Dear Arie and others What you have described is the classic "dominant zone" pathology, which I described in 1975 at the Amsterdam Congress and many times subsequently.
The problem (and opportunity) here is that two of the reciprocal lattice vectors (let's call them <a> and <b>) and hence the associated three constants (a*, b* and gamma*) become very well defined, while the remaining vector <c> becomes poorly defined and in an extreme case may not be sampled at all in the first 20 (or 30, etc.) observed lines. That makes a figure of merit like M20 completely useless for ranking trial solutions, since the first 20 lines may all belong to hk0 and so can be explained using just the three 2-dimensional dominant-zone parameters (a*, b*, gamma*, or whatever you have chosen to call them). The same will be true for F(N) [where often N=30], if the zone is a bit more dominant and all or nearly all the first 30 lines belong to hk0. Actually it is sufficient for 19 of the first 20 to belong to hk0 for alpha* and beta* to become completely indeterminate. But note that I've described this situation as not just a problem but also an opportunity. That's because the more dominant the hk0 zone, the more confidence we have that we know its three parameters, reducing the general triclinic indexing solution space from 6 to just 3 dimensions. The SIW (i.e. Shirley-Ishida-Watanabe) dominant-zone heuristic then allows us to assign any one of the lower-angle unindexed hk1 lines arbitrarily to be 001. We've thus determined a 4-parameter "basis set" [a*,b*,c*,gamma*] and reduced the unknown parameters to just 2 - the remaining two angles alpha* and beta*. There are several indexing programs specialised for this 2-dimensional search of alpha* and beta*, all of them available within Crysfire: LZON, LOSH and Mmap (and in the Crysfire 2003 beta release, also Hmap). Note that you *must* extend your search dataset to sufficiently high 2Theta to include enough hk1 lines (8-10 for example) for this process to work. That may mean including 30-40 lines. Unfortunately the summary file entries for LZON and LOSH currently still report only M20, so are not as helpful as they should be in these cases if the hk0 lines have been included. This does affect Mmap and Hmap, which report their FoM for as many lines as were actually used. Note too that in such searches which rely on mid-angle lines, you will be getting into quite delicate territory within solution space, where it becomes very important to reduce uncorrected 2Theta-zero or specimen- displacement errors to a minimum, if the search is to remain stable. A trick worth remembering is that, once the numerous low-angle hk0 lines have been used to determine the basis set, they do not contribute any further information in the search for alpha* and beta*, so can then be omitted. This may well give a much sharper and more informative signal, and also allows "M20" (for the first 20 lines in your search dataset rather than the full pattern) to be used once more as a criterion. There are many tools in Crysfire to assist with such cases, including selecting index bounds for calc hkl so as to exclude e.g. l=0, etc. It's also worth remembering that, as Armel has suggested, it may well be possible to solve your structure in projection from the dominant zone reflections alone, since by definition, the structure must be approximately planar and so well resolved in projection down the short c- axis (or whatever you've called it). However, notwithstanding Peter Stephens' advice, don't count on your specimen being monoclinic and projected down a short b-axis except in special cases. The resulting 90-degree alpha and gamma angles would force the packing to place bumps opposite bumps and hollows opposite hollows, which doesn't make for good space-filling. Instead, expect your sample to be triclinic with angles to the short axis that are sufficiently oblique to slide along the next layer of molecules so that bumps are recessed into hollows, so that the structure packs well. But if it *isn't* triclinic, you may find that there's actually a glide- plane in the dominant zone, so that one or more of its cell sides needs to be doubled to account for general hkl reflections (it can become very frustrating to try to index such a pattern without realising this!). Also it's possible to have pseudo-symmetry. One insidious form this can take is for even "dominant-zone" levels hk0, hk2, etc., to be systematically strong while the odd ones, particularly hk1, are systematically weak. In other words, the "short" c axis might really be doubled and thus the hk0 zone actually as dominant as it looked. This should be visible with a single-crystal but might well not be so easy to see in a powder pattern (especially if its quality is poor, which one often finds in such cases). The bottom line is that for a *pure* and *well-calibrated* sample with *high-resolution* measurements and *no pseudo-symmetry*, someone who uses these more specialised programs (they're all in Crysfire and documented in its user guide) can usually solve dominant zone cases. Good luck. Robin Shirley P.S. Watch for further developments and new software for indexing these and other pathological cases, to be discussed this summer at ECM in Budapest and EPDIC in Prague (assuming that the new stuff has reached a demonstrable state by then...). On 4 Jun 2004 at 13:07, A. van der Lee wrote: Dear all, It is generally assumed that a high value of the M20 index gives a high probability that the solution is correct. I have a particular problem for which I have a couple of different solutions with M20 between 40 and 100. The problem resides in the fact that the a and c axes of the monoclinic cell are much larger (both around 20 A) than the b-axis (3-6A?) The solution depends therefore on the angular range which is taken for the indexation process. Taking the first 20 reflections with significant intensity gives a 6A b-axis with the 010 reflection as the last one in the list. Taking 5 reflections more, the length of the b-axis decreases and the 010 remains the last in the list. And so on. The compound is organic and there is not much scattering left beyond 2Theta=30degr, giving a total of 31 reflections to be used for the indexation. How to pick up the right solution between these high M20 solutions? Thanks in advance, Arie ******************************************* A. van der Lee Institut Européen des Membranes (UMR 5635) Université de Montpellier II - cc 047 Place E. Bataillon 34095 Montpellier Cedex 5 FRANCE visiting address: 300 Av. Prof. E. Jeanbrau tél.: 00-33-(0)4.67.14.91.35 FAX.: 00-33-(0)4.67.14.91.19 *******************************************
