The X-Ray Diffraction Method

The X-ray diffraction method is applicable to solids and provides such detailed views of crystal geometry as those shown for sodium chloride solid in Figure 5-10, p. 81. 

As has been shown by the X-ray diffraction method the parent metals (i.e. Pd or Ni), the a-phase, and /3-phase all have the same type of crystal lattice, namely face centered cubic of the NaCl type. However, the /9-phase exhibits a significant expansion of the lattice in comparison with the metal itself. Extensive X-ray structural studies of the Pd-H system have been carried out by Owen and Williams (14), and on the Ni-H system by Janko (8), Majchrzak (15), and Janko and Pielaszek (16). The relevant details arc to be found in the references cited. It should be emphasized here, however, that at moderate temperatures palladium and nickel hydrides have lattices of the NaCl type with parameters respectively 3.6% and 6% larger than those of the parent metals. Within the limits of the solid solution the metal lattice expands also with increased hydrogen concentration, but the lattice parameter does not depart significantly from that of the pure metal (for palladium at least up to about 100°C). 

A rough estimation of the critical temperatures of coexistence of the (a + /3)-phases in two Ni-Cu-H systems containing 59 at. % and 63 at. % nickel was made by Majchrzak (26). Both phases, a and /8, were identified by the X-ray diffraction method. The presence of the /3-phase was not seen above 47°C for the alloy with 63 at. % Ni and above 20°C for the alloy with 59 at.% Ni. Though this method gives only approximative numerical values, one can make conclusions of a general character, e.g. that the critical temperature of the Ni-Cu-H system increases sharply with a growing content of nickel in the Ni-Cu alloy, and that one might expect the critical temperature of the coexistence of the a- and /8-phases... 

The direct proof of hydride formation in situ in a reaction vessel is in principle possible. One can follow changes of resistance (of a film, a wire, etc.) or of magnetic susceptibility of a catalyst. Hydride identification by means of the X-ray diffraction method requires a catalyst sample to be taken out from a reaction vessel, and eventually frozen in order to avoid a rapid decomposition of the hydride under ambient conditions (67). 

Oxidation of aknadinine with silver nitrate gave a pair of dimeric compounds, one of which was identical to the naturally occurring bisaknadinine (8) and the other assumed to be a stereoisomer arising from an axial chirality concerning the mode of biphenyl linkage (21,22). It was impossible, however, to determine from ORD and CD measurements whether the isomer is of natural bisaknadinine (8). Therefore, unambiguous proof of the stereochemistry was achieved, using the X-ray diffraction method, and the... 

The molecular structure of 1,2,9,10-tetrastanna[2.2]paracyclophane 22 was determined by the X-ray diffraction method. The crystal belongs to the space group P2,/a, and the data collection was carried out at 13°C. The ORTEP drawing of 22 is shown in Fig. 8. 

A series of aggregation structures of bilayer forming azobenzene amphiphiles, CnAzoCmN+Br, both in single crystals and cast films was determined by the X-ray diffraction method and uv-visible absorption spectroscopy. From the relationship between chemical structures and their two-dimensional supramolecular structure, factors determining the molecular orientation in bilayer structure were discussed. Some unique properties based on two-dimensional molecular ordering were also discussed. 

As the effects of an annealing step on the properties of cellulose acetate membranes, the increase of crystallinity by means of the X-ray diffraction method (12, 13) and the changes of pore sizes by the BET adsorption method l5) have been reported. 

The oxepin ring structure (8) appeared to be formed in preference to the arene oxide tautomer according to the NMR spectrum, and the oxepin form was unequivocally established by X-ray structure analysis (78AG(E)12l). Unfortunately the molecular dimensions of the oxepin ring in structure (8) were not included in the original report. In contrast, the valence isomeric arene oxide form of oxepin (9) was found to predominate and detailed information about the arene oxide molecular geometry was provided by the X-ray diffraction method (Table 3) (80LA1889). 

X-ray and neutron diffraction methods and EXAFS spectroscopy are very useful in getting structural information of solvated ions. These methods, combined with molecular dynamics and Monte Carlo simulations, have been used extensively to study the structures of hydrated ions in water. Detailed results can be found in the review by Ohtaki and Radnai [17]. The structural study of solvated ions in lion-aqueous solvents has not been as extensive, partly because the low solubility of electrolytes in 11011-aqueous solvents limits the use of X-ray and neutron diffraction methods that need electrolyte of -1 M. However, this situation has been improved by EXAFS (applicable at -0.1 M), at least for ions of the elements with large atomic numbers, and the amount of data on ion-coordinating atom distances and solvation numbers for ions in non-aqueous solvents are growing [15 a, 18]. For example, according to the X-ray diffraction method, the lithium ion in for-mamide (FA) has, on average, 5.4 FA molecules as nearest neighbors with an... 

Conclusion. This book is concerned with optical and X-ray methods but there are of course other methods of studying the structures of crystals and molecules. The diffraction of electrons and of neutrons depends on the same general principles as that of X-rays or visible light but there are important theoretical differences, and the expert mental arrangements are very different. It is not proposed to deal with either of these subjects here, but a few remarks will be made on their relation to the X-ray diffraction method. 

