Elementary biophysics: selected topics elementarybiophy00epst Year: 1963 X-RAY DIFFRACTION 95 To detector Figure 47 Consider the three measurable parameters indicated in the sketch: L, the distance from the crystal to the film; sh the distance from the undeflected beam to the individual lines; X, the wavelength of the x-rays. Since in practice the angles are always small, sin 20 « 2 sin 0 and Si L X = 2d sin 0 « 2d -Sf « ^ • Thus, as indicated earlier in this section, the spacing d can readily be computed from the measured quantities. For the simple monatomic crystal we are discussing, it
Elementary biophysics: selected topics elementarybiophy00epst Year: 1963 X-RAY DIFFRACTION 95 To detector Figure 47 Consider the three measurable parameters indicated in the sketch: L, the distance from the crystal to the film; sh the distance from the undeflected beam to the individual lines; X, the wavelength of the x-rays. Since in practice the angles are always small, sin 20 « 2 sin 0 and Si L X = 2d sin 0 « 2d -Sf « ^ • Thus, as indicated earlier in this section, the spacing d can readily be computed from the measured quantities. For the simple monatomic crystal we are discussing, it is only moderately difficult to relate the calculated spacings to the distances between atoms, but it is beyond the scope of this presentation. It remains to indicate how the intensities can yield the structures of molecules placed at the crystal positions. To this end we return to Fig. 44 and, as in Fig. 47, insert atoms midway between the planes. It is true that there will now be some new powder lines, but we shall neglect them for the present and consider only what happens to the already existing powder lines. In the case presented in the sketch, the extra distance traveled by ray III is just one-half that for ray II. Since the latter dis- tance is exactly one whole wave more than for ray I in the case of ray reinforcement, ray III travels exactly one half wave more than ray I. Thus it cancels ray I because its troughs are superposed on the crests of ray I, and vice versa. In this instance, then, the line will be missing. Now, if the extra atoms are not placed so that their contribution is pre- cisely one half wave different, then there will not be a total cancellation of ray I. In general, then, the insertion of the extra atoms will diminish
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