4.6. - Sectors
Sectors correspond to different
symmetry transformations of
(2 , , , )
and may be of help in avoiding blind
spots.
Sectors can also be useful for samples in cryostats or
ovens.
All modes
can have the positions chosen for the motors
further influenced by the choice of sector.
However, the modes
azimuth-fixed , "alpha-fixed" and "beta-fixed" only allow sectors numbered zero through three, below.
For a given pair of incident and scattered X-ray beams,
k [i] and
k [f], there are
eight orientations of the crystal in the spectrometer that give
the same scattering since they present equivalent projections to the
incident and scattered beams.
The eight orientations
are labeled as sectors 0 through 7.
Four of the orientations
come from the symmetries of a pair of vectors.
They correspond to
the identity operation (i.e.,
the current diffraction angles),
a rotation of 180° about
k [i], a rotation of 180° about the bisector of
k [i] and
k [f], and
a rotation about
z
by 180° - 2.
The last two symmetries are based on interchanging the role of the
entrance angle and the exit angle of the X-rays on the sample.
These four symmetries give sectors 0, 2, 4 and 6 in
fourc.
For each of these
four positions another position can be obtained by increasing by 180°,
decreasing by -180° and changing the sign of .
Since a
rotation of 180 and of -180
are the same, both and can be increased by 180.
These orientations
give sectors 1, 3, 5 and 7.
Studying these operations shows that sectors
2, 3, 6 and 7 have opposite signs of 2 from the current position.
Sectors 2, 3, 4 and 6 have flipped the
up
direction of the sample
(normal to the scattering plane)
to the
down
direction.
The value of
g_sect determines in which sector of reciprocal space the diffractometer
operates.
The actual transformations of the angles are:
| |
 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
| 2 -> |
|
2 |
2 |
-2 |
-2 |
2 |
2 |
-2 |
-2 |
| -> |
|
|
- 180° |
- |
180° - |
- |
180° - |
|
- 180° |
| -> |
|
|
- |
- 180° |
180° - |
180° - |
- 180° |
- |
|
| -> |
|
|
- 180° |
|
- 180° |
- 180° |
|
- 180° |
|
In addition,
a sector 8 is defined that can be
used when the and
circles of the diffractometer are
arc segments in contrast to the complete circle.
Sector 8 minimizes
| - 90°| and
||.
|
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