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Scanning Tunneling Microscopy and Scanning Tunneling Spectroscopy Studies of Powdery Palladium/Graphite Model Catalysts† J. Schneider,*,‡ C. Wambach,§ B. Pennemann,§ and K. Wandelt‡ Institut fu¨ r Physikalische und Theoretische Chemie der Universita¨ t Bonn, Wegelerstrasse 12, D-53115 Bonn, Germany, and Bayer AG Leverkusen, Zentrale Forschung, Germany Received November 16, 1998. In Final Form: April 23, 1999 Powdery Pd/graphite model catalysts were studied with transmission electron microscopy (TEM), scanning tunneling microscopy (STM), and scanning tunneling spectroscopy (STS), with the later two techniques in air. In contrast to TEM images, STM/STS data are representative of the very surface and are therefore more relevant for an interpretation of the catalytic properties of these kind of catalysts. Besides spherical clusters and layered structures, also platelike and diffuse structures could be distinguished in the STM images. An assignment of the different objects to one of the main elementssgraphite and palladiumswas possible with STS. The I(V) curves on graphite are always much narrower on the V axis than those on palladium, and their slope dI/dV is, thus, larger. Utilizing this distinction, “chemical maps” were determined by taking I(V) data over a grid of surface points and assigning each point the value of the integral under its dI/dV curve. The comparison of such a chemical map with the topographic STM picture of the same area shows that only the spherical cluster structures consist of palladium, in accordance with the TEM pictures. The layered and platelike structures are identified as graphite, and the diffuse structures probably belong to impurities. In any case, the latter consist neither of graphite nor of palladium. A statistical analysis of the cluster morphology reveals that at low Pd loads the clusters are of spherical shape whereas the average width-to-height ratio increases at higher concentrations. The clusters at higher Pd concentrations exhibit a more elliptical shape.
Introduction Generally, STM and STS investigations on powdery samples are problematic because of the enormous sample roughness. Therefore, to date only a few publications deal with scanning probe investigations on systems with powdery graphite substrates.1-4 Nevertheless, there is great interest in such systems on the part of the chemical industry, where carbon is used as a heterogeneous catalyst support in a wide range of applications (see, for example, ref 5). In order to optimize these catalytic reactions, many unknown processes concerning the reaction itself and the synthesis of the catalysts have to be clarified. Because of their rugged structure, real catalysts with activated carbon or soot as support are regarded as quite unsuitable for investigations using scanning probe techniques. Hence, highly oriented pyrolytic graphite (HOPG) with large atomically flat terraces is often used as a model substrate for STM or STS investigations on carbon-deposited metal clusters.6-11 Due to its nearly perfect crystalline structure, HOPG exhibits less unsaturated carbon bonds and † Presented at the Third International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Poland, August 9-16, 1998. * Corresponding author. Telephone: +49 228 73 2504. Fax: +49 228 73 2551. E-mail:
[email protected]. ‡ Institut fu ¨ r Physikalische und Theoretische Chemie der Universita¨t Bonn. § Bayer AG Leverkusen.
(1) Shaikhutdinov, S. K.; Kochubey, D. I. Catal. Lett. 1994, 28, 343. (2) Hoffman, W. P. Carbon 1992, 30 (3), 315. (3) Atamny, F.; Reller, A.; Schlo¨gl, R. Carbon 1992, 30 (7), 1123. (4) Cadete Santos Aires, F. J.; Sautet, P.; Fuchs, G.; Rousset, J.-L.; Fuchs, P.; Me´linon, P. Microsc. Microanal. Microstruct. 1993, 4, 441. (5) Ro¨ mpp Chemie Lexikon; Thieme Verlag: 1988/92. (6) Clark, G. W.; Kesmodel, L. L. J. Vac. Sci. Technol. B 1993, 11 (2), 131. (7) Tong, X. Q.; Aindow, M.; Farr, J. P. G. J. Electroanal. Chem. 1995, 395, 117.
