Neutron diffraction patterns

To answer this question we need to consider the kind of physical techniques that are used to study the solid state. The main ones are based on diffraction, which may be of electrons, neutrons or X-rays (Moore, 1972 Franks, 1983). In all cases exposure of a crystalline solid to a beam of the particular type gives rise to a well-defined diffraction pattern, which by appropriate mathematical techniques can be interpreted to give information about the structure of the solid. When a liquid such as water is exposed to X-rays, electrons or neutrons, diffraction patterns are produced, though they have much less regularity and detail it is also more difficult to interpret them than for solids. Such results are taken to show that liquids do, in fact, have some kind of long-range order which can justifiably be referred to as a structure . 

Fig. 51. Continuous random network fit to the neutron diffraction pattern of H20 (as) (from Ref. 82>). Experimental data-, Theory----...

The structure derived from a Rietveld fit of a neutron diffraction pattern of a 6-line ferrihydrite which showed more and sharper lines (Fig. 2.9, lower) than an XRD pattern, was in agreement with the structure proposed by Drits et al. (1993) except that it was not necessary to assume the presence of hematite in order to produce a satisfactory fit (Jansen et al. 2002). The unit cell of the defect free phase had a = 0.29514(9) nm and c = 0.9414(9) nm and the average domain size derived from line broadening was 2.7(0.8) nm. Since forced hydrolysis of an Fe solution at elevated temperatures will ultimately lead to hematite, it is likely that incipient hematite formation may occur under certain synthesis conditions. Neither these studies nor Mbssbauer spectroscopy, which showed only a singular isomer shift at 4.2 K characteristic of Fe, supported the presence of " Fe (Cardile, 1988 Pankhurst Pollard, 1992). However, the presence, at the surface, of some Fe with lower (<6) coordination, perhaps as tetrahedra (Eggleton and Fitzpatrick, 1988) which may have become unsaturated on heating, has been suggested on the basis of XAFS results (Zhao et al. 1994). 

The compound EuO has the NaCl structure and is paramagnetic above 70 K but magnetically ordered below it. its neutron diffraction patterns at high and low temperatures are identical. What is the nature of the magnetic ordering ... 

As reported by Blanco et al. (1999), neutron diffraction patterns of powder and bulk polycrystalline samples of GdCu were obtained for both structures in the cubic CsCl type of structure, which orders antiferromagnetically at 7n 150 K, a propagation vector of ( j 0) has been found with the moments probably parallel to the c-axis (note that other noncollinear magnetic structures might give rise to the same neutron-diffraction pattern). In the orthorhombic low temperature phase (7n 45 K) the available diffraction patterns... 

At present therefore, the details of most atomic structures must be discovered indirectly. The experimental material for the purpose is the X-ray diffraction pattern. Electron diffraction patterns and neutron diffraction patterns are similar, and have been used for the same purpose but the great majority of investigations of crystal structure are based on X-ray diffraction patterns. The interpretation of these diffraction patterns falls into two stages—first, the determination of the shape and dimensions of the unit cell (see Chapter II), and second, the discovery of the positions of the atoms in the unit cell. 

Fig. 2.5 A neutron diffraction pattern of Sr rOg measured by the tlme-cFfltght method. The arrangement is similar to that in X-ray diffraction (Fig. 1.6). except that the detector angle is fixed, and neutron wavelengths are separated according to their velocity.

Figure 10. Elastic neutron diffraction pattern from a 0.4-layer nitric oxide film adsorbed on a recompressed graphite powder Papyex (431. Background scattering from the substrate has been subtracted. The molecules are assumed to be lying down as shown in the unit cell (inset). The arrows indicate the position and relative intensities of the Bragg peaks calculated for this structure.

In the case of the ethane (45) and butane (46) monolayers adsorbed on graphite, it has been possible to analyze the neutron diffraction patterns using all three Euler angles of the molecule as orientational parameters. Here we limit discussion to the butane monolayer which we have taken as a model system and whose vibrational spectrum was discussed in Sec. II. 

Figure 11. (a) Elastic neutron diffraction pattern from a 0.8-layer butane film... 

Hulmes, D. J. S., Miller, A., White, S. W., Timmins, P. A., and Berthet-Colominas, C. (1980). Interpretation of the low angle meridional neutron diffraction patterns from collagen fibres in terms of the amino acid sequence. Int. J. Biol. Macromol. 2, 338-345. 

