Beyond Classical Rietveld Analysis using Le Bail fitting Lachlan M. D. Cranswick CCP14 (Collaborative Computation Project No 14 for Single Crystal and Powder Diffraction) Department of Crystallography; Birkbeck College, University of London, Malet Street, Bloomsbury, London, WC1E 7HX, UK. E-mail: l.m.d.cranswick@dl.ac.uk WWW: http://www.ccp14.ac.uk Armel Le Bail Laboratoire des Fluorures - CNRS ESA 6010 Université du Maine, Faculté des Sciences Avenue Olivier Messiaen 72085 LE MANS Cedex 9, France Tel: (33) 02 43 83 33 47 Fax: (33) 02 43 83 35 06 E-mail: alb@cristal.org WWW: http://www.cristal.org/

Using diffraction methods to solve the problems of the world Agenda Was there anything before Le Bail Analysis? Invention of Le Bail fitting and Le Bail extraction The spread and impact of Le Bail fitting A modern application of the Le Bail method : Does the Earth’s outer core contain oxygen (determining the volume of fluid Oxygen at high temperature and pressure) Slide 2 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Before Le Bail analysis “was the void” Not exactly - 1981 - Pawley method - "Unit-cell refinement from powder diffraction scans", (G.S. Pawley J. Appl. Cryst. 14 (1981) 357-361) Unlike “classical” Le Bail fitting - Pawley fitting provides a correlation matrix Not easily implemented in existing Rietveld software When developed, was not matched up with the weak computer power due to each HKL being a parameter in the least squares matrix (1000 HKLs and 10 pattern/profile parameters = 1010 x 1010 least squares matrix) Available early implementations had a reputation of being unstable and difficult to control Only relatively recently that methods have improved to make the Pawley method a going concern and rival in usability to Le Bail method (all are restricted access and/or commercial(?)) Slide 3 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Invention of Le Bail fitting and Le Bail Extraction July 1987 “came during a long and lonesome night experiment at ILL (Institute Laue-Langevin, Grenoble, France)” “It seemed so simple that my first thought was that probably either it was already done or it did not work at all. But at least everybody used it successfully for only one cycle when extracting the so-called "|Fobs|" at the end of any Rietveld refinement. These "|Fobs|" being used for RBragg calculation and Fourier difference purposes though it was long recognized that they were biased due to partitioning according to the Fcalc, hence the quotes.” Slide 4 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

What is the Le Bail method “Iterating the Rietveld decomposition formula, starting from a set of identical |F|s instead of |Fcal|s" : That is the way. The programmer knowing how to implement the Rietveld method will see how to do it.” To implement is simple. At the point where calculated |F| are entered in the Rietveld decomposition formula (SUMMAT subroutine in old code), put instead a set of identical |F|, let the program do as usual, then, when getting the "|Fobs|" from this decomposition formula, use them as if they were the new |Fcalc| and continue to iterate this way...." Slide 5 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Some more Le Bail history Called the "Le Bail method" for the first time in 1992, either in : D.E. Cox, High resolution powder diffraction and structure determination, Chapter 9 in Synchrotron Radiation Crystallography, P. Coppens, Academic Press (1992) 186-254. or in the Nature paper, "Determination of complex structures by combined neutron and synchrotron X-ray powder diffraction, R.E. Morris, W.T.A. Harrison, J.M. Nicol, A.P. Wilkinson & A.K. Cheetham, Nature 359 (1992) 519-522" Slide 6 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

The spread and impact of the Le Bail Method More than 350 citations of the 1988 original paper, according to ISI (Web of Science data) Among these, more than 200 structure determinations by powder diffractometry Other citations are from review papers or use for cell parameter refinements, space group confirmation, evaluation of ODF (Orientation Distribution Functions) or evaluation of electron-density distributions by the maximum entropy method, etc. Slide 7 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

