Crystals Manual

Chapter 5: Reflection Data Input

5.1: Scope of the Reflection Data Input section of the Reference Manual

5.2: Reflection Data

5.3: Simple input of F or Fsq data - LIST 6

5.4: Printing LIST 6

5.5: Punching LIST 6

5.6: Advanced input of F or Fsq data - LIST 6

5.7: Reflection Parameter Coefficients

5.8: Storage of reflection data

5.9: Compressed reflection data

5.10: Intensity Data - HKLI

5.11: Intensity Decay Curves \LIST 27

5.12: Printing the decay curve

5.13: Data Reduction - Lp

5.14: Systematic absence removal - \SYSTEMATIC

5.15: Sorting of the reflection data - \SORT

5.16: Merging equivalent reflections - \MERGE

The areas covered are:

 Reflection Data
 Simple input of F or Fsq data               - \LIST 6
 Advanced input of F or Fsq data             - \LIST 6
 Reflection Parameter Coefficients
 Storage of reflection data
 Compressed reflection files
 Intensity data                              - \HKLI
 Standard Decay Curves                       - \LIST 27
 Data Reduction                              - \LP
 Systematic absence removal                  - \SYSTEMATIC
 Sorting data                                - \SORT
 Merging equivalent reflections              - \MERGE

If fixed-format input is used, the user must supply a FORTRAN format statement. This specifies the width of the input fields, where the decimal points are, and any fields to be skipped. Even though the indices are usually integer values, CRYSTALS read them as floating point numbers. Note that if the input figures contain decimal points, these will over-ride values given in the format statement.

      Examples - ^ represents a space.

      FORMAT (3F4.0, 2F8.2)      ^^^1^^12^^^3^^^47.23^^^^9.32

      FORMAT (3F4.0, 2F8.0)      ^^^1^^12^^^3^123456.^^312.16

      FORMAT (3F4.0, 3X,2F8.0)   ^^^1^^12^^^3STD^123456.^^312.16

LIST 6 will accept reflection data either as F or Fsq. For routine work, a pre-specified set of coefficients

      h k l Fobs sigma(Fobs)

 \LIST 6
 READ F'S=
 FORMAT EXPRESSION=
 END

 \ The OPEN instruction connects the reflection file
 \OPEN HKLI REFLECT.DAT
 \LIST 6
 READ F'S=FSQ
 FORMAT (3F4.0, 2F8.0)
 END
 \ Close the reflection file
 \CLOSE HKLI

      FSQ
      FO   -  Default

The reflections can be output to listing file as follows :
 
\PRINT 6 mode
Mode controls the type of output.

        - The reflections are in compressed format, on the scale of Fo.
      A - The reflections are in compressed format, on the scale of Fo.
      B - The reflections are in compressed format, on the scale of Fc.
      C - A general print of all the data stored for each reflection. 
          This value should be used with caution.

LIST 6 can be punched as an ASCII file in several formats.
 
\PUNCH 6 mode
Mode controls the format of the output.

        - Output the reflections in a compressed format
      A - Output the reflections in a compressed format
      B - Output the reflections ic 'cif' format
      C - Output Fo, Fc, phase information in tabulated format
      E - Output Fo and other input information in tabulated format

LIST 6 is also output by the links to the direct methods programs. In these files, the magnitudes of Fo or Fsq are scaled so that the largest fits the format statement. The SHELX file contains Fsq, the SIR file contains Fo.
 

LIST 6 will accept reflection data either as F or Fsq. The data may be in free or fixed format. For routine work, a pre-specified set of parameters is stored for each reflection. This may be expanded for non-routine work by INPUT and OUTPUT coefficients.

