From the: Structure Determination by Powder Diffractometry (SDPD) mailing list
To: sdpd@egroups.com From: cxia@cec.uchile.cl Date: Fri, 15 Dec 2000 06:09:51 Chile/Continental Subject: [sdpd] Best Cell? Dear All, I wish to know what are criteria for verifying the best cell suggested by autoindexing. Especially, when there are cells with V, 2V, 4V. Thank you very much! Sincerely Yours, Xia Changtai |
From the: Structure Determination by Powder Diffractometry (SDPD) mailing list
From: Armel Le Bail [armel@fluo.univ-lemans.fr] Date: Fri, 15 Dec 2000 17:03:10 +0100 Reply-To: sdpd@egroups.com Subject: Re: [sdpd] Best Cell? >I wish to know what are criteria for >verifying the best cell suggested by >autoindexing. Especially, when there >are cells with V, 2V, 4V. The principle is that you have to choose the proposition with the highest symmetry explaining all your reflections. It is always possible to index the reflections corresponding to a high symmetry cell with a A, B, C, I, F or R Bravais lattice by a smaller symmetry P cell with smaller volume. Example, a rhombohedral cell can always be described by a monoclinic C-centered cell with 2/3 volume ; a C-centered monoclinic cell is equivalent to a triclinic cell with 1/2 volume, etc. It is also always possible to index an hexagonal or trigonal cell by an orthorhombic cell with a doubled volume. Most indexing programs will recognize automatically such special conditions. However, be very careful, having in mind the above possibilities. Hope Robin Shirley agrees, he is probably writing a better answer than mine. A pity that so many experts prefer to stay at long distance (almost infinite ;-) from the Internet. Best, Armel Le Bail http://sdpd.univ-lemans.fr/course/ |
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To: sdpd@egroups.com From: "L. Cranswick" [L.M.D.Cranswick@dl.ac.uk] Date: Fri, 15 Dec 2000 16:36:56 +0000 (GMT) Subject: Re: [sdpd] Best Cell? > I wish to know what are criteria for > verifying the best cell suggested by > autoindexing. Especially, when there > are cells with V, 2V, 4V. Going via a graphical button pushing route to help you select good cells: One suggestion which may help is to make use of the latest bleeding edge beta test of the Chekcell for Windows program: http://www.ccp14.ac.uk/ccp/web-mirrors/lmgp-laugier-bochu/bleeding_edge_beta_versions/chekcell.zip The standard Chekcell uses "parsimony of extra" reflections on all available cell and spacegroup combinations as a selection criteria of useful cells that could potentially be the "best cell". The latest beta version also links into LePage (using ported source code originally written by A.L. Spek and A. Meetsma) which suggests sub and super cells that can be checked via "parsimony of extra" plus gives the true "reduced" cell. This (plus the enhanced Truecell feature) can help get around the bias of indexing programs to suggest low symmetry, low volume cells. Many indexing programs do not reliably give the "reduced" cell as they are based on the Delaunay reduction. Refer: http://www.ccp14.ac.uk/solution/indexing/reduced_cell.html ----------- Check cell tutorials (now slightly out of date) are at: http://www.ccp14.ac.uk/tutorial/lmgp/#chekcell Another new feature is a GUI based cell transformation option similar to the WinGX transformation interface. With this you can be performing common point and click cell transformations (Hexagonal to Rhombohedral - Obverse/Reverse, etc) as well as manually defining the transformation matrix. Lachlan. -- Lachlan M. D. Cranswick Collaborative Computational Project No 14 (CCP14) for Single Crystal and Powder Diffraction Daresbury Laboratory, Warrington, WA4 4AD U.K Tel: +44-1925-603703 Fax: +44-1925-603124 E-mail: l.cranswick@dl.ac.uk Ext: 3703 Room C14 http://www.ccp14.ac.uk |
From the: Structure Determination by Powder Diffractometry (SDPD) mailing list
