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CAD4/MACH3
User manual |
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Introduction
X-ray optics
Without a monochromator
in the primary beam
With a monochromator
in the primary beam
Alignment without monochromator
Initial alignment procedure
Final alignment procedure
Alignment using the monochromator
Introduction
Initial alignment procedure
Final alignment procedure
The alignment program
Test crystal data
The major task of the alignment procedure described in this Chapter
is to direct the primary X-ray beam through the center of the goniometer
and through the center of the receiving aperture when positioned at THETA=0.
The alignment is done using a suitable crystal that must be well centered
on the
goniometer. The test crystal is generally used for this task.
The goniometer has been carefully manufactured and checked; phi, kappa
and omega axes intersect within a sphere, the radius of which is less than
10 microns. The connecting line between the centre of this sphere and the
center of the collimator lies in the equatorial plane of the goniometer
and points towards the OMK=0 position. The center of the detector aperture
can be moved in the equatorial plane. Alignment of the goniometer is achieved
when the correct positions of the focal spot, the
sample crystal and the horizontal center of the detector aperture have
been set. The alignment of the goniometer must be checked any time the
tube is changed. Readjustment could also be necessary after using one tube
for extended periods of time, as the position of its focal spot might change
slightly.
Each CAD4 goniometer has its characteristic constants. The success of any alignment attempt will depend on the use of the correct series of constants. These constants have been supplied with the goniometer and the aperture system. To check or to modify the constants read Chapter VII section C.
Before starting the alignment procedure check on the correct setting of the radiation detection equipment. Read Chapters XIII and VII (section C) to check and/or modify the radiation detection constants.
Supplied with the diffractometer is a spherically ground test crystal (ammonium bitartrate, for characteristic values, read Section F of this Chapter). This test crystal is well suited for doing the alignment. Of course other appropriate crystals could be used as well. These crystals should have the following properties:
1. Small size (0.2mm maximum diameter) and regular sphere; enable accurate
optical centering.
2. Some reflections with high intensity; enable fast measurements.
3. Small mosaic spread; give rise to properly shaped reflection profiles.
4. High symmetry; allow comparison of many symmetry-equivalent reflections.
5. Low absorption coefficient; enable comparing the intensities of
symmetry equivalent reflections.
The test crystal should be kept mounted permanently on the goniometerhead with the scattering vector of a useful reflection directed along the goniometer phi-axis. The orientation matrix should be known and the results of an alignment procedure should be well documented and saved for later comparison. This will provide a good working standard for the instrument.
In this chapter the CAD4 alignment procedure will be described. For this alignment it will be necessary to make adjustments to the hardware of the CAD4 goniometer. We refer to the drawings at the end of this manual for the position of the adjustment screws. Always use a measuring gauge when doing the alignment.
The four most important adjustments are:
B.1 Without a monochromator in the primary beam
The primary beam passes through a collimator and is directed in the horizontal plane towards the center of the diffractometer. The function of the collimator is not to provide a "parallel" beam, but only to reduce the angle of X-ray emission from the X-ray tube window. The collimator is an X-ray shield; it limits the divergence of the primary beam. The choice of the collimator has no influence on the intensity in the center of the beam. Similarly, the receiving aperture in front of the detector and the secondary beamtunnel must permit all diffracted beams to enter the detector window.
The collimator chosen should match both the size of the sample crystal and the size of the focal spot; it should minimize the size of the unused parts of the beam. On the other hand, it should be possible for all parts of the focal spot to be seen from all parts of the sample crystal. This should also apply when the focal spot is slightly out of position during the final steps of the tube alignment.
The width of the focal spot as seen by the sample crystal can be changed
in the horizontal direction by changing the take-off angle. The take-off
angle is adjusted (using a special key(4.10) from the CAD4 accessory box)
by a screw at the rear of the goniometer (see Technical
user manual). The take-off
angle can be locked by tightening the hex-socket screw below the X-ray
tube support (see Technical
user manual). For most applications the optimum take-off angle is such
that the focal spot shape appears square. An axial rotation of the tube
filament is occasionally observed. This causes a change of spot
shape from a square to a diamond. For fine focus tubes the theoretical
optimum is 2.9 degrees take-off angle; i.e. a square focus of 0.4*0.4mm.
