# Symmetries in silicon

by Kreck
Tags: silicon, symmetries
 Emeritus Sci Advisor PF Gold P: 11,155 As far as I can see, the principal axes are normals to the {110} family of planes (i.e., lines joining edge-center and opposite edge-center) as they have a 4-fold rotation symmetry. That automatically makes the 3 planes in the {110} family the $\sigma _h$ planes. I don't see any reason that the {100} family needs to make up the $\sigma _h$ planes. The point group is defined by the symmetry elements, which are independent of the co-ordinate system.
 Sci Advisor PF Gold P: 1,474 Symmetries in silicon Its not....the vectors will not be orthogonal in the {110} set of planes. Remember that silicon $\Gamma$ -point is 48 fold symmetric.