Crystallite shape

We have studied the effea of preparation procedure, crystallite shape and size, and oxidation conditions on the oxidation behavior of silicon micro- and nanopowders. The oxidation process is shown to occur in two steps, with a transition at a certain thickness of the oxidized layer, which depends on the oxidation time, particle shape, and particle size. The composition and physicochemical properties of the oxide films have been detennined in relation to the shape and size of the silicon particles. The results indicate that the silicon micro- and nanopowdeis differ in oxidation mechanism from singlecrystal silicon. 

Crystallite shape transformations, due to adsorbed reactants, may affect the steady-state kinetics of catalytic reactions. Such effects can be studied phenomenologically by employing the Wulff rule [39] in order to find the optimum crystallite shape. The use of this rule implies that the crystallite reshaping time scale is shorter than the experimental time scale. The latter can be very long in practical systems. 

It is not expected to be significant because of the three-dimensional metal oxide framework (see Figure 6.32), and not a layered structure as was always the case in the three previous examples. Yet the obvious anisotropy of the crystallite shapes (see the inset in Figure 6.31) suggests that the possibility of a complex preferred orientation cannot be completely excluded. 

Jf-Ray Methods. - A -ray line-broadening is often used to estimate the mean size of supported metal crystallites and introductory accounts of the technique in relation to catalyst examination are available. Recently, more detailed information is being extracted, e.g., the distribution of crystallite size, the presence of strain, and an indication of crystallite shape. The crystallite size distribution obtained from X-ray line-profile analysis can be complicated by spurious oscillations. A method for the smoothing of crystallite size distribution by use of a least-squares procedure with a stabilization scheme has been described (with references to other methods). One such correction procedure was appUed to obtain crystallite size distributions in... 

Pt/Si02,Al203 H2, N2, CO I Crystallite shape and surface free energy depend on 850-1200°C 1 atm high temp, annealing produces spherical particles SAM, SEM, 1 with (100) and (111) facets. N2 has little effect in H2 theoretical calcns. 1 (100) facets grow in CO Pt (210) facets grow. 37... 

Surface adsorbates and adatoms serve to restmcture surfaces, especially at high temperatures. At sufficiently high temperature, equilibrium crystallite shape and surface free energy vary with atmosphere. Metal clusters and crystallites are observed to form epitaxial layers on supports this epitaxy can contribute to a stronger metal-support interaction. 

This Et has the same signification as the defined below from the Fourier analysis. In both cases, the true mean size is the product of the apparent dimension by the Scherrer constant relative to the variance, K . Tournarie and Wilson have tabulated K for different crystallite shapes as a function of the Miller indices hkl. 

The expression is different for other (hkl) and crystallite shapes, thus providing intensity profiles with different width and shape. 

The SEM is a powerful tool for study of overall topographySample preparation is not demanding, so that practical catalysts arc easily handled. Resolution limitations, however, restrict the technique to crystallites larger than S nm in size. Above this level, crystallite shape, size, and size distributions are easily obtained. SEM investigations have been made on many systems and are useful, not only in crystallite characterization but also in pore structure sludies. ... 

A more precise analysis and characterization of the M0O3 crystallites shape have shown that in fact the better plane for propene oxidation to acrolein corresponds to the (IkO) plane as schematised in fig. 1 [7]. It is then suggested that the propene activation (H abstraction) into the 3t-allyl intermediate occurs on the side (100) plane while the O atom insertion occurs on the (010) basal plane. As a matter of fact it is worth noting that due to the layered structure of M0O3, the lattice oxide ions are much more labile in the (OkO) plane than in the others. Recently such a structure sensitivity was also derived for the partial oxidation of methane to formaldehyde 8],... 

Figure 6.6 The effect of crystallite shape on the form of a diffraction spot (a) square or cube (b) sphere (c) elliptical needle (d) thin film...

It should also be mentioned, that crystallite shape transformations due to adsorbed reactants may affect the steady-state kinetics of catalytic reactions. 

Degree of polarization (nonresonant photo excitation) < 0.2 decreases with increasing detection wavelength (Cullis et al. 1997 Bisi et al. 2000) Can be anisotropic (effect of crystallite shape)... 

Ruthven, D.M., and Loughlin, K.F., Effect of crystallite shape and size distribution on diffusion measurements in molecular sieves, Chem. Eng. Sci., 26(5), 577-584 (1971). 

It is well known that the introduction of a larger eation such as Cs in the zeolitic framework can cause a modification on the zeolite framework and therefore on the XRD pattern. A sharp decrease in intensity of the diffraction lines situated at low angle values is observed (fig.l). The crystallite shapes of starting NaFAU particles (not shown here) are multi facetted spherulites, which are not altered by ion exchange. In the case of HFAU, it seems that a partial breakdown of the zeolite lattice occurs. 

The first attempts in the 1960s and 70s proposed to predict elastic properties by using simple analytical models derived from the analysis of fiber-filled media. Takayanagi [210] described the elastic behavior of miidirectional oriented processed fibers. Halpin and Kardos [211] proposed to use the Halpin-Tsai model [212]. Phillips and Patel [213] also applied this model to PE with an adjustable paiameter linked to the crystallite shape ratio. However, these models require the assmnptiou that lamellae be regarded as fibers. Moreover, they are known to fit only the experimental data at low volume fr actions of filler and this is not the case for semicrystalline materials, for which the crystallinity can often reach 60 to 70%. 

Considering PET at ambient temperature which shows a low contrast in terms of elastic behavior between amorphous and crystalline phases, several models have proven to provide similar results (Figure 1.20). Here, micromechanics models are only slightly sensitive to the crystallite shape ratio parameters. It explains why models with no crystallite shape ratio, such as the U-inclusion model [183], still apply. Therefore, the obtained results in the case of glassy amorphous phases ai e contrasted. In terms of absolute values, the Yomig s modulus is decently approached by the models but in terms of the shape of the cm ve, the convexity of the experimental data is poorly represented. 

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