A pinhole photograph of the X-ray source will reveal the shape,
the size and the intensity distribution of the spot. This pinhole (preferably
30 or 40 microns) should be placed as close to the X-ray tube window as
possible and a photograph should be taken. The film plane should be as
far from the crystal as possible for a good magnification. Use the supplied
pinhole
alignment pipe with the pinhole to the source end of the collimator
bed. It is not possible to take a useful pinhole with a normal collimator
B.2 With a monochromator in the primary beam
The monochromating material diffracts the primary beam, producing a
beam of "filtered" radiation. The surface of the monochromator is considered
to replace the focal spot. In the CAD4 the diffraction plane of the monochromator
can be perpendicular, parallel or anti-parallel to the horizontal diffraction
plane of the goniometer. Depending on this the dispersion is vertical (perpendicular
setting) or horizontal (
(anti)parallel setting). The monochromator is a flat 10*10 mm square
plate of oriented graphite with a mosaic spread of about 0.4 degree used
at the 0,0,2 reflection with a lattice spacing of 3.354 Angstrom. The monochromated
beam contains both the LAM1 and the LAM2, because the mosaic spread of
the monochromator and the focal spot size are too large. A fluorescent
screen placed in the beam leaving the
monochromator shows a flat but very wide spot. This can be interpreted
as a wide virtual source rather than a divergent beam from a point virtual
source. The second hole of a collimator(placed in that beam) is used to
limit the "cross-fire". Without this restriction the divergence of the
beam in the horizontal plane would be too large. The intensity distribution
of the beam in vertical direction does not have a
wide plateau. This limits the size of the crystals that can be analysed
to 0.3mm using fine focus tubes. Here, a traditional pinhole photograph
of the monochromated beam is unsuitable for analysing the virtual source.
This stems from the fact that a "parallel" beam leaves the monochromator;
the points of the
virtual source do not radiate in all directions. Therefore a pinhole
placed on a goniometer head in the center of the goniometer must be scanned
horizontally and vertically through the beam if it is desired to map the
intensity distribution.
If the monochromator is used for Ag radiation, the Bragg angle(THETAm) is 4.8 degrees. In that case diffraction occurs across a very large part of the surface of the graphite plate. The height adjustment of the monochromator is therefore critical in positioning the virtual source in the equatorial plane of the diffractometer.
Diffraction by a monochromator produces a beam which is partially polarized. For ideally imperfect monochromating material the polarization factor is:
P =[(cos(2THETAm))**2 + (cos(2THETA))**2]/[1 + (cos(2THETAm))**2]
Where THETAm equals the Bragg angle for the monochromator and THETA equals the Bragg angle for the sample crystal. For a perfect monochromator the polarization factor is:
P =[cos(2THETAm) + (cos(2THETA))**2]/[1 + cos(2THETAm)]
The difference is not significant for Ag- and Mo-K radiation (<0.5% for 2THETA below 90 degrees).
Table XII.1 Summary of diffraction angles for oriented graphite.
| Chemical
symbol |
LAM1
Angstrom |
LAM2
Angstrom |
sin(T1) | sin(T2) | THETA1
degr |
THETA2
degr |
| Ag | 0.5594075 | 0.563798 | 0.0834 | 0.0840 | 4.78 | 4.82 |
| Cu | 1.5405620 | 1.544390 | 0.2297 | 0.2302 | 13.28 | 13.31 |
| Mo | 0.7093000 | 0.713590 | 0.1057 | 0.1064 | 6.07 | 6.11 |
However, for very accurate intensity measurements using Cu-K radiation,
it may be necessary to determine the appropriate form of the polarization
factor.
For further reading refer to Cole, Chambers and Wood, J.Appl.Physics,
32, 1942 (1962).
C. Alignment without monochromator
C.1 Initial alignment procedure
Normal operation of equipment producing X-rays should be done by experienced
personnel only. Care must be taken to avoid inexperienced personnel to
enter the CAD4 room during the alignment of the diffractometer. One should
be aware also that while the beam stop is removed back scattering can be
substantial.
Mount the X-ray tube and set the high voltage and tube current (see
FR590
Technical user manual). Although safety interlocks are provided to
ensure the correct positioning of collimator and X-ray port (or
monochromator housing), it is strongly recommended to check there is
no radiation leakage between the tubeshield and the collimator assembly.
The purpose of the initial alignment is to bring the focal spot to the position where the final alignment using the test crystal can be started. The initial alignment should be done quickly and safely. Accuracy is the aim of the final alignment procedure.
The focal spot is brought into approximate position by setting the detector to directly intercept the primary beam by removing the backstop cap and setting THETA to ZERO. This is a dangerous thing to do, thus all attention must be paid to safety. It should be emphasized, that the scintillation detection equipment may be damaged, if it is exposed to a too high intensity of X-rays for too long.
Procedure stepwise:
1. Switch off the high voltage
2. Set the high voltage selection switch at 20 kV for a Cu tube, at
23 kV for a Mo tube or 25 kV for an Ag tube.
3. Set the mA selection for the tube at the minimum current.
4. Set the beta filter at the tubeshield; Ni for a Cu tube, Zr for
a Mo tube or Rh for an Ag tube.
5. Remove the beamstop.
6. Position the detector at 2THETA = 0.
7. Check attenuator in front of the detector; Ni for Cu, Zr for Mo
or Rh for Ag radiation.
8. Set the HV of the pre-amplifier and the window to the suggested
value, using the pocket terminal (see CAD4
general operator rules). If no information is present on the correct
settings, a fluorescent screen should be used to find approximate settings
for the tube and the monochromator. Then an approximate value for the HV
setting can be found using LL=150 and WD=750 (see also CAD4
control).