Peak Breadths And Reflection Profile Function. As has been mentioned, the individual reflection profiles tend to be broad for polymers. With both x-ray and neutron radiation the peaks exhibit large peak-widths. In a neutron diffraction pattern of isotactic polypropylene (A. Immirzi, work in progress) the peak width at half maximum, K j, had values ranging from 0.60° at 20= 14° to 1.00° at 26= 43° (X= 1.542 A), whilst, with the same... 

In this technique, structural parameters are refined to fit the overall profile of the powder, neutron-diffraction pattern, which is assumed to consist of Gaussian-shaped peaks, centered at the Bragg-angle positions. The data consist of the point-intensity counts over the angular scan, and overlapping peaks are treated separately, using their contributions to the point intensities. 

Measurements of Crystal Structures. - (a) Zeolites. Improved understanding of the catalytic behaviour of zeolites has tended to proceed in parallel with improvements in their structural characterization. The recent advent of magic-angle spinning n.m.r. (m.a.s.n.m.r.)for instance, has reawakened interest in the ordering of the Si and A1 atoms in zeolites and its catalytic consequences. This renewed interest has in turn lead to a re-examination of the neutron diffraction patterns of certain zeolites in order to obtain confirmatory evidence for the the predictions of the n.m.r. experiments. A useful introduction to the benefits of using neutrons rather than X-rays for powder diffraction can be found in ref. 55. 

FIGURE 18 The neutron diffraction pattern of Tb11B44Si2 at 4 K (top) together with the difference pattern (bottom) which was obtained by subtracting the intensities of the 300 K pattern from those of the 4 K pattern. The asterisks indicate the strong peak positions of B2O (Mori et al., 2004a). 

X-ray and neutron diffraction patterns can be detected when a wave is scattered by a periodic structure of atoms in an ordered array such as a crystal or a fiber. The diffraction patterns can be interpreted directly to give information about the size of the unit cell, information about the symmetry of the molecule, and, in the case of fibers, information about periodicity. The determination of the complete structure of a molecule requires the phase information as well as the intensity and frequency information. The phase can be determined using the method of multiple isomor-phous replacement where heavy metals or groups containing heavy element are incorporated into the diffracting crystals. The final coordinates of biomacromolecules are then deduced using knowledge about the primary structure and are refined by processes that include comparisons of calculated and observed diffraction patterns. Three-dimensional structures of proteins and their complexes (Blundell and Johnson, 1976), nucleic acids, and viruses have been determined by X-ray and neutron diffractions. 

Neutron diffraction patterns of powder samples were taken on a neutron diffractometer (X = 1.085 A) mounted on the thermal column of a WR-SM nuclear reactor [3]. The DBW-3.2 program for the Rietveld neutron diffraction line shape analysis was used in calculations and structure refinement [4]. A DRON-3M X-ray diffractometer (CuK - radiation) was used to measure X-ray powder diffraction patterns. 

Figure 1. Neutron diffraction patterns of TiN0 26Ho 15, solid solution samples quenched from 1170 K (a) 1070 K (b) and 890 K (c) (points show data points, the solid line is the fitted curve, and A= I exp. - I cak)-...

Figure 2. Neutron diffraction patterns of TiN0 26Do 15 (ss) annealed at (a) 1270 K, (b) 1190 K, and (c) 900 K. Dots show measured reflections. The solid curves are simulated patterns.

Based on the neutron diffraction reflections (Fig. 2a) for TiN0.26D0.i5 (ss) samples quenched from 1270 K (001 reflections with 14- 2n are absent space group P63/mmc), the hexagonal structure is the L3 type, which was possessed by disordered TiNo. Ho.is (ss) [2]. Processing the neutron diffraction pattern for the intact solid solution in terms of space group P63/mmc (the a-phase) showed that... 

Figure 5. Neutron diffraction patterns of TiN0.26H0.075D0.075 (ss) quenched from 1270 K. Conclusions...

Unlike TiN0.26H0.15, in TiN0.26D0.15, the appearance of superstructural reflections in the neutron diffraction patterns is not preceded by diffuse scattering. 

Figure 7. Neutron diffraction pattern of ball-milling amorphic C o (—) and polycrystal C co...

Figure 10. Neutron diffraction patterns as LDA (top, T = 1) transforms to HDA (bottom,...

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