functional groups. Since several models for the bonding between palladium and carbon supports are based on the existence of those unsaturated bonds12,13 or oxygencontaining groups,14,15 a comparison between Pd clusters on HOPG and metal particles of real heterogeneous Pd/ graphite catalysts is, in most cases, not justified. This article, therefore, reports about results from powdery Pd/graphite model catalysts. Size distributions of the metal clusters on those powdery supports are mostly extracted from electron microscopic images.10 These images, however, provide only the projected area of the particles. By contrast, STM investigations are purely surface sensitive and give additionally information about the dimension perpendicular to the sample surface. Thus, with sufficient statistics it is possible to provide evidence about changes concerning the cluster shape and their dependence on different parameters. The various types of powdery graphite used as support for the present model catalysts can be seen as bridging the gap between HOPG and the “real” materials, such as activated carbon. There is no difference between the synthesis of the model catalysts discussed here and the real ones. Even the catalytic applicability of the model substances is comparable to that of the real catalysts, as confirmed by test reactions16 and quantified below. (8) Shaikhutdinov, S. K.; Kochubey, D. I. Chem. Rev. 1993, 62 (5), 409. (9) Sartre, A.; Phaner, M.; Poite, L.; Sauvion, G. N. Appl. Surf. Sci. 1993, 70/71, 402. (10) Aiyer, H. N.; Vijayakrishnan, V.; Subanna, G. N.; Rao, C. N. R. Surf. Sci. 1994, 313, 392. (11) Bettac, A.; Ko¨ller, L.; Rank, V.; Meiwes-Broer, K. H. Surf. Sci. 1998, 402-404, 475. (12) Ryndin, Yu. A.; Alekseev, O. S.; Simonov, P. A.; Likholobov, V. A. J. Mol. Catal. 1989, 55, 109. (13) Semikolenov, V. A. Russ. Chem. Rev. 1992, 61 (2), 168. (14) Prado-Burguete, C.; Linares-Solano, A.; Rodrı´guez-Reinoso, F.; Salinas-Martinez de Lecea, C. J. Catal. 1989, 115, 98. (15) Suh, D. J.; Park, T.-J. Carbon 1993, 31 (3), 427.
10.1021/la9816003 CCC: $18.00 © 1999 American Chemical Society Published on Web 06/30/1999
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Figure 1. (a) SEM image (28 µm × 22 µm) of RFL graphite. (b) SEM image (28 µm × 22 µm) of Edelgraphite.
Experimental Section Preparation of the Model Catalysts. Two different kinds of graphite were used for the synthesis of the present model catalyst: (1) RFL graphite with a BET surface area17 of 0.75 m2/g and a carbon content greater than 99.5% and (2) Edelgraphite with a BET surface area of 14.5 m2/g and a carbon content greater than 99.5%. The differences concerning the BET surfaces between the two graphites are clearly shown by typical scanning electron microscopy (SEM) images displayed in Figure 1. Images of the RFL graphite show relatively large graphite flakes with dimensions up to 20 µm (Figure la) while the Edelgraphite consists of smaller graphite flakes with maximum sizes up to 2 µm (Figure lb). Although these graphites have a morphology not nearly as fragmented as that of soot or activated carbon, the finding of more or less extended flat regions oriented perpendicular to the tunneling tip was still the main problem during the STM investigations. Frequently, crashes of the tip into protruding parts of the sample caused significant loss of resolution, which sometimes could be restored by applying a voltage pulse to the STM tip. Excepting those crashes, we never observed any morphological changes (e.g. movement of particles18 or oxidation with atomic oxygen created in the tip-sample field19) due to tip-sample interactions; in our measurements two images scanned in succession always looked identical. Even after detection of several hundreds of spectroscopy curves within one region, no morphological changes had occurred. In general, on the Edelgraphite the possible scan areas were smaller than 100 nm × 100 nm. In the first step of the catalyst synthesis, the graphite was oxidized with 65% nitric acid followed by stirring at 80 °C, washing with water, and drying. This pretreatment served to oxidize the impurities and to wash them out. Additionally, the number of functional groups like carboxyl, phenol, carbonyl, or lactonic groups acting as fixing points for the metal clusters was increased, (16) Wambach, C. Ph.D. Thesis, University of Bonn, 1998. (17) A method for measuring the surfaces of porous materials developed by Brunauer, Emmett, and Teller. (18) Coratger, R.; Chaboun, A.; Ajustron, F.; Beauvilain, J.; Erard, M.; Amalric, F. Ultramicroscopy 1990, 34, 141. (19) Rabe, J. P.; Buchholz, S.; Ritcey, A. M. J. Vac. Sci. Technol. 1990, 8, 679.
