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In Section 7.4 we acknowledged that, for physiological and biochemical reasons, it can be insightful to conceptually split the elements away from one another. If we examine the stuff of life (the live and dead biotic components of the biosphere plus nutrients; Section 7.3) and sort through these materials by elemental content, then budgets can be assembled. We have seen (Section 7.2) that such budgets help assess the status and health of Earth. These scienti c exercises tally the sizes of nutrient pools and the uxes of materials between them. Figures 7.16 7.18 portray global elemental cycles of carbon, sulfur, and nitrogen for terrestrial, atmospheric, and marine compartments of the globe.

If your font doesn t have the accented characters you need, you may be able to create them by kerning accent marks over the letters. See 16 for detailed information on kerning.

Figure 15-8 X-ray tomographic time series of blending of radiopaque grains in a double-cone blender is representative of several new techniques available for on-line and in situ assays of blending mechanisms. (From Chester et al., 1999.)

FIGURE 16-18: The camera is excellent at macro photography without the plain glass to replace the IR-blocking filter.

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range of X-ray wavelengths (see Section 6.3.2). A visual/mathematical depiction of complete Bragg law re ection from stacks of hkl-lattice planes is the reciprocal lattice. The reciprocal lattice has imaginary dimensions a , b and c that are inversions of the a, b and c dimensions of the unit cell. Each reciprocal lattice point corresponds to an hkl re ection that satis es the Bragg law from a given stack of hkl-lattice planes that bisect the unit cell. In effect, a given reciprocal lattice represents a complete theoretical diffraction pattern. The Ewald sphere was developed as a tool to construct the directions of X-ray scattering. However, it also serves as a means to determine how to sample the vast majority of reciprocal lattice points, or in other words sample the intensity of X-rays scattered by re ection from every possible stack of hkl-lattice planes. In order to construct an Ewald sphere, an incident beam of X-rays is considered as being directed towards the origin O of the reciprocal lattice. A sphere is then constructed that cuts the origin O on its surface but whose centre M marks the position of the crystal. The radius MO is 1/ , where is the wavelength of incident X-rays (Figure 6.4). Only reciprocal lattice points that sit on the surface of the sphere correspond to X-ray re ections that may be detected given the orientation of the crystal with respect to the incident X-ray beam and the wavelength of the incident X-rays. If the orientation of

8.5.3.1 A Paraboloidal Array. We take as an example an array of elements on a general paraboloid of revolution (GPOR). The radiating elements are assumed to have element patterns corresponding to those of short dipoles in free space (cosine patterns) and their polarization characteristics are also assumed to be those of short dipoles. Mutual coupling is neglected. Since it is not possible to create a regular lattice of elements on a doubly curved surface, an approximation according to the following rule is used. A minimum spacing d along the surface is defined from grating-lobe considerations (typically d 0.5 ). One element is placed at the vertex position. The first ring of elements is spaced d from the first element. Within such a ring, as many elements as possible are placed at regular angle ( ) intervals. However, the spacing along the ring is not less than d. The procedure is then continued with the next ring, and so on. The first elements of each ring are initially positioned along the same generating curve (at the same angle, thus on a parabolic arc). However, every second ring is then rotated one-half interelement spacing in order to spread the elements more evenly. An example of an element layout for a 14-ring array on a paraboloid as seen from the symmetry axis is shown in Figure 8.33. In order to spread the first elements evenly along the parabolic arc (at constant ) we need to know the total parabolic length from the vertex. This length normalized to the focal distance is

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