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Additional info for Infrared and Raman selection rules for molecular and lattice vibrations: the correlation method

Example text

Here, only one typical example of the X-ray diffraction intensities for an amorphous substance (a glass) is given in Fig. ^"^^ The diffuse scattering, resulting in a typical diffuse halo, is mainly due to the predominant contribution of the third term in Eq. 34, which in turn results from the oscillations of the function P(r), which correspond to the length of the most common S i - 0 bond (ca. 6 A) and the 0 - 0 and Si-Si separations. The function differs in this respect from that of liquid (cf.

Since it results from an inelastic collision between an X-ray photon and an electron (cf. Fig. e. at zero scattering angle. 19) fmn is an exchange term due to interaction of the mth and nth electrons. RED is the BreitDirac electron recoil factor. Where the double summation term may be omitted in practice, and at zero scattering angle, since E I fmm 1^ is equal to Z, /inco is zero. i increases, /inco also increases to give a continuous intensity distribution. 1) Compton scattering factors for some important atoms are given in Table 4 of the Appendix.

P. 3(A^3) for the Laue diffraction function (the expression in brackets in Eq. 44) where, G = L^L2^L^^. e. if M, A^2, and N3 are at least of the order of 100, G (or L^) has the value N1N2N3 only over a very small solid angle (cf. Fig. 20) and the X-ray diffraction amplitude Acr, as mentioned above, is zero except in those 42 2. X-Ray Scattering, Interference and Diffraction directions where the Laue conditions are satisfied. ^^^ It is also instructive, however, to consider the form of G (or L^) when M,A^2and A^3 are fairly small, as they are for very small crystals.

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