TasUBMatrix

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JSPWiki v2.0.52


UB Matrix for Triple Axis Instruments

> CELL a b c alpha beta gamma

set unit cell constants. If b or c are omitted, the same value as for a is used, if angles are omitted, they are set to 90 degress. Without arguments, the cell constants are listed.

> addauxref qh qk ql

Define the vectors for the scattering plane.

> REF qh qk ql a3 a4 sgl sgu Ei Ef

Make an entry in the list of peaks. For angles and k-values not given, the current motor positions are used. The peak number and the peak data are returned.

> REF AUX qh qk ql Add an auxiliary reflection to the list of reflections. A4 is calculated from the cell constants, the current ei and ef values are used. A3 is left alone or is calculated to have the right angular difference to the previous reflection. Using auxiliary reflections is a help during setup of the instrument or in powder mode.

The sequence:

ref clear all
cell aa bb cc alpha beta gamma
addauxref ax ay az
addauxref bx by bz
makeub 1 2
with ax, ay, az being the first plane vector and bx, by, bz being the second plane vector creates a UB matrix which allows to drive Q positions and qm. But be aware that a3, sgu and sgl values are still invalid.

> REF CLEAR peak

Remove a peak.

> REF CLEAR ALL

Remove all peaks.

> REF

List all peaks.

> MAKEUB peak1 peak2

Calculate, activate and print out the UB matrix, as well as the peak list with qhkl values calculated back. peak1 is used as the main peak, i.e. driving to the angles given for this peak will correspond to a QHKL which may only differ by a scalar factor of about one, if the cell constants are not correct. peak2 is used only for determining the scattering plane.

It has to be checked that this is fully compatible with the TASMAD specification. In principle, AX,AY,AZ should correspond to peak1 and BX,BY,BZ to peak2.

>MAKEUBFROMCELL

Calculate and activate a UB which has been calculated from the cell constants alone. This is useful to get a4 when no reflection has yet been found to calculate a proper UB.

>MAKEAUXUB qh qk ql

Calculate a UB matrix from the first reflection and an auxiliary second reflection specified through the miller indices qh , qk, ql. The auxiliary reflection will have the same angles as the first reflection, except a3 and a4 will be adjusted to match the requirements from the crystalls geometry.

Markus Zolliker: there should be a an easy way helping the user to correct the cell constants (for example due to thermal contraction) according to the measured peak.

> LISTUB

List the UB matrix, the cell constants and all stored reflections.

Out Of Plane Operation

This formalism allows to drive out of the scattering plane using the tilt motors of the sample stage. Some cryostats cannot stand this. Therefore driving out of plane can be switched off and on.

> TASUB OUTOFPLANE 1

This command switches out of plane operation on.

> TASUB OUTOFPLANE 0

This command switches out of plane operation off.

> TASUB OUTOFPLANE

lists the current value of the outofplane variable

Example session:
(Some numbers might not be correct, as this module does not yet work in this form).

We enter cell values

   > CELL 2.88 2.88 2.88 90 90 90

   > MAKEUBFROMCELL

MAKEUBFROMCELL builds a UB matrix from the cell only. With this you can drive to 2 0 0
   
   > drive qh 2 0 0

This will get you the correct two-theta == a4. You have to search the peak in a3, sgu and sgl and optimize it. 

Once we are at the maximum:

   > REF 2 0 0
   Peak   QH     QK     QL      A4      A3     SGL     SGU
   1    2.00   0.00   0.00   65.31  -87.21    1.25   -5.22

   > makeauxub 0 4 4
   > dr qh 0 4 4 
Make an axiliary UB and drive to the theoretical position for 0 4 4

Find the peak 0 4 4 and optimize it.

   ...

Once we are at its maximum:

   > REF 0 4 4
   Peak   QH     QK     QL      A4      A3     SGL     SGU
   1    0.00   4.00   4.00   65.31  -87.21    1.25   -5.22
   
Show again the peak list:

   > REF
   Peak   QH     QK     QL      A4      A3     SGL     SGU
   1    2.00   0.00   0.00   65.31  -87.21    1.25   -5.22
   2    0.00   4.00   4.00   99.45   20.39    4.25   -1.22

Calculate the UB matrix, with 2 0 0 as primary peak and 0 4 4 as
secondary peak.

   > MAKEUB 1 2
   UB   2.456   0.530  -0.200
       -0.530   2.456  -0.090
        0.200   0.090   2.456
   Peak    QH     QK     QL      A4      A3     SGL     SGU     QH     QK     QL
   1 A   2.00   0.00   0.00   65.31  -87.21    1.25   -5.22   2.03   0.00   0.00
   2 B   0.00   4.00   4.00   99.45   20.39    4.25   -1.22   0.02   3.95   4.03

the last 3 columns above show the Q values calculated back from the angles.
We drive now to the 2 0 0 peak

   > DR QH 2 0 0
   > PR A4 A3 SGL SGU
   A4 =  64.218
   A3 = -87.515
   SGL =  2.258
   SGU = -3.217

The value of A4 has changed, because the cell constants do not match the values
given for the first peak. The value of A3 has changed by the same reason, and
in addition, because the the plane given by 2 0 0 and 0 4 4 is now tilted back
into in the scattering plane. For the latter reason SGU and SGL have changed also.

   > DR QH 3 3 3
   > PR A4 A3 SGL SGU
   A4 =  82.516
   A3 = -31.215
   SGL =  2.258
   SGU = -3.217

note that the values for SGU and SGU have not changed. The will not change
as long as we stay in the scattering plane (no drives to Q3) and as long
as the UB matrix has not changhed.

   > REF 3 3 3
   Peak   QH     QK     QL      A4      A3     SGL     SGU
   3    3.00   3.00   3.00   82.32  -31.25    2.26   -3.22
   > MAKEUB C B
   UB   2.456   0.530  -0.200
       -0.530   2.456  -0.090
        0.200   0.090   2.456
   Peak    QH     QK     QL      A4      A3     SGL     SGU     QH     QK     QL
   1     2.00   0.00   0.00   65.31  -87.21    1.25   -5.22   2.03   0.00   0.00
   2 B   0.00   4.00   4.00   99.45   20.39    4.25   -1.22   0.02   3.95   4.03
   3 A   3.00   3.00   3.00   82.32  -31.25    2.26   -3.22   3.00   3.00   3.00

We have calculated a new UB matrix, based on the peak 3 3 3 as primary and the
0 4 4 as secondary peak. The UB matrix has not changed, as we were already exactly
at 3 3 3.


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This page last changed on 12-Dec-2007 12:25:12 CET by Niedermayer.