in Figure 4 as a function of σ2gb. All of the σ2meas values increase linearly with increasing values of σ2gb. The σ2meas values are fitted by a linear function (lines in Figure 4). As mentioned above (Figure 1d), the σ2meas value extrapolated to the intercept on the vertical axis 2 ) corresponds to σ2obj + σ2probe, which does not (σmeas_gb)0 include the artificial blurring effect. As expected, the slopes of the lines in Figure 4 are close to 1, with some random clusterto-cluster variation that may derive, in part, from the effects on the Gaussian fits of noise, background, and variations in cluster shape and orientation on the surface. Because the points contributing to each straight-line fit are not statistically independent, it is not strictly possible to derive the uncertainty in σ2meas from standard data analysis theory. Instead, we estimate uncertainties by analyzing calculated σ2meas values from an ensemble of independent clusters, as we now show. Figure 5 shows a histogram and a series of kernel density estimators (KDE) of the measured rms radii with all known systematic effects removed for 30 clusters indicated in the STEM images. As shown by the results of Figure 5, the clusters can be divided into three groups, designated I, II, and III, in order of size. The KDE is a substitute for the better-known histogram, providing similar information while being less wasteful of information and less sensitive to bin size and centering artifacts that can plague histogram analysis for small data sets.18 The KDE is a continuous function that estimates the probability density of a distribution from a discrete list of n sampled points {xi}. It does this by superposing kernel functions, one centered on each point xi. In our case, we used a Gaussian kernel 2 (σmeas-x
KDE(x) )
1
n
∑
n i)1
1
x
2πσ2KDE
(
exp -
)
(x - xi)2 2σ2KDE
(9)
A heuristic formula for the optimum kernel width is given by Silverman18
σKDE ) 0.9min (σsample,IQ/1.34)n-1/5
(10)
where σsample is the sample standard deviation of the list of {xi} and IQ is the interquartile range (the difference between the (3n/4)th and (n/4)th elements in the sorted list of data points).
Figure 5. Distributions of measured particle rms radii with all known systematic effects removed. (a) Histogram with 0.04 nm bins and 0.01 nm offsets. Although three peaks are clearly determined for this choice, they are less clearly defined when equally valid choices are used. (b) Gaussian-kernel probability density estimators with a varying rms kernel width (offset for visibility); 0.037 nm is the optimum according to Silverman’s criterion.18
This width is intended to suppress random noise while leaving statistically reliable information intact. Use of the KDE helped to confirm the validity of the classification of the clusters suggested by the histogram. Three peaks are evidently both necessary and sufficient to describe the statistical distribution of the 30 clusters. Parameters for these peaks were derived from the maximumlikelihood (ML) method by using a sum of three Gaussian distributions as a model19 and varying the height, width, and position of each peak to maximize the likelihood of the complete set of 30 measured values. This procedure eliminates the need for assuming that any specific measurement belongs to any specific peak (and we emphasize that similar results were obtained by making this assumption for each of the 30 values and calculating the means and standard deviations within each group). Table 1 is a summary of the means and (sample) standard deviations of rms radii for each group determined by the ML calculation. The ML calculation indicates that group I contains 6 clusters drawn from a distribution with a mean radius of 0.201 nm and a standard deviation of 0.021 nm; group II contains 14 clusters with a mean radius of 0.311 ( 0.031 nm; and group III contains 10 clusters with a mean radius of 0.416 ( 0.014 nm.
