Reciprocal patterns

Maisonpierre PC, Bellusicio L, Squinto S, et al. NT-3, BDNF and NGF in the developing rat nervous system parallel as well as reciprocal patterns of expression. Neuron 1990 5 501-509. 

The lanthanide abundance pattern for Shergotty (table 9, fig. 7) is unique among meteorites and indicates a complex prehistory in the Martian mantle from which they appear to have been derived, as basalts, by partial melting. The enriched pattern of the heavy lanthanides (Gd-Lu) resembles that of pyroxenes (the parent rocks appear to have been pyroxene cumulates). It provides no evidence that garnet was a residual phase in the source from which these basalts were derived, for, if so, the reciprocal pattern would be displayed. Leaching experiments show that most of the lanthanides are contained in accessory phases (whitlockite and apatite) rather than in the major mineral phases. 

Figure Bl.21.4. Direct lattices (at left) and reciprocal lattices (middle) for the five two-dimensional Bravais lattices. The reciprocal lattice corresponds directly to the diffraction pattern observed on a standard LEED display. Note that other choices of unit cells are possible e.g., for hexagonal lattices, one often chooses vectors a and b that are subtended by an angle y of 120° rather than 60°. Then the reciprocal unit cell vectors also change in the hexagonal case, the angle between a and b becomes 60° rather than 120°.

The reciprocal lattices shown in figure B 1.21.3 and figure B 1.21.4 correspond directly to the diffraction patterns observed in FEED experiments each reciprocal-lattice vector produces one and only one diffraction spot on the FEED display. It is very convenient that the hemispherical geometry of the typical FEED screen images the reciprocal lattice without distortion for instance, for the square lattice one observes a simple square array of spots on the FEED display. 

One of the spots in such a diffraction pattern represents the specularly reflected beam, usually labelled (00). Each other spot corresponds to another reciprocal-lattice vector = ha + kb and is thus labelled (hk), witli integer h and k. 

Diffraction is usefiil whenever there is a distinct phase relationship between scattering units. The greater the order, the better defined are the diffraction features. For example, the reciprocal lattice of a 3D crystal is a set of points, because three Laue conditions have to be exactly satisfied. The diffraction pattern is a set of sharp spots. If disorder is introduced into the structure, the spots broaden and weaken. Two-dimensional structures give diffraction rods, because only two Laue conditions have to be satisfied. The diffraction pattern is again a set of sharp spots, because the Ewald sphere cuts these rods at precise places. Disorder in the plane broadens the rods and, hence, the diffraction spots in x and y. The existence of streaks, broad spots, and additional diffuse intensity in the pattern is a common... 

These reciprocal lattice vectors, which have units of and are also parallel to the surface, define the LEED pattern in k-space. Each diffraction spot corresponds to the sum of integer multiples of at and at-... 

Reactions that fit this model are called ping-pong or double-displacement reactions. Two distinctive features of this mechanism are the obligatory formation of a modified enzyme intermediate, E, and the pattern of parallel lines obtained in double-reciprocal plots (Figure 14.19). 

Figure 3-68. Reciprocating pump discharge flow patterns. (Courtesy the Aldrich Pump Co.)...

Significant Features in Reciprocating Pump Arrangements, 215 Performance, 217 Discharge Flow Patterns, 218 Horsepower, 218 Pump Selection, 221. 

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