 | Acta Crystallographica Section E Acta Crystallographica Section E CRYSTALLOGRAPHIC COMMUNICATIONS |
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![[Figure 7]](oi2031fig7mag.jpg)
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Figure 7
The above illustration shows how Fourier analysis graphs can be used to derive a general rule for the appearance of the 210 reflection in the ordered CsCl-type variant, and its disappearance in the disordered bcc-type variant. In this case, the entire contents of the unit cell must be projected onto the line, as shown. Note the point symmetry with the grey B atom at the centre, which means that all B coefficients after summation of the individual scattering amplitudes will be zero. As in the example shown in Fig. 3 ![[link]](../../../../../../logos/arrows/e_arr.gif){kind=small} , therefore, only the A coefficient must be considered. As each of the B atoms (blue) shown represents two atoms in projection along the [001] direction, these must be counted twice. However, as each corner atom belongs to eight unit cells in the three-dimensional crystal structure, its contribution to the summation of the individual amplitudes must be weighted by the factor 1/8. Thus, the effective weighting factor for the B atoms is 1/8 × 2 = 1/4, as indicated. As the A atom at the centre of the structure is not shared with other unit cells, it is assigned a weighting factor of 1. As can now be seen for the 210 reflection, if all the atoms have the same scattering amplitude, as in the disordered bcc-type structure, the four blue B atoms with a positive contribution will cancel out the negative contribution from the one grey A atom in the centre due to the 180° phase difference between the two sets of atoms. If ordering takes place and the CsCl-type structure is formed, either the sum of the B atoms (= fB) will exceed the contribution of the A atom in the centre [A(210) is positive and the structure factor will be zero], or vice versa [A(210) is negative and the structure factor will be 180°, see look-up table in Appendix A]. In both cases, the structure-factor amplitude will be non-zero, and a weak reflection will be observed in the diffraction pattern. |
![[Figure 7]](oi2031fig7.jpg)
| CRYSTALLOGRAPHIC COMMUNICATIONS |
ISSN: 2056-9890
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