Organization: Psychology Dept, Surrey Univ. U.K. To: sdpd@egroups.com Priority: normal From: "ROBIN SHIRLEY (USER)" [R.Shirley@surrey.ac.uk] Date: Fri, 15 Dec 2000 20:21:10 GMT Subject: Re: [sdpd] Best Cell? > Hope Robin Shirley agrees, he is probably writing a better answer > than mine. In fact I do pretty much agree, both with your reply and with Lachlan's, (though don't hexagonal cells give alternative *V/2* orthorhombic settings rather than 2V ones?). > The standard Chekcell uses "parsimony of extra" reflections on all > available cell and spacegroup combinations as a selection criteria > of useful cells that could potentially be the "best cell". Regarding this criterion, used in Chekcell and referred to by Lachlan... Something very similar was tried around 1970, by early zone-indexing programs from the Delft group, for selecting zones according to what they called "maximum coverage". When these programs evolved into ITO, this was abandoned and a (somewhat over-optimistic) probability estimate used instead. In its turn, this became supplanted in LZON and FJZN6 by the Japanese PM criterion. This "parsimony" or "coverage" criterion has its attractions, but can also sometimes mislead, since it makes little use of the quantitative goodness of fit between the observed and calculated patterns. Another methodological problem (shared by those versions of M20 that allow the exclusion of "unindexed lines") is that the decision as to whether or not an observed line is "indexed" by a theoretical (calculated) one is essentially arbitrary, involving some threshold or cut-off point in Q or 2Theta difference, beyond which, quite abruptly, indexing is disallowed. By contrast, criteria like PM make a much smoother transition and handle unindexed lines more gracefully. I hope to have time, next year perhaps, to explore the potential of PM (or related criteria) for solution evaluation, and perhaps implement them in further releases of Crysfire. > A pity that so many experts prefer to stay at long distance (almost > infinite ;-) from the Internet. Not personally guilty, I hope. I'm a moderately frequent contributor to these discussions (when I feel I have have something relevant to say), and of course the free non-profit release of Crysfire is published entirely on the Internet via the CCP14 website. Best wishes and a merry Xmas to all sdpd indexers Robin Shirley P.S. If you index protein powder patterns (or any cells with volumes greater than c.5000 A**3), check out my new UNSCALE program which restores the original scaling to rescaled Crysfire summary files. This will be available shortly from the CCP14 website. |
To: sdpd@egroups.com From: Armel Le Bail [armel@fluo.univ-lemans.fr] Date: Fri, 15 Dec 2000 22:47:42 +0100 Subject: Re: [sdpd] Best Cell? >(though don't hexagonal cells give alternative *V/2* >orthorhombic settings rather than 2V ones?). in lenght a(o)=a(h) b(o)=a(h)x1.732 c(o)=c(h) or in vectors : a(o)=a(h)+b(h) b(o)=b(h)-a(h) c(o)=c(h) V(o)=2V(h) And many compounds like beta-AlF3 in the large HTB (Hexagonal Tungsten Bronze) family are really orthorhombic, pseudo hexagonal : very hard to determine the exact structure either from powder or single crystal (systematically twinned) data. A well known pathology. The orthorhombic cell is C-centered (Cmcm space group in the beta-AlF3 case). Apart from the V, 2V, 2/3V, 3V, 4V pitfall, another one is to not recognize I-centered cells in monoclinic settings, etc. A good one is also the rhombohedral cell with large c parameter, and first reflection being the 006 when programs have max l value = 2 or 4 for the first tested hkl... You have to fall down in all these pitfalls in order to known them. Programs need help sometimes. An advice is to test a/b, a/c, etc, ratios in order to see if there are not 1.414 or 1.732 values. Best regards, Armel Le Bail http://sdpd.univ-lemans.fr/course/ |
To: sdpd@egroups.com From: Robin Shirley [R.Shirley@surrey.ac.uk] Date: Thu, 21 Dec 2000 14:41:41 GMT Subject: Re: [sdpd] Best Cell? Robin Said: >> (though don't hexagonal cells give alternative *V/2* >> orthorhombic settings rather than 2V ones?). Armel Said: > in length > a(o)=a(h) > b(o)=a(h)x1.732 > c(o)=c(h) > or in vectors : > a(o)=a(h)+b(h) > b(o)=b(h)-a(h) > c(o)=c(h) > V(o)=2V(h) I wasn't using sufficiently careful terminology. I should have referred to the V/2 orthorhombic cell of a *derivative* lattice rather than just an alternative orthorhombic setting of the hexagonal lattice. The distinction is an important one, since, as I shall show, this issue *always* arises when trying to index a hexagonal powder pattern, and can easily result in the hexagonal cell being overlooked. For every hexagonal lattice, there