Possible Point of Confusion -First and Second Settings
Now, let's discuss a few of the potentially confusing details about Bravais lattices and unit cells.
What's this stuff about "first" and "second" settings of monoclinic cells? I believe this is associated with a historical artifact that's simply part of the tradition of crystallography. In early versions of the International Tables, only one setting was presented for monoclinic cells. This was what's now called the second setting. It's the one with b as the unique monoclinic axis. In higher symmetry lattices like tetragonal or hexagonal, c is the unique axis parallel to the four-fold and six-fold axes. To be consistent, you'd think c should also be the unique axis in monoclinic systems, and this has become the officially sanctioned "first" setting in the later editions of the Tables. However, tradition also continues to rule, and most published structure determinations in monoclinic cells, have b as the unique axis.
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