Clustered particle distribution

One of the recent advances in magnetic studies is that it enables not only the estimation of the average volume v of clusters from the LF and HF approximations of the Langevln function, but also enables to compute particle size distribution based on an assumed function. By judiciously combining the parameters of the Langevln and of the "log normal function, we obtained a particle (cluster) size distribution of Y Fe203 in ZSM-5. The essential features of such computation are shown in Fig. 6. 

Experiments with radioactive cluster compounds ( Au) allowed precise analyses of the particles distribution in the cells. In case of melanoma BLM it was found that 57.5% of the radioactive gold was in the cytoplasma... 

The cluster size distribution in the limit of small mass [x < s(f)] depends on the properties of the agglomerates undergoing fragmentation. If infinitesimal particles are formed on a single breakage, that is, b(r) r", then... 

Thus, we plot M(x,t)IMi vs xls(t). As noted earlier, the cluster size distribution and the first moment of the size distribution are averaged over the entire journal bearing. As indicated by the behavior of P in Fig. 39b, the cluster size distribution becomes self-similar when the average size is about 10 particles per cluster. 

Kim and Thompson—site blocking by formates/carbonates over Au/ceria catalysts linked to deactivation. Kim and Thompson437 reported on the deactivation of Au/ceria catalysts. The ceria was prepared by the decomposition of cerium carbonate (BET SA ceria calcined at 400 °C = 203 m2/g) or obtained from Rhodia (BET SA ceria calcined at 400 °C = 155 m2/g). Au was added by precipitation of HAuC14, resulting in a particle distribution between 1 and 10 nm, with the majority of clusters between 2 and 7 nm, as examined by HR-TEM. The experimental catalyst was tested with respect to the Sud-Chemie water-gas shift catalysts, consisting of Cu-Zn-Al with surface area 60 m2/g, and results are reported in Table 87. 

The particular striking discrepancy between the exact and the Smolu-chowski solution is observed, however, for the non-uniform, clustered distribution of particles A (Fig. 5.17) [89] - in a line with what was said above (Section 3.2) about shortcoming of the use of Kirkwood s superposition approximation for initially strongly correlated particle distributions. 

Fig. 5.17. Exact results (full curves) and Smoluchowski theory (dashed curves) for the A + A —> 0 reaction in one-dimension for (a) random particle distribution (curves 1), equidistant particle distribution (curves 2) and clustered distribution (b) [89],...

In the case of diffusion-controlled A + B —> 0 reaction distinctive spatial distributions of reactants observed in computer simulations (e.g., [21]) are qualitatively the same as were presented earlier in Figs 1.20 and 1.21. Quite similar aggregation of similar particles into loose clusters occurs in agreement with a distinctive block-structure characterized by the diffusion length Id = f Dt shown in Fig. 2.8. When the reaction is controlled by the particle diffusion, these clusters (domains) are less pronounced since diffusion is known to smooth nonuniform particle distribution created in a course of reaction. 

Figure 4.6a, b shows the substitutional carbon and SiC particle distributions, respectively in a cross section of the solidified ingot. It can be seen that the particle precipitation begins at the center, when the fraction solidified reaches about 30%. The SiC particles are clustered at the center-top region of the ingot, where the concentration of substitutional carbon is almost constant. This distribution pattern is due to the m-c interface shape, which is concave to the solid side throughout the solidification process. 

As a result, the substitutional carbon and SiC particle distributions are obtained in a cross plane of the solidified ingot as shown in Fig. 4.8. Both substitutional carbon and SiC particles are clustered in a smaller periphery-top region of the ingot. This indicates that we can control the distributions of impurities in the solidified ingot by optimizing the process conditions or furnace configurations. 

As an illustration, we consider the cluster-size distribution for a monodis-perse Lennard-Jones fluid (particle diameter a, interaction cut-off 2.5(t) at a rather arbitrary density 0.16monotonously decreasing function of cluster size at high temperatures, it becomes bimodal at temperatures around 25% above the critical temperature. The bimodal form is indicative of the formation of large clusters. 

It turns out to be possible to influence the cluster-size distribution by placing the pivot in a biased manner. Rather than first choosing the pivot location, a particle is selected that will become the first member of the cluster. Subsequently, the pivot is placed at random within a cubic box of linear size 5, centered around the position of this particle. By decreasing (5, the... 

The distribution of doublets at E>1019 3 eV (Fig.3c) is more isotropic. It is possible that at these energies the formation of doublets starts at the expense of superheavy nuclei fragmentation. To appreciate the origin of doublets we considered the distribution of showers parallel with the distribution of doublets (Fig3b) in the same energy interval. In the distribution of showers the some maxima are observed at b <3° (exceese of the number of showers relative to expected is 2.7g=(29-17.5)/, at 21°>b>15° etc. However, the maximum in the distribution of doublets is seen at b <3° only. This means that the maximum number of doublets appears where there is the exceed particle flux. Other maxima in the particle distribution are most likely formed by accident and therefore maxima from these directions in the distribution of doublets do not observed. So, the arrival directions of doublets (clusters) can be an indicator of cosmic rays anisotropy. It is important in the case when the cosmic ray anisotropy cannot be detected because of the small statistic. 

Figure 10.11. Cluster size distribution for I lO. particles in injection molded PP. [Data from Burke M, Young R J, Stanford J L, Plast. Rubb. Comp. Process. Appln., 20, No.3, 1993, 121-35.]...

When aerosol particles in the size range [ai er than 10 nm are present, the size distribution is composed of these particles and the equilibrium cluster size distribution. The mass concentration of foreign p irtidcs is normally many times greater than that of the clusters. 

The transmission electron micrograph represented in Figure 1 shows a typical carbon-supported precious metal catalyst. Activated carbon contains very small clustered particles beside carbon flakes. A flake is indicated in the micrograph. Precious metal particles are usually present only at the edges of the flakes. On the small carbon particles fairly uniform distribution of small precious metal particles has been achieved. Two clusters of platinum particles can also be seen in the micrograph of Figure 1. 

Further, a point-pattern analysis was applied. This is especially suitable for the quantification of particle distribution patterns [Tanaka et al., 1989], The nearest-neighbor center-to-center distance and effective coordination number (number of cell sides of corresponding Voronoi polygons) of dispersed particles were measured. For a ternary system, PPE/PA/rubber, TEM micrographs were analyzed to estimate the randomness and the degree of clustering [Hayashi et al., 1992]. 

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