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Morphic Effects

The morphic effects are those that arise from a reduction of the symmetry of the system caused by the application of an external force, for example: an electric field or a magnetic field. The new system, the crystal + applied force correspondes to a new symmetry group (group-subgroup related) that leave the new system invariant.

Once it is known the point group of the initial system and the extended one (crystal + applied force) one can cancluate the correlation relations between the point groups and study their behaviour of the IR, Raman and Hyper-Raman modes.

Electric Field or Uniaxial Stress

The electric field can be represented as a vector. A vector is invariant under the rotations along
its axes, the planes which contains that vector leave also it invariant as one can observe in the figure.
Taking this into account one can say that there are infinity rotations and planes which leave the
vector invariant
. In this case, a vector can be represented by the point group: C∞v (∞m).

One can calculate the new point group of the crystal + electric field by the intersection
of the initial point group (G) and the point group which represent the electric field (GE):

G ∩ GE  =  G'  ⊂   G

where GE is the point group C∞v (∞m)   and G' is the point group of the crystal + electric field
and it is a subgroup of the initial point group.


Example:

Supose that the point group of the crystal without electric field is G = D4h (4/mmm) and it is applied an
electric field along the direction (0 0 1). The point group of the crystal with an electric field applied is:

G ∩ GE  =  C4v (4mm)


Imagine that the electric field is applied in the direction (1 0 0):

G ∩ GE  =  C2v (mm2)


Once the point group of the extended system is known it is easy to calculate the correlation relations between
the point groups and their behaviour.

Magnetic Field

The magnetic field can be represented as an axial vector or a pseudovector. An axial vector is invariant
under the rotations along its axes, the plane perpendicular to this axes also leaves invariant the axial vector
as it is shown in the figure. Taking this into account one can say that there are infinity rotations and one
perpendicular plane which leave an axial vector invariant
. In this case, a vector can be represented by the
point group: C∞h (∞/m).

One can calculate the new point group of the crystal + magnetic field by the intersection of the initial point group
(G) and the point group which represent the magnetic field (GM):

G ∩ GM  =  G'  ⊂   G

where GM is the point group C∞h (∞/m)   and G' is the point group of the crystal + magnetic field and it is a subgroup
of the initial point group.


Example:

Supose that the point group of the crystal without magnetic field is G = D4h (4/mmm) and it is applied a magnetic
field along the direction (0 0 1). The point group of the crystal with a magnetic field applied is:

G ∩ GM  =  C4h (4/m)


Imagine that the magnetic field is applied in the direction (1 0 0):

G ∩ GE  =  C2h (2/m)


One the point group of the extended system is known it is easy to calculate the correlation relations between the
point groups and their behaviour.


Input of the program:

This program calculates the reduction of the symmetry when an electric field or a magnetic field is applied and the behaviour between the modes of the high and low symmetries. The information that one has to introduce is:

Output of the program:

The output of the program has three parts:

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