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Re: proposal for valence items

  • To: Multiple recipients of list <coredmg@iucr.org>
  • Subject: Re: proposal for valence items
  • From: Howard Flack <Howard.Flack@cryst.unige.ch>
  • Date: Mon, 4 Dec 2000 17:30:04 GMT

> ;              A unique identifier for each domain detected in the sample.
> ;

  might be better as:

 ;              A unique identifier for each domain state whose presence
is assumed to be permissible.

   I think it should be 'domain state' instead of 'domain' although it
depends on the exact definition of the terms one is using and I'm not
quite sure what is the most official source. The problem is as follows,
taking the simple case of inversion twinning in the crystal as an
example e.g. a crystal structure in space group P2 with an entirely
general metric for the lattice. In this case there are two 'domain
states' i.e. two crystal structures related one to another by space
inversion. The number of domains (n) may be any non-negative integer. If
n=0, there is no crystal. If n=1, the sample is an untwinned single
crystal whose structure is that of one of the two domain states. If n=2,
there is one domain with structure of one of the domain states and
another domain with the structure of the other. etc etc etc. Of course
since in the data names and elsewhere the term twin has been used, it
might be advisable to use the term 'twin component' instead of 'domain'
or 'domain state' but again one has to be sure what exactly the 'twin
component' is.
  I changed the wording from 'detected' to 'permissable' because a
domain state whose twin fraction turns out from the refinement to be
zero can not be said to have been detected.


> ;              The matrices that generate the Miller indices of each domain
> from the Miller indices of the first one:

 might be clearer as:

  ;  The set of twin-law matrices in which the ith matrix transforms the
Miller indices of a reflection in the first domain state into those of
the twin-equivalent reflection resulting from the ith domain state. A
twin law transformation of Miller indices is written in matrix form as:

> The twin matrices are referred to the basis reciprocal to that given by 
> _cell_length_ and _cell_angle_. All the twin matrices including the identity 
> should be entered. 

  might be nicer as:

The twin-law matrices are referred to the basis reciprocal to that
derived from 
_cell_length_ and _cell_angle_. It is mandatory to specify all twin-law
matrices, including that of the identity. 


> ;              An identifier for the refined twin fractions. It must match a
> corresponding _diffrn_reflns_twin_id.
> ;

 might be nicer as:

;              The identifier of one domain state. This must be
identical to a   _diffrn_reflns_twin_id.

  I do it this way because surely what needs identifying is not the twin
fraction but the domain state itself.

  The range on the possible values of the twin fractions should be
specified either in the text or in the evaluation range. The Flack
parameter data item has suitable wording for this and you can cut and
paste it in here.
>  F^2^~c~=s^2^ Sumi k(i)F^2^~c,i~    (i=1,n)
  |F|^2^~c~=s^2^ Sumi k(i)|F|^2^~c,i~    (i=1,n)

AND I would like to add the second equation:
   Sumi k(i) = 1    (i=1,n)

> where F~c~ is the calculated structure factor,
  A structure factor is a complex quantity but the thing on the
left-hand side of the equation is real (and not even non-negative as
implied by the square - refined k values can go negative). I'm not too
keen either that the same letter F should be used for the untwinned and
for the twinned intensities. The equation as written applies to the
intensity of one reflection of the twinned sample. In some analyses it
is interesting to write down similar equations for all the
twin-equivalent twinned intensities. This means that one needs
subscripts on the left-hand side and the nomenclature does not allow one
to distinguish between twinned and untwinned intensities. So I suggest:

  G~c~=s^2^ Sumi k(i)|F|^2^~c,i~    (i=1,n)
  where G~c~ is the calculated twinned intensity for reflection h1 h2
> F~c,i~ the calculated structure factor of domain i
  F~c,i~ the calculated structure factor of domain state i

> and n the number of domains.
  and n the number of domains states.

> The sum of twin fractions must be unity
  I prefer the equation.

> and therefore only k(2)...k(n) are refined.
   I have problems here. It gives the impression that k(1) is invariable
which is not the case. Its value is constrained to satisfy the
constraint equation Sumi k(i) = 1  (i=1,n). For me, the value of k(1)
has been refined. Also as written Gotzon is here insisting for the first
time that the domain states must be ordered so that the first one is the
constrained one. His definitions however only give an identifier to each
domain state and nowhere is an order required. Further using the
constraint equation in the form:
   k(1) = 1 - Sumi k(i)    (i=2,n)
is not the only way of doing things. Is it necessary in CIF to insist
that k(1) is special? Is k(1) necessarily that twin fraction
corresponding to the twin-law of identity? This is nowhere stated.  I
think that what is necessary instead of:
> The  sum of twin fractions must be unity and therefore only k(2)...k(n) are
> refined.
> However all the twin fractions including k(1) should be entered.

 should be (assuming you put in the constraint equation):

It is mandatory to specify the refined twin fractions of all domain


> ;              A description of the method used to calculate the "observed"
> structure factor of the first domain used to evaluate the difference Fourier 
> map.
> ;

 ;              A description of the method used to calculate the
Fourier coefficients used in electron density calculations.

  I don't think you should talk at all about the first domain state here
since it implies that the electron density calculation is being
evaluated only on partial data deriving from that particular domain
state. If you have good software, Fourier coefficients contain
contributions from all domain states.

Hope these comments are useful,

Howard Flack        http://www.unige.ch/crystal/ahdf/Howard.Flack.html
Laboratoire de Cristallographie               Phone: 41 (22) 702 62 49
24 quai Ernest-Ansermet             mailto:Howard.Flack@cryst.unige.ch
CH-1211 Geneva 4, Switzerland                   Fax: 41 (22) 702 61 08

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