The spread and impact of the Le Bail Method -2 Number of published structures solved by powder methods Cumulative total of 592 up to end of 2001 Slide 8 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world The spread and impact of the Le Bail Method - 3 Comparison with other methods Totals Le Bail = 134 Pawley = 43 No cell constraint = 49 Other / Unspecified = 92 Slide 9 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Some of the most complex structures solved from Le Bail method data 1992 - Nature 359, 519-522 SYNCHROTRON + NEUTRON R.E. Morris, W.T.A. Harrison, J.M. Nicol, A.P. Wilkinson & A.K. Cheetham Ga2(HPO3)3.4H2O 29 independent atoms, 86 coordinates refined 1993 - J. Solid State Chem. 103, 287-291 CONVENTIONAL X-RAY A. Le Bail -Ba3AlF9 29 independent atoms, 74 coordinates refined 1994 - J. Solid State Chem. 111, 52-57 SYNCHROTRON + NEUTRON R.E. Morris, J.J. Owen, J.K. Stalick & A.K. Cheetham La3Ti5Al15O37 60 independent atoms, 178 coordinates refined Slide 10 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Some organic structures solved from Le Bail method data 1998 - Fluorescein Diacetate K. D. Knudsen, P. Pattison, A. N. Fitch, R. J. Cernik Angew. Chem. Int. Ed. 37 (1998) 2340-2343. C24H16O7 Solved by direct methods (EXTRA/Sirpow) 2000 - The Structure of Malaria Pigment (beta-Haematin), S. Pagola, P. W. Stephens, D. S. Bohle, A. D. Kosar and S. K. Madsen, Nature, 404 (2000) 307-310. Solved by simulated annealing (PSSP) Slide 11 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Recent example (Mg,Fe2+)3(Al,Fe3+)4(PO4)4(OH)62H2O Gormanite Triclinic 19 independent atoms Solved by direct space method (ESPOIR) from 500 extracted structure factors Synchrotron data In spite of 3 impurities (10% of the sample) A. Le Bail, P.W. Stephens, F. Hubert, European Journal of Mineralogy, in press Slide 12 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world A recent application involving the Le Bail method Can there be Oxygen in the Earth’s outer core Project headed by Professor Dave Walker of the Lamont-Doherty Earth Observatory of Columbia University, New York, USA Use energy dispersive X-ray diffraction; and high pressure / high temperature phase transitions to help determine the volume of fluid Oxygen at high pressure and temperature (~550°C and 2 to 9 GPa). Then see if the volume this has interesting implications for Oxygen being involved in the Earth’s Outer Core Slide 13 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

What do we need from the data? Accurate Unit Cell volumes to obtain the “equations of state” (EOS) of the phases of interest (how the volume of the phases change with pressure and temperature) T - RbClO4 = B2-RbCl + 2O2 4 R-KClO3 = 3 O-KClO4 + B2-KCl O-KClO4 = B2-KCl + 2 O2 O2 from the differences in the unit cell volumes Thus use powder diffraction Slide 14 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

