Average particle-size estimations

As with other diffraction techniques (X-ray and electron), neutron diffraction is a nondestructive technique that can be used to determine the positions of atoms in crystalline materials. Other uses are phase identification and quantitation, residual stress measurements, and average particle-size estimations for crystalline materials. Since neutrons possess a magnetic moment, neutron diffraction is sensitive to the ordering of magnetically active atoms. It differs from many site-specific analyses, such as nuclear magnetic resonance, vibrational, and X-ray absorption spectroscopies, in that neutron diffraction provides detailed structural information averaged over thousands of A. It will be seen that the major differences between neutron diffraction and other diffiaction techniques, namely the extraordinarily... 

The average particle sizes estimated from the TEM are consistent with the values obtained from the XRD patterns. The indexed SAED pattern shown in Fig. 7(a) suggests the particles to be crystalline. The pattern could be indexed on the basis of the Fmlm space group. The HREM image of a 6 nm NiO particle, shown as an inset in Fig. 7(b), shows a lattice spacing of 2.09 A, corresponding to the interplannar distance between the (100) planes. 

The palladium dispersion on the activated charcoal (AC) was somewhat different when compared to that observed on the CNTs catalyst. On the activated charcoal, palladium was present in agglomerate shape instead of individual particles as observed on the CNTs, which led to a less homogeneous dispersion of the metal particles on the support. However, the average particle size estimated fi om TEM was similar to that of the palladium supported on the CNTs, i.e. 5 nm. 

Figure 22.1 shows the surface of Carbotron P (J) by scanning electron microscopy (SEM). X-ray powder diffraction (XRD) patterns of these carbons, measured on Rigaku RAD-C diffractometer with roter-flex and Cu-Ka radiation, are shown in Fig.22.2. The interlayer distances and the crystallite size factors (Lc) calculated from XRD(002) reflection using Schener formula" are given in Table 22.1. Figure 22.3 also shows the particle size distributions of these three carbons. The average particle sizes estimated from distributions are shown in Table 22.1.

The pelobischofite-surfactant mixtures emulsifying ability was estimated by measurements of the phase immiscibility time for standard oil in water emulsion. The measurements of emulsion particles size were also carried out. The experiments showed the essential increase of phase immiscibility time with the pelobischofite contents increase. Some decrease in average particles size of standard emulsion was also registered. The emulsifiability of other magnesium containing preparations was at least twice worse. 

Niobium oxide obtained by plasma chemical decomposition is an ultra-fine powder with a specific surface area, as determined by the BET method, of about 20-30 m2/g. The estimated average particle size does not exceed 0.1 pm. 

Figure 3.8. Kinetic data from molecular beam experiments with NO + CO mixtures on a Pd/MgO(100) model catalyst [70]. The upper panel displays raw steady-state C02 production rates from the conversion of Pco = PN0 = 3.75 x 10-8 mbar mixtures as a function of the sample temperature on three catalysts with different average particle size (2.8, 6.9, and 15.6 nm), while the bottom panel displays the effective steady-state NO consumption turnover rates estimated by accounting for the capture of molecules in the support. After this correction, which depends on particle size, the medium-sized particles appear to be the most active for the NO conversion. (Reproduced with permission from Elsevier, Copyright 2000).

A sludge is to be clarified in a thickener that is 50 ft in diameter. The sludge contains 35% solids by volume (SG = 1.8) in water, with an average particle size of 25 pm. The sludge is pumped into the center of the tank, where the solids are allowed to settle and the clarified liquid overflows the top. Estimate the maximum flow rate of the sludge (in gpm) that this thickener can handle. Assume that the solids are uniformly distributed across the tank and that all particle motion is vertical. 

In a batch thickener, an aqueous sludge containing 35% by volume of solids (SG = 1.6), with an average particle size of 50 pm, is allowed to settle. The sludge is fed to the settler at a rate of 1000 gpm, and the clear liquid overflows the top. Estimate the minimum tank diameter required for this separation. 

The specific surface area of a powder can be used to estimate the average particle size if the particle shape is known. 

The Pt/LTL [. ], Pt/LTL [0.47, small], Pt/ASA and Pt/HT catalysts all have highly dispersed Pt particles. Based on the Htotai/Pt and Nptpt results, the average particle size for all these catalysts was estimated < 1 nm. The particle size for the Pt/ASA catalyst as revealed with HRTEM (1.5 nm) seems in contradiction with the other techniques. However, it has to be noted that with HRTEM the lower detection limit for Pt/ASA is approximately 8-10 A, and that on the HRTEM pictures taken only a small amount of particles was visible. In other words, with HRTEM the smallest particles, which make up the majority of all Pt in the Pt/ASA catalyst, are invisible. The relation between particle sizes as determined with HRTEM, H2 chemisorption and EXAFS was extensively described by de Graaf el a/35. 

Figure 9.5 Comparison of modeled and observed smectite/illite conversion found in CRWU Gulf Coast Well 6 shale (Howeret al. 1976). Kinetic mode predicts the conversion using the estimated temperature and age at each depth. Line is the modeled result. Symbols represent average particle sizes of the initial clay + - <0.1 /xm, O = 0.1 to 0.5 fxm, =...

The metal dispersion and the average particle sizes calculated from the hydrogen chemisorption data are listed in Table 2 and are in close correspondence with the TEM estimated values. The reproducibility of the HDP procedure was checked several times and always high dispersions and rutheirium particles were found with TEM in the 1-2 nm range. 

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