 \LIST 6
 READ NCOEFFICIENT= TYPE= F'S= NGROUP= UNIT= CHECK=
 INPUT COEFFICIENT(1)= COEFFICIENT(2)= .  .
 STORE NCOEFFICIENT= MEDIUM= APPEND=
 OUTPUT COEFFICIENT(1)= COEFFICIENT(2)=  .  .
 FORMAT EXPRESSION=
 MULTIPLIERS VALUE=
 END

 \ The OPEN instruction connects the reflection file
 \OPEN HKLI REFLECT.DAT
 \LIST 6
 READ NCOEF=5 FORMAT=FIXED UNIT=HKLI F'S=FSQ
 FORMAT (3F4.0, 2F8.2)
 INPUT H K L /FO/ SIGMA(/FO/)
 STORE NCOEF=7
 OUTPUT INDICES /FO/ SQRTW /FC/ BATCH/PHASE RATIO/JCODE SIGMA(/FO/)
 END
 \CLOSE HKLI

      H K L FOBS SIGMA(F)

      FIXED     -  Fixed format card images
      FREE      -  Free format card images  -  default value
      COMPRESSED-  See 'Compressed Reflection Data' below
      COPY      -  LIST 6 is copied from the current input device to the
                   output device designated on the STORE directive with
                   the number of coefficients given on the OUTPUT and
                   COEFFICIENT directives.

      FSQ
      FO   -  Default value

      HKLI   -  Default value.
      DATAFILE

HKLI indicates that the reflection data are in a separate file from the main input data. The local implementation may set up default names for this file, or the \OPEN directive can be used to connect the file to CRYSTALS.

DATAFILE indicates that the reflections follow the directives for '\LIST 6' in the normal data input stream. If this is the case, the directives for \LIST6 must be terminated by the directive END, otherwise the reflection cards will be processed as normal directive cards associated with the \LIST6 instruction, and generate a large number of input errors.

By default, the data are assumed to come from the alternative HKLI channel.
CHECK This parameter determines whether reflections are rejected on input if they have a zero or negative value for Fo.

      YES
      NO -  Default value.

This directive defines the coefficients that are to be read in. The number of coefficients is given by the NCOEFFICIENT parameter above, or its default value.
COEFFICIENT(1)= COEFFICIENT(2)= Defines the coefficients and their input order. The coefficients must be selected from the following list

      H             K             L             /FO/
      SQRTW         FCALC         PHASE         A-PART
      B-PART        TBAR          FOT           ELEMENTS
      SIGMA(F)      BATCH         INDICES       BATCH/PHASE
      SINTH/L**2    FO/FC         JCODE         SERIAL
      RATIO         THETA         OMEGA         CHI
      PHI           KAPPA         PSI           CORRECTIONS
      FACTOR1       FACTOR2       FACTOR3       RATIO/JCODE

      INDICES /FO/ SQRTW /FC/ BATCH/PHASE RATIO/JCODE SIGMA(/FO/)
      CORRECTIONS ELEMENTS

      FILE        A named or scratch ASCII serial file
      INPUT       A file of the same type as the input reflection source
      DISK   -    Default - The current structure data base

   2
 

      YES      The input reflections are appended to existing reflections
      NO   -   Default - The input reflections replace any existing reflections

This directive defines the coefficients that are to be stored. The number of coefficients is given by the NCOEFFICIENT parameter above, or its default value, and the coefficiens selected from the list above.
 
If the OUTPUT directive is omitted, as many of the default coeficients as are required by NCOEFFICIENT are used as output coefficients :
 
If the OUTPUT directive is omitted and NCOEFFICIENT is greater than 9, it is reset to 9 so that the coefficients above can be used.
 

 

 
FORMAT EXPRESSION=

This directive allows the user to define a format statement if fixed format input is being used. This directive is only valid if the TYPE on the READ card is FIXED .
EXPRESSION= This parameter defines the format to be used. Normally this keyword is omitted, so that the directive card looks like a FORTRAN format card, except that there must be at least one space between the 'FORMAT' and the expresion, to terminate the directive. Since all the data are read as real numbers, the format expression can only contain F , E , and X field definitions.
 

 

 
MULTIPLIERS VALUE=

This directive allows the user to define the multipliers to be applied to the data if they are being read in compressed format. This directive is only valid if the TYPE on the READ card is COMPRESSED .
VALUE= This parameter, whose default value is unity, is repeated READ-card NCOEFFICIENT times on this card. The order is the same as the INPUT coefficients.
 

