Disordered structure models distribution

The location of boron or aluminum sites in zeolites is of utmost importance to an understanding of the catalytic properties. Due to the inherent long-range disorder of the distribution of these sites in most zeolites, it is difficult to locate them by diffraction methods. The aforementioned methods to measure heteronuclear dipolar interactions can be utilized to determine the orientation between the organic SDA and A1 or B in the framework. The SDA location may be obtained by structure refinement or computational modeling. For catalytic reactions, the SDA must be removed from the pores system by calcination. 

The driving force behind the rapid development of powder diffraction methods over the past 10 years is the increasing need for structural characterization of materials that are only available as powders. Examples are zeolite catalysts, magnets, metal hydrides, ceramics, battery and fuel cell electrodes, piezo- and ferroelectrics, and more recently pharmaceuticals and organic and molecular materials as well as biominerals. The emergence of nanoscience as an interdisciplinary research area will further increase the need for powder diffraction, pair-distribution function (PDF) analysis of powder diffraction pattern allows the refinement of structural models regardless of the crystalline quality of the sample and is therefore a very powerful structural characterization tool for nanomaterials and disordered complex materials. 

Structures of powdered P-rhombohedral boron and amorphous boron were investigated with pulsed neutron diffraction techniques (Delaplane et al. 1988). To avoid intensive neutron absorption by °B nuclei, samples were "B isotopically enriched up to 97.1% and 99.1%, respectively. Earlier neutron diffraction studies based on nuclear reactor data did not permit the derivation of a meaningful radial distribution of atoms in amorphous material due to limited range of the neutron wave vector (<10.8 A" ). The obtained static structural factor and derived radial distribution function supported a structural model of amorphous boron based on building blocks of B,2 icosahedra resembling those found in p-rhombohedral boron, but with disorder occupying in the linking between ico-sahedral subunits. The intensity data indicated that amorphous samples contained 5% of a mixture of crystalline a- and p-rhombohedral boron. 

In this paper, the electronic structure of disordered Cu-Zn alloys are studied by calculations on models with Cu and Zn atoms distributed randomly on the sites of fee and bcc lattices. Concentrations of 10%, 25%, 50%, 75%, and 90% are used. The lattice spacings are the same for all the bcc models, 5.5 Bohr radii, and for all the fee models, 6.9 Bohr radii. With these lattice constants, the atomic volumes of the atoms are essentially the same in the two different crystal structures. Most of the bcc models contain 432 atoms and the fee models contain 500 atoms. These clusters are periodically reproduced to fill all space. Some of these calculations have been described previously. The test that is used to demonstrate that these clusters are large enough to be self-averaging is to repeat selected calculations with models that have the same concentration but a completely different arrangement of Cu and Zn atoms. We found differences that are quite small, and will be specified below in the discussions of specific properties. 

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