as verified by using the adsorption titration method established by Boehm (see ref 20). After the described oxidation process, the concentration of nearly all mentioned groups was higher than before; only the concentration of carbonyl groups was decreased after the oxidation. This supports the correlation between the presence of these functional groups and a dispersive cluster distribution after impregnation, because, without preoxidation of the support material, the Pd particles formed huge conglomerates with diameters larger than 100 nm.16 The preoxidized graphites were suspended in water and once again stirred at 80 °C after addition of an H2PdCl4 solution. After reduction with formaldehyde in an alkaline medium (pH 8-9 adjusted by addition of sodium hydroxide), the solid phase was filtered and washed with plenteous water to get rid of the chloride; the complete removal of chloride was checked with AgNO3. Finally, drying completed the synthesis. By this preparation method catalysts with different palladium loads between 0.1 and 5.0 wt % relative to the graphite were produced, choosing the concentration of the H2PdCl4 solutions accordingly. Note, however, that these concentrations do not have to be identical with the deposited amounts of Pd. The real metal loads of the final catalysts are a priori unknown. Therefore, the different catalyst samples studied in this work are only labeled by the concentration of the respective H2PdCl4 solution employed to prepare the catalyst. As mentioned above, the catalytic applicability of our model catalysts was determined by test reactions. For example, the hydrogenation of phenol to cyclohexanol with cyclohexanone as an intermediate product was catalyzed by our model substances. Compared to that of a commercial catalyst, the activity of our samples was lower by a factor of 2; however, especially those catalysts with small Pd clusters (diameters < 3 nm) showed a (20) Boehm, H. P.; Diehl, E. Z. Elektrochem., Ber. Bunsen-Ges. Phys. Chem. 1962, 66, 642. To measure the concentration of alkaline groups, 300 mg of support material was degased for 3 days under vacuum conditions and then stirred with 25 mL of a 0.05 N hydrochloric acid solution for 2 days. After filtration the remaining liquid phase was titrated with 0.05 N sodium hydroxide. The amount of sodium hydroxide needed corresponds to the number of alkaline functional groups. Likewise, treatments with specific alkaline solutions (Na2CO3 or NaHCO3 instead of HCl) give evidence about the concentrations of the different acidic groups (carboxyl, phenol, etc.).
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Figure 2. STM image (29 nm × 29 nm) of RFL graphite with a palladium load of 1.0 wt %. Pd clusters with a spherical shape are marked by an S. On top of a graphite flake, flattened clusters (P) are visible. five times improved selectivity toward the preferential production of cyclohexanone. Instrumental TEM, STM, and STS Setups. Besides the STS and STM investigations, transmission electron microscopy (TEM) images of the prepared catalysts were taken with a Phillips EM 400 T microscope at Bayer AG Leverkusen, which also included the option of carrying out energy-dispersive X-ray spectroscopy (EDX). Two different microscopes were used for the scanning probe investigations. Most of the STM images were taken with a homebuilt “beetle”-type scanning tunneling microscope operating in air. These images constitute the data set for the topographical analysis which will be discussed later on. Since this home-built scanning tunneling microscope did not allow us to carry out any spectroscopy investigations, the STS measurements were done with a commercial AFM/STM setup (Omicron Vakuumphysik) also in air. In all cases electrochemically etched Pt/Ir(90/10) wires were chosen as tunneling tips. The preparation method for the tips, which consists of two successive etching steps in 2.0 M KOH solution, is very similar to the one described by Musselman et al.21 With the Omicron scanning tunneling microscope two kinds of spectroscopy are available: (1) After or during a topographic scan a spectroscopic curve is registered at a defined position on the sample. In the following this mode will be called the “singlepoint spectroscopy” mode. (2) During an STM scan spectroscopic curves are registered at a number of points, forming a grid across the scanned area (“grid spectroscopy” mode). In principle, several kinds of tunneling spectroscopy are possible,22 but in the two modes described above only one kind was used. Namely, I(V) curves with a bias voltage scan from -1.5 to +1.5 V were taken while the distance between tip and sample was kept constant. From these spectra the respective conductance curves (dI/dV versus V) were generated by numerical differentiation and assigned to the respective surface points. (21) Musselman, I. H.; Russel, P. E. J. Vac. Sci. Technol., A 1990, 8 (4), 3558. (22) Bonnell, D. A. Scanning Tunneling Microscopy and Spectroscopy; VCH Publishers, Inc.: New York, 1993.
