Distribution of the particle sizes

From the slopes of the straight lines, the strain distribution (fi2(/)) is obtained. Furthermore, knowing the shape of the particles, it is possible to have the distribution of the particle sizes [39,40]. 

The distribution of the particle size must be as tight as possible, especially for hard materials such as alumina. A typical particle size distribution curve for alumina used in tungsten slurries is shown in Fig. 2a (data taken by the laser scattering method). However, from time to time the particle size distribution in a slurry may be out of control, so that a long tail will appear at the large particle end (Fig. 2b). These large particles may become a source of CMP scratches. 

Numerous techniques have been applied for the characterization of StOber silica particles. The primary characterization is with respect to particle size, and mostly transmission electron microscopy has been used to determine the size distribution as well as shape and any kind of aggregation behavior. Figure 2.1.7 shows a typical example. As is obvious from the micrograph, the StOber silica particles attract a great deal of attention due to their extreme uniformity. The spread (standard distribution) of the particle size distribution (number) can be as small as 1%. For particle sizes below SO nm the particle size distribution becomes wider and the particle shape is not as perfectly spherical as for all larger particles. Recently, high-resolution transmission electron microscopy (TEM) has also revealed the microporous substructure within the particles (see Fig. 2.1.8) (51), which is further discussed in the section about particle formation mechanisms. 

P(r) can be transformed into a distribution of the particle size as defined by the hydrodynamic radius Rh. But only for TDFRS, and not for PCS, a particle size distribution in terms of weight fractions can be obtained without any prior knowledge of the fractal dimension of the polymer molecule or colloid, which is expressed by the scaling relation of Eq. (39). This can be seen from the following simple arguments ... 

However, TEM measurements performed on a Pt0 83Sn017/C (Figure 9.15) indicated that the increase of the metal loading on the carbon support led to the formation of a multimodal distribution of the particle size. Then, to overcome this problem, colloidal methods were also developed in our laboratory. 

The frequency distribution of the particle size is related to the number of particles eluting at volume v as follows ... 

Packing materials are characterized by the average diameter of their particles and the distribution of the particle size around the average value. 

Various compounds have been prepared by solvothermal reactions metals, metal oxides, chalcogenides, - ° nitrides, - -" phosphides, open-framework structures, - oxometalate clusters, - organic-inorganic hybrid materials, - - and even carbon nanotnbes. - Most of the solvothermal products are nano- or microparticles with well-defined morphologies. The distribution of the particle size of the prodnct is nsnally qnite narrow, and formation of monodispersed particles is freqnently reported. - When the solvent molecules or additives are preferentially adsorbed on (or have a specific interaction with) a certain surface of the products, growth of the surface is prohibited and therefore products with unique morphologies may be formed by the solvothermal reaction. - - Thus nanorods, wires, tnbes, and sheets of various types of products have been obtained solvothermally. 

Cascade Impactor Characteristics. If the cascade impactor is to be used to obtain information on the diameters of particles in the atmosphere, then the distribution of the particle sizes on each stage must be known. Two approaches were used to obtain these data. The first used an empirical equation derived for this impactor (26,27,28) ... 

The uniform distribution of the particle size (Fig. 93) and also the (partly) spherical particle structure (Fig. 94 and 95) make copovidone free flowing and easy to handle in dry processes. 

Alkalinity also has an important influence on the crystallization rate of zeolites. A remarkable example is the crystallization of zeolite A (LTA) from the precursor gel with a batch composition of 5Na20 Al203 2Si02 (100-200) H20.[13] Figure 3.8 shows the effect of different alkalinity (H2O/Na2O=20, 30,40) on the crystallization rate (including induction period and growth rate) and particle size of the product. Clearly, with an increase of alkalinity the crystallization process is speeded up, the particle size is decreased, and the distribution of the particle size is narrowed due to an increased nucleation rate and an increased polymerization rate between polysilicate and aluminate anions. 

Particle size distribution (PSD) is another unique feature of crystals. Crystals have different shapes and different sizes. PSD function is a very effective way to describe the distribution of the particle size of crystals over a wide range of sizes. Although crystals have a three-dimensional length, the one-dimensional PSD function is frequently used in practice. Extending the one-dimensional PSD function to two-dimensional or three-dimensional PSD functions may be closer to reality. But these functions are definitely more complex, and their advantages over the one-dimensional PSD function are not always apparent. 

Many works have been devoted to investigate the deactivation causes of the supported palladium catalysts in methane oxidation [13,21-23]. The inhibition of the catalytic sites by water through the formation of palladium hydroxide [21], the change in the distribution of the particle sizes [13], the extensive oxidation of the palladium oxide [22]... 

It is now seen that the fluorescence lifetime measurements on a single particle are much more informative than the similar measurements on a packed or suspended sample in a conventional cell. In fact, when the distribution of the particle size is rather broad, our technique will allow us to differentiate particle-size dependent phenomena from the others. 

The structured absorption spectrum in the case of CdS (Fig. 3a) indicates the existence of a narrow distribution of the particle sizes. The maxima in the absorption spectra represent excitations of an electron from the valence band to the first and the second excited state (ref. 20). 

The value of x is used as the average particle size of the powder, while r is a measure of the spread in the distribution of the particle size. In a random (Gaussian) distribution, about two thirds of the particles have sizes within the range of x s. 

The photocatalytic properties of a semiconductor depend on the position of the energetic levels, on the mobihty and mean lifetime of the photogenerated electrons and holes, on the hght absorption coefficient and on the nature of the interface. Moreover, the photoactivity depends on the methods of preparation of the powders which allows varying many physico-chemical properties of the semiconductor as the crystalline structure, the surface area and the distribution of the particle size. 

After sulfidation, no change in the distribution of the particle size is evidenced some large particles coexist along with a population of evenly spread-over clusters. EDX analysis was performed over several zones of variable area in order to determine the sulfur-to-nickel ratio as a function of the localization. The resulting data are summarized in figure S. 

As example, the GPC trace of CSi in toluene is presented in Fig. 2, which shows a monomodal, narrow distribution of the particle sizes. 

Qi is the cumulative surface area distribution of the particle sizes. From this the material loss of a size fraction can be deduced as... 

The investigations are carried out in a ISO mm diameter column filled with plastic Hiflow packing Type 15 PP, in which a suspension of Ca(OH)2 or CaCOa is circulating by means of a circulation pump. The gas, mixture of air and CO2 wifti a constant concentration for ch experiment, is preliminary humidified in an additional packed column, to prevent evaporation in the investigated apparatus. The distribution of the particle size is presented in Fig. 1. 

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