Indexing of powder diffraction patterns is considered as the most difficult part among the procedures of ab-initio powder structure determination.  Recently, we devised a new indexing algorithm that can search rapidly and thoroughly for the possible solutions. 

Topograph is a connected tree in the graph theory, which is a collection of relation formula given by Q(h1+h2) + Q(h1-h2) = 2 * ( Q(h1) + Q(h2) ).  Although this formula is already known as Ito's equation and used in Ito's algorithm, it seems to have not yet displayed its real merit.  We report on how it is efficient to construct an algorithm that is not affected by the extinction rule.

We proved this algorithm works completely at least for lattices of dimension 2.  Although we are trying to extend this to the case of dimension 3, some uncertain part still remains.

Out method does not use any assumptions on Bravais lattice. It is efficient even if there is a false peak in the powder diffraction pattern or the material is not a single phase.

The detail of the method and some results are introduced.

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1. iMATERIA - versatile neutron diffractometer at J-PARC