Sample Preparation. In order to make the powdery samples suitable for scanning probe studies, two different sample preparations were tested: (1) After the sample holder, consisting of a steel plate, was covered with a thin film of conducting glue, the powdery model catalyst was strewed on the glue. A few minutes later, when the glue had begun to dry, the powder was slightly pressed with another previously cleaned steel plate. Finally, any excess material was removed by simply shaking the sample holder. (2) For the second method of sample preparation a conventional IR tablet press (maximum pressure ) 9 tons/cm2) was employed to produce pressed pieces with a diameter of 13.0 mm and a thickness of approximately 1.0 mm. Subsequently, these pressed pieces were fixed with the above-mentioned conducting glue on the sample holder. Depending on the chosen sample preparation, a morphological change of the cluster structures could be observed. The ratio between the width and the height of the detected palladium clusters was determined from line profiles. For clusters on unpressed powdery samples, which were glued to the sample holder, the average ratio was significantly smaller than that for particles on pressed tablets with identical Pd coverages. As an example, Figure 2 shows a 29 nm × 29 nm large STM image of such a pressed sample with several Pd clusters (as identified spectroscopically; see below). Most of them, in particular those on the lower terrace, are of a spherical shape (marked by an S), but others on the upper terrace seem to be flattened, as verified by a reduced height (P). In some cases the width-to-height ratios for clusters on pressed samples were up to 10 times larger than those from the nonpressed ones. Thus, an influence of the pressing process on the cluster morphology cannot be excluded, in agreement with other cases where morphological changes due to mechanical pressure have been observed. For instance, Manivannan et al. found atomically resolved 50 nm2 large areas of (111)-oriented monocrystalline facets on a polycrystalline silver wire only after a pressure treatment.23 Without this treatment no such monocrystalline facets were detected. Atamny et al. also suppose an influence of a press treatment on the structure of their carbon substrate.24 (23) Manivannan, A.; Cabrera, C. R. Appl. Surf. Sci. 1993, 72, 435.
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Figure 3. TEM image (260 nm × 180 nm) of RFL graphite with a palladium load of 1.0 wt %. Two Pd clusters are marked by arrows. In order to exclude such an influence on the morphology of our Pd clusters, only nonpressed samples were used for all further investigations. Several hundred STM images were taken in order to enable a statistical analysis of the cluster shapes and their distribution as a function of the respective total Pd load. All images were obtained in the constant-current mode with bias voltages between 20 and 600 mV and typical tunneling currents between 0.5 and 2.0 nA. Variations of the scan parameters within these ranges did not lead to any qualitative changes of the images. The first part of the following section focuses on the various structures observed in these images and their identification by means of STS. The second part is devoted to the results of a statistical analysis of the cluster shapes.
Results and Discussion Chemical Identification. Figure 3 shows a typical 260 nm × 180 nm large TEM image of RFL graphite with a Pd load of 1.0 wt %. The individual Pd clusters (marked by arrows) appear as black dots with a lateral size between 2 and 15 nm whereas the graphite essentially forms a uniform background of different darkness depending on the thickness of the underlying graphite plates. The identification of the black dots as Pd clusters was performed by EDX measurements. Most clusters in Figure 3 are fixed along the graphite step (edge between bright and dark parts of the picture); fewer particles seem to be located away from any graphite step. STM images of the same model catalyst also exhibit both types of structures. Figure 4a shows an example of pure RFL graphite without Pd coverage; the layer structure of the graphite substrate is clearly visible. On samples with Pd deposition, additional spherical particles are observed (Figure 4b). Since their lateral extension (24) Atamny, F.; Kollmann, H.; Bartl, W.; Schlo¨gl, R. Ultramicroscopy 1993, 48, 273.
(1-8 nm) is similar to that in the TEM images, these structures are assigned to Pd clusters. On all samples conglomerations of these clusters could be detected, but no systematic dependence between the probability of their occurrence and the given Pd concentration was found. Instead, with increasing Pd concentrations the STM images showed a change of cluster shape. A detailed discussion of this topic will be given later on. Besides the graphite flakes and the Pd clusters, which both can be identified because of their distinct morphology, two additional structures were detected, namely, platelike objects with circular shapes up to 30 nm diameter and heights between 1 and 3 nm (Figure 5a) and diffuse structures like those in Figure 5b in the lower right corner and at the top of this STM image (marked by arrows). Under the conditions (air atmosphere) deliberately used in this work, contamination cannot be excluded. It is, thus, impossible to assign especially the latter two observed structures to palladium or graphite merely on the basis of their morphologies. However, because of their different electronic structures, a distinction between palladium and graphite by STS measurements is possible. In order to perform such identifications, I(V) measurements were taken at individual points on bare graphite plates as well as on palladium clusters. Figure 6 gives an example of such a “single-point spectroscopy” measurement. In the upper part of Figure 6 an STM image showing graphite flakes and steps is visible. Additionally, a 28 nm large conglomeration of clusters is located in the lower left corner of the image. The lower part of Figure 6 exhibits three conductance curves detected in the same scan area. I(V) spectra on clean graphite areas are reproducibly much narrower on the V axis than those on Pd clusters. Thus, the respective conductance curves (dI/dV versus V) calculated from these I(V) spectra have different opening angles, as can be seen in the lower part of Figure 6.
