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Re: [sdpd] more info on the method of harmonics !!!

Finding the (instrument + sample displacement) zeropoint 
(or calibrating a powder pattern) is usually done by two methods :
   - mixing the unknown sample with a reference compound,
     then the difference in obs and calc angular positions of the
     reference is transmitted for correction to the unknown compound
     peak positions. That method is quite sure.
   - using the harmonic method : much more risky. It may be 
      employed if you have not enough sample for losing a part
      of it by mixing with a reference.

I am surprised to see how that method of harmonics may pose
problems. It can be made automatically by a software like
PowderX, and there is even a publication about it :
- Correction of zero shift in powder diffraction patterns using the 
reflection-pair method, Dong C.  Wu F.  Chen H. 
J. Appl. Crystallogr. 32 (Part 5):850-853, 1999. 

Why using only pairs if you can find more harmonics ? No reason.
Finding a large series of harmonics is usual when dealing with
lamellar compounds, and if you induce preferred orientation
by pressing the sample on the holder. Then a zeropoint can be
estimated by using a cell parameter refinement program (CELREF,
LAPOD...). The series of harmonics may correspond to a 00l
series, i.e. to a cell parameter, but not necessarily. If not (and if
the structure of the compound is unknown, you cannot be sure,
obviously), you may consider a "fictitious cell parameter". If you 
are lucky, you may (think to) have found 3 series of different 
harmonics, and refine 3 "fictitious cell parameters" in order to
estimate the zeropoint. I do not really recommend it, but with
experience, this may prove to be efficient. 

 >And what about the space group? It is still unknown. 

A fictitious cell has no (need for a) space group. In a cell parameter
refinement, you have not to enter any space group, nor in a "fictitious 
cell parameter" refinement.

 >Do I have to have exact x/2,x/3, x/4 reflections or an error 
 >of 0.02 deg is tolerable?

That is all the problem with this method. You don't know
the zeropoint, so that you don't know what error is
tolerable. However, if you have put the sample on its holder
by yourself, and if you already know the part of the 
zeropoint associated with the instrument, then you may have
an idea of the usual total zeropoint which will depend on
the following : the sample surface was above or below
or exactly in the diffracting plane (a few microns of error in
the surface position may lead to a few 1/100th of 2-theta 
degrees zeropoint error). 

Best wishes,

Armel Le Bail
http://www.cristal.org/course/