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Re: proposal for twin terms

  • To: Multiple recipients of list <coredmg@iucr.org>
  • Subject: Re: proposal for twin terms
  • From: Howard Flack <Howard.Flack@cryst.unige.ch>
  • Date: Wed, 18 Oct 2000 09:38:39 +0100 (BST)
Dear David,

> I would like to propose as an addition to the Core some items concerning
> twinned samples.

I agree to this. Here are a few thoughts. 

> In priciple only a few items would be necessary:
> -twinning matrices

   One needs to be clear on what these rotation matrices operate. From
the analysis of the diffraction pattern, its best to have them operate
on hkl. From the point of view of understanding the twin laws and the
interrelations of the domain orientations, it is probably better to have
them in direct space. One has the choice of providing for the two
different ways or being a dictator and insisting that there is one
'best' way. Moreover I just wonder whether one should not include a
translation vector so that antiphase domains can be treated in the same
formalism. Twinning only deals with rotations but in the treatment of
phase transitions, the coset representatives in the decomposition of the
high symmetry space group with respect to the low symmetry spae group
will also give information on the translations.

> -volume fractions

  I think I would prefer to call them mass fractions (or perhaps twin
fractions or perhaps mole fractions) and that the twinning matrices and
the mass fractions need to be in a loop where both items must be
present. As far as I know most least-squares programmes work by assuming
that the model structure is that of the first component (with an assumed
twinning matrix of identity) whose mass fraction is constrained to be (1
- sum of all the other refined mass fractions). This means that authors
do not specifically report the mass fraction of the basic component
which is in general the largest one. Should one then insist that the
mass fractions of all components including the one with the identity
matrix as twin matrix be reported.
  It goes without saying that the mass fraction must be reported with a
standard uncertainty. As the sum of the mass fractions is contrained to
be equal to 1.0, the covariance terms are large, and important in the
calculation of derived quantities. Should CIF provide a mechanism for
reporting the full variance-covariance matrix of the mass fractions? I
only know of one calculation (See section 8 of Absolute Structure and
Absolute Configuration. H. D. Flack and G. Bernardinelli (1999). Acta
Cryst. A55, 908-915. http://www.iucr.org/cgi-bin/details/actaa/v55/p908
- BTW that form of the URL is a general way of finding papers in the
IUCr journals from the 'ordinary' literature reference) where one makes
linear combinations of twin fractions in order to calculate something of
physical significance. However in that particular case, CIF has already
the necessary data items for reporting the quantity and its su.

> I do not know if some
> additional items (perhaps pointers to indicate the contribution of each
> domain to a given intensity) are required to cover with generality this
> topic.

  Very very tricky to get something that is general and useable at the
same time. Even in the case of 'merohedral' twinning (there are ''
because one has to be absolutely sure what one means by this term) space
group Pa-3 is unique. For the 0kl (and hk0, h0l) reflections there is
the condition for reflection k = 2n with no corresponding condition on
l. This means that in the crystal twinned by a two-fold axis along
[011], one gets reflections with observable intensity from the twin
domain overlapping space group absent reflections from the basic
component. How should one index such reflections? Split reflections are
the same kettle of fish.

  In section 1 of Absolute Structure and Absolute Configuration. H. D.
Flack and G. Bernardinelli (1999). Acta Cryst. A55, 908-915.
http://www.iucr.org/cgi-bin/details/actaa/v55/p908, there is a glossary
of terms. I would like to see these included in the coreCIF dictionnary.
Comments please.
  N.B. What I am asking is for a breakaway in the use of CIF. CIF data
names will have to be provided for the items in my glossary but
presumably nobody will ever use them in a real live CIF. They should
however be used in the definition of other data items within the coreCIF

  Actually I did not make it to the CODATA 2000 conference in Baveno
near Stresa in Italy this week. Due to the numerous murderous landslides
and terrible flooding in the Alps both on the Italian and Swiss sides,
there was no way for me to get to Baveno. I sent an e-mail and then a
fax to the conference hotel in Baveno to say I was having trouble with
travelling. When I phoned to say I could not make it, the line was down!
I wonder whether Brian is really there and having a nice time swimming
in the Lago Maggiore? As a result of my need to search through numerous
sources of information to try and find out what was going on, I now have
an even clearer idea about running a valid web information service. E.g.
24 hours after the road over the Simplon pass was blocked by a
landslide, the Swiss TCS (automobile club) web site was still saying it
was open. 24 hours later, all one could get out of it was that the
server was overloaded. Its all full of Java stuff that flashes false
messages at you all the time. Useless. The Swiss railways put up special
messages every two hours, but their route planer still offered me on the
'timetable for today' a journey over a stretch of railway that was
closed. The Italian railway web site continued unabated as though
nothing had happened. The only thing working was their web site.

Best wishes,

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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