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Figure 4. (a) STM image (210 nm × 240 nm) of pure RFL graphite. (b) STM image (62 nm × 62 nm) of RFL graphite with a palladium concentration of 1.0 wt %.
Additionally, the conductance curves taken on Pd clusters show some fine structure between (0.5 and (1.2 eV relative to the Fermi level EF. These features are more likely due to a Coulomb blockade effect25,26 rather than to quantum size effects.11 The above results are in perfect agreement with those of Clark et al.,6 who performed STS studies of vapordeposited Pt clusters on HOPG. Also these authors found that the I(V) curves measured on the graphite are much narrower on the V axis than those on the metal particles. In the following the integral under a conductance curve between two fixed limits and not the respective opening angle is used as a criterion for a distinction between palladium and graphite. Under the very rough ap(25) Dubois, J. G. A.; Gerritsen, J. W.; Shafranjuk, S. E.; Boon, E. J. G.; Schmid, G.; van Kempen, H. Europhys. Lett. 1996, 33, 279. (26) Scho¨nenberger, C.; van Houten, H.; Donkersloot, H. C. Europhys. Lett. 1992, 20, 249.
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Figure 5. (a) STM image (80 nm × 80 nm) containing platelike structures on RFL graphite with a palladium concentration of 0.1 wt %. (b) STM image (100 nm × 100 nm) of diffuse structures (marked by arrows) on Edelgraphite with a palladium load of 1.0 wt %.
proximation that the tunneling resistance R can be treated as an Ohmic one, the value of this integral represents the reciprocal value of the tunneling resistance: +U dI dU ) ∫-U ∫-U+U dU 0
0
0
0
dI )
∫-U+U R1 dU ) 0
0
2U0 1 ∝ R R
According to this equation, a large value of the integral indicates an area with a relatively low tunneling barrier while a low value of the integral is found at sites with a relatively high tunneling barrier. By using the “grid spectroscopy” mode described in the instrumental section, a two-dimensional visualization of the spectroscopic data is possible. Each grid point where an I(V) spectrum was detected is assigned its respective integral value, with the obvious correlation that a larger work function usually
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Figure 6. STM image (100 nm × 100 nm) of RFL graphite with a palladium concentration of 1.0 wt % and three conductance curves detected within the same scan area.
corresponds to a larger barrier height. In such a “chemical map”, graphite patches always appear brighter than palladium clusters because polycrystalline palladium has a work function of 5.5 eV,27 which is 0.5 eV higher than the work function of graphite (5.0 eV).28 The comparison of such “chemical maps” with the topographic pictures of the same region enables an assignment of all observed structures. Figures 7 and 8 show two examples of this identification procedure. Figure 7a exhibits graphite layers and one step running from the upper left to the lower right corner of the image. In the respective spectroscopic image (Figure 7b) the step edge is also visible because at a step the work function is lower than on a flat graphite region due to the disturbance of the semimetallic band structure of graphite; the step appears as a bright stripe in the “chemical map”, whichsin this caseshas an 81 times lower resolution than the topographic image. Such a graphite step is also visible in the lower right part of the images in Figure 8 (marked by an S). In this case the spectroscopic grid (Figure 8b) is only 25 times more coarse than the STM image (Figure 8a). Besides the graphite step (S) and the bare graphite regions (C), two kinds of palladium deposits are visible: clusters with lateral dimensions of about 10 nm (Pd) and a palladium seam decorating one of the graphite steps (Pd(S)). This elemental identification is possible because both structures appear in the STM image as protrusions and in the “chemical map” darker than the graphite. Many such pairs of spectroscopic and topographic images also clearly show that the above-mentioned platelike structures are identical (27) Eastman, D. E. Phys. Rev. B 1970, 2, 1. (28) Venkateswaran, N.; Sattler, K.; Mu¨ller, U.; Kaiser, B.; Raina, G.; Xhie, J. J. Vac. Sci. Technol., B 1991, 9 (2), 1052.
