Average crystallite size

Table 4 Degree of Crystallinity and Average Crystallite Size of Differently Drawn PET Fibers...

Draw ratio Degree of crystallinity Lattice disorder coefficient (k) Average crystallite size perpendicular to the crystallographic plane (hkl) Dhki (nm) ... 

Figure 15 Electrostatic charge of PET fiber versus average crystallite size perpendicular to the chain direction.

The second phenomenon, i.e. the change in catalytic activity or selectivity of the active phase with varying catalyst support, is usually termed metal-support interaction. It manifests itself even when the active phase has the same dispersion or average crystallite size on different... 

This analysis gives satisfactory results concerning the average crystallite sizes even in unfavorable experimental conditions such as overlapped or very weak and noisy peaks, and it allows an easy treatment of non-perfect monochromaticity of the radiation. But, it is important to emphasize that it is almost impossible to obtain the promised detailed description of the crystallite size and strain distributions. This is a fundamental problem related to the adopted procedure that is based on the a priori choice of the peak shape that inevitably imposes the general shape of such distributions [40]. For these reasons, the average dimension and strains remain the only reliable information. 

CdSe, CdTe. CdSe films have been grown from complexed (with tartaric acid and triethanolamine) cadmium acetate or cadmium sulfate solutions and sodium selenosullale.1272 81 84 The films were amorphous or nanocrystalline with an average crystallite size of 6nm. The optical band gap was 1.8-2.1 eV, and the electrical resistivity was of the order 104-106Qcm. 

CatalysU Unit Cell Parameter of die Support Oxide (nm) Average Crystallite Size of the Support Oxide (nm) Average Crystallite Size of CuO (nm) Sbet (tn /g)... 

Average crystallite sizes can be estimated from peak widths (e.g., see [22]) using the Scherrer equation ... 

Sample designation Milling time (h) XRD analysis" Average crystallite size D (nm) " BET surface area (mVg) Chemical composition LaxCOyF Cz03-5 ... 

TiOj, both anatase and rutile structures were found. On the contrary, the TiO (ST) sample showed only anatase structure. The average crystallite size was 9.3 nm for TiOj (ST) samples by using Scherrer s equation [8], which was significantly smaller compared to the P25 powder, with an average crystallite size between 15 and 25 nm [9]. 

Fig. 9. X-Ray diffraction data of a-iron oxide samples in Fig. 8 collected by pulse-counting mode using MoK, radiation for samples of average crystallite size of (A) 14.5 nm, (B) 25 nm, (C) 7.5 nm, and (D) 9.5 nm. For spectrum C, the region from 13 to 16° was counted for 1000 sec/step. From ref. 56, reprinted with permission, copyright 1984 by the American Chemical Society.

The Ti02 used here was supplied from Ishihara Techno Corp. (type ST-01, average crystallite size, 7 nm specific surface area, 320 m2 g"1). The activated carbon (type 3GS 1350 m2 g 1 pore size, 2.0 nm) from Kuraray Chemicals Co. was ground into particles (<0.15 mm diameter). 

Figure 16. Computed intensity profiles for the first three orders of a 001 reflection for 501 crystallites with 5007 layer planes of mean spacing 0.4 nm, the number average crystallite size being 4.0 nm and the r.m.s. distortion 5%...

Unfortunately another factor complicates the measurement of true crystallite size. The K parameter is also a function of both crystallite size and of lattice distortion. We recently studied the effect of crystallite size and distortion on the K parameter using optical transform methods with simulated lattice images drawn by a computational method (26). The Scherrer K parameters given in Table X may be used to obtain a true number average crystallite size by any of the methods quoted, but will only be valid for crystallites with a number average size in the range 8 to 15 layer planes and a lattice distortion of 4-6%. The mixed function method (3) appears to give the best estimate of true crystallite size (K = 1.0) and the Hosemann method (4) the best estimate of lattice distortion. 

FIGURE 18 Average crystallite size measurement by X-ray line broadening. The width of characteristic X-ray lines decreases markedly as cerium dioxide powder is sintered. The crystallites grow from an initial size of 50 to 400 A after heating in air for several hours. 

Chemisorption, transmission electron microscopy, and XRD line broadening do not necessarily result in the same calculated dispersion for a given catalyst. Chemisorption may be biased toward a lower average crystallite size and line broadening toward a higher size. In fact, line broadening and chemisorption methods are not directly comparable unless Fourier analysis is applied to the X-ray data. Chemisorption and transmission electron microscope results are directly comparable. 

Figure 8. A comparison of X-ray diffraction lines for AuSn particles upon heating to 275 °C and 450°C. (a) as received, 18 nm average crystallite size (b) 275°C, 25 nm (c) 450°C, 36 nm (according to Scherrer Treatment of crystallite sizes).

Nanocrystalline copper with an average crystallite size of about 50nm can be obtained without additives in the ionic liquid 1-butyl-l-methyl-pyrrolidinium bis(trifluoromethylsulfonyl)imide ([BMP]Tf2N) [92], Because of the limited solubility of the tested copper compounds in this ionic liquid, copper cations were introduced into the ionic liquid by anodic dissolution of a sacrificial copper electrode. The electrodeposition of copper was also investigated in the ionic liquid... 

Two results of practical interest follow from the above reasoning. Firstly, the smaller the number of viable nuclei the larger will be the average crystallite size in the final crop of crystals. Secondly,... 

In utilizing the Scherrer equation, care must be exercised to properly account for instrumental factors which contribute to the measured peak width at half maximum. This "intrinsic" width must be subtracted from the measured width to yield a value representative of the sample broadening. When the experimental conditions have been properly accounted for, reasonably accurate values for the average crystallite size can be determined. Peak shapes and widths, however, can also provide other information about the catalyst materials being studied. For example, combinations of broad and sharp peaks or asymmetric peak shapes in a pattern can be manifestations of structural disorder, morphology, compositional variations, or impurities. 

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