9. Remove the collimator and put in its place the central pinhole collimator(pinhole
end towards the center of the goniometer).
10. Turn on the generator at the low setting of steps 2 and 3. Now
there will be a moderate primary beam, of which only the fraction passing
the pinhole enters the detector. The pinhole acts as a reference point.
When the focal spot is moved, the image of it on the detector will move
in the opposite direction.
11. Position the vertical slit in front of the detector(SV), set the
attenuator(SA) and open the shutter(SO). If the shutter does not open,
it must be closed first(SC), then the collimator must be pushed inwards
against a safety contact. Take care not to cover the outlet of the collimator
with your finger. Now it can be tried to open the shutter again(SO). If
the count rate is above 50.000 c/s, immediately close the shutter and lower
the kV setting. Move the focal spot horizontally and leave it where the
maximum count rate is obtained. Close the shutter(SC).
12. Position the horizontal slit in front of the detector(SH), set
the attenuator(SA) and open the shutter(SO).
13. Move the focal spot vertically and leave it at the place where
the maximum count rate is obtained. Close the shutter(SC).
If the focal spot was far out of position, repeat from step 11 and finally also remove the attenuator(RA).
14. Switch off the high voltage.
15. Move the detector out of the zero position and remount the beamstop.
16. Remove the pinhole collimator and mount the collimator that you
wish to use later on.
17. If no values are available for setting the radiation detection
chain these settings can now be determined (read Chapter XIII).
18. Turn on the generator and set kV and mA to the proper operating
settings.
19. Open the shutter and check with a fluorescent screen the position
of the beamstop. If necessary adjust the position of the beam catcher.
The beam catcher support can be locked and unlocked by a securing nut at
the tube shield end of the support; it is visible from the crystal position.
This finishes the initial alignment.
The fine alignment is done with the test crystal. The scattering vector
of the reflection to be used should be directed along the phi-axis. However,
it is not necessary to align it precisely. The scattering vector may make
an angle of upto 10 degrees with the phi-axis, then it is still possible
to make a full (360o) azimuthal rotation. The procedure is conducted by
the program ALIGN. It sets up the symmetry equivalent reflections, performs
the optimazation of the setting angles and calculates the offsets of the
X-ray
tube, the missetting of the sample crystal and the detector. For a
complete description refer to section E of this chapter. Apply the corrections
indicated by the program using a measuring gauge for TubeHo and TubeVe.
Repeat this procedure until the deviations calculated are less than 0.01mm.
Finally, Deterr should be adjusted mechanically. This completes the fine
alignment of the primary beam.
This procedure is similar to the one described in the literature (for a review see: W.C. Hamilton in International Tables for X-ray Crystallography, Vol.IV, Kynoch Press, Birmingham, 1974, p. 282).
D. Alignment using the monochromator
In fact, this alignment procedure is equivalent to the procedure without the monochromator; the monochromator surface replaces the tube focus. However, especially when molybdenum or silver radiation is used, the vertical tube adjustment is much more critical. An important complicating factor, is the interdependence of the vertical tube adjustment and the monochromator vertical and theta adjustments. The origin of these interactions is described and a strategy for alignment is proposed here. It should be noted that, apart from at the first installation of the equipment, there is no need for pre-aligning without the monochromator.
Imagine the equipment is aligned perfectly (cf. Fig.XII.1). Now the effect of changes will be analysed.
Fig.XII.1 Optimum position of monochromator(and tube focus).
Adjustment 1:
2THETA movement of the tube focal spot (2THETA-tube); a rotation of
the tube focal spot around the monochromator axis. When the focal spot
is misplaced by its 2THETA-adjustment, the reflection area on the monochromator
surface shifts vertically. The vertical position of the beam changes, whereas
the
direction of the beam in the goniometer remains unchanged. The direction
of the beam, as determined from the reflections of the test crystal, still
seems to be correct and unchanged. However, the beam has a limited width;
i.e. most of the primary beam is lost in the monochromator housing.
The total intensity that reaches the crystal will be reduced and the reflections have a lower intensity.
Fig.XII.2 Effect of "adjustment 1".
Adjustment 2:
Height adjustment of the monochromator housing. This adjustment can
be made by the lever (item 5 drawing figure 7) on the monochromator axis;
it doesnot move the monochromator vertically, but under an angle of approximately
6 degrees with the monochromator plane. The effective height adjustment
range is therefore only +0.12 mm. When the monochromator crystal is misplaced
in vertical direction the
result is identical to that of adjustment 1.
Fig.XII.3 Effect of "adjustment 2".