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TABLE 1: Means and (Sample) Standard Deviations of rms Radii Obtained by the Maximum Likelihood Method;18 Crystallographic Values for Groups I and II are for Os3(CO)12 and [Os10C(CO)24]2-, Respectively
group (see text)
number of clusters in group
I II III
6 14 10
mean rrms (nm)
standard deviation of rrms (nm)
sample standard error of the mean (nm)
crystallographically determined rrms (nm)
microscopycrystallography discrepancy, standard deviations
0.201 0.311 0.416
0.021 0.031 0.014
0.009 0.0085 0.0046
0.202 0.295
0.1 1.8
From these values we may estimate sample standard errors of the means by dividing each peak’s standard deviation width by (N - 1)1/2, with N being the number of clusters contributing to the peak.19 These values, equal to 0.009, 0.0085, and 0.0046 nm for groups I, II, and III, respectively, indicate the statistical precision to which the mean has been determinedsalso correcting for the downward bias in peak width inherent in ML calculations. Recalling that the theoretical rms radii of Os3(CO)12 and [Os10C(CO)24]2- are 0.202 and 0.295 nm, respectively, we identify these with groups I and II, with measured mean values of 0.201 ( 0.009 and 0.311 ( 0.0085 nm, respectively. Thus, the deviations between the microscopically measured values and those determined by crystallography (and consistent with EXAFS spectra of the supported species), after correction for all known systematic effects, amount to 0.1 and 1.8 standard deviations for the two cases. These values are so small that we believe they are consistent with a random error. In the future, larger data sets will be collected to check whether there may yet be systematic errors that need correcting. The coexistence of the Os3(CO)12 and [Os10C(CO)24]2clusters (groups I and II) is as expected because some of the precursor Os3(CO)12 clusters were expected not to have been converted to the larger clusters.13 The group III clusters, with a rms radius of 0.416 ( 0.0046 nm, are likely to be agglomerated clusters consisting of pairs or perhaps triples of the original clusters, as are expected to form at the 548 K treatment temperature used in the sample preparation. This inference can be checked by tomographic analysis. These clusters are however of much less practical interest than are the nonagglomerated group I and group II clusters and therefore have not been considered further in this paper. In summary, the size distribution of MgO-supported osmium nanoclusters was determined from HAADF-STEM images with a new blurring propagation method of data analysis. The method is precise enough to distinguish populations of different-sized clusters and to determine their rms radii to within ∼15 pm. The results indicate the existence of both the precursor Os3(CO)12 clusters and the [Os10C(CO)24]2- clusters formed from them.
The method described in this letter can be used to generate detailed information about particle size distributions of isolated nanoclusters and shed light on the relationships between the size of clusters and their properties. Acknowledgment. This work is supported by the National Science Foundation under GOALI Grant Number CTS-0500511 performed in collaboration with ExxonMobil and by the Japan Society for the Promotion of Science for Young Scientists. The work was performed in part under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. References and Notes (1) Gates, B. C. Chem. ReV. 1995, 95, 511. (2) Guzman, J.; Gates B. C. J. Chem. Soc., Dalton Trans. 2003, 17, 3303. (3) Boudart, M. AdV. Catal. 1969, 20, 153. (4) Pennycook, S. J.; Jesson, D. E.; McGibbon, A. J.; Nellist, P. D. J. Electron Microsc. 1996, 45, 36. (5) Batson, P. E.; Dellby, N.; Krivanek, O. L. Nature 2002, 418, 617. (6) Singhal, A.; Yang, J. C.; Gibson, J. M. Ultramicroscopy 1997, 67, 191. (7) Yang, J. C.; Bradledy, S.; Gibson, J. M. Microsc. Microanal. 2000, 6, 353. (8) Yang, J. C.; Bradledy, S.; Gibson, J. M. Mater. Charact. 2003, 51, 101. (9) Barnard, C. F. J.; Bennett, S. C. Platinum Met. ReV. 2004, 48, 157. (10) Johansson, M.; Linde´n, A. A.; Ba¨ckvall, J.-E. J. Organomet. Chem. 2005, 690, 3614. (11) Bhirud, V. A.; Iddir, H.; Browning, N. D.; Gates, B. C. J. Phys. Chem. B 2005, 109, 12738. (12) Allard, L. F.; Panjabi, G. A.; Salvi, S. N.; Gates, B. C. Nano Lett. 2002, 2, 381. (13) Lamb, H. H.; Gates, B. C. J. Phys. Chem. 1992, 96, 1099. (14) Jackson, P. F.; Johnson, B. F. G.; Lewis, J.; Nelson, W. J. H. J. Chem. Soc., Dalton Trans. 1982, 1982, 2099. (15) Corey, E. R.; Dahl, L. F. Inorg. Chem. 1962, 1, 521. (16) NIST Standard Reference Database 64: NIST Electron ElasticScattering Cross-Section Database, V. 3.1, 2003 (copyright U.S. Secretary of Commerce). http://www.nist.gov/srd/ (accessed July 4, 2007). (17) Bhirud, V. A.; Panjabi, G.; Salvi, S. N.; Phillips, B. L.; Gates, B. C. Langmuir 2004, 20, 6173. (18) Silverman, B. W. Density Estimation for Statistics and Data Analysis; Chapman and Hall: London, 1986. (19) Bevington, P. R. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, 1969; Chapters 2 and 5.
