Help Morphic

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 (G_E):

G ∩ G_E = G^' ⊂ G
where G_E 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 = D_4h (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 ∩ G_E = C_4v (4mm)

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

G ∩ G_E = C_2v (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 (G_M):

G ∩ G_M = G^' ⊂ G
where G_M 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 = D_4h (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 ∩ G_M = C_4h (4/m)

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

G ∩ G_E = C_2h (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:

The initial point group:

One can select directly the point group from the table, one can also select the space group.

The field and the direction in which is going to be applied:

The next page is where one have to select the field (electric or magnetic) and the direction in which is going to be applied.

Output of the program:

The output of the program has three parts:

Input information:

In this part of the output one can find which are the parameters one has introduced: the filed, the direction and the point group.

There is a direct link to the program POINT which gives us information about the initial point group (character tables, point subgroups, ...).

Reduction of the point group:

Here one can find which is the new point group of the crystal + applied field and the transformation matrix which relates the initial whit the final point group.

There is another direct link to the program POINT which gives us information about the reduced point group (character tables, point subgroups, ...).

Correlation relation table:

In the last part of the output one can find the correlation relations between the initial crystal and the extended one.

Taking into account this table, one can say:

The modes A_1g, B_1g, B_2g and E_g which are Raman active in the high symmetry group remains Raman active and
they are also Hyper-Raman active in the low symmetry group.

The modes A_1g and E_u which are not IR active in the high symmetry group are active in the low symmetry group.

The mode A_1u which is Hyper-Raman active in the high symmetry group remains active in the low symmetry group.

The mode A_2g which is a silent mode in the high symmetry group is Hyper-Raman active in the low symmetry group.

The modes A_2u, B_1u, B_2u and E_u which are Hyper-Raman active modes in the high symmetry group are Raman and
Hyper-Raman in the low symmetry group.

Using this table one can predict the behaviour of the modes when it is applied and external field in a certain direction.

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