An Introduction to X-Ray Crystallography by M. Woolfson

By M. Woolfson

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1 A general description of the scattering process 33 this case, the intensity of the scattered radiation will depend on the distance from 0 and there will be an inverse-square law fall-off of intensity with distance. The intensity of the scattered radiation is thus usually described as the energy scattered per unit time per unit solid angle in a particular direction and is therefore a measure of what is happening at the scatterer itself. 1) where v is the frequency of the radiation and A its amplitude.

1 there are plotted the functions sin2(7ina#s) and sin2(7ia's) for n = 5. It is evident that the ratio of these two functions will be periodic with a repeat distance of unity so that if (Kn)2 = n2 for a*s = 0 it is also equal to n2 for a#s = h, where h is any positive or negative integer. In fig. 2, for the range a*s = 0 to 1 the function (Kn)2 is shown graphically for n = 3, 5 and 7. The vertical scale of these graphs has been adjusted to reveal more clearly the relative variation of (Kn)2 as a*s changes.

In fig. 32(a) these basic symmetry elements are shown together with the general structural pattern produced by them. It can be found by inspection that other symmetry elements arise; Ax is related to AA and A2 to A3 by glide planes which interleave the original set. The pairs of units A4, A2 and Al9 A3 are related by a centre of symmetry at a distance \c out of the plane of the paper and a whole set of centres of symmetry may be found which are related as those shown in fig. 25(a). The International Tables gives this space group with the unit-cell origin at a centre of symmetry and the structure pattern and complete set of symmetry elements appears in fig.

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