EM studies of the size of clusters: diameter and mass

As one of the major parameters of the nanocluster, size can affect many of its properties, from its melting point and atomic structure to the catalytic activity.41,52,53,58,110 Therefore, size measurement is always an important part of the study on the cluster. Because of the low resolution requirement, the cluster or nanoparticle size measurement should be the earliest function of the electron

microscopy in cluster study.

Figure 1.14 (a) Example electron microscopy image of the colloidal Au clusters. The magnification of the image is 50,000. (b) The size distribution of the colloidal Au clusters with the condition: 0.5ml sodium citrate (up), 1ml sodium citrate (middle) and 2.5ml sodium citrate (lower). (c) The size distribution of colloidal Au clusters with different dilutions of reagents.¹¹¹ The figure is from ref [111].

In 1951, Turkevich et al. used electron microscopy to study the colloidal cold cluster’s sythesis.¹¹¹ They detected the variation of the cluster size distribution with the different sythesis conditions. In the sodium citrate sols synthesis, the cluster’s size is significantly affected by the synthesis temperature, sodium citrate amount and reagents dilution. The decreasing synthesis temperature results in a slightly smaller average cluster size, from ~20nm at 100^oCto ~18nm at 70 ^oC. As the amount of the sodium citrate decreases, the average cluster size decreases first, then rapidly

increases. For the reagent dilution’s effect, the cluster mean size increases with the diluting reagents. The example of the gold cluster electron microscopy image and the distribution with the variable conditions are shown in Figure 1.14.¹¹¹

Figure 1.15 (a) A HAADF-STEM image of a Pd cluster supported on TiO2, where the flat shape can be clearly seen. (b) Single crystal X-ray crystallography determined the atomic structure of Au38(SR)18 cluster, showing the aspherical feature.¹⁰⁷ The figure is from ref [107].

The diameter measurement by electron microscopy is a very common and fundamental method to determine the size now. It has been successfully employed in many different studies on nanoclusters. However, there is a significant disadvantage of this method. The diameter reflects that the cluster size is based on the assumption that the nanocluster has a spherical 3D shape. It works well for most situations,

however in some special cases, the cluster cannot be treated as spherical. Many studies reported that the support clusters (supported catalysts) tend to be flat on the support materials (as shown in Figure 1.15(a)). It can be recognized when we observe them on the side, but if the view point is above the clusters, we cannot easily identify whether they are spherical or flat. Another case is the very small cluster (<100 atoms).

In this size region, the cluster’s atomic structure is not always spherical, and the influence of the surface atoms on the diameter cannot be ignored. The example is shown in Figure 1.15(b).¹⁰⁷

Figure 1.16 (a) HAADF-STEM image of Re8 clusters. (b) The integrated HAADF intensity distribution of the Re8 clusters. The figure is from ref [112].

To overcome these drawbacks, a new method of measuring the nanocluster’s size is required. With the application of the field emission electron source, the scanning transmission electron microscopy (STEM) became a more practical technique. One of the most interesting parts of this technology is the HAADF imaging. In this

incoherent imaging mode, the intensity is only due to the high angle scattered electrons and it is dependent on the atomic number Z, so this mode is also called the Z-contrast imaging. So, for a mono-metallic nanocluster, its integrated HAADF intensity can directly reflect its mass. Yang et al. successfully employed the first HAADF-STEM analysis on the supported cluster in 1996.¹¹² The integrated HAADF intensities of Re clusters were measured, and the result matched well the theoretical calculation. The long time exposure was utilized to confirm the high stability of the Re6 clusters under the electron beam. Figure 1.16 shows the example HAADF image of Re8 clusters and the corresponding integrated HAADF intensity distribution.

Figure 1.17 The representable HAADF-STEM image of size-selected: (a) Au147, (b) Au2057, and (c) Au6525 clusters. (d) The cluster’s integrated HAADF intensity as a function of cluster size. The inset is the log fit of the HAADF intensity against the cluster size.¹¹³ The figure is from ref [113].

With the development of the size-selected cluster formation, the relationship between the integrated HAADF intensity of the clusters and the corresponding mass was studied by Young et al.¹¹³ They used the HAADF-STEM to image the size-selected Au clusters with a size range up to 30000 atoms. The integrated HAADF intensities of the clusters were measured after the background subtraction, due to the resolution limit, the measured area is big enough to include all the atoms in the HAADF intensity counting. The integrated HAADF intensity of the clusters as a function of the cluster size (number of atoms) is shown in Figure 1.17. We can see that the relationship between the integrated HAADF intensity and the cluster size displays good linearity in the small size range. For the bigger size clusters, their integrated HAADF intensity increases a little slower than the smaller clusters, which is mainly due to the multiple scattering.¹¹³ A similar study was carried out by Zhiwei et al, who used the different elemental size-selected cluster (Au and Pd) to find out the dependency of the integrated HAADF intensity on the size and element. The quantitative STEM analysis on the Pd cluster shows a good linear relationship between the integrated HAADF intensity and the cluster size. Such a similar linearity also suggests the relationship is not element-specific.¹¹⁴

The finding of the linear relationship between the cluster’s integrated HAADF intensity and size provides the possibility to use the known size clusters as the mass standards to calculate the other cluster size in the HAADF-STEM study. Zhiwei et al.

reported using the size-selected Au clusters as mass balances to weigh the monolayer-protected Au38 cluster.¹¹⁵ Three different sized clusters (Au25, Au38 and Au55) were utilized to eliminate the possible size effect on the quantitative analysis.

The ligand’s contribution on the integrated HAADF intensity must be taken account of. With the calibrated exponent “n” in the Zⁿ dependent intensity, the ligands’

contribution was calculated as 8.7 Au atoms. After the subtraction of the ligand contribution, the numbers of Au atoms in the monolayer-protected Au38 clusters were calculated to be 38.6±2.8, 38.4±2.9 and 37.5±2.9 with the corresponding Au25, Au38

and Au55 clusters, respectively, as the mass standard.¹¹⁵

Figure 1.18 Schematic of cluster weighing with size-selected clusters. (a) The monolayer-protected clusters and size-selected clusters were deposited separately on the same TEM grid. The representative HAADF-STEM images of (b) size-selected cluster and (c) monolayer-protected cluster. The integrated HAADF intensity distribution of monolayer-protected cluster with: (d) Au38 clusters, and (e) Au25

clusters.¹¹⁵ The figure is from ref [115].