Arrays of complex objects

Notice that only one plane of the three-dimensional diffraction pattern is superimposed on the film. With the crystal in the orientation shown, reflections shown in the plane of the film (solid spots) are the only reflections that produce spots on the film. In order to measure the directions and intensities of 

Each reflection can be assigned three coordinates or indices in the imaginary three-dimensional space of the diffraction pattern. This space, the strange land where the reflections live, is called reciprocal space. Crystallographers usually use h, k, and l to designate the position of an individual reflection in the reciprocal space of the diffraction pattern. The central reflection (the round solid spot at the center of the film in Fig. 2.11) is taken as the origin in reciprocal 

Alternatively, actual distances, rather than reflection indices, can be measured in reciprocal space. Because the dimensions of reciprocal space are the inverse of dimensions in the real space of the crystal, distances in reciprocal space are expressed in the units A 1 (called reciprocal angstroms). Roughly speaking, the inverse of the reciprocal-space distance from the origin out to the most distant measurable reflections gives the potential resolution of the model that we can obtain from the data. So a crystal that gives measurable reflections out to a distance of 1/(3 A) from the origin should yield a model with a resolution of 3 A. 

The crystallographer works back and forth between two different coordinate systems. I will review them briefly. The first system (see Fig. 2.4) is the unit cell (real space), where an atom s position is described by its coordinates x,y,z. 

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