CRYSTALS has a very flexible procedure for storing reflection information, enabling the user to optimise disk space use. The user must indicate to the program what inforamtion is available in the input data, and what information is to be stored. Storage space may also be reserved for data yet to be computed.

During data reduction, space is reserved for relavent coefficients. These coefficients ( e.g. setting angles) may not be needed during structure analysis, so they are not normally preserved beyond reduction.
 

 
Special Reflection storage

The user might need to arrange special refection storage under the following conditions:
 

 
Refinement using a partial model

If the users is experiencing difficulties a small part of an otherwise well behaved large structure, the real and imaginary parts of the structure factors due to the well behaved part can be precomputed and stored and these atoms removed from the atom list (LIST 5). The user then only needs recompute the contributions from the varying fragment. The total Fo, Fc, real and imaginary parts are stored with the keys

      /FO/      /FC/      APART      BPART

When twinned structures are being refined, the user need to store Fc, the total twinned observation FOT, the extracted structure factor for one twin element, Fo, and the indices of the twin elements contributing to each reflection.

      /FC/      /FOT/      /FO/      ELEMENTS

 Coefficients recognised are:
 H            Reflection index h
 K            Reflection index k
 L            Reflection index l
 INDICES      Packed reflection indices
 /FO/         The observed intensity, Fsq or Fo value
 /FOT/        The observed intensity, Fsq or Fo value for a twinned crystal
 /FC/         The calculated structure factor
 SIGMA(/FO/)  Standard deviation of the input obsevation
 SQRTW        Sqrt of weight to be given a reflection durinf least squares
 A-PART       Real part of structure factor
 B-PART       Imaginary part of structure factor
 PHASE        phase angle, radians
 BATCH        An integer associated with reflections measured in batches
 BATCH/PHASE  Packed Batch and Phase
 SINTH/L**2   (Sintheta/lambda)**2
 FO/FC        Fo/Fc
 ELEMENTS     Integers coresponding to twin elements
 SERIAL       Serial number of reflection
 JCODE        Refelction quality code. See RC93 manual
 RATIO        Ratio Fo**2/sigma(Fo**2)
 RATIO/JCODE  Packed ratio and jcode
 TBAR         Absorption weighted X-ray path length
 THETA        Bragg angle
 OMEGA        setting angle
 CHI          setting angle
 PHI          setting angle
 KAPPA        setting angle
 PSI          setting angle
 CORRECTIONS  Composite correction factor for Fo
 FACTOR1      Individual correction factor for Fo
 FACTOR2      Individual correction factor for Fo
 FACTOR3      Individual correction factor for Fo
 NOTHING      A spare location for programmers use

If an output coefficient is specified without the corresponding input coefficient, it value is set to zero except for BATCH (default is 1.0) and SINTH/L**2 (value computed from cell parameters). Packed INDICES are restricted to +/- 127, packed RATIO to range 0.0 - 999.0, JCODE to range 0 - 9.
 

Reflections may be stored either in the structure data base (the DSC file), or as external binary serial files. The latter is used mainly during data redunction (see later).

When a change is made to most other data lists, they are either completely overwritten (LIST1 , cell parameters), or a new list created in additon to the old list (LIST 5, atom parameters). Because the reflections are special, they are handled differently. A small piece of information (called the LIST 6 Header) is created to hold information about the rest of the reflection list, and new headers are stored each time the main body is updated. The main body of the reflection list is modified in-situ if the only changes are ones which can easily be recomputed ( e.g. Fc, phase, sqrtw), thus reducing the disk activity. If an error occurs during the updating of the body, the list becomes inacessible to other processes, and the failing process must be re-run correctly. If the changes involve a change in size of the list, then a new body is created.

During raw data processing (Data reduction) the size of the reflection list can change a lot (coefficients being added or removed, reflections being merged or rejected). To prevent the .DSC file growing too large, binary serial files are used to hold the body of the reflection list. One is used for input and one for output at each stage, the roles being reversed after each stage. The Header is kept in the .DSC file, and keeps track of the bodies. When data reduction is complete, the body must be copied to the .DSC file.