For Cu radiation, when using fine focus X-ray tubes, the reflection
spot on the monochromator is relatively small, roughly 2 mm or more (depending
on filament positioning and take-off angle). Vertical adjustment of the
beam can be achieved by adjustment 1 only. If molybdenum or silver radiation
is used, however, the reflecting area on the monochromator has an elliptical
shape and will have a minimum
size of 4 and 5 mm, respectively. Thus both adjustment 1 and adjustment
2 may cause the reflection to fall off the monochromator. Therefore, in
these cases, a combination of both adjustments is necessary to change the
height of the beam. Firstly, the beam is moved up (A--->B) and secondly
the focal spot is adjusted (2THETA-tube) to bring back the entire reflection
onto the graphite surface (C--->D).
Fig.XII.4 Effect of "adjustments 1 and 2".
Adjustment 3:
Theta adjustment (THETAm) of the monochromator surface. The angle between
the beam and the horizontal plane can be adjusted by the monochromator
theta rotation.
Fig.XII.5 Effect of "adjustment 3".
Using the monochromator, two vertical errors of the primary beam may
occur, one of which is detected as a vertical tube offset. This one has
to be adjusted by the monochromator theta rotation. The other vertical
error, which cannot be detected in the alignment procedure (see remarks
adjustment 1) has to be
corrected by carrying out a combination of adjustments 1 and 2.
Final adjustment:
Adjustment 3 will reduce the vertical tube error, but as a consequence
the beam may pass under the crystal; by adjusting the monochromator angle
the focal spot moves over the monochromating surface and results in either
too high or too low a beam position. Now, adjustment 1 (Cu-K(alpha)-radiation)
or adjustments 1 and 2 (Mo- or Ag-K(alpha)-radiation) should be used
to move the beam into the horizontal plane, thereby retaining the right
direction of the beam.
D.2 Initial alignment procedure
Procedure stepwise:
1. Switch off the high voltage.
2. Set the high voltage selection for the tube at 20kV for a Cu tube,
or at 23kV for a Mo tube and 25kV for an Ag tube.
3. Set the mA selection for the tube at minimum current.
4. Set the tubeshield beta filter disk at zero.
5. Remove the beamstop.
6. Position the detector at 2THETA=0.
7. Check the material of the attenuator in front of the detector; Ni
for copper, Zr for molybdenum and Rh for silver radiation.
8. Set the HV of the pre-amplifier and the window to the suggested
value, using the pocket terminal(see CAD4
general Operator rules). If no information is present on the correct
settings, a fluorescent screen should be used to findapproximate settings
for the tube and the monochromator. Then an approximate value for the HV
setting can be found using LL=150 and WD=750 (see also CAD4
Operate group).
9. Remove the mounted collimator and put in its place the central pinhole
alignment collimator (pinhole end towards the center of the goniometer).
10. Cu : Remove the X-ray port and mount the monochromator unit (THETAm
= 13.3° and 2THETA-tube = 26.6°).
10. Mo : Remove the X-ray port and mount the monochromator unit (THETAm
= 6.1° and 2THETA-tube = 12.2°).
10. Ag : Remove the X-ray port and mount the monochromator unit (THETAm
= 4.8° and 2THETA-tube = 9.6°).
11. Turn on the generator at the low setting of steps 2 and 3. Now
there will be a moderate primary beam, of which only the fraction passing
the pinhole enters the detector. The pinhole acts as a reference point.
When the focal spot is moved, the image of it on the detector will move
in the
opposite direction.
12. Position the vertical slit in front of the detector(SV), set the
attenuator(SA) and open the shutter(SO). If the shutter does not open,
it must be closed first(SC), then the collimator must be pushed inwards
against a safety contact, without covering the outlet of the collimator
with a finger. Now it can be tried to open the shutter again(SC). If the
count rate is above 50.000 c/s, immediately close the shutter and lower
the kV setting. Move the focal spot horizontally and leave it where the
maximum count rate is obtained. Close the shutter(SC).
13. Position the horizontal slit in front of the detector(SH), set
the attenuator(SA) and open the shutter(SO).
14. Move the focal spot vertically by a repeated sequence of THETAm
and 2THETA-tube adjustments until the maximum count rate is obtained. The
maximum countrate should be noted for further reference.
If the focal spot was far out of position, repeat from step 12.
15. For Cu-radiation switch off the generator and continue with point
17.
16. For Mo and Ag radiation open the shutter(SO) and monitor the intensity(ABS.)
while moving the height adjustment lever. Readjust THETAm and 2THETA-tube.
Set the lever for the heighest intensity, close the shutter(SC), remove
the attenuator(RA) and switch off the generator.
17. Move the detector out of the zero position and remount the beamstop.
18. Remove the pinhole collimator and mount the proper collimator.
19. If no values are available for setting the radiation detection
chain these settings can now be determined (read Chapter XIII).
20. Turn on the generator and set proper operating kV and mA settings.
21. Open the shutter(SO) and check with a fluorescent screen the position
of the beamstop. If necessary adjust the position of the beam catcher.
The beam catcher support can be locked and unlocked by a securing nut at
the tube shield end of the support; it is visible from the crystal position.
This finishes the initial alignment.
