Bravais nets

Figure 1 Unit meshes and 20 Miiier indices, (a) Exampies of 20 Bravais nets (b) exam-pies of famiiies of rows with Miiier indices referenced to the unit mesh vectors. (11) and (31) famiiies of rows are shown.

There are 17 two-dimensional space groups arising from five Bravais nets associated with translation over a surface [28]. A Ceo molecule adsorbed onto a surface will therefore be subject to a local symmetry belonging to one of ten possible site symmetries Cev, Ce, C4V, C4, Csv, C3, Cxv, C2, Q, and Ci. None of these site groups support triply degenerate irreps and so the Ti LUMO will be split whenever Ceo... 

The Bravais lattice can be identified, on some specific Zone-Axis Patterns, from the observation of the shift between the reflection net located in the ZOLZ and the one located in the FOLZ. This shift is easily observed by considering the presence or the absence of reflections on the mirrors. Thus, in the example given on figure 1, some reflections from the ZOLZ are present on the four mi, m2, m3 and mirrors. This is not the case in the FOLZ where reflections are present on the m3 and m4 mirrors but not on the mi and m2 mirrors. Simulations given in reference [2] allow to infer the Bravais lattice from such a pattern. It is pointed out that Microdiffraction is very well adapted to this determination due to its good angular resolution (the disks look like spots). 

Example 16.1-1 Find the Bravais lattices, crystal systems, and crystallographic point groups that are consistent with a C3z axis normal to a planar hexagonal net. 

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