Scherrer

X-ray powder diffraction studies are perfonned both with films and with counter diffractometers. The powder photograph was developed by P Debye and P Scherrer and, independently, by A W Hull. The Debye-Scherrer camera has a cylindrical specimen surrounded by a cylindrical film. In another commonly used powder... 

David Vietti Micheal Scherrer Morton International, Inc. 

Institute for Water and Environmental Problems SB RAS, Molodezhnaya 1, 656038 Barnaul, Russia E-mail papina iwep.asu.ru -Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Department of Chemistry and Biochemistry, University of Bern, Ereiestrasse 3,... 

Scherrer equation to estimate the size of organized regions Imperfections in the crystal, such as particle size, strains, faults, etc, affect the X-ray diffraction pattern. The effect of particle size on the diffraction pattern is one of the simplest cases and the first treatment of particle size broadening was made by Scherrer in 1918 [16]. A more exact derivation by Warren showed that. 

The CRO pitch sample (Fig. 9) and the PVC samples (Fig. 10) show well formed (002) peaks which first broaden, and then sharpen, as the heating temperature is increased. The KS pitch sample shows a very similar result. Diamond [35] noticed this effect in his work on carbonization of coals. Figures 9 and 10 show that the widtli and position of the (002) peaks do not change dramatically upon heating in this temperature range for the pitch and PVC samples. These peak widths are consistent with stacks of order 5 to 7 layers accordmg to the Scherrer equation assuming d,oo2) is about 3.5A. 

Powder X-ray diffraction and SAXS were employed here to explore the microstructure of hard carbon samples with high capacities. Powder X-ray diffraction measurements were made on all the samples listed in Table 4. We concentrate here on sample BrlOOO, shown in Fig. 27. A weak and broad (002) Bragg peak (near 22°) is observed. Well formed (100) (at about 43.3°) and (110) (near 80°) peaks are also seen. The sample is predominantly made up of graphene sheets with a lateral extension of about 20-30A (referring to Table 2, applying the Scherrer equation to the (100) peaks). These layers are not stacked in a parallel fashion, and therefore, there must be small pores or voids between them. We used SAXS to probe these pores. 

Scherrer, R.A. U.S. Patent 3,13B,636 June 23,1964 assigned to Parke, Davis Company... 

Data taken with a 143.2-mm diameter Debye-Scherrer camera using Cu Ka radiation (X 1.5418 A). 

In addition, an interesting, although negative, result has come from powder diffraction studies of the hexachloro compounds. We have examined Debye—Scherrer photographs of several samples known to contain predominantly hexachlorodibenzo-p-dioxins and have identified the patterns of at least three crystalline phases therein. (There are 10 possible isomers of hexachlorodibenzo-p-dioxin.) These patterns have been checked carefully against the calculated d-spacings and intensities of the 1,2,3,7,8,9-hexa isomer described by Cantrell, Webb, and Mabis (I) and also against an observed pattern supplied by Cantrell and believed to be from the low temperature phase of the same material. Yet to date we... 

R ratio(H2O/TTIP)=150, synthesis temperature=180°C(HNO3) and 160 C(TENOH), dried at 105 C. obtained by Scherrer equation, apparent first-order constants(A ) of orange n. rutile structure... 

Figure 1 is a TEM photograph of the Cu (10wt%)/Al2O3 catalyst prepared by water-alcohol method, showing the dispersed state of copper and was confirmed the particle sizes from XRD data. Figure 2 is X-ray diffraction patterns of above-mention catalysts, was used to obtain information about phases and the particle size of prepared catalysts. Metal oxide is the active species in this reaction. Particle sizes were determined fix)m the width of the XRD peaks by the Debye-Scherrer equation. 