 \LIST 6
 READ TYPE=COPY
 END

CRYSTALS can produce files containing reflections is a 'compressed' format. This might be useful for archiving data. The compressed data is headed by the correct information for its reinput.

The file contains information for h, k, l, /FO/ or /FOT/, RATIO/JCODE and elements. For each KL pair, the K value is given for this group of reflections, then the L value for the group, followed by the H and /FO/ and other values for the first reflection, the H /FO/ and other values for the second reflection, and so on, finishing with 512, which is the terminator for this KL pair. This pattern is repeated for all the KL pairs, the terminator for the last KL pair being -512, and indicates the end of the reflection list. Take care if you try to edit these files, and note that K and L are the two constant indices for each group, while H changes most rapidly.
 

 

Raw intensity data require more processing than F or Fsq values. The instuction '\HKLI' is related to '\LIST 6', but has different default coefficients and additional directives for geometrical corrections.

 \HKLI
 READ NCOEFFICIENT= TYPE= F'S= NGROUP= UNIT= CHECK=
 INPUT COEFFICIENT(1)= COEFFICIENT(2)= .  .
 STORE NCOEFFICIENT= MEDIUM= APPEND=
 OUTPUT COEFFICIENT(1)= COEFFICIENT(2)=  .  .
 FORMAT EXPRESSION=
 CORRECTIONS NSCALE NFACTOR
 FACTORS COEFFICIENT(1)= COEFFICIENT(2)=  .  .
 ABSORPTION PRINT= PHI= THETA= TUBE= PLATE=
 PHI NPHIVALUES= NPHICURVES=
 PHIVALUES PHI= .........
 PHIHKLI H= K= L= I[MAX]=
 PHICURVE I= .........
 THETA NTHETAVALUES=
 THETAVALUES THETA=
 THETACURVE CORRECTON= ........
 TUBE NOTHING OMEGA= CHI= PHI= KAPPA= MU=A[MAX]=
 PLATE NOTHING OMEGA= CHI= PHI= KAPPA= MU=A[MAX]=
 END

 \ The OPEN instruction connects the reflection file
 \OPEN HKLI REFLECT.DAT
 \HKLI
 READ NCOEF=12 FORMAT=FIXED UNIT=HKLI F'S=FSQ CHECK=NO
 INPUT H K L /FO/ SIGMA(/FO/) JCODE SERIAL BATCH THETA PHI OMEGA KAPPA
 FORMAT (5X,3F4.0,F9.0,F7.0,F4.0,F9.0,F4.0,4F7.2)
 STORE NCOEF=6
 OUTPUT INDICES /FO/ BATCH RATIO/JCODE SIGMA(/FO/) CORRECTIONS SERIAL
 ABSORPTION PHI=YES  THETA=YES PRINT=NONE
 THETA 16
 THETAVALUES
 CONT 0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
 THETACURVE
 CONT 3.61  3.60  3.58  3.54  3.50  3.44  3.37  3.30
 CONT 3.23  3.16  3.09  3.02  2.96  2.91  2.86  2.82
 PHI 26  1
 PHIVALUES
 CONT   6  16  21  26  31  36  41  61  66  76
 CONT  81  86  91  96 111 121 131 136 141 146
 CONT 151 156 161 166 171 176
 PHIHKLI    -3   -1    0    28392
 PHICURVE
 CONT    26887   25377   24608   23990   23445   23049
 CONT    22867   22801   22782   22937   23104   23368
 CONT    23713   24129   25669   26836   27892   28250
 CONT    28291   28256   28101   28009   28204   28373
 CONT    28392   28203
 END
 \CLOSE HKLI

 NCOEFFICIENT= 12
 TYPE=FIXED
 F'S=FSQ
 NGROUP=1
 UNIT=HKLI

This directive defines the coefficients that are to be read in. The number of coefficients is given by the NCOEFFICIENT parameter above, or its default value.
 
The default input coefficients are:

      H K L /FO/ SIGMA(/FO/) JCODE SERIAL BATCH THETA PHI OMEGA KAPPA

      INDICES /FO/ SQRTW /FC/ BATCH/PHASE RATIO/JCODE SIGMA(/FO/)
      CORRECTIONS ELEMENTS

This directive is only valid if the TYPE on the READ card is FIXED .
EXPRESSION= If the diffractometer type indicatd in LIST 13 is CAD4, the default corresponds to RC93 or RC85 output, otherwise an expression must be given.
 