The fine alignment is done with the test crystal using the same list of reflections as given for the alignment without monochromator. A suitable reflection should be in the CRYSTAL file (see Test Crystal Data). Then the command ALIGN can be used to set up the list necessary to conduct the measurements and the calculations. Apply the corrections produced by the program using a measuring gauge for TubeHo and the scale on the THETAm-wheel for MonDeg. One scale division on the wheel equals 0.061° (one full rotation equals 1.22°). Repeat this procedure until the deviations calculated are of the order of magnitude of 0.01 mm or 0.003°. Then check for the optimum position of the monochromator height and 2THETA-tube. When the initial alignment has been carried out carefully very little further adjustment should be required. Now Deterr should be adjusted. This completes the fine alignment of the primary beam.
Principles
If a reflection is found at the angles Theta, Phie, Ome and Chie a set
of 8 reflections can be generated, so that the arcs of the goniometerhead
will be horizontal and vertical during centering. Theta is represented
as Thr (Thetareal), Omega as Tho (Thetaomega) + a factor A or B. The difference
in Thr and Tho is related to the zero-error in the Omega-axis. X is either
Chie-positif or Chie-negatif.
| 1. | h | k | l | Theta1= Thr | Phie1= 0 | Ome1= Tho+Al | Chie1= X-C |
| 2. | -h | -k | -l | Theta2=-Thr | Phie2= 0 | Ome2=-Tho+A | Chie2= X-C |
| 3. | h | k | l | Theta3= Thr | Phie3=180 | Ome3= Tho-A | Chie3= X+C |
| 4. | -h | -k | -l | Theta4=-Thr | Phie4=180 | Ome4=-Tho-A | Chie4= X+C |
| 5. | -h | -k | -l | Theta5= Thr | Phie5= 90 | Ome5= Tho+B | Chie5=-X+D |
| 6. | h | k | l | Theta6=-Thr | Phie6= 90 | Ome6=-Tho+B | Chie6=-X+D |
| 7. | -h | -k | -l | Theta7= Thr | Phie7=-90 | Ome7= Tho-B | Chie7=-X-D |
| 8. | h | k | l | Theta8=-Thr | Phie8=-90 | Ome8=-Tho-B | Chie8=-X-D |
Once these positions have been entered the reflections can be centered using SETANG. From the results the following parameters can be determined:
1. Horizontal and vertical offsets of the focal spot.
2. The horizontal offset of the detector.
3. The offset of the test crystal from the center of the goniometer
in three coordinates.
4. The difference between Chie=90 position and Chie=-90 position can
be calculated and is called the Chizero error.
5. The constants that control the transformation between kappa angles
and eulerian angles can be verified. When the constants used are wrong
for this diffractometer, then all chie values, as converted from actual
kappa angles, come out too high or too low. In this check it is called
Chininety; it should be equal to 90.00 degrees.
The parameters are computed using the following formulas:
PRVERT = (Chie1-Chie2+Chie3-Chie4+Chie5-Chie6+Chie7-Chie8)/8
Move the focal spot up 9.33*PRVERT*sin(Theta1)mm
PRHOR = (Ome1+Ome2+Ome3+Ome4+Ome5+Ome6+Ome7+Ome8)/8
Move the tube 3.78*PRHOR mm to the negative theta side.
DETERR = (Theta1+Theta2+Theta3+Theta4+Theta5+Theta6+Theta7+Theta8)/4
+(-Ome1-Ome2-Ome3-Ome4-Ome5-Ome6-Ome7-Ome8)/8
Move the detector 3.02*DETERR mm on its support to the positive theta
side. For the detector mounted on the extension arm use 6.42 instead of
3.02. Use a measuring gauge mounted on the
detector support.
CrystX=1.17*(Chie1-Chie2-Chie3+Chie4)*sin(Theta1)mm
CrystY=1.17*(Chie5-Chie6-Chie7+Chie8)*sin(Theta1)mm
CrystZ=0.189*(Theta1+Theta2+Theta3+Theta4-Theta5-Theta6-Theta7-Theta8
+Ome1+Ome2+Ome3+Ome4-Ome5-Ome6-Ome7-Ome8)mm
Chizero=(Chie1+Chie2+Chie3+Chie4+Chie5+Chie6+Chie7+Chie8)/8
Chininety=(Chie1+Chie2+Chie3+Chie4-Chie5-Chie6-Chie7-Chie8)/8
The above formulas are valid for positive values of Chie. In the case negative values have to be used the program (ALIGN) will choose other algorithms.
ALIGN is a routine which generates a set of eight reflections according to the list as described above. As the parent reflection for the set to be generated, a single reflection or a number of reflections from the list may be used, provided for every reflection 80.0°<Chie<100.0° or -100.0°<Chie<-80.0°.
Selection of the parent reflections is done using an 'ALIGN' status.
Any list entry can be selected by setting the proper code during ALIGN.