exists a derivative orthorhombic lattice with a unit cell having half the volume of the hexagonal cell: V(o) = V(h)/2. This forms what Mighell & Santoro called a "geometrical ambiguity" - two different though related lattices that have distinct reduced forms but give identical powder patterns. For the theoretical basis of this, see Mighell & Santoro (1975), "Geometrical Ambiguities in the Indexing of Powder Patterns", J.Appl.Cryst.,8,372-374, and specifically Table 1 on p.373. The Hexagonal to Derivative Orthorhombic transformation matrix is given there as [.5,.5,0 / .5,-.5,0 / 0,0,-1], the determinant of which is 0.5, hence V(o) = V(h)/2 as stated. This result can readily be verified by indexing any convenient hexagonal powder pattern using an exhaustive program such as DICVOL or TAUP (=POWDER). Provided that the search is continued far enough, these programs should find the correct hexagonal solution of volume V, plus an orthorhombic solution of volume V/2. If monoclinic searches are enabled, one or more additional V/2 monoclinic settings of that orthorhombic cell are also likely to be found. For example, the first 20 lines to Qmax = 7500 QU. of a constructed hexagonal pattern with cell 4x4x5A (hence volume 69.282A**3) also gives a V/2 orthorhombic solution (with volume 34.641A**3). The dimensions of the derivative orthorhombic cell are 2 x 3.4645 x 5A (i.e. a/2, a*sqrt(3)/2, c). For this test pattern (which has also been given a few small, simulated measurement errors to keep the figures of merit manageable), and using all Crysfire defaults, TAUP v3.2c gave the following solutions: I20 Merit Volume V/V1 BL Pedig a b c al be ga 20 167.46 34.639 1.00 P Ort_1 1.9997 3.4644 5.0000 90 90 90 20 85.67 69.277 2.00 P Hex_1 3.9999 3.9999 5.0000 90 90 120 Similarly, DICVOL91 reports as the two best solutions: I20 Merit Volume V/V1 BL Pedig a b c al be ga 20 220.8 34.646 1.00 P Mon_1 3.4646 5.0000 2.0000 90 89.975 90 20 202.6 69.278 2.00 P Hex_1 3.9999 3.9999 5.0000 90 90 120 For reasons of its own that I didn't have time to investigate, DICVOL91 missed the V/2 orthorhombic cell during its orthorhombic search, then found it later in a monoclinic approximation. But one can see from the values reported for the cell constants that is actually orthorhombic. DICVOL91 reports two further monoclinic settings of this V/2 cell. Both programs also report a 5V tetragonal supercell. If TAUP is allowed to pursue a hexagonal pattern into low symmetry (not recommended), it usually reports copious additional monoclinic and triclinic settings of these cells. The differences in the figures of merit variously reported by the programs carry no significance, and result from minor details such as different policies regarding how far symmetry-equivalent lines should be eliminated before reporting that result and moving on to the next. The complete logfile for the two runs is attached as HEXDTEST.LOG, and the CRYS dataset as HEXDTEST.CDT, in case anyone wishes to verify these calculations (apologies for including them as [ASCII] attachments, which are generally discouraged in postings, but this was necessary to stop them being corrupted by word-wrap, and in any case they are quite small). In this example, because the cell volumes are so small, both the V/2 and V solutions lie within DICVOL's first 400A**3 volume shell, so both are found automatically. However, one cannot rely generally on hexagonal cells being small enough for this to happen. More usually, DICVOL91 will halt after the first volume shell that contains the V/2 orthorhombic cell, and won't go on to report the presence of a hexagonal solution. A manual restart starting from the next volume shell is thus usually required to check that no hexagonal solution with twice that cell volume (i.e. with volume V) is present. Anyone using DICVOL91 on patterns that may well give hexagonal cells (and other analogous high-symmetry cases - see Mighell & Santoro) needs to be aware of this consequence of DICVOL's strategy of searching outwards through solution space in successive volume shells. It is a very efficient strategy for the majority of situations, but can cause confusion in high-symmetry cases where lower-volume derivative cells exist that can cause the search to halt prematurely. Robin Shirley |