![]() |
![]() |
![]() |
![]() |
![]() |
Previous: 3.5 Effect of Strain on Symmetry Up: 3.5 Effect of Strain on Symmetry Next: 3.5.2 symmetry |
The point group of the unstrained diamond structure is denoted by according to
the Schönfließ notation, and contains 48 symmetry elements listed in
Table 3.2 [Yu03]. The symmetry elements are given
in terms of rotations and rotations followed by the inversion operation (I
). The
following notation for the point operations is chosen:
E | unity operation |
n![]() |
clockwise rotation of angle ![]() ![]() |
n![]() |
counter-clockwise rotation of angle ![]() ![]() |
I | inversion |
![]() |
clockwise rotation of angle ![]() ![]() |
![]() |
counter-clockwise rotation of angle ![]() ![]() |
![]() |
Of all the point symmetry groups of the crystal lattice, the
group
possesses the highest symmetry. The symmetry group
of the Bravais lattice of the strained crystal is a subgroup of the symmetry
group
of the unstrained crystal and does not generally belong to
the same crystal class as
. It contains only those symmetry elements which
are preserved under strain. The effect of a homogeneous strain on the symmetry
of the Bravais lattice depends on the specific form of applied strain.
By successively lowering the symmetry, one can go from to point group
on two distinct paths [Bir74]:
![]() |
![]() |
(3.35) |
![]() |
![]() |
(3.36) |
From (3.34) it can be concluded that the higher the point
symmetry of the crystal lattice, the smaller is the volume of the irreducible
wedge. In the following, the symmetries of the band structure and the shape of
the irreducible wedge in terms of the irreducible wedge of the unstrained
crystal are given for the crystal systems
, and
.
![]() |
![]() |
![]() |
  | ![]() |
Previous: 3.5 Effect of Strain on Symmetry Up: 3.5 Effect of Strain on Symmetry Next: 3.5.2 symmetry |