Structure and X-ray diffraction Some examples

X-ray diffraction works wonders when applied to crystals, but is also useful in the study of other materials. In order to provide some understanding of how the internal structure of a condensed phase is portrayed in its diffraction pattern, a few computational examples on typical states of matter will now be given. 

The succinic anhydride molecule is used as a computational guinea pig. Consider first the unit cell of the succinic anhydride crystal, with four molecules with all atomic coordinates known. Consider then a slab carved out of the succinic anhydride crystal structure (Fig. 5.14(a)) containing 224 unit cells (896 molecules, 9,856 atoms). For the sake of the computational experiment, consider also a box made by 864 succinic anhydride molecules (9,504 atoms) arranged in a more or less regular fashion (Fig. 5.14(b)) this is a semi-crystalline system. The latter box has then been ther-malized by a molecular dynamics calculation (see Chapter 9), and frames have been extracted from the simulation after 1 ps (Fig. 5.14(c)), 5ps, and46ps (Fig. 5.14(d)) [7]. The progressive loss of structure is clearly visible, until in Fig. 5.14(d) molecules are completely at random, a true liquid state. The position of all atoms in the crystal unit cell and in each of these computational boxes is known to the computer. 

Consider first the true crystalline state. Using the unit cell information, all the structure factors, equation 5.27, can be calculated and a graph can be prepared where each Bragg reflection appears with its intensity at the proper 0 location in a 0/intensity plot. A visually conspicuous, overall landscape view of the distribution of Bragg reflections in 0-space is thus obtained. This corresponds to the pattern obtained experimentally by diffraction from finely ground crystalline material, in which crystallites are oriented at 

For the simulation, intensities /hki(0), equation 5.31, are calculated, using an average thermal B factor. The complete powder profile is then prepared by placing each Bragg peak at its calculated position 0°, with an exponential spread  

The calculation of the powder diffraction pattern can be done also using Debye s equation 5.21, as the position of all atoms and hence all the atom-atom distances 

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