(5X,3F4.0,F9.0,F7.0,F4.0,F9.0,F4.0,4F7.2) This directive is only valid if the TYPE on the READ card is
 

 
Directives not found in LIST 6 Instructions are:
 
CORRECTIONS NSCALE= NFACTOR=
NSCALE= Set to 1 or 2 to select the first or second scale factor in LIST 27. The default is 2.
NFACTOR= Up to three correction per reflection to be applied to the input observations can be included in the input file. This keyword specifies how many to use. The default is 0.
 

 
FACTORS COEFFICIENT(1)= COEFFICIENT(2)= . . The permitted coefficients are FACTOR1, FACTOR2 and FACTOR3. These are applied to the input observation before any other action (including square rooting if requested) is performed.
 

 
ABSORPTION PRINT= PHI= THETA= TUBE= PLATE= This directive controls approximate absorption corrections to be applied during input. They are only suitable if the diffractometer used is one of those permitted in LIST 13.
PRINT= Permitted levels are

      FULL                  Two lines of inforamtion per reflection
      NONE    - Default     No output is produced
      PARTIAL -             Summary for each reflection

      NO      - Default
      YES

      NO      - Default
      YES

      NO      - Default
      YES

      NO      - Default
      YES

If each reflection has been assigned a serial number (or some other incrementing value, such as total X-ray exposure time) then CRYSTALS can apply a correction which is linked to this value. The corrections, on the scale of Fsq, are held in LIST 27. Two correction factors can be stored, but only one used. In Oxford, these are the actual corrections computed from the decay of the standard reflections, and those obtained from 3-point smoothing. The applied scale factor is obtained by interpolating between those given scale factors with serial numbers above and below the serial number of the current reflection. If there is a dramatic change in scale (for example due to remeasurement of some very strong reflections with attenuated X-rays), it is important not to interpolate over this discontinuity. To achieve this, a dummy scale factor is inserted at this point with scale values the same as the current scales, but with the same serial number as the first scales after the discontinuity - see the example.

 \LIST 27
 READ NSCALE=
 SCALE SCALENUMBER= RAWSCALE= SMOOTHSCALE= SERIAL=
 END

 \LIST 27
 READ NSCALE=16
 SCALE   1      1.000  1.000    1
 SCALE   2      1.066  1.066    4
 SCALE   3      1.074  1.053   57
 SCALE   4      0.997  1.018   83
 SCALE   5      1.003  1.003  564
 SCALE   6      0.370  0.370  564
 SCALE   7      0.372  0.371  617
 END

This directive is repeated once for each scale factor that is to be read in.
SCALENUMBER This parameter indicates the number of the scale factor, starting from one. There is no default for this parameter, which currently is not used.
RAWSCALE This parameter gives the initial scale factor, computed directly from the intensities of the standard relections. There is no default.
SMOOTHSCALE This parameter gives the scale factor after the raw scale factors have been smoothed, so that a continuous curve is fitted to all the data. There is no default.
SERIALNUMBER This parameter gives the serial number of the first standard reflection contributing to this scale. The data reduction programs use the SERIAL to locate the correct scales to use for a given reflection. There is no default.
 

 

This Instruction prints the decay curve. There is no instruction to punch LIST 27.
 

 

This instruction causes the Lp correction to be calculated for each reflection.

The diffraction geometry, wavelength, etc. are taken from LIST 13. If LIST 13 is input incorrectly, or has to be generated by the system, the message 'illegal diffraction geometry flag' will be output and the job terminated. If the user has forced the storage of Fsq values in \HKLI, it is necessary to indicate this to the Lp correction.

 \LP
 STORE MEDIUM= F'S=
 END

 \LP
 END

      FILE              A serial file
      INPUT - Default   The same as the input medium
      DISC              The .DSC file.

      FO      -      Default
      FSQ            Indicating that square roots were not taken at
                     input time.