A great amount of information about the structure of crystals has been obtained by use of the x-ray diffraction method. The diffraction of x-rays by crystals was discovered by Max von Laue in 1912. Shortly thereafter W. L. Bragg discovered the Bragg equation, and in 1913 he and his father, W. H. Bragg, published the first structure determinations of crystals. 

The X-ray diffraction method utilizes a monochromatic beam of X-rays to which a solid material is exposed. The beam of radiation interacts with the solid, and is both reflected and diffracted. The reflection pattern is recorded by a detector system sensitive to the X-radiation. Until recently, this involved an intricate mechanical device whose complex... 

The infrared spectroscopic method is the same as the X-ray diffraction method, except that the infrared band absorptions are used instead of diffraction intensities. As in the X-ray analysis method, the dependence of the spectrum on temperature or on the presence of diluent can be used to determine which bands are due to the crystalline regions, and which to the amorphous. 

Here, the evaluation of the residual stresses in the electrolyte of the anode-supported cell at room temperature is reported. The X-ray diffraction method is used to measure the residual stresses in the electrolyte of the anode-supported cell, and a synchrotron radiation is used as an excellent X-ray source this enables the estimation of the residual stresses in the electrolyte with a high accuracy. It is clarified that the measured stresses are close to the calculated stresses. 

To derive Equation (10.44), it is assumed that the sample is isotropic and elastic. In addition, there is no stress perpendicular to the sample surface, because only the stresses near the sample surface are measured using the X-ray diffraction method. 

At present the X-ray diffraction method is used mostly to determine atomic positions in a crystal. However, X-ray scattering amplitudes depend directly on the electron-density distribution in a crystal, from which atomic positions can be derived on the assumption of coincidence of the nuclear positions and the center of gravities of total electron densities around atomic nuclei. 

X-ray analysis has been successfully used for elucidation of the structures obtained in the oxidation and alkylation reactions of 5-phenyl-l,2,3,4-thiatriazole <1976ACA351>, and to determine the place of protonation and alkylation of l,2,3,4-thiatriazole-5-thiolate <2004IC1370>. The structures of l,2,3,4-thiatriazol-5-thiolate derivatives as heterocyclic pseudohalides were carefully studied by the X-ray diffraction method <2000JA9051, 2004IC1370>. 

A clean and dry 20-gallon reactor was charged with 17.4 gallons of deionized water and 4.44 L of concentrated hydrochloric acid, to give a 0.77 M solution. To the solution was added 4.44 kg of the anhydrous 5-(2-(4-(l,2-benzisothiazol-yl)-l-piperazinyl)-ethyl)-6-chloro-l,3-dihydro-2H-indol-2-one free base. The slurry was warmed to 65°C and held for 18 hours. The slurry was cooled to room temperature. The product was filtered and washed with 2x5-gallon portions of deionized water, and then air dried at 50°C for 30 hours. The dried product contained 4.4% water and the x-ray diffraction method confirmed that the desired product was obtained. 

If untreated paper samples are examined, the X-ray diffraction method appears presently to be limited to the determination of those major inorganic components constituting more than about... 

Fig. 11(a) shows the AFM image of an 11-layer mixed-stack CT film of octadecyl-TCNQ and (Me)2P scanned at room temperature with a scan area of 2x2 pm2 [29]. It can be seen from the image that the CT film consists of platelet microcrystal domains of a few micrometers in size in which a multi-layered structure with many steps is observed. An analysis of the cross-sectional profile revealed that the layered platelet microcrystal domains have a step of 3.3 nm thickness [29]. This is in good agreement with the d value measured by the X-ray diffraction method [28]. Therefore, it seemed that the X-ray diffraction peaks originate from the multi-layered structure inside the domains. Each layer in the domains apparently consists of biomolecular layers of octadecyl-TCNQ and (Me)2P because the layer thickness of 3.3 nm is larger than the molecular length (3.0nm) of octadecyl-TCNQ. The biomolecular layer structure also supports that the CT film is in a mixed-stack pattern. 

In a recent publication on the performance of single crystals Pulvari (30) wrote It is essential, therefore, to distinguish between the skin and bulk properties of a crystal. Thus he explained the discrepancies found by different authors with respect to the lattice parameters for BaTi03. According to his findings, the lattice parameters change from the skin to the bulk, so that the x-ray diffraction method produces values which are functions of the particle size The c-axis decreases while the a-axis increases nearly linearly with crystal thickness. The skin thickness was found to be practically independent of the dimensions of the crystals. 

Synthesized copolymers were studied by the X-ray diffraction method. Diffraction patterns of amorphous polymers (Figure 9) show that the interchain distance reaches its maximum (t/i=10.24 A) at short lengths of flexible dimethylsiloxane backbone, n. As the length of dimethylsiloxane backbone increases ( = 21), the interchain distance decreases and for copolymer 5 reaches 7.54 A (Table 6). 

The complexes are similar to complexes cited with carbonyl ligands. The similarities are particularly the anion coordination possibility and the different coordination numbers for complexes with a given ligand depending upon the anion. All the complexes have the group L-O, where L = P, As, N, S and the coordination to the metal is through oxygen, Ln-O-L where L = N, S, P, As. The evidence for this is based on infrared spectra for most of the complexes and the X-ray diffraction method of determination of some structures. 

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