The ALIGN status can be:
| * | This reflection is not used and/or not suitable to be used by ALIGN |
| A | This reflection is used for ALIGN and/or will be used in the forthcoming attempt |
| D | This reflection is used by ALIGN and will NOT be used in forthcoming attempt |
| K | Empty list entry |
Allowable modifications during ALIGN are:
| * to A | A to D | A to * | D to A |
The reflection setting angles calculated are optimized by the SETANG centering routine. Please note that SETANG uses the scan and aperture information stored (see Reflection centering). For ALIGN the angle status is irrelevant. If SR=1XXX, the optimized setting angles Theta, Phie, Ome and Chie are printed on the terminal together with IRNPI, RSCAN and RSCINT (attenuator setting/scan speed parameter, scan angle and net intensity (see The reflection list)). The offsets for the tube and detector are calculated and printed on the terminal.
The calculations are made using the following formulas:
TubeHo = RS*2pi*PRHOR/360 mm
Deterr = RADIUS*2pi*DETERR/360 mm
TubeVe = RS*tan[2.70*PRVERT*sin(2Theta)] mm
The monochromator adjustment(THETAm) is calculated from PRVERT. The
THETAm adjustment equals 5.40*TubeVe*sin(Theta) degrees. RS is the distance
between the focal spot and the center of the
goniometer, i.e. 216.5mm in the standard setup. Depending on whether
a monochromator is used or not the value of MonDeg or TubeVe should be
used respectively to apply the corrections.
Terminal output is controlled by SR=2XXX and SR=1XXX.
Operation:
The program prompts '*******A************KKKKK OK?'
The operator may answer Y<CR> or he must label the list entries
he intends to use as parent reflections with an 'A'. Then all 'A' entries
are being checked for validity of the Chie angle and the program returns
an output line indicating which of the requested entries are allowed. Any
status may now be changed
again or the operator may enter the centering stage by typing Y<CR>.
No further input is required.
If switch 1XXX is selected the results for each member of the set of
8 reflections are printed as one line comprising the setting angles (in
eulerian), scan speed, scan angle and net intensity. Furthermore, for each
set of 8 reflections the results are given (not dependant on the switch
setting). The first line gives Theta (Thr), Omega (Tho) and the parameters
A, B, C & D as described in the list of 8 reflections. The second
line gives expressed as the offsets for the detector Deterr, for the
X-ray tube in horizontal TubeHo and vertical TubeVe direction (in mm),
the angular offset of the monochromator Mondeg in degrees and the offsets
of the crystal from the center of the primary beam, Crystx, Crysty and
Crystz (in mm).
To apply a correction in x to the crystal place the crystal in VIEW
0 (or VIEW 2) position and adjust the crystal looking through the microscope.
The positive x-axis is on the right side. The same procedure applies to
the correction for a misplacement in the y-direction using a Phie position
+90 degrees further from the VIEW 0 (or VIEW 2) position. The z direction
can always be adjusted.
Note: The results of ALIGN are expressed as the current settings of the diffractometer and the crystal, i.e. the misalignment. When for example CrystY = -0.0059, the correction to be applied is in the positive y direction.
Example 1 ALIGN:
CD0> ALIGN<CR>
************************* OK?
AAAAAAAAAA<CR>
*A*********************** OK?
Y<CR>
2 1 23.753 -0.000 28.951
-85.708 2. 0.60 11792.6
2 2 -23.753 -0.000 -18.549 -85.695
2. 0.59 11883.0
2 3 23.753 -180.000 18.541 -94.301
2. 0.59 11498.0
2 4 -23.747 -180.000 -28.952 -94.308
3. 0.54 17560.7
2 5 23.747 90.000 28.024
95.212 2. 0.61 12290.3
2 6 -23.752 90.000 -19.466
95.211 2. 0.56 12148.5
2 7 23.749 -90.000 19.466
84.775 2. 0.61 12081.7
2 8 -23.755 -90.000 -28.028 84.776
3. 0.53 17441.0
Theta Omega
A B
C D
2 23.7512 23.7472 5.2034
4.2798 4.3017 5.2179
Deterr TubeHo TubeVe CrystX
CrystY CrystZ Mondeg
2 -0.0016 0.0060 0.0024 0.0002 -0.0059
-0.0041 0.0006
Average values:
-0.0016 0.0060 0.0024 0.0002 -0.0059
-0.0041 0.0006
CD0>
Example 2 ALIGN:
CD0> ALIGN<CR>
A**KKKKKKKKKKKKKKKKKKKKKK OK?