 \SYSTEMATIC
 STORE MEDIUM= F'S= NEWINDICES=
 END

 \SYST
 END

This routine uses the symmetry operators in LIST 2 to identify systematic absences, which are listed and rejected. It can also use the symmetry operators to transform indices to that the reflections fall into a unique part of the reciprocal lattice. The unique set is bounded by the maximum range in 'l', maximum range of 'k' given the 'l' range, and maximum range of 'h', given the 'k,l' range.

Friedels Law may be invoked, depending on the flag in LIST 13. It is important NOT to use Friedels Law for structures which have strong anomalous scatterers, since reflections related by friedel's law are not equivalent in this case and should not be merged together. Similarly, if orientation dependent corrections are to be made ( e.g. DIFABS),original indices should be preserved. Note that in this case, only exactly equivalent reflections will be merged, and care must be taken when computing Fourier maps. See the sections on Fourier maps and DIFABS.
 

 

 
\SYSTEMATIC

 

 
STORE MEDIUM= F'S= NEWINDICES=
MEDIUM= Determines the output medium.

      FILE              A serial file
      INPUT - Default   The same as the input medium
      DISC              The .DSC file.

      FO      -      Default
      FSQ            Indicating that square roots were not taken at
                     input time.

      YES  -  Default  Permits transformaiton of indices.
      NO

 \SORT
 STORE MEDIUM=
 END

 \SORT
 END

This routine sorts the data so that the reflections are placed in a predetermined order, in which reflections with the same indices are adjacent in the list. Upon output, the reflections are arranged so that they are in groups of constant L , starting with the group with the smallest L value. Within any L group, the reflections are ordered in groups of constant K , starting with the group with the smallest K value. Within each KL group, the reflections are arranged with the smallest H value first and the largest last in ascending order.

The method of sorting is a multi-pass tree sort, in which as many reflections as possible are held in memory during each pass. If all the reflections with a given value of L cannot be in memory at the same time, the program will terminate in error.
 

 
\SORT

 

 
STORE MEDIUM
MEDIUM= Determines the output medium.

      FILE              A serial file
      INPUT - Default   The same as the input medium
      DISC              The .DSC file.

 \MERGE
 STORE MEDIUM=
 REFLECTIONS NJCODE= LIST= LEVEL= F'S=
 JCODE NUMBER= VALUE=
 REJECT RATIO= SIGMA=
 WEIGHT SCHEME= NPARAMETERS= NCYCLE=
 PARAMETERS P .....
 END

 \MERGE
 WEIGHT SCHEME=2
 PARAMETERS .5  3.0  1.0  2.0  .01 .00001
 END

The merge routine takes a list of reflections and combines groups of adjacent reflections with exactly the same indices to produce a single mean structure amplitude.

\SYST and \SORT produce a suitable list, and if either of them have been omitted, it is extremely likely that the list of reflections produced by the merge process will contain duplicated entries for certain reflections.

It is possible to combine equivalent reflections in several different ways, depending upon how each individual contributor is weighted when the mean is computed. Several different weighting schemes are provided, and these are described in the next section (the WEIGHT directive).

Reflections which have JCODES that differ from unity and are thus thought to be inaccurate, can be down-weighted or eliminated during the merge process (the JCODE directive). Note that JCODES MUST be positive and less than 10.

Although under normal circumstances LIST 6 contains /Fo/ data rather than /Fo/**2 data, the calculations performed during the merge are done on the scale of /Fo/**2. This means that r-values are computed which refer to /Fo/**2, and that reflections can be rejected on the basis of the ratio of /Fo/**2 to its standard deviation. If for some reason the LIST 6 contains /Fo/**2 data rather than the normal /Fo/ data, it is necessary to use the "F's" parameter to inform the system of this fact.

During the merge process, the system calculates and then prints a set of merging r-values, which are defined as follows :

 R = 100*SUM[ Sd(i) ]/SUM[ M(i) ],
             where 'i' runs over all reflections.


 Sd(i) = SUM[ <Fsq(i)> - Fsq(j) ],
             summed over 'j' contributors.

 and

 M(i) = SUM[ <Fsq(i)> ],
            summed 'j' times for 'j' contributors.

