 | Acta Crystallographica Section E Acta Crystallographica Section E CRYSTALLOGRAPHIC COMMUNICATIONS |
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![[Figure 10]](oi2031fig10mag.jpg)
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Figure 10
Model for the cubic diamond structure in projection along the [001] direction with corresponding one-dimensional Fourier analysis graphs for the 200 and 400 reflections. Atoms shown in dark grey refer to atoms of the underlying fcc lattice that was assumed by the Braggs in their 1913  investigation. The green atoms refer to atoms on the tetrahedral sites of the cubic unit cell. The numbers beside the atoms denote their weighting in the numerical summation, e.g. atoms on the corners of the unit cell are in fact two atoms projected on top of each other, where each of the atoms is part of 8 unit cells ( ), and atoms at the face centres belong to two unit cells and thus are weighted by
1/2. As seen in the 200 graph, the four atoms from the fcc sub-lattice match all with the maxima, so the remaining four atoms must be placed in between at the minima to yield extinction. Acknowledging that the same situation is met if the unit cell is rotated in plane by 90° makes extinction of the 200 (and 020) reflection only possible if the four (green) carbon atoms are placed at xy = ¼ ¼; ¼ ¾; ¾ ¼; ¾ ¾ as shown. The corresponding graph for the 400 (or 040) reflection shows that this arrangement results in a positive amplitude for all atoms (all atoms scatter in phase), yielding the strong 400 peak in Fig. 9(b). As this analysis can be repeated for any other equivalent projection of 〈001〉, it must be concluded that the four carbon atoms will be located on the tetrahedral sites of the cubic unit cell. However, a cubic unit cell has eight tetrahedral sites in total, but at this stage only four atoms are remaining to be distributed among them. Thus, a symmetrical distribution can only be obtained by a diagonal distribution of the carbon atoms at each level as shown in Fig. 12. This also agrees with the model of the projection along [001] in Fig. 10, where each of the tetrahedral sites is only occupied by one atom (note that in fact two of the tetrahedral sites in three dimensions fall on top of each other in the two-dimensional projection). The model derived thereby is in perfect agreement with the finding that the 200 reflection is extinguished and that 400 is the first strong reflection (see Fig. 9). |
![[Figure 10]](oi2031fig10.jpg)
| CRYSTALLOGRAPHIC COMMUNICATIONS |
ISSN: 2056-9890
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