Y<CR>
1 1 10.691 -0.000 15.428
-85.617 2. 0.63 12286.2
1 2 -10.681 -0.000 -5.934 -85.823
2. 0.66 13093.2
1 3 10.687 180.000 5.935
-94.404 2. 0.67 10526.5
1 4 -10.679 180.000 -15.429 -94.149
2. 0.67 10563.3
1 5 10.680 90.000 14.935
94.803 2. 0.64 11833.3
1 6 -10.687 90.000 -6.417
94.739 2. 0.70 12518.7
1 7 10.677 -90.000 6.416
85.202 2. 0.67 11196.3
1 8 -10.690 -90.000 -14.958 85.278
1. 0.66 5605.9
Theta Omega
A B
C D
1 10.6840 10.6815 4.7469
4.2648 4.2783 4.7655
Deterr TubeHo TubeVe CrystX
CrystY CrystZ Mondeg
1 -0.0069 0.0111 0.0103 0.0209 0.0725
-0.0107 0.0027
Average values:
-0.0069 0.0111 0.0103 0.0209
0.0725 -0.0107 0.0027
CD0> ALIGN<CR>
A**KKKKKKKKKKKKKKKKKKKKKK OK?
Y<CR>
1 1 10.690 -0.000 15.427
-85.592 2. 0.62 11910.3
1 2 -10.677 -0.000 -5.928 -85.834
2. 0.64 12576.9
1 3 10.684 180.000 5.935
-94.398 2. 0.62 9641.0
1 4 -10.681 180.000 -15.430 -94.154
2. 0.64 9927.0
1 5 10.681 90.000 14.935
94.801 2. 0.60 10971.2
1 6 -10.689 90.000 -6.417
94.726 2. 0.66 11852.6
1 7 10.678 -90.000 6.416
85.199 2. 0.62 10637.9
1 8 -10.690 -90.000 -14.957 85.272
2. 0.64 10644.2
Theta Omega
A B
C D
1 10.6838 10.6806 4.7483
4.2647 4.2813 4.7639
Deterr TubeHo TubeVe CrystX
CrystY CrystZ Mondeg
1 -0.0043 0.0094 -0.0000 0.0221 0.0764
-0.0107 -0.0000
Average values:
-0.0043 0.0094 -0.0000 0.0221 0.0764
-0.0107 -0.0000
CD0> VIEW 0<CR>
CD0>
CD0> ALIGN<CR>
; corrections X 0.5 sd, Y 0.5 sd
A**KKKKKKKKKKKKKKKKKKKKKK OK?
Y<CR>
1 1 10.686 -0.000 15.417
-85.681 2. 0.61 10857.4
1 2 -10.678 -0.000 -5.938 -85.706
2. 0.64 11346.3
1 3 10.687 180.000 5.941
-94.296 2. 0.56 10423.3
1 4 -10.677 -180.000 -15.419 -94.289
2. 0.64 11474.6
1 5 10.680 90.000 14.957
94.787 2. 0.59 10917.5
1 6 -10.686 90.000 -6.402
94.745 2. 0.62 11295.9
1 7 10.679 -90.000 6.395
85.254 2. 0.57 10546.0
1 8 -10.690 -90.000 -14.974 85.260
2. 0.62 11032.8
Theta Omega
A B
C D
1 10.6829 10.6803 4.7395
4.2835 4.2994 4.7544
Deterr TubeHo TubeVe CrystX
CrystY CrystZ Mondeg
1 -0.0082 0.0111 -0.0094 0.0064 0.0061
-0.0136 -0.0025
Average values:
-0.0082 0.0111 -0.0094 0.0064 0.0061
-0.0136 -0.0025
CD0> VIEW 1<CR>
CD0> ALIGN<CR>
; correction Z 0.25 sd
A**KKKKKKKKKKKKKKKKKKKKKK OK?
Y<CR>
1 1 10.683 -0.000 15.534
-85.752 2. 0.59 10804.0
1 2 -10.680 -0.000 -5.818 -85.815
2. 0.61 11125.1
1 3 10.682 180.000 5.816
-94.220 2. 0.57 10384.0
1 4 -10.680 -180.000 -15.544 -94.206
2. 0.61 10827.3
1 5 10.683 90.000 14.871
94.913 2. 0.61 10926.4
1 6 -10.679 90.000 -6.479
94.866 2. 0.59 10755.5
1 7 10.683 -90.000 6.483
85.135 2. 0.62 10888.7
1 8 -10.684 -90.000 -14.882 85.132
2. 0.61 10697.9
Theta Omega
A B
C D
1 10.6818 10.6785 4.8609
4.1976 4.2148 4.8778
Deterr TubeHo TubeVe CrystX
CrystY CrystZ Mondeg
1 -0.0126 0.0088 -0.0175 0.0071 0.0119
0.0015 -0.0046
Average values:
-0.0126 0.0088 -0.0175 0.0071 0.0119
0.0015 -0.0046
CD0> VIEW 1<CR>
CD0> ALIGN<CR>
; correction Y 0.125 sd
A**KKKKKKKKKKKKKKKKKKKKKK OK?
