Determination of Crystallite Size

The ciystallite size of a mineral, from its X-ray diffractogram, has been evaluated by applying Scherrer s relationship. However, assigning values and units of variables (viz., peak width and difiEraction angle) in this relationship is contentious and such computations are quite cumbersome and time consuming. Hence, development of a Took up chart using d-spacing, peak width and crystallite size of a mineral would be quite pmdent, for materials like fly ash and its residues obtained from the alkali activation. 

With due reference to the previous researchers much attention was given to clarify selection and utilization of appropriate units of the main variables [38-41], used in Scherrer s formula, presented in Eq. 5.7. 

Accordingly, /I (i.e., full width at half maximum in 26°) adopted from the X-ray diffractograms was converted to radian, while cos 6, used in Eq. 5.7 was calculated by using the value of 6 in radian. Also, (=1.540 A), was converted to nm unit (i.e., X = 0.154 nm), before substituting it in Eq. 5.7. Here K is equal to 0.9 (the average shape factor for a spherical crystallite). 

The conventional way of getting a correct value of CS is a cumbersome task and it might also yield manual errors, as well, particularly if proper units of the variables are not input in Eq. 5.7. With this in view and for the precise and quick determination of CS, as listed in Table 5.32, look up chart has been developed, as depicted in Fig. 5.8. Each chart exhibits a regular trend of variation between the CS and d-spacing (corresponding to the 20°) of various minerals present in the samples, for different (ranging from 0.0502 to 1.0706 in 20° unit) values. Thus getting the value of CS from Fig. 5.8 looks very simple, except for an interpolation in case of an intermediate value of P, between adjacent plots. 

Common minerals and zeolites (legends used in the XRD) d-spadng (A) of strong Unes in descending order of peak intensity PDF number 

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Langford, J.I., and Wilson, A.J.C., Scherrer after 60 years—survey and some new results in determination of crystallite size, J. Appl. Crystallogr, 11, 102, 1978. 

Metal Dispersion by Chemisorption and Titration Selective Chemisorption. - This is the most frequently used technique for determining the metal area in a supported catalyst and depends on finding conditions under which the gas will chemisorb to monolayer coverage on the metal but to a negligible extent on the support. Various experimental methods, conditions, and adsorbates have been tried and studies made of catalyst pre-treatment and adsorption stoicheiometry, viz, the (surface metal atom)/(gas adsorbate) ratio, written here as Pts/H, Bh jQO,etc., and reviews to about 1975 are available. A summary is given in Table IV of ref. 2 of methods used to confirm the various adsorption stoicheiometries proposed, sometimes from infrared studies. These include chemisorption on metal powders of known BET area or, more satisfactorily, one of the instrumental methods reviewed in Section 3 for the determination of crystallite size distributions. For many purposes, a relative measurement of metal dispersion is sufficient, conveniently expressed as the ratio (number of atoms or molecules adsorbed)/(totfl/ number of metal atoms in the catalyst), e.g., H/Ptt. 

DEL 82] DELHEZ R., DE KEIJSER T.H., MITTEMEIJER E.J., Determination of crystallite size and lattice distorsions through x-ray diffraction line profile analysis , Fresenius Z Anal. Chem., vol. 312, p. 1-16, 1982. 

KEI 83] de KEIJSER Th.H., MITTEMEIJER E.J., ROZENDAL H.C.F., The determination of crystallite size and lattice strain parameters in conjunction with the profile refinement method for the determination of crystal structure , J. Appl. Cryst, vol. 16, p. 309-316,1983. 

Schonfdd A, Wilke W (1972) Determination of crystallite size and lattice distortion in extended chain polyethylene and their change after oxidative degradation. Kolloid Z. Z. Polym. 250 496... 

The Au NPs-rGO composites material was characterized by powder X-ray diffraction (pXRD) (as shown in Figure 4.6). pXRD is an essential characterizing device to resolve difficulties related to crystal structure of solid, determination of crystallite size, orientation of crystal, detection of unidentified material, etc. In the area of NPs characterization, XRD holds... 

This example is to illustrate that a single determination of crystallite sizes is of extremely limited value as no distinction is possible between contributions from size and contributions from strain. The unchanging graphitic microcrystallite model carmot explain these phenomena. 

J. I. Langford and A. J. C. Wilson, Scherrer after Sixty Years A Survey and some New Results in the Determination of Crystallite Size, J. Appl Crystal ., 11,102-113 (1978). 

The activity loss measured here is caused by recrystallizations. This was demonstrated by using scanning electron microscopy to determine nickel crystallite size in the same catalyst samples. These tests revealed that the catalyst used in demonstration plants has only a slight tendency to recrystallize or sinter after steam formation and loss of starting activity. 

The amount of variation in reactivity which may be tolerated is small, since a reasonable balance has to be struck between rapid and uniform reaction on the one hand and practical working times on the other. Sorrell Armstrong (1976) found that the mean crystallite diameter could be determined adequately by X-ray diffraction, using line-broadening as an indication of crystallite size, and also by electron microscopy. These techniques were able to distinguish between suitable and unsuitable oxide powders. 

