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.

> PEAK qh qk ql a4 a3 sgl sgu

Make an entry in the list of peaks. For angles not given, the current motor positions are used. If the given qhkl triple already exists, its list entry is overwritten. If not, a new entry is made, and the new peak name is returned. Peak names are single letters starting from A. It is therefore possible to save the information about up to 26 reflections.

> PEAK peak qh qk ql a4 a3 sgl sgu

The same as above, but a named entry is overwritten. If another entry with the same qhkl triple already exists, it is deleted.

> PEAK CLEAR peak

Remove the named peak.

> PEAK CLEAR

Remove all peaks.

> PEAK

List all peaks.

> CALCUB peak1 peak2

Calculate 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.

> CALCUB peak1 peak2 CHEAT

The same as above, but the cell constants a, b and c are scaled in order to make peak1 perfectly fitting.

> CALCUB peak1 peak2 peak3

The cell constants are calculated back from the three peaks and printed out.

> CALCUB

Just list again the UB matrix and the full peak list.

> MAKEUB peak1 peak2 ...

Calculate the UB matrix and make it active. The arguments are the same as in CALCUB.

> MAKEUB

Without arguments, the last UB matrix calculated by CALCUB is used.

> LISTUB

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

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

Find the peak 2 0 0 and optimize it

   ...

Once we are at the maximum:

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

Find the peak 0 4 4 and optimize it.

   ...

Once we are at its maximum:

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

   > PEAK
   Peak   QH     QK     QL      A4      A3     SGL     SGU
   A    2.00   0.00   0.00   65.31  -87.21    1.25   -5.22
   B    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.

   > CALCUB A 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
   A 1   2.00   0.00   0.00   65.31  -87.21    1.25   -5.22   2.03   0.00   0.00
   B 2   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

   > MAKEUB

make the calculated UB matrix active. 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.

   > PEAK 3 3 3
   Peak   QH     QK     QL      A4      A3     SGL     SGU
   C    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
   A     2.00   0.00   0.00   65.31  -87.21    1.25   -5.22   2.03   0.00   0.00
   B 2   0.00   4.00   4.00   99.45   20.39    4.25   -1.22   0.02   3.95   4.03
   C 1   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.