Y<CR>
1 1 10.682 -0.000 15.537
-85.774 2. 0.59 10441.5
1 2 -10.683 -0.000 -5.823 -85.785
2. 0.59 10749.5
1 3 10.681 180.000 5.817
-94.200 2. 0.59 10887.0
1 4 -10.680 -180.000 -15.540 -94.198
2. 0.57 10391.3
1 5 10.684 90.000 14.871
94.908 2. 0.59 10554.0
1 6 -10.677 90.000 -6.481
94.855 2. 0.59 10614.0
1 7 10.684 -90.000 6.485
85.122 2. 0.57 10211.9
1 8 -10.687 -90.000 -14.881 85.127
2. 0.61 10756.3
Theta Omega
A B
C D
1 10.6822 10.6793 4.8592
4.1965 4.2099 4.8786
Deterr TubeHo TubeVe CrystX
CrystY CrystZ Mondeg
1 -0.0082 0.0072 -0.0104 0.0091 0.0020
0.0005 -0.0027
Average values:
-0.0082 0.0072 -0.0104 0.0091 0.0020
0.0005 -0.0027
CD0> ALIGN<CR>
A**KKKKKKKKKKKKKKKKKKKKKK OK?
Y<CR>
1 1 10.682 -0.000 15.536
-85.771 2. 0.63 10977.7
1 2 -10.683 -0.000 -5.827 -85.788
2. 0.59 10727.5
1 3 10.683 180.000 5.818
-94.197 2. 0.59 10634.0
1 4 -10.678 -180.000 -15.538 -94.205
2. 0.59 10673.5
1 5 10.682 90.000 14.868
94.890 2. 0.57 10478.2
1 6 -10.679 90.000 -6.484
94.856 2. 0.59 10949.0
1 7 10.683 -90.000 6.485
85.152 2. 0.57 10441.8
1 8 -10.686 -90.000 -14.881 85.135
2. 0.61 10827.1
Theta Omega
A B
C D
1 10.6820 10.6796 4.8571
4.1950 4.2106 4.8649
Deterr TubeHo TubeVe CrystX
CrystY CrystZ Mondeg
1 -0.0112 0.0108 -0.0133 0.0026 0.0017
-0.0007 -0.0035
Average values:
-0.0112 0.0108 -0.0133 0.0026 0.0017
-0.0007 -0.0035
CD0>
The molecular structure of ammonium bitartrate has been reported long ago by Prof. J. Bijvoet (Acta Cryst. 11 (1958) 61). The cell parameters for ammonium bitartrate are a=7.648, b=7.844 and c=11.068 Angstrom. The space group is P212121 (orthorhombic). The asymmetric unit contains 20 atoms; the molecular formula C4H9O6N applies. The fractional coordinates are given in Table XII.2
Table XII.2 Fractional coordinates for ammonium bitartrate
| Atom | x/a | y/b | z/c |
| N 1 | .1655 | .3217 | .4671 |
| C 1 | .9576 | .6401 | .7349 |
| C 2 | .7706 | .5761 | .7246 |
| C 3 | .6682 | .6878 | .6360 |
| C 4 | .4792 | .6243 | .6307 |
| O 1 | 1.0447 | .6210 | .6335 |
| O 2 | 1.0174 | .7017 | .8259 |
| O 3 | .6885 | .5775 | .8398 |
| O 4 | .6828 | .8622 | .6670 |
| O 5 | .4560 | .4693 | .6103 |
| O 6 | .3583 | .7306 | .6492 |
| H 1 | 1.166 | .653 | .648 |
| H 2 | .782 | .461 | .695 |
| H 3 | .657 | .465 | .856 |
| H 4 | .713 | .675 | .560 |
| H 5 | .641 | .877 | .742 |
| H 6 | .244 | .342 | .416 |
| H 7 | .134 | .418 | .491 |
| H 8 | .094 | .251 | .434 |
| H 9 | .178 | .259 | .543 |
The nett intensity for some of the reflections of ammonium bitartrate are given in Table XII.3.
Table XII.3 Intensities for some classes of reflections for Cu radiation
h k l I(nett)
h k l I(nett)
-----------------------------------------------
2 0 0 2360
2 2 2 7620
4 0 0 3450
3 3 3 210
6 0 0 5630
4 4 4 330
8 0 0 350
5 5 5 870
0 2 0 11800
0 0 2 >50000
0 4 0 6270
0 0 4 >40000
0 6 0 20
0 0 6 13100
0 8 0
5 0 0
8 1770
0 2 1 >50000
0 0 10 1720
1 1 1 8350
0 0 12 10
Table XII.4 Suggested 24 high angle reflections for orientation
matrix determination
| h k l | h k l |
| 0 -2 -9 | -3 -6 0 |
| 0 2 -9 | 3 6 0 |
| 0 -2 9 | -5 -4 -2 |
| 0 2 9 | -5 -4 2 |
| -5 3 -5 | -6 -2 -3 |
| -5 -3 5 | -6 2 -3 |
| -5 -3 -5 | -5 0 -6 |
| -5 3 5 | 5 0 -6 |
| 6 1 4 | -6 -1 -4 |
| -6 1 4 | 6 -1 -4 |
| 6 -1 4 | -6 1 -4 |
| 6 1 -4 | -6 -1 4 |
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