Crystallite distribution

The mechanistic implications of the GPLE have been only partially discussed. Standard models cannot be used to justify the use of a steady-state distribution because they were developed using only aggregation kernels. However, there is no fundamental reason why steady-state configurations do not exist as shown by Puentes and Gamas [6] based on an analysis of the surface free energy corresponding to a crystallite distribution. 

When plotted versus crystallite size, independently of the support used, a similar crystallite size effect appears to exist for all three adsorbates— heats of adsorption increase somewhat as crystallite size decreases from 6 nm to below 2 nm. All Pd crystallite sizes were based on hydrogen chemisorption and the assumption of 1. 2 x 10 9 Pdam2-1 (f)). At this time we believe there is a possibility that the values reported for the most poorly dispersed samples—particle sizes of 10 nm and higher—may actually represent a bimodal crystallite distribution because of their preparation by sintering in H2. Consequently, the observed AH(aq) values would be higher than expected for large supported Pd crystallites. Characterization by TEM is now underway to better characterize these catalysts. Further study is necessary to determine the reasons for this apparent crystallite size effect on heats of adsorption, especially since the trend is opposite to that found in supported Pt catalysts (16.1J). 

Crystallite size, crystallite distribution, and crystallite perfection... 

As we have seen, the orientation of crystallites in a thin film can vary from epitaxial (or single crystalline), to complete fiber texture, to preferred orientation (incomplete fiber texture), to randomly distributed (or powder). The degree of orientation not only influences the thin-film properties but also has important consequences on the method of measurement and on the difficulty of identifying the phases present in films having multiple phases. 

Fig. 6. Size-distribution of metal crystallites on the surface of Co-silica made by precipitalion-ion-exchange method.

Similarly to the previously considered case of the first-order transitions, the above picture applies to a specific situation in which the sample exhibits just one type of crystallites, all of the same size, and where we neglect the effects of energetical heterogeneity that are bound to be present at the crystallite boundaries. In real samples one expects to find a distribution of the crystallite sizes, and hence more complex behavior. 

The effects due to the finite size of crystallites (in both lateral directions) and the resulting effects due to boundary fields have been studied by Patrykiejew [57], with help of Monte Carlo simulation. A solid surface has been modeled as a collection of finite, two-dimensional, homogeneous regions and each region has been assumed to be a square lattice of the size Lx L (measured in lattice constants). Patches of different size contribute to the total surface with different weights described by a certain size distribution function C L). Following the basic assumption of the patchwise model of surface heterogeneity [6], the patches have been assumed to be independent one of another. 

The quantitative assessment of the degree of crystallite orientation by x-ray examination is not free of ambiguity. From a comparative analysis [23] in which results obtained from the consideration of (105) and from three different variations of equatorial reflection were compared, the conclusion was that the first procedure can lead to underrated results, i.e., to the underestimation of the orientation. However, it can be assumed that this does not result from an incorrect procedure, but from ignoring the fact that the adjacent (105) reflex can overlap. The absence of the plate effect of the orientation is characteristic of the orientation of crystallites in PET fibers. The evidence of this absence is the nearly identical azimuthal intensity distributions of the diffracted radiation in the reflexes originating from different families of lattice planes. The lack of the plate effect of orientation in the case of PET fiber stretching has to do with the rod mechanism of the crystallite orientation. 

Figs. 2 and 3 shows typical SEM pictures and XRD patterns of crude VOPcs obtained at ISO °C for 4 h in the amventional and microwave synthrais. As shown in Fig. 2, the smaller particle size and nairowra size distribution are obtained in the microwave synthesis, compared to conventional one. From XRD results in Fig. 3, it can be c culated that the crystallite sizes of onde VOPcs obtained by the conventional and microwave synthesis are about 44 nm and 48 nm, respectively. Thus, the tact that particle size is snutller and crystallite size is larger in microwave sample, compared to conventional sample is probably caused by the microwave non-thramal eflfect [3]. 

Zinc sulfide, ZnS, has been epitaxially deposited by the dual bath approach on Au(lll) surface and studied by STM and XPS [48]. The first complete ECALE cycle resulted in the formation of nanocrystallites of ZnS randomly distributed across Au(l 11) terraces, on account of lattice mismatch induced strain between ZnS and Au(lll) - although the mismatch is only 0.13% for ZnS/Au(lll). Atomically resolved STM images showed the ZnS/Au(lll) monolayer to be sixfold symmetric. The average diameter of the crystallites was 10 5 nm and the apparent coverage 0.38. 

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