Getting Cell Parameters from Powder Diffraction Data Armel Le Bail Université du Maine, Laboratoire des Oxydes et Fluorures, CNRS UMR 6010, Avenue O. Messiaen, 72085 Le Mans, FranceEmail : firstname.lastname@example.org
Outline The Indexing Problem(s) Indexing Software Indexing Benchmarks Demonstrations (screen shots) Live Demonstrations
The Indexing Problem(s) 1 to 6 unknownsmaximum :a, b, c, , , Data :20 first peak positions Problem overdetermined,looks simple…
Difficulties come from : - inaccuracy in peak positions (due to zeropoint error, sample misplacement, low resolution, bad crystallinity), - the presence of impurities providing spurious additional peaks, - the possibility to miss some large high-symmetry cells which can also be described in smaller sub-cells of lower symmetry, - the fact that one of the a, b, c parameters can be very short if compared to the two others (dominant zone) so that the first diffraction peak involving it through the hkl Miller indices may not be included among the first 20 which will be exclusively h0l lines for instance (if b is small), - etc.
INDEXING SOFTWARE The best description is in this 2003 Robin Shirley paper :
From Robin Shirley Underlined are inside the CRYSFIRE package
Bergmann, J., Le Bail, A., Shirley, R. & Zlokazov, V. Zeitschrift für Kristallographie219 (2004) 783-790.
Demonstrations - Screenshots WinPLOTR, PowderX(peak position hunting, and more) McMaille, TREOR, DICVOL(indexing) CHEKCELL(visualization, and more) FULLPROF(cell-constrained whole pattern fitting, and more)
Typical data for indexing in automated mode with McMaille Y2O3! Wavelength, zeropoint and NGRID (NGRID=3: black box mode) 1.54056 0.000 3! List of 2theta positions, intensity (min.=20) 20.504 1411. 29.157 11198. 33.791 2632. 35.910 531. 37.921 135. 39.848 606. 41.700 118. 43.488 881. 46.889 271. 48.528 4213. 50.120 230. 51.685 66. 53.207 506. 54.697 117. 56.169 404. 57.614 2603. 59.035 563. 60.433 471. 61.811 194. 63.178 149.
McM20 = [100./(RP*N20)] * Br * Sy, N20 is the number of possibly existing lines up to the 20th observed line (for a primitive P lattice). Br is a factor arbitrarily set to 6 for F and R Bravais lattices, 4 for I, 2 for A, B, C and 1 for P. Sy is a factor equal to 6 for a cubic or a rhombohedral cell, 4 for a trigonal/hexagonal/tetragonal cell, 2 for an orthorhombic cell, and 1 for a monoclinic or triclinic cell.
Examining with Chekcell the list of most probable -AlF3 cells from McMaille
Pawley or Le Bail methods are used for a penultimate proof of the cell quality(the ultimate being the structure solution and refinement)
The Le Bail fit of the -AlF3 conventional laboratory powder pattern by using FULLPROF and the P4/mmm space group, showing the possible (hk0, h+k = 2n) extinction rule
The Le Bail fit of the C28H24O8 synchrotron powder pattern by using FULLPROF selecting the P21/c space group Another plague of SDPD : anisotropic line broadening
Live Demonstrations Once a (good) powder pattern is recorded,and if the compound(s) remain unidentified, the time needed for a successful indexing is somewhere between 15 minutes and never…