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Re: Absolute structure

  • To: Multiple recipients of list <coredmg@iucr.org>
  • Subject: Re: Absolute structure
  • From: Howard Flack <Howard.Flack@cryst.unige.ch>
  • Date: Tue, 31 Mar 1998 17:13:13 +0100 (BST)
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I wish to submit a slight modification of my previous suggestion of 
   _reflns_Friedel_completeness

 (1) I now prefer to call this _reflns_Friedel_coverage
 (2) and define it so that it takes values ranging from 0.0 (bad - 
     centrosymmetric) to 1.0 (very good - the complete coverage possible
in 
     space group P1.)
   
 The definition is like this:



data_reflns_Friedel_coverage
    _name                        '_reflns_Friedel_coverage'
    _category                    reflns
    _type                        numb
    _enumeration_range           0.0:1.0
    _definition
;              _reflns_Friedel_coverage is defined as being the quotient
               [N(Crystal class) - N(Laue symmetry)] / N(Laue symmetry) 
               where working from the _diffrn_refln_ list
               N(Crystal class) is the number of reflections obtained on 
               averaging under the symmetry of the crystal class and
               N(Laue symmetry) is the number of reflections obtained on 
               averaging under the Laue symmetry.
               Examples:
                 (a) For centrosymmetric structures its value is
necessarily equal
               to 0.0 as the crystal class is identical to the Laue
symmetry.
                 (b) For whole-sphere data for a crystal in the space
group P1,
               _reflns_Friedel_coverage is equal to 1.0, as no
reflection h k l
               is equivalent to -h -k -l in the crystal class and all
pairs
               {h k l; -h -k -l} have been measured.
                 (c) For whole-sphere data in space group Pmm2, 
               _reflns_Friedel_coverage attains a value less than 1.0
               because although reflections h k l and -h -k -l are not
equivalent
               for general non-zero values of h k and l nevertheless h k
0 and 
               -h -k 0 are equivalent in the crystal class.
                 (d) For a crystal in the same space group Pmm2 as
example (c),
               measurements of the two inequivalent octants h >= 0, k
>=0, l 
               lead to the same value of _reflns_Friedel_coverage as
example (c) 
               whereas measurements of the two equivalent octants 
               h >= 0, k, l >= 0 lead to a value of zero for
_reflns_Friedel_coverage.
                 

 
;

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