Crystallite size, limited

CURRENT PROBLEMS IN STUDYING PHYLLOSILICATE EVOLUTION AT THE LOWER CRYSTALLITE-SIZE LIMITS OF MINERALS... 

Many studies have been made of the rates of water evolution from layer-type silicate minerals which contain structural hydroxyl groups (clays and micas). Variations in composition of mineral specimens from different sources hinders comparison of the results of different workers. Furthermore, the small crystallite sizes and poor crystallinity that are features of clays limit and sometimes prevent the collection of ancillary observations (e.g. microscopic examination and diffraction measurements). 

X-Ray diffraction has an important limitation Clear diffraction peaks are only observed when the sample possesses sufficient long-range order. The advantage of this limitation is that the width (or rather the shape) of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow, see for example the (111) and (200) reflections of large palladium particles in Fig. 4.5. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The two XRD patterns of supported Pd catalysts in Fig. 4.5 show that the reflections of palladium are much broader than those of the reference. The Scherrer formula relates crystal size to line width ... 

Anodization generally results in the formation of films with limited thickness, uncertain composition, defects, and small crystallite size. Thus, the barrier nature of the n-type semiconducting CdS film obtained in the previous manner makes it too thin to form the basis of Cu2S/CdS or CdTe/CdS solar cells by the normal dipping process. Heterojunction cells of low efficiency have, however, been made by anodization followed by vacuum deposition of the added layer (CU2S). 

What happens is that the crystallites melt and fuse into a small tip. If we do this carefully, we will have our "seed". The tip s small size limits regrowth of the remelted part to that of a single crystal. Then, when we return the seed to the melt, we can initiate the growth of a much Icurger single crystal, provided that growth-conditions are suitable. 

It is worth noting that within a range of 20 %, five different methods of analyzing the crystallite size, viz., (a) microscopic inspection, (b) application of Eq. (3.1.7) for restricted diffusion in the limit of large observation times, (c) application of Eq. (3.1.15) to the results of the PFG NMR tracer desorption technique, and, finally, consideration of the limit of short observation times for (d) reflecting boundaries [Eq. (3.1.16)] and (e) absorbing boundaries [Eq. (3.1.17)], have led to results for the size of the crystallites under study that coincide. 

The hydrogenation of para-substituted anilines over rhodium catalysts has been investigated. An antipathetic metal crystallite size effect was observed for the hydrogenation of /Moluidinc suggesting that terrace sites favour the reaction. Limited evidence was found for catalyst deactivation by the product amines. Catalysts with pore diameters less than 13.2 nm showed evidence of diffusion control on the rate of reaction but not the cis trans ratio of the product. 

In all films there is a distribution of crystallite diameters. An example is shown in Fig. 2 for the film with a specific weight of 0.12 fig cm-2. The smallest particles whose diameters can be measured in a micrograph (and then only very approximately) have diameters of about 10 A, and this is the lower size limit used in Fig. 2. However, particles smaller than this can readily be observed in the micrograph, and there is no doubt that this type of film contains some crystallites down to the limit of microscopic resolution (about 8 A in our case), and presumably beyond. However, their number appears to be relatively small. It is interesting to compare the specific film weight of these ultrathin platinum films with the amount of platinum per unit actual surface area of support for typical supported platinum catalysts. A typical supported catalyst would have 1% (w/w) of platinum on a... 

When both the component metals have reasonably high melting points, as in Pd-Rh alloys, then the variation of crystallite size with composition (60) is limited, despite the use of high substrate temperatures (400°C). 

Lc 1 nm or Lc>20 nm). Highly graphitic materials (<7002 within 0.335 -0.338 nm and Lc>30 nm) show some increase of the capacity when the lowest limit of d002 is achieved and Lc increases. The specific reversible capacity vs crystallite size or vs treatment temperature diagrams are often published. They look as smooth curves with a minimum within medium temperatures or medium crystallite sizes [7,11,17]. 

The activity of the Pt-exchanged catalyst for n-C f, transformation increases when the crystallites size increases, which was totally unexpected. External diffusional limitations cannot be invoked since the size of the grains of catalyst is the same. Moreover, this would lead to the opposite result. Other experiments showed that the activity of zeolite-... 

Zeolite crystal size can be a critical performance parameter in case of reactions with intracrystalline diffusion limitations. Minimizing diffusion limitations is possible through use of nano-zeolites. However, it should be noted that, due to the high ratio of external to internal surface area nano-zeolites may enhance reactions that are catalyzed in the pore mouths relative to reactions for which the transition states are within the zeolite channels. A 1.0 (xm spherical zeolite crystal has an external surface area of approximately 3 m /g, no more than about 1% of the BET surface area typically measured for zeolites. However, if the crystal diameter were to be reduced to 0.1 (xm, then the external surface area becomes closer to about 10% of the BET surface area [41]. For example, the increased 1,2-DMCP 1,3-DMCP ratio observed with decreased crystallite size over bifunctional SAPO-11 catalyst during methylcyclohexane ring contraction was attributed to the increased role of the external surface in promoting non-shape selective reactions [65]. 

Assuming that Ti(IV) is distributed statistically in all tetrahedral positions, it can be easily seen that even for crystallite sizes of 0,2 m the great majority of T1(IV) is located inside the pore structure. Assuming that every Ti(IV) is a catalytic centre with equal activity, diffusion limitations for molecules of different sizes should be observed. This is in fact the case. It has been shown [27] that the rate of oxidation of primary alcohols decreases regularly as the chain length increases, while for iso-butyl alcohol a sudden drop in the rate is observed. Also the reactivity order of olefins on TS-1 is different from the order observed with homogeneous electrophilic catalysts, while as already indicated very bulky molecules are unreactive when TS-1 is used as the catalyst. All these facts can only be interpreted as due to diffusion limitations of the larger molecules, which means that the catalytic sites are located inside the pore structure of the solid. 

Crystallite Size Effects upon AP Catalyst Selectivity. Previous studies have shown that with the pellet sizes investigated, gross particle size does not affect activity or selectivity. If there are diffusional limitations, they must be intracrystalline and therefore a function of the crystallite size of the zeolite component. 

The first spectrum could be recorded 25 s after admission of alcohol to the catalyst. For all the zeolite samples of various crystallite sizes (Table I) at 296 K, the adsorption was complete within 25 s for sec- and isobutyl alcohols. The dehydration process of these alcohols in the zeolitic pores was, however, slower. For a given alcohol (/ -, sec-, or iso-) the kinetics of water elimination were identical for catalysts of different crystallite sizes. This firmly establishes the absence of any diffusion limitation for dehydration for these three alcohols. 

For all four alcohols in the zeolitic catalysts with small enough crystallite sizes—when diffusion limitations also disappear—dehydration kinetics are well approximated by the exponental function, a fact that is explicable in terms of the unimolecular decay of molecules of butyl alcohol adsorbed on identical active sites. With isobutyl alcohol, for example, the rate coefficient k may be written... 

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