POWDER DIFFRACTION

POWDER DIFFRACTION converts 2-D powder rings from a flat detector to 1-D profiles whilst taking account of spatial distortion and detector tilt [10]. The command TILT/CENTRE BEAM (see Section 17.26, Page ) can be used to determine the tilt and optionally the beam centre. If a semi-transparent beam-stop is used the beam centre can be found be fitting a suitable function e.g. 2-D Gaussian (see Section 17, Page ). Other commands may also be useful e.g. the PIXEL X/Y option within the DISPLAY sub-menu of the graphics menu of the IMAGE command (see Section 3.5, Page ).

A choice of equal orthogonal detector pixel distance or equal diffraction angle bins is available.

The re-binned 1-D profile can be output into a ``Powder Diffraction Standard'' (PDS) format file⁵⁵ within this command, or will be saved in the memory for further manipulation or output in a alternative form⁵⁶.

Below is the log file from FIT2D of the present user interaction. The documentation will be fully written when the algorithm and user inputs are stable:

Main menu: ENTER COMMAND [INPUT DATA]:fit
Fit sub-menu: ENTER COMMAND [INPUT PARAMETERS]:powd
INFO: The current pixel coordinates for the beam centre = 256.500 256.500
INFO: The current pixel sizes (microns) =    100.000   100.000
INFO: The current sample to detector distance (millimetres) =    315.000
INFO: The rotation angle of the tilt plane =     .000
INFO: The tilt angle of the detector =     .000
CHANGE BEAM CENTRE AND/OR TILT VALUES [NO]: 
CORRECT FOR X-RAY BEAM POLARISATION [YES]: 
BEAM POLARISATION (AT SAMPLE) (Range: -1.00000 to 1.00000)
 [.99000]:?
Enter the "polarisation" of the main beam on the sample. This is defined as
(I_h - I_v) / (I_h + I_v),  where I_h is  the horizontal component  of  the
intensity and I_v is  the vertical.  (The horizontal should correspond with
the X-direction on  an image.  Normally for  a synchrotron the polarisation
is positive and approaches 1.0.  e.g. Station 9.6 at  the SRS Daresbury has
been measured to  have  a polarisation of 0.86.  This  is  a value which is
dependent on the X-ray source, beam-line mirrors, and on the monochromator.
The beam-line scientist should  be  able  to  give  a good estimate of this
number.
BEAM POLARISATION (AT SAMPLE) (Range: -1.00000 to 1.00000)
 [.99000]:.95
TYPE OF LORENTZIAN CORRECTION TO APPLY [NONE]:?
Enter the type of "Lorentz" correction which you want to apply to the
output intensities. At present the following choices are available:
 
   NONE: No correction factors applied
   PARTIAL POWDER (2-THETA SCAN): Correct intensities to be equivalent to
      a 2-theta scan with a single counter. This allows standard powder
      diffraction software to apply their own Lorentz corrections.
TYPE OF LORENTZIAN CORRECTION TO APPLY [NONE]:part
PRODUCE EQUAL ANGLE PIXEL SCAN [YES]:?
Enter: "YES" if you want to produce a 1-D scan as a function of equal
       angle pixels.
       "NO" if you want to produce a 1-D scan as a function of equal
        radial distance pixels (on an orthogonal detector).
(The two are not the same.)
The best choice will depend on the capabilities on any further
processing software. e.g. If a Rietveld program requires equal angle
pixels then this is clearly the choice. If either type of scan may be
treated then the equal radial re-binning is probably preferable.
PRODUCE EQUAL ANGLE PIXEL SCAN [YES]: 
2 THETA SCAN ANGULAR PIXEL STEP (DEGREES)
 (Range: 1.000E-03 to 10000.0) [1.800E-02]:?
Enter required angle step between bins for the calculation of the 1-D
2 theta scan. (The default value corresponds to the angular size of
the average pixel size at the beam centre.)
2 THETA SCAN ANGULAR PIXEL STEP (DEGREES)
 (Range: 1.000E-03 to 10000.0) [1.800E-02]: 
TAKE ACCOUNT OF SPATIAL DISTORTION [NO]:?
YES: if a the detector spatial distortion has been characterised and is
to be taken into account. If you answer "YES" you will be required to
input the name of a valid spatial distortion interpolation file.
TAKE ACCOUNT OF SPATIAL DISTORTION [NO]: 
INFO: Starting to re-bin 2-D data to a 1-D profile, this can take some
      time for large arrays.
INFO: Number of rows treated =    300 ( 58%)
 
INFO: Minimum fractional intensity decrease owing to polarisation = .96
INFO: (The reciprocal value is applied to the data.)
SAVE DATA IN "POWDER DIFFRACTION STANDARD" FORMAT [YES]: 
Enter name of output file
FILE NAME [scan.pds]:

Note:

• The default pixel size for equal angular pixel size scans is an exact multiple of one thousandth of a degree (V7.37). This is because the PDS format saves the angular step to this precision. Since thousands of scan bins may be output, a small error can build up to be relatively large angle. It is recommended to only use pixel bin sizes which are exact multiples of a thousandth of a degree when outputting data to PDS files.

• For the Polarisation correction to be correct, the image must have been input in the correct orientation. i.e. The horizontal on the displayed image should correspond with the horizontal on an upright detector in line with the direct beam.

• The ``Lorentz'' correction allows data from a flat 2-D detector, which has been re-binned into a 1-D ``2$\theta$ scan'' to be corrected for geometrical differences between this scan and a true 2$\theta$ scan (V7.31). Following this correction, the normal Lorentz corrections present in Rietveld refinement and other refinement programs should be appropriate.