If the crystal is twinned, this will affect the merge. See the section on twinned crystals.

If the data is in Batches with different BATCH sale factors, this will affect the merge. See the section on Batched data input.
 

 
WEIGHTING SCHEMES FOR THE DATA MERGE

At present there are three different weighting schemes available for merging equivalent reflections. These are :

      1.      Each reflection is given equal weight (unit weights).
      2.      Weights based on a Gaussian distribution.
      3.      W(i) = 1.0/Sigma(i)  for each reflection.

Unit and statistical weights (schemes 1 and 3) are more or less equivalent unless some reflections have been remeasured under very different regimes ( e.g. with an attenuator set, mA turned down, different crystal)

Scheme 2 is designed to discriminate against outliers, -i{i.e. refections lying farther from the mean than might be expected. For this scheme, a weighted mean value of Fsq is determined iteratively, starting from unit weights. At each iteration, the weights are recomputed to discriminate against outliers and the contributing reflections are given a new weight w(i) given by :

      w(i) = exp [ (-log(a) * q(i)**2)/(b**2 * e(i)**2) ]

 Where

     q(i)  is the deviation of the particular Fsq(i) from the current average.
     e(i)  Is a predicted mean deviation of the reflection 'i' from the
           current mean and is given by a function similar to that used
           in Least Squares :

           e = c + d*Sig(Fsq) + g*Sig(Fsq)*/Fo/ + h*Sig(Fsq)*Fsq

     a,b,c,d,g,h  are 6 input parameters provided by the user

'a' and 'b' define the Gaussian distribution. 'a' is the weight to be given to a reflection which has a deviation given by 'q(i) = b*e(i)'. Suggested values of 'a' and 'b' are 0.5 and 3.0 respectively, so that if for example, 'e(i) = 3*Sig(Fsq)' (d=3, c=g=h=0), a deviation q(i) of 6*Sig*fsq will assign a reflection a weight of 0.5.

'c' Provides the bias necessary to allow for failures in the counting statistics at low count rates.

'd' is a scaling constant.

'g' and 'h' allow for the increased dispersion of strong reflections.

 For a conventional diffractometer, suggested values for the parameters are :

      a = .5      b=3.0      c=1.0      d=2.0      g=.01      h=.00001

It is recommended that the Gaussian scheme be used, as it discriminates against zero or widely dispersed intensities very efficiently.
 

 
Standard deviations produced by the merge

After the equivalent reflections have been merged two different standard deviations are computed and can be output :

 SIGMA1 = Sqrt (sum [ w(i)*q(i)**2 ] / sum [ w(i) ])
             that is, the weighted r.m.s. deviation.

 SIGMA2 = Sqrt (sum [ w(i)*s(i)**2 ] / sum [ w(i) ])
             that is, the weighted standard deviation.

      FILE              A serial file
      INPUT - Default   The same as the input medium
      DISC              The .DSC file.

      OFF
      MEDIUM  -  Default value
      HIGH

      FO      -      Default
      FSQ            Indicating that square roots were not taken at
                     input time.

This directive allows reflections whose jcode number differs from unity to be down-weighted or eliminated from the merge. It is repeated once for each jcode that is read in.
NUMBER= The number of the jcode must be given. There is no default value for this parameter.
VALUE= This is the absolute weight, associated with the jcode number, that is given to the reflection. If this parameter is omitted a default value of zero is assumed, indicating that the reflection is to be eliminated and not included in the merge at all.
 

 
REJECT RATIO= SIGMA=

This directive causes reflections whose mean intensity is less than ratio*e.s.d. to be eliminated.
RATIO= The default value for this parameter is -10. Use LIST 28 to suppress the use of reflections with RATIOs below a suitable threshold.
SIGMA=
 

      1
      2  -  Default value

This directive determines the weighting scheme to be used in merging equivalent reflections.
SCHEME= This parameter determines which of the weighting schemes defined above is to be used in the merging of equivalent reflections, and must take one of the following values:
 

      1  -  Default value (unit weights)
      2                   (modified Gaussian)
      3                   (statistical)