5Uniforme todo el perímetro

Diameter measurements were taken for all clusters with a circular projection under the electron beam. Due to the circular projection, the diameter measurement could be performed simultaneously with that of integrated intensity. By tracing the perimeter of the cluster, the area, A, of it can be determined easily via the program ImageJ. This area

can then be converted into a diameter measurement due to the relationship A = πr2, where r is the radius and is equal to half the diameter.

For clusters seen that did not have a circular projection an alternative method of defining the cluster shape was required. Within the literature, defining irregular morphology uses different methods. An interesting use of two dimensionless determinations is that used by Korolev and Isaac [137] in determining the roundness and aspect ratio of ice clouds. Here many irregular morphologies are seen so just using the aspect ratio of the structure does not give a true representation of ice cloud morphology. This is where the roundness value, β comes in; it is determined by:

β = 4Smeas πD2

max

, (4.18)

where Smeas is the area of the projection of the object and Dmax is the maximum

dimension of the object shape. Alternatively, Bele et al [138] defines the circularity of clusters as the equivalent circular circumference over the particle perimeter. Values for this range from 0 for totally irregular clusters to 1 for an ideal circular cluster. This study also utilised a computational method known as local adaptive threshold (LAT) to study many more clusters from TEM images than would normally be done using the by-eye by-hand method [138]. LAT used more complex methods to determine the cluster perimeters than is needed in Z-contrast imaging due to the nature of contrast for bright field images.

In this thesis, clusters seen to have non circular projections under the electron beam have been analysed using two methods, that of aspect ratio and cirularity. For the case of size selected Pd clusters the method used was to define the aspect ratio. In this case, the clusters were not irregular or asymmetric in projection, but all appear elongated along one axis. Therefore the choice of aspect ratio analysis is relevant as the results symbolise the magnitude of the deviation along the elongated axis. If circularity was used, then the resultant data would only signify the deviation from circular projection. For example, a cluster elongated along one axis may have the same circularity value as a cluster with a very asymmetrical projection, but where elongation has occurred in multiple directions. So circularity would not quantify the data for size selected Pd clusters in the correct manner. This data can be found in chapter 6. For Pd catalytic

particles investigated using the Jeol 2100F microscope, however, some were found to be very irregular in shape. In this case the aspect ratio measurement is not suitable as it would not represent the deviations away from either the defined x or y axis. Circularity is used in order to quantify the deviation from circular projection. Figure 4.21 displays examples of two clusters where both aspect ratio (a) and circularity (b) were required for different purposes.

Aspect ratio measurements were taken by drawing a multiline profile (11 lines) over a cluster’s shortest dimension but passing through the central point of the cluster. The line profile produced was a projection of the intensity over the length of the line and the edge of the cluster was easily visible due to Z-contrast making Pd easily distinguishable from the a-C support. This length was determined by taking 10th width full maximum at each end of the profile. The length value was displayed within the image processing software by positioning the mouse at the required spot, and then clicking and dragging it to the opposite end of the profile. This step was then repeated for the clusters longest dimension. The aspect ratio is given by the longest length of the cluster divided by the shortest length. Aspect ratios of 1 represent circularly projected clusters, ratios of 1.1 to 1.5 maybe thought of as egg-shaped in projection and values above this elongated. This type of measurement could be performed using both ImageJ and DM. Circularity measurements were calculated by taking the equivalent circular area of the particle and dividing it by the projected area of the particle. The perimeter of the particle was traced to obtain the projected area measurement and the circular projection was drawn surrounding the particle in question. This is best described by illustration and can be seen in figure 4.21 (b). The area inside the circle surrounding this cluster is the measurement taken.

For the measurement of atomic distances when analysing images taken with atomic resolution the program DM was used. A multi line profile can be drawn over atomic columns of the cluster seen in the image. The distance between the peaks of the atomic column profiles can then be measured using the same method as used to determine the length of the aspect ratio profiles.

Figure 4.21: HAADF-STEM micrographs of clusters (a) Pd10000and (b) Pd catalyst

particle on Al2O3taken with the Jeol 2100F with Cscorrector microscope. The cluster

in (a) is suitable for aspect ratio analysis. The cluster in (b) is suitable for circularity analysis. The circle shown in (b) represents the equivelant circular area of the particle.

See text for details.