[sdpd] Re: UPPW-5 solution - UPPW-6 problem

[Alan Coelho <alan.coelho...@attglobal.net>]

hello to all

First I would like to praise Armel for bringing indexing into the 
spotlight. Now I would like to comment on Armel's statement "Have the 
most recent indexing software outmatched the old established ones ? 
Perhaps, hard to say".

I don't think that these examples are going to show up progress on 
whether new algorithms succeed; they do however show when they fail. I 
do enjoy the challenge so don't stop Armel.  The reason for being 
pessimistic is the fact that if a new method does find a correct 
solution to a difficult unknown then who is to know if the correct 
solution was indeed found. As much as I think that "real" data is 
necessary for testing methods I do think that there is no substitute for 
simulated test data where the solutions are known. There is also no 
substitute for understanding the methods rather than trusting their 
implementations.

UPPW-5 is a case where powder data does not yield a unique solution. 
When multiple solutions yield similar "perfect" Pawley/Le Bail fits with 
similar de Wolff  values then it is not a matter of failure of the 
programs/methods but rather a failure of the data to yield a unique 
solution. In my view it is therefore not possible for any indexing 
method to resolve the ambiguity. This is not to say however that the 
door should be closed to new methods. The way forward is to go 
backwards. Back tracking could mean recollecting the data on a higher 
resolution instrument (ie. Peter Stephens), annealing the sample or 
trying some SEM/TEM analysis. If all this fails then it is really a 
matter of trying structure solution for each of the possible lattice 
parameters.

Excuse the long mail but while I am at it I would like to correct a 
misconception regarding the idea of an "exhaustive" search and in the 
process state the reason why I developed an indexing algorithm. I have 
heard the term "exhaustive" used so much in indexing that I am beginning 
to believe that I got something wrong. So please enlighten me if you can.

On data with small 2Th errors then a method can claim to be exhaustive. 
However, on data with large errors due to say peak overlap on a dominant 
zone problem then the term  "exhaustive" looses meaning. The successive 
dichotomy method, a stroke of genius by Daniel Louër to use it, is often 
regarded as being exhaustive. For data with large errors the delta-2Th 
values would need to be set large for the dichotomy method to proceed to 
the correct solution. If the delta-2Th were indeed set large enough then 
there would be many solution ranges returned (note I am defining a 
solution range as a solution with +- delta-2Th). Thus sure enough the 
solution range would be there but the correct range would be impossible 
to define. If the correct range could somehow be identified then in my 
view an iterative least squares estimate between the observed and 
calculated d-spacings is the best solution choice within a particular 
range. Note multiple Palwey/Le Bail fits would not be feasible if the 
delta-2Th were large; this brings me to my own algorithm (dare I say its 
Topas) which returns iterative least squares solutions. Now having said 
that no method is going to resolve ambiguity, it is my opinion that a 
combined ITO and DICVOL probably solves more than 90% of every thing 
thrown at it. Thus new algorithms are only filling a small gap and to 
find this gap is presumably what UPPW is all about - or is it? If not 
then it's a lot of fun in any case.     
cheers
alan





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