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Notes: We show here that a static disordered binary alloy in which one of the impurities is prevented from clustering in the lattice as a result of strong repulsive interactions, e.g., will possess a localization–delocalization transition regardless of the spatial dimension. We show explicitly that (N)1/2 of the electronic states are completely unscattered by the disorder and lead to superdiffusive transport with a mean-square displacement growing in time as t3/2 over a wide range of the static disorder in one dimension. The model is shown to be applicable to electron transport in Fibonacci lattices fabricated from two kinds of materials such as GaAs and AlAs. It is shown explicitly that transient grating experiments can be used to probe the location of the unattenuated states in the energy band. We propose that this model can be used to design molecularly based electronic filters.

Notes: Impurity tracer diffusion coefficients for Co and Hf were measured in a series of amorphous NixZr1−x alloys at various temperatures for 0.3〈x〈0.7. The diffusion coefficients for Co, an impurity with small atomic radius were, depending on alloy composition and temperature, two to four orders of magnitude larger than those for Hf, an impurity with large atomic radius. Whereas the Hf tracer diffusion coefficients are independent of alloy composition, those of Co decrease strongly with increasing Ni concentration. These results suggest that the diffusion mechanisms for atoms with small or large atomic radii are different in amorphous Ni-Zr alloys.

Notes: To validate the yearly periodicity of annulus formation in the otolith of the eel, the structure of annuli in otoliths of the European eel, Anguilla anguilla, stocked for 7 and 12 years in Lake Ommen on the east coast of southern Sweden, was examined. The population was stocked from elvers imported both from France (Bay of Biscay) in April 1979 and England (River Severn) in March–April 1984. The microstructure of an annulus consisted of single, double and/or composite tings depending on the location in the otolith. The counts of annuli in otoliths of these eels were approximately consistent with the expected age. However, supernumerary false annuli and/or annulus underestimation frequently occurred. The methodology for annulus discrimination with light and scanning electron microscopes is described.

Notes: The relation between the form of the scattering particles and the outer part of the small-angle X-ray scattering curve has been studied. The particles are assumed to be independent, identical, and randomly oriented and to have a uniform electron density and a smooth, strictly convex boundary surface. The electron density of the solvent is also assumed to be uniform. As earlier calculations by the authors and others have shown, the effects of the particle shape on the scattered intensity can often be conveniently described by a function called the chord, or intersect, distribution G(M). A chord, or intersect, is a straight line that has both ends on the particle boundary surface, and G(M) is defined to have the property that G(M)dM is the probability that the chord length will lie between M and M+ dM. The outer part of the scattering curve is shown to depend on the form of G(M) only in the neighborhoods of M = 0 and of any M values at which G(M) or G′(M) are discontinuous. Methods are developed for finding where these discontinuities occur and for calculating the form of G(M) in the neighborhood of these M values. In the outer part of the scattering curve, the intensity I(h) is shown to have the limiting form I(h) = \pi I_{e}\rho^{2}h^{-4}\Bigg[2A+j_{-2}h^{-2}+ \sum_{i=0}^{N+1} j_{i} {{sin (hD_i + \phi _{i})}\over (hD_{i})^{\mu}_{\kern4pt i}}\Bigg] where h = 4πλ −1 sin (&thgr;/2), 2 is the X-ray wavelength, &thgr; is the scattering angle, Ie is the intensity scattered by a single electron, A is the particle surface area, the Di are the values of M at which G(M) or G′(M) is discontinuous, and j−2 and the ji, &phgr;i, and μi are quantities which can be calculated from the principal curvatures and other properties of the surface at the two points where it contacts the chord with length Di. The values of the μi are shown to lie in the interval 0 ≤ μi ≤ 1. In this equation the assumption is made that only the term or terms which vanish least rapidly as h increases are to be retained. In addition to the assumptions which conventionally are made in the analysis of the small-angle X-ray scattering from dilute suspensions, the limiting expression for the intensity for large h requires only that the particle boundary be smooth and strictly convex. This approximation is useful for determining the effect of the particle shape on the outer part of the scattering curve. In addition, the equation can be employed for numerical calculations for large h, where other methods of computation often are unwieldy or inapplicable.

Notes: Structure determination of macromolecules often depends on phase improvement and phase extension by use of real-space averaging of electron density related by noncrystallographic symmetry. Although techniques for such procedures have been described previously [Bricogne (1976). Acta Cryst. A32, 832–847; Johnson (1978). Acta Cryst. B34, 576–577], modern computer architecture and experience with these methods have suggested changes and improvements. Two unit cells are considered: (1) the p-cell corresponding to the actual crystal structure(s) being determined (there would be more than one of these if the molecule crystallizes in more than one crystal form) and (2) the h-cell corresponding to the molecule in a standard orientation with respect to which the molecular symmetry axes are defined. Averaging can proceed entirely within the p-cell, referring to the h-cell only in as far as knowledge of the molecular symmetry is required. It is also possible to place the averaged molecule back into the h-cell, where it can be used to redefine the molecular envelope or for displaying a suitably chosen asymmetric unit of the molecule. Techniques are discussed for automatically selecting a molecular envelope which is consistent with packing considerations within the p-cell and which retains the symmetry of the molecular point group. The electron density map to be averaged is divided into bricks for storage in virtual memory. Roughly as many bricks as there are noncrystallographic asymmetric units per crystallographic asymmetric unit need to be retained in memory at one time. This procedure minimizes paging problems and avoids double sorting. Use of eight-point interpolation permits storing the map at grid points separated by no more than 1/2.5 of the resolution limit to obtain rapid convergence.