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By M. Woolfson
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Extra resources for An Introduction to X-Ray Crystallography
The maxima of(Kn)2 lie close to the maxima of sin2(7i/ia*s), being closer Fig. 1. The functions sin2(5ita*s) and sin2(7ia*s). 5 Diffraction from a crystal 52 Fig. 2. The intensity of scattering from rows of 3, 5 and 7 scatterers as functions of a*s. 0 the larger the value of n and the faster the variation of sin2(7trca-s) compared to sin2(7ia*s). As n tends to infinity, when the two sets of maxima tend to coincide, we may write the positions of the maxima of (Kn)2 as 2m + 1 a*s = — , m = 1 to n — 2.
Thomson. Fig. 5. A phase-vector diagram for six non-identical scatterers. 2nrh • s The scattering of X-rays 38 The basic mechanism of Thomson scattering is simple to understand. When an electromagnetic wave impinges on an electron the alternating electric-field vector imparts to the electron an alternating acceleration, and classical electromagnetic theory tells us that an accelerating charged particle emits electromagnetic waves. Thus the process may be envisaged as the absorption and re-emission of radiation and, although the incident radiation is unidirectional, the scattered radiation will be emitted in all directions.
1) where v is the frequency of the radiation and A its amplitude. The scattered wave will have a displacement at the point P (fig. 1) which will depend on a number of factors: (i) The distance OP ( = D) will introduce a phase shift with respect to the scattered wave at O of —inD/X where X is the wavelength of the radiation. This can also be expressed as —2nDv/c where c is the velocity of propagation of the radiation. (ii) The scattering process itself may introduce a phase shift so that the scattered wave at O will be retarded with respect to the incident wave at O.
An Introduction to X-Ray Crystallography by M. Woolfson