Figure 7. (a) STM image (50 nm × 50 nm) of RFL graphite with a palladium load of 1.0 wt %. (b) Corresponding spectroscopic image (“chemical map”).
to graphite flakes while the so-called diffuse structures consist neither of graphite nor of palladium. The latter always appear brighter than graphite in a chemical map, and therefore they are probably due to impurities. Analysis of Cluster Shape. Having shown the possibility of an identification of the observed structures even on powdery samples by means of STS, the last part of this article reports about a statistical analysis of the Pd cluster shapes. Although the STS and the STM measurements were performed on two different kinds of graphite powder, the following results refer exclusively to model catalysts based on RFL graphite, because these samples expose more flat surface regions. As a consequence, the number of meaningful images is larger, resulting in better statistics. In fact, roughly 400 images were taken on the model catalyst based on RFL graphite with three different palladium concentrations, and the size of all clusters visible in these images was determined by line profiles.
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Figure 9. Histogram showing the size distribution of clusters on RFL graphite with 0.1% palladium.
Figure 10. Histogram of the width-to-height ratio of the same clusters as used for the histogram in Figure 9.
Figure 8. (a) STM image (100 nm × 100 nm) of RFL graphite with a palladium load of 1.0 wt %. (b) Corresponding spectroscopic image (“chemical map”). Table 1. Summary for Three Different Pd/Graphite Model Catalysts (Samples 1, 2, and 3) of Their Respective Pd Concentrations, the Total Scanned Area, and the Number, the Average Lateral Size, and the Average Width-to-Height Ratio of the Characterized Clusters Pd conc (wt %) scanned area (µm2) no. of characterized clusters avg lateral size (nm) avg width-to-height ratio
sample 1
sample 2
sample 3
0.1 5.58 215 2.51 1.2
1.0 4.39 346 2.76 1.6
5.0 1.42 233 3.49 2.1
In the case of conglomerates the individual particles were measured separately. Table 1 contains for three different model catalysts with the given Pd concentration the total scan area of all corresponding images, the number of clusters which were characterized by a line scan, their average lateral size, and the average width-to-height ratio.
Figure 9 and 10 show detailed histograms based on the data set of the clusters on sample no. 1 (see Table 1). Figure 9 reflects the lateral size distribution of the detected clusters while Figure 10 displays the ratios of width to height. The clusters on this model catalyst with 0.1% Pd coverage have an average lateral extension of 2.51 nm and a quite spherical shape, as demonstrated by an average width-to-height ratio of 1.2. As reflected by the numbers in Table 1, these values do not dramatically change by enlarging the palladium concentration by a factor of 10. In this case the clusters have an average size of 2.76 nm (see also Figure 11, which shows the corresponding size distribution) and the average width-toheight ratio is shifted to 1.6, with 2/3 of the particles having width-to-height ratios between 0.6 and 1.6 (black bars in Figure 12), representing once again a nearly spherical shape. It should be mentioned that the particle dimensions measured here are comparable to those of Pd clusters which were deposited on an HOPG crystal from a colloid solution by an electrophoretical process29 but quite different from the sizes of vapor-deposited clusters.30 An interesting aspect becomes visible if the data set for the histogram in Figure 11 is reduced. Including exclusively clusters with lateral sizes less than 4.0 nm (white bars in Figure 12), only those particles with width-toheight ratios larger than 2.8 are noticeably reduced. Hence, it follows that beyond a certain cluster size the width(29) Breuer, N. Ph.D. Thesis, University of Bonn, 1995. (30) Humbert, A.; Dayez, M.; Sangay, S. J. Vac. Sci. Technol., A 1990, 8 (1), 311.
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Figure 11. Histogram showing the size distribution of clusters on RFL graphite with 1.0% palladium.
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Figure 13. Histogram of the width-to-height ratios of clusters on RFL graphite with 5.0% palladium. Black bars represent the complete data set, and white bars show the distribution for the reduced data set, including clusters with lateral sizes less than 4.0 nm only.
palladium loads, clusters with diameters below 1.0 nm are rare. Furthermore, clusters of larger lateral size tend to have a larger ratio of width to height; that is, while the smaller clusters (