What do we need from the diffraction experiment Ability to penetrate high a “large volume” high pressure cell - high temperature cell (in this case a multi-anvil Walker Cell) Ability to get the X-ray beam in and out of tight spaces Thus Energy Dispersive Diffraction can be advantageous for these types of problems. Slide 15 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Energy Dispersive Diffraction E(keV) = 6.199 / (d_space * sin(theta_angle of Energy Dispersive detector)) Schematic Diagram Slide 16 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Energy Dispersive Diffraction : Advantages Can see “inside” unconventional sample environments Within limits: can have steel or other materials shielding the sample at pressure and/or temperature thus samples can also be immersed in gas or liquid (hydrothermal synthesis) in-situ studies - reactions / explosions / properties under stress. Particle flows within gases and fluids. Reactions in gas/fluid flow lines. Only see diffraction in the volume (nick-named the “lozenge”) defined where the detector collimator subtends onto the incident white X-ray beam Spatial Resolution inside the sample environment Can narrow down the beam and collimator - and move the sample : thus obtaining diffraction patterns from different spatial volumes inside the sample environment Fast data collection times minutes to fractions of a second Slide 17 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Energy Dispersive Diffraction Beamline 16.4 at Daresbury X-ray Synchrotron, Cheshire, UK In high pressure mode and Walker Cell and Press installed All the hardware can make for a crowded and complicated environment. Slide 18 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Energy Dispersive Diffraction : Example of High pressure/temp. sample assembly for the multi-anvil Walker Cell Slide 19 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Energy Dispersive Diffraction : Example datasets at high pressure and high temperature Slide 20 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world What do we need from the data to help us determined if there can be Oxygen in the Earth’s outer core? What do we want? “Accurate” Unit-cell volumes to obtain equations of state (EOS) When do we want it? Now!! - and/or in a timely fashion (not 6 months to 5 years later!) Slide 21 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Synchrotron Hardware Fixation Syndrome (SHFS) Diagnosis: A neurotic spending of all effort on custom novel synchrotron hardware without consideration and similar effort put into software analysis requirements Effects: Beamlines can have very low productivity due to data analysis being unnecessarily problematic and taking months or years of analysis (kludging together a software solution) Slide 22 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Thus the next problem : Software Analysis: Difficulties that need to be considered: Energy Dispersive Diffraction setup and calibration can be very ad-hoc and problematic Possible Detector instability over short time spans Possible “other” detector problems (more neurotic of these problems only obvious when doing whole pattern Le Bail fitting) Slide 23 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Other Problems that need to be considered Poor resolution data with multiple sources of spurious peaks Phase transitions give unknown cells Track how diffraction patterns are changing through the experiments Slide 24 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

3 x Problems that need to be overcome Overlapping multi-phase powder patterns Large amounts of raw diffraction data! (collecting 3 patterns each 5 to 300 seconds) Intensities are near meaningless no incident intensity spectrum particle statistics problems preferred orientation problems X-ray absorption Slide 25 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Le Bail fitting is a solution! Peak numbers and shifts are constrained by cell and spacegroup Le Bail method does not care about intensities Can handle multiple phases Is graphical in modern software Speedy and easy (very important when you have 100’s to 1000’s of XRD patterns) Impurities and spurious peaks are often very obvious Slide 26 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Performing the Le Bail fit Rietica Rietveld for Windows by Brett Hunter http://www.rietica.org/ Newish: Easy to use mass Le Bail fitting of angular and energy dispersive data All files are ASCII Files Handles alpha 1 /alpha 2 (if relevant) Flexible : can manually edit Le Bail ASCII HKL files to delete reflections Powerful option when dealing with overlapping phases and multiphase samples where trace peaks of one phase can overlap with major peaks of another. Le Bail HKL intensities can be subject to damping factors Slide 27 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Rietica Rietveld for Mass Le Bail fitting to get cell volumes Example of 3 phase setup : KClO3; KClO4, B2-KCl Easy to use and setup via GUI Easy to add and delete structures Database for adding and recalling structures / unit cells Slide 28 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Rietica Rietveld for Mass Le Bail fitting At simplest: 3 step process after initial setup has been done Some beamlines give the option of converting into 2-theta space or refining native in KeV (2-theta can be convenient for using search match and related software) Le Bailing Sequence: 1. Copy over INP and HKL file (using windows explorer) 2. Perform whole profile LB fit 3. Access / plot results - (check need to add or delete phases) 4. Repeat above Slide 29 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 1 of 10 Before the phase transition - only Potassium Chlorate is present Slide 30 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 2 of 10 In the phase transition No completely freestanding peak for KCl Slide 31 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 3 of 10 Repeat as required No completely freestanding peak for KCl Slide 32 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 4 of 10 Repeat as required No completely freestanding peak for KCl Slide 33 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 5 of 10 Repeat as required Still no completely freestanding peak for KCl Slide 34 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 6 of 10 Repeat as required Slide 35 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 7 of 10 Repeat as required Slide 36 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 8 of 10 Repeat as required Slide 37 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 9 of 10 Repeat as required Slide 38 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail fitting 10 of 10 Done!!! Just have to repeat for a few more 100 to few 1000 datasets Slide 39 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Rietica Rietveld for Mass Le Bail : Graphing up “some” results Using Traditional Methods Using Le Bail fitting Slide 40 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world 1. Rietica and Le Bailing : problems with stability of the Energy Dispersive Detector(?) NaCl / Halite at Room Temperature and Pressure (thus is not crystal strain) Very nasty miss-fits on peak positions Possible instability in the detector Peaks cause detector to become unstable in the region of high counts(?) Other problems? Slide 41 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

