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(Bravais?) lattice with one angle equal 90

  1. Sep 17, 2014 #1
    I have seen in some books that the triclinic bravais lattice ( a≠b≠c , α≠β≠γ ) excludes explicitly the option that one angle equal 90°. For instance 90°≠α≠β≠γ=90°.

    If I got the definition of α, β and γ correctly, it would be a primitive cell with a pair of parallel faces as rectangles, and rhoumbuses in the other two pairs.

    The question is: Why this lattice is not included in the bravais lattices? Is possible to redefine the vectors, such that they turn into one of the Bravais lattices?
     
  2. jcsd
  3. Sep 19, 2014 #2
    A lattice with just one angle at 90 deg does not have a special symmetry (unlike a monoclinic lattice with two 90 deg angles).

    Therefore the 90deg does not have any significance and would only be "accidental" rather than locked by the appearance of a symmetry operation.

    You can see this from looking at the point groups for the triclinic and monoclinic space groups: As soon as
    there is a 2-fold rotation axis or mirror plane or both you are in the monoclinic lattice with two 90deg angles.

    http://en.wikipedia.org/wiki/List_of_space_groups
     
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