Diffraction data, film

The structure of alumina on NiAl(l 1 0) was the subject of a surface X-ray diffraction study by Stierle et al. [46]. The model derived by Stierle et al. from the analysis of the X-ray diffraction data was based on a strongly distorted double layer of hexagonal oxygen ions, where the Al ions are hosted with equal probability on octahedral- and tetrahedral-coordinated sites the resulting film structure was closely related to bulk k-A1203. An attractive feature of Stierle s model was that it provided a natural explanation of the domain structure of the alumina overlayer, which is induced by a periodic row matching between film and substrate lattices. However, as pointed out recently by Kresse et al. [47], this structure model has two bonds with... 

Electron diffraction by lamellar, single crystals leads to a two-dimensional, tetragonal unit-cell with a = b = 22.9 A (2.29 nm). From X-ray diffraction data obtained from a film of sedimented, lamellar crystals, it was found that the c axis spacing (7.8 A 780 pm) is equivalent to that in 6-fold and 7-fold amylose helices. The true helical diameters of the 1-butanol, isopropyl alcohol, and 1-naphthol complexes were calculated from experimental data. The ratios of 6 7 8 indicated that the 1-naphthol complex has eight D-glucose residues per turn. The diversity of helical orientations in V-amylose crystals was discussed. 

Structural characterizations of the immobilized bilayer assemblies are essential for the molecular design of the functional materials. On the bases of the systematic crystallographic investigation of single crystals of double-chain ammonium amphiphiles [9], Okuyama wrote a computer simulation program for the calculation of bilayer structures in cast bilayer films and bilayer thicknesses estimated from the repeating period in the X-ray diffraction data have been exclusively used for structural discussions [10,11]. 

In the case of straight-chain alcohols or fatty acids, A0 is almost 20 A2, which is the same as found from the x-ray diffraction data of the packing area per molecule of alkanes. This equation is thus valid when A A0. The magnitude of n is 0.2 mN/m for A = 2000 A2, for ideal film. However, n will be about 0.2 mN/m for A = 20 A2 for a solid-like film of a straight-chain alcohol. 

Fig. 68. Schematic representation of three types of anionic porphyrins in a cast multibilayer film of 33. For simplicity, counterions are not shown. The bilayer packing is based on the X-ray diffraction data. Type I porphyrins (Fig. 66) assume random orientations. Type II and III porphyrins stay horizontally on the bilayer surfaces [445]...

Figure 2.1. Application of the reciprocal lattice to the analysis of electron diffraction data, (a) The vector corresponding to the incident wave is drawn through the origin of the reciprocal lattice, O, in the direction that the wave is travelling and has a length, XO, equal to 1/X. For diffraction to take place Q must correspond to 2ir times the vector joining O to another point in the reciprocal lattice, P, and distance XO must be equal to XP. Clearly this situation can only be satisfied by freak conditions. However, (b) illustrates what happens for the real case of a thin film in which the reciprocal lattice points become extended in the direction normal to the plane of the film.

Various efforts have been made to form LB films of fatty acids using a subphase containing trivalent cations. Reference has already been made to the pioneering work of Wostenholme and Schulman [77J and the review article by Binks [78], Two recent attempts have been made to carry out such a programme by Prakash et al. [146J and Ohe et al. [147]. Both groups of workers made use of trivalent iron in the subphase and had some success, but X-ray diffraction data showed that the films obtained were far less well ordered than films dipped over divalent cations. 

As in the case of low-molecular liquid crystals the majority of information about the structure of LC polymers is obtained from their optical textures and X-ray diffraction data. Because of high viscosity of polymer melts, which results in retardation of all structural and relaxation processes it is quite difficult to obtain characteristic textures for LC polymers. As is noted by the majority of investigators smectic LC polymers form strongly birefringent films as well from solutions, as from melts11 27-... 

Schlesinger and Marton (15) studied the nucleation and growth of electrolessly deposited thin nickel (Ni-P) films. These studies were later extended and complemented by the studies performed by Cortijo and Schlesinger (19, 20) on radial distribution functions (RDFs). RDF curves were derived from electron diffraction data obtained from similar types of films as well as electrolessly deposited copper ones. Those studies, taken together, have elucidated the process of crystallization in the electroless deposition of thin metal films. 

Figure 2.5 depicts the collection of X-ray diffraction data. A crystal is mounted between an X-ray source and an X-ray detector. The crystal lies in the path of a narrow beam of X rays coming from the source. A simple detector is X-ray film, which when developed exhibits dark spots where X-ray beams have impinged. These spots are called reflections because they emerge from the crystal as if reflected from planes of atoms. 

Although film for data collection has largely been replaced by devices that feed diffraction data (positions and intensities of each reflection) directly into computers, I will continue to speak of the data as if collected on film because of the simplicity of that format, and because diffraction patterns are usually published in a form identical to their appearance on film. I will discuss other methods of collecting data in Chapter 4. 

Accurate Fiber X-ray Diffraction Data from Films... 

For many films exposed in the region of density <2.5, the optical density of a diffraction spot is often proportional to exposure and inversely proportional to the log Q of transmission coefficient. Thus, accuracy of reflection measurements tended to be reasonably uniform over the full range of density. The technique proved usable in estimating diffraction data on patterns on low background and reflections of moderate intensity, generally of photographic density < 1.0 and has been found to yield an error of 15-20% (14). 

Film diffraction data can be obtained by several techniques flat plate camera, cylindrical camera or precession camera. We chose the latter, because it records a relatively undistorted "slice" of diffraction transform (reciprocal space) (19,20). We felt that this characteristic of the precession technique outweighed the disadvantages of longer exposure times (this was lessened by use of a Helium atmosphere in the camera enclosure). For potassium bromide amylose, the fiber studied, this required exposure of a 79y x 79y x 300y fiber specimen for 45 hours (35kv,... 

In the last few years rapid advances have been made in the field of computational crystallography, so that it is now possible to produce highly refined computer models of a wide variety of polymeric materials using X-ray diffraction data. Unfortunately, these achievements have been negated to some extent because the techniques used to collect the data for such refinement programs have not advanced at a comparable rate. In this contribution we describe a computer program which facilitates the reduction of intensity and d-spacing data obtained by the multiple film-pack method, and attempts to quantify the errors associated with such measurements. 

It will be assumed here that the X-ray diffraction data were collected on flat films with a point focus camera. This simplifies the theoretical presentation. The TMV data analyzed in the results section were collected on cylindrical films with Guinier cameras, but positions on the cylindrical films can be mapped onto positions on a flat film by a simple geometric transformation. In general, the form of the optical density, D(r,), in a fiber diffraction pattern can be expressed in film coordinates as the sum of contributions from all reflections, I (r,iJ> ), plus a background term, B(r,) ... 

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