2. Rietica and Le Bailing : problems with stability of the Energy Dispersive Detector(?) Le Bail fitting Non-unit weighting of reflections Isotherm data of different temperatures colliding Inappropriate to use Le Bail fitting on this data Though Le Bail can detect these problems on the beam-line!! Traditional Unitcell refinement Unit weighting of reflections (over a wide KeV range - the data is “on average” linear) Isotherm data no longer overlapping Slide 42 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Using XFIT and UNITCELL for traditional Unit-cell refinement and EOS using unit weighting of HKLs http://www.ccp14.ac.uk/solution/xfit-95/ and http://www.esc.cam.ac.uk/astaff/holland/ Slide 43 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Using XFIT and UNITCELL for EOS of NaCl and KCl : But:Le Bailing can make sure correct HKLs are assigned to the correct peaks and phases - greater than 5 phases (spurious peaks can be easily identified) Slide 44 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Volume of Oxygen as a function of Pressure Energy Dispersive XRD: vol O2 ~10 cc/mol Established vol O2 from shockwave experiments: ~15 cc/mol (50% difference) Slide 45 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Implications of the volume of fluid Oxygen and the earth’s other core 15 cc/mol means there cannot be Oxygen in the Earth’s outer core (the results from shockwave / molecular dynamics) 10 cc/mol (EDX result) means there can be Oxygen in the Earth’s outer core - and has implications for “outer core” “lower mantle” interactions Slide 46 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Warning: a new volume of fluid oxygen at high pressure that is 50% different from the established value is up for debate When submitted to the journal Science with the suggestion that these diffraction results be taken as seriously as the shock wave results, because the new results disagree with the dynamic techniques, 2 out of 3 reviewers believed this to be dangerous nonsense, from which the community deserves protection. "Synthesis and thermal decomposition of tetragonal RbClO4 and volume of fluid O2 from 2 to 9 GPa" D. Walker, G. Hughes, L. M. D. Cranswick, S. M. Clark, and S. Buhre, Geochemistry, Geophysics, Geosystems (G3) Vol 2, October 2001. "O2 volumes at high pressure from KClO4 decomposition: D" as a siderophile element pump instead of a lid on the core." D. Walker , S.M. Clark, L.M.D. Cranswick1, M.C. Johnson, R.L. Jones, Geochemistry, Geophysics, Geosystems (G3), (in press) Slide 47 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world For those who believe in Shockwave / Molecular Dynamics / Impulsively Stimulated Scattering Measurements over Diffraction Methods Is possible that dynamic methods : Have problems with systematic errors / interpolation Are accurate but have locked into an inappropriate phase of Oxygen Slide 48 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk

Using diffraction methods to solve the problems of the world Summary The Le Bail method has allowed a major advance in crystallography using powder diffraction, not only in terms of solving structures, but also the ability to fit problematic data for a variety of applications. Due to its ease of implementation, ease of use, and availability in a wide range of available software, it is still having a major impact. Le Bail method full saga webpage: http://sdpd.univ-lemans.fr/iniref/lbm-story/ Other information about the Le Bail method at: http://www.ccp14.ac.uk/solution/lebail/ Thanks: Brett Hunter - Rietica Rietveld Slide 49 Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick (l.m.d.cranswick@dl.ac.uk) http://www.ccp14.ac.uk