Table 1 shows that the physicochemical properties of the support material were modified by the pre-treatment process. The particle sizes. Dp, which are summarized in the Table 1 were calculated from the X-ray diffraction patterns of prepared catalysts and a commercial catalyst(30 wt% Pt-Ru/C E-TEK) by using Scherrer s equation. To avoid the interference from other peaks, (220) peak was used. All the prepared catalysts show the particle sizes of the range from 2.0 to 2.8nm. It can be thought that these values are in the acceptable range for the proper electrode performance[7]. For the prepared catalysts, notable differences are inter-metal distances(X[nm]) compared to commercial one. Due to their larger surface areas of support materials, active metals are apart from each other more than 2 3 times distance than commercial catalyst. Pt-Ru/SRaw has the longest inter-metal distances. 

The properties of titania particles were investigated using X-ray diffraction (XRD, Model D/MAX-RB, Rigaku Ltd.), scanning electron microscopy (SEM, Model 535M, Philips Ltd.), transmission electron microscopy (TEM, Model 2000EX, JEOL Ltd.). The crystallite sizes were estimated by Scherrer s equation and the composition of rutile phase in titania were estimated from the respective integrated XRD peak intensities. 

X-Ray diffraction has an important limitation Clear diffraction peaks are only observed when the sample possesses sufficient long-range order. The advantage of this limitation is that the width (or rather the shape) of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow, see for example the (111) and (200) reflections of large palladium particles in Fig. 4.5. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The two XRD patterns of supported Pd catalysts in Fig. 4.5 show that the reflections of palladium are much broader than those of the reference. The Scherrer formula relates crystal size to line width ... 

X-ray diffraction has been employed for a very long time to attempt to characterize supported catalysts. For the most part, and until recently, only the width of a wide-angle peak has been employed. From the Scherrer equation, this width yields a "size". However, it has not been recognized that such a procedure faces many problems ... 

For materials which are available not in the form of substantial individual crystals but as powders, the technique pioneered by Debye and Scherrer is employed (Moore, 1972). The powder is placed into a thin-walled glass capillary or deposited as a thin film, and the sample is placed in the X-ray beam. Within the powder there are a very large number of small crystals of the substance under examination, and therefore all possible crystal orientations occur at random. Hence for each value of d some of the crystallites are correctly oriented to fulfil the Bragg condition. The reflections are recorded as lines by means of a film or detector from their positions, the d values are obtained (Mackay Mackay, 1972). 

XRD on battery materials can be classified as powder dififaction, a technique developed by Peter Debye and Paul Scherrer. In powder dififaction the material consists of microscopic crystals oriented at random in all directions. If one passes a monochromatic beam of X-rays through a fiat thin powder electrode, a fraction of the particles will be oriented to satisfy the Bragg relation for a given set of planes. Another group will be oriented so that the Bragg relationship is satisfied for another set of planes, and so on. In this method, cones of reflected and transmitted radiation are produced (Fig. 27.2). X-ray diffraction patterns can be recorded by intercepting a... 

FIGURE 27.2 Debye-Scherrer powder method. Cones of reflected and transmitted radiation are produced. In this example the pattern is recorded with photographic film. Alternatively,... 

Schmickler, Wolfgang, 673 Schottky, Walter, 135 Schweizer, E.K., 680 Semenchenko, Vladimir K., 124 Senda, M., 614 Sevcik, Augustin, 202 Scherrer, Paul, 471 Shirakawa, Hideki, 457 Shlygin, Aleksandr I., 173 Siemens, Werner von, 694 Sinha, S.K., 477... 

We will give here a short overview of the most common XRPD techniques used to study the microstructure of materials, starting from the most used and simple Scherrer method to the quite complex Warren-Averbach method, which is able to extract all the information available on sample microstructure and defects. 

The Crystallite Size and the Scherrer Formula. The Scherrer formula is based on a restricted assumption assuming that the peak shape is dominated by size effects. The problem of Bragg line broadening, originating from particle size, was first investigated by Scherrer [30] who derived the well-known and widely used law ... 

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