Ten![]() Calculations with tensors and characters M. Ephraim, T. Janssen, A. Janner and A. Thiers |
Dimension | 3 |
Rank | 1 |
Point group | m (unique axis y) |
Permutation symmetry | 0 |
Basis transformation | Identity |
Type | Pseudotensor |
The result: One free parameter, T, T
=T
=0.
Dimension | 2 |
Rank | 2 |
Point group | 3 |
Permutation symmetry | (0 1) |
Basis transformation | Identity |
Type | Tensor |
The group is generated by a threefold rotation which is represented on a lattice basis
by the matrix
Dimension | 3 |
Rank | 2 |
Point group | 4 |
Permutation symmetry | (0 1) |
Basis transformation | Identity |
Type | Tensor |
There are two free parameters:
Dimension | 3 |
Rank | 4 |
Point group | 4 |
Permutation symmetry | ((0 1)(2 3)) |
Basis transformation | Identity |
Type | Tensor |
Result:
There are seven free parameters. For the standard notation where 1=, 2=
, 3=
,
4=
, 5=
, 6=
the elastic tensor becomes the 6
6 matrix
Dimension | 3 |
Rank | 2 |
Point group | 4 |
Permutation symmetry | [0 1] |
Basis transformation | Identity |
Type | Pseudotensor |
There is one free parameter:
Dimension | 3 |
Rank | 2 |
Point group | mm2 (unique axis z) |
Permutation symmetry | 0 1 |
Basis transformation | Identity |
Type | Pseudotensor |
There are two free parameters, and the elements of the invariant tensor are
,
,
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