*** For details on how to be removed from this list visit the ***
*** CCP4 home page http://www.ccp4.ac.uk ***
Hai Sue,
Should the intensity distribution look twinned in P3(1)21? Will the
moments look twinned? Or will the anomalies only appear when the data
scaled in P3(1)?
In P3(1)21 the data will look twinned. Both the moments and the N(Z)
plots will behave as if the data is perfectly twinned I think:
Say you have twin related intensities I1 and I2. the miller indices H1
and H2 are related by a two-fold axis, that is a 'twin law' in P3(1) and
is considered a symmetry operator if you process your data in P3(1)21.
Say that you have a twin fraction of alpha, and error-free untwinned
intensities J1 and J2.
Then :
I1 = alpha J1 + (1-alpha) J2
I2 = (1-alpha) J1 + alpha J2
If you would merge your data in space group P3(1)21, you basically
declare I1 and I2 to be the same (call it I(1,2) ), and you average
them in order to get a
more accurate estimate of the intensity. this is what would happen:
I(1,2) = 0.5*I1+0.5*I2 = 0.5*J1 +0.5*J2
i.e.the distribution of I(1,2) (i.e. the intensity distribution in
P3(1)21 ) would look like you have a perfect twin.
Note that you have a number of options for twinning when you have
spacegroup P3(1)
The possible "point groups" and possible systematic absense consistent
(*) space groups are
P 3 -> P3(1) P3(2)
P 3 2 1 -> P3(1) 2 1, P 3(2) 2 1
P 3 1 2 -> P 3(1) 1 2, P 3(2) 1 2
P 6 -> P6(1), P6(5), P6(2), P6(4)
P 6 2 2 -> P6(1)22, P6(5)22, P6(2)22, P6(4)22
(*) the systematic absenses of P31 fall in the systematic absenses of
the listed groups. The converse is not neccesarily true.
The relations between the various point groups are shown in a picture I
just put on the web:
http://cci.lbl.gov/~phzwart/p31.png
Finding candidate twin laws and the proper spacegroup will be a matter
of processing the data carefully and I guess the decision is
relatively straightforward if the data is not perfectly twinned. If it
is perfectly twinned, it will be difficult to distinguish between
symmetry in the
intensities due to the symmetry of the untwinned unit cell or due to
twinning. I think trial and error might be the only option you have in
that case.
Note that if you have NCS parallel to one of the other potential twin
axes, things can get difficult. You might even end up in a situation
where you
mistake a twin law for a symmetry axis and NCS relations between
intensities for a twin operator. I am not sure what will happen when you
try to
refine in those situations, but I guess it would not make one happy ....
If I decide I have a twinning problem, and wish to try the shelx
refinement, which space group do I refine in? (I haven't tried this
yet, so I don't have an empirical answer.)
That would be P3(1) if you have the twinning you described.
HTH
Peter
