Changing the UB matrix

Working in q space requires a UB type GQE, called UB_MATRIX. One part of this GQE is the matrix which is used to calculate the diffractometer angles from q space positions and vice versa. This involves the orientation of the sample (the UB matrix itself and the offset angles), as well as information about the scan mode (scan mode, constant psi value, constant plane vectors, ASN).

The UB_MATRIX GQE also contains data used by the refinement procedures: This involves entries for wavelength, zero offsets, the direct lattice parameters and a list of reflections.

Three refinement procedures can be invoked by the change menu: A fast algorithm which needs only two reflections and the direct lattice constants, the code from Klaus Eichhorns (now at Universität Karlsruhe) DIF4 and the program RAFIN 17

A UB_MATRIX is created by:

ONLINE> create/ub ub_matrix

The elements of the UB GQE can be changed by command (set ub_matrix/... , *=attr(ub_matrix, ...)) or with the help of a menu. Details about the command line interface can be found in the Spectra manual, in the commands reference section: set, set the attributes of UB matrices. The keywords for the attribute() function that returns parameter values are the same as those used for the set command. The menu that modifies a UB GQE is invoked by:

ONLINE> change ub_matrix

This command creates a full screen menu which displays the items of the queue element 9.1.

Table 9.1: Changing an UB Matrix

 

 UB:  1.0       CHROM
 Wavelength      1.562694      N_Refl: 2
 Zero Offsets:
         Theta:  0             Omega:  0               Chi:    0
 UB-Matrix:
         UB11:   0.012554      UB12:   -0.120158       UB13:   0.131217
         UB21:   -0.0981989    UB22:   -0.114373       UB23:   -0.0953385
         UB31:   0.148367      UB32:   -0.0655318      UB33:   -0.0742038
 Scan Mode:      Const. Pl.    Param.  : 0             ASN:    2
 Cent. Mode:     CMS
 Constant Plane Vector
         H11:    1             H12:    0               H13:    0
         H21:    0             H22:    1               H23:    1
 The Lattice
         a:      5.60653       b:      5.60653         c:      5.60653
         alpha:  90            beta:   90              gamma:  90
 The Reciprocal Lattice
         a:      0.114604      b:      0.131614        c:      0.187591
         alpha:  90.00001      beta:   67.5641         gamma:  89.99998
  ON_LINE>
--------------------------------------------------------------------------------
 PF1 - Calc. Latt. Par.   | PF2 - UB from RAFIN.LPT | PF3 - Ed Reflections
 KP- - cre & ed RAFIN.DAT | KP7 - Start RAFIN       | KP9 - Ed RAFIN.LPT
 KP5 - UB from two refl.  | KP1 - UB a la DIF4      |

The description of the menu items:

 Wavelength:
Input parameter to RAFIN or DIF4 only. Updated whenever a reflection is added to the list of reflections.

 N_Refl:
The size of the list of reflections.

 Zero offsets:
Offset angles for $two\_theta, \omega$ and $\chi$ ($\phi$ has by definition arbitrary zero point; an offset is therefore meaningless).

 UB matrix:
The matrix elements.

 Scan mode:
There are 3 coordinates in q space but 4 diffractometer angles. This leaves one degree of freedom which needs to be constraint in order to uniquely determine the angles. Three types of constraints have been implemented so far (for other types of constraints call an expert):

1. Bisecting: $two\_theta = 2\omega$.

2. Fixed Psi: The sample is rotated around the scattering vector by a fixed value. The zero point $\psi=0$ corresponds to the bisecting position.

3. Const. Plane. The scattering vector is kept in the horizontal plane together with two other reference reflections. If the specified vector is not (quite) in the plane $\omega$ is calculated from the projection and $\chi$ and $\phi$ set so that the specified vector is horizontal (that is: in the Bragg condition).

4. Fixed Phi

5. Fixed (omega - two_theta/2). Corresponds to the omega definition of Busing and Levy. The fixed-phi and fixed-omega mode has been coded by Ulrich Gebhardt, MPI Stuttgart.

 Param.:
The value that is used for q-movements in the fixed psi, fixed phi and fixed (omega - two_theta/2) mode.

 ASN:
Angle set number, the constant plane constraint still leaves four possible solutions for the motor positions. This number selects one of them (number between 1 and 4).

 Cent. Mode:
Used by scan/refl.

 Constant Plane Vector:
The two vectors, which define the plane for the constant plane mode.

 The direct lattice:
Can be calculated form the UB matrix (PF1). Is also used as input/output to RAFIN and as input to FAST CALC.

 The Reciprocal Lattice:
Calculated form the UB matrix (PF1).

 PF1
The lattice parameters are calculated from the UB matrix.

 PF2
The UB matrix is read from the RAFIN output.

 PF3
Edit the list of reflections.

 KP_MINUS
Prepare the input file for RAFIN.

 KP7
Start RAFIN.

 KP9
Inspect the output file of RAFIN.

 KP5
Calculate the UB matrix from 2 reflections (and the lattice). If the UB matrix contains more than 2 reflections, the first two are used. This operation can also be triggered by set ub_matrix/ub_form_two.

 KP1
Invokes the refinement procedure from Klaus Eichhorn (now at Universität Karlsruhe). This code does not support offsets of the diffractometer angles.

Note that if ONLINE finds a reflection with negative $two\_theta$ value, it makes the following transformation:

• $two\_theta = - two\_theta$
• $\omega = - \omega$
• $\chi = \chi + 180$. The value of $\chi$ is then mapped into the range from -180 to 180 degrees.
• $\phi = \phi$

This transformation is necessary because the UB matrix formalism works for positive $two\_theta$ angles only.

BW5, PETRA2: Accordingly the symbol SIGN_OF_ANGLES can be set to -1, if one wants to make q-movements with negative $two\_theta$ values.