Coincidence schematic illustrations

Fig.11.14. Schematic illustration of time-to-pulse-height conversion used for lifetime measurements with delayed coincidences...

Figure 9.17b schematically represents a cross-sectional view of the surface of a solid and represents the topmost layer of atoms by shaded circles. The open circles represent molecules in an ordered pattern on the solid substrate. Since the adsorbed molecules are ordered, their structure on the surface is characterized by what is called a supernet. Suppose we define <50 as the characteristic spacing of the substrate and 8S the equivalent quantity for the supernet. Then the two arrangements in Figure 9.17b are described by the ratios 5/60 = 4/1 and 8s/80 = 4/3. Building on the notion of reciprocal distances as developed in the discussion of Figure 9.15, it follows that the adsorbed layer with 8/80 = 4/1 should produce spots with a separation that is 1/4 that of the substrate. Likewise, for the case when 8s/80 = 4/3, a pattern of spots with a separation that is 3/4 that of the substrate is predicted. Thus, if the substrate produces spots at, say, 0 and 1, extra spots would be expected at 1/4, 2/4, and 3/4 for the 6/60 = 4 case, and at 3/4, 6/4, and 9/4 when 8s/80 = 4/3. The cases illustrated here are called coincident structures since the two patterns coincide periodically. When there is no correlation between two structures, they are said to be incoherent. 

Measurements of daPs/dQ for positron-argon scattering have also been made by Finch et al. (1996a, b) and Falke et al. (1995, 1997) and for positron-krypton scattering by Falke et al. (1997). The principle of the experiments, involving the detection of the positronium in coincidence with an atomic ion, is illustrated schematically in Figure 4.28. More details of the system used by Finch et al. (1996a), which has also been used to study the differential ionization cross section, can be found in section 5.6. 

Assume, however, that the asymmetric unit is composed of two or more identical copies of a molecule. These may be related by exact rotational symmetry, such as a dyad or triad, that is not coincident with any crystallographic operator and, hence, is not a part of the space group symmetry. The molecules may also be related by some completely general rotation plus translation. The asymmetric unit will give rise, in either case, to a continuous transform that is essentially a superposition of the transforms of the two independent molecules. This is illustrated schematically in Figure 8.9. The two molecular transforms are identical because the two molecular structures are the same, but the two transforms will be rotated relative to... 

Fig. 11.38 shows the density of the located AE events in projection to the three coordinate planes (x-y-plane at top, z-y-plane in the middle, and x-z-plane at bottom) in this as5munetric compression test as schematically shown in Fig. 11.39. The crack growth is illustrated in four stages (al to a4) of approximately 130 located events each and the final stage a5 of stress accumulation after the pre-fracture (290 events). The y-z-plane represents a view onto the macroscopic fracture plane, which is growing from top left to about 10 mm above the bottom surface. The x-y-plane shows that the contour lines of high event density coincide with the locus of maximum shear stress from finite element calculations. After the complete shear fracture formation the AE activity shifted to the remaining part of the specimen.

Cure is illustrated schematically in Figure 1 for a material with co-reactive monomers such as an epoxy-diamine system. Reaction in the early stages of ciu-e (a to b in Fig. 1) produces larger and branched molecules and reduces the total number of molecules. Macroscopically, the thermoset can be characterized by an increase in its viscosity r] (see Fig. 2 below). As the reaction proceeds (lb to Ic in Fig. 1), the increase in molecular weight accelerates and all the chains become linked together at the gel point into a network of infinite molecular weight. The gel point coincides with the first appearance of an equilibrium (or time-independent) modulus as shown in Figure 2. Reaction continues beyond the gel point (Ic to Id in Fig. 1) to complete the network formation. Macroscopically, physical properties such as modulus build to levels characteristic of a fully developed network. 

If the reaction kinetics of the electrode is assumed to be very rapid, mass transfer and ohmic resistance are the dominant resistances. Assuming a reaction zone that coincides with the electrode-electrolyte interface, the diffusion fluxes in stationary operation can be expressed simply in terms of bulk gas partial pressures and gas-phase diffusivities. This is illustrated schematically in Figure 11.8, which compares anode- and cathode-supported cell designs for the simple case of a H2/O2 fuel cell. The decrease in concentration polarisation at the cathode, rjcc- is obvious in the case of an anode-supported cell, while the model shows that concentration polarisation at the anode, tiac is relatively insensitive to anode thickness. The advantage of the mass transfer-based approach is that analytical expressions are obtained for the polarisation behaviour. These are rather simple if activation overpotential is excluded but may still become elaborate in the case of an internally reforming anode where a number of reactions (discussed in Section 11.3) may occur simultaneously within the pores of the anode. 

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