Spin-Lattice and Spin-Spin Relaxations. In order to determine the content of these crystalline and noncrystalline resonances, the longitudinal and transverse relaxations were examined in detail. It was first confirmed that the noncrystalline resonance of all samples is associated with Tic in an order of 0.45-0.57 s. Hence, the noncrystalline component of all samples comprises a monophase, in as much as judged only by Tic. However, it was found that the noncrystalline component of drawn samples generally comprises two phases with different T2C values amorphous and crystalline-amorphous interphases. The dried gel sample does not include rubbery amorphous material it comprises the crystalline and rigid noncrystalline components. However, the rubbery amorphous phase with T2C of 5.5 ms appears by annealing at 145 °C for 4 minutes. For the orthorhombic crystalline component, three different Tic values, that suggest the distribution of crystallite size, were recognized for each sample, as normal for crystalline polymers [17,54, 55]. The Tic and T2C of all samples examined are summerized in Table 6. 

PtRu catalysts with controlled atomic ratios were prepared by adjusting the nominal concentrations of platinum and ruthenium salts in the solution, whereas different mean particle sizes could be obtained by adjusting some electric parameters of the deposition process, e.g., ton (during which the current pulse is applied) and toff (when no current is applied to the electrode), as determined by different physicochemical methods (XRD, EDX, and TEM) [40], Characterization by XRD led to determine the crystallite size, the atomic composition and the alloy character of the PtRu catalysts. The atomic composition was confirmed using EDX, and TEM pictures led to evaluate the particle size and to show that PtRu particles formed small aggregates of several tens of nanometers (Figure 9.10). 

The average values of crystallite size were determined by the integral width of the diffraction maximums corresponding to the... 

A brief review of the diffraction phenomenon and the effect of crystallite size is presented. Applications of XRD to catalyst characterization are illustrated, including correlation of XRD powder patterns to molecular structural features, determination of Pt crystallite size and others. Factors that affect the appearance of XRD powder patterns, such as framework structure perturbations, extra-framework material, crystal morphology, impurities, sample preparation, instrument configurations, and x-ray sources, are discussed. 

Crystallite Size. From the width of the peaks the computer can determine the size of the crystallites in the sample. The smaller the crystallite size, the broader are the diffraction peaks. This kind of analysis is important for determining particulate size of certain materials (eg, silica) where a range of crystallite size may be a health hazard if inhaled into the lungs. 

Another example of nanoparticle size analysis via EXAFS is the work of Frenkel (1999) on Pt and Pt-Ru particles supported on carbon. This study utilizes the longer absorber-neighbor distances within nanocrystals, showing that determinations of the relative numbers of these farther neighbors are more sensitive to crystallite size than closer neighbors. In the best case all neighbor coordinations can be used to obtain a good estimate of crystallite size and shape even without the added information provided by polarized studies (Fig. 28). 

Both, SAXS and XRD, are indirect methods but offer the advantage of providing reliable statistical information on particle size. XRD is particularly attractive as it can be performed on a very basic laboratory-based powder diffractometer, and for this reason is the most commonly used method. The technique involves measuring the peak broadening of the diffraction lines which, for perfect crystals, would be sharp except for a very small inherent broadening due to the uncertainty principle (i.e., there is not an infinite number of diffracting planes). In practice, however, these are broadened due to the instrumental optics and crystallite size. The most common approach to determining the crystallite size is to use the Scherrer relationship [170-172] ... 

It is commonly recognized that a comprehensive understanding of the properties of a new material is an essential prerequisite to finding its new applications. In this respect, the study of ultrafine diamond is incomplete and its properties remain to be fully elucidated. For example, the nature of the surface functional groups and the method of their modification the nature of the agglomeration of ultrafine crystallites and effective methods of de-agglomeration to prepare mono-dispersed suspension the crystalline and surface structures of the nano-scaled diamond, etc., are appropriate subjects of research An efficient method for the determination of particle size distributions and structures of nano-sized particles in suspension is very important, and is worth developing in the near future. 

Calculation of mean crystallite size, lattice strain and frequency distributions of crystallite sizes from the same XRD line-profiles used for crystallinity determinations. In addition to the application of the Scherrer equation, two single-line methods were used the variance method of Wilson (1963) (Akai and To th 1983 Nieto and Smchez-Navas 1994), and the Voigt method of Langford (1978) in combination with single-line Fourier analysis (Akai et al. 1996, 1997, 2000 Warr 1996 Jiang et al. 1997 Li et al. 

The catalysts were characterized by transmission electron microscope(TEM, Hitachi H9000UHR) operated at 300 kV for the direct observation of the particle size and the distribution of Mg species, X-ray photoelectron spectroscopy ( XPS, PHI Quanteta SXM) for the examination of surface Ce/Zr concentration and valence of Ce species, X-ray diffractometer (XRD, Rigaku RINT02000) operated at 30 kV and 20 m A for the determination of crystallite structures. 

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