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. WWW: Armel Le Bail Laboratoire des Fluorures - CNRS ESA 6010 Université du Maine, Faculté des Sciences Avenue Olivier Messiaen LE MANS Cedex 9, France Tel: (33) Fax: (33) WWW:

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 2 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)

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 3 Before Le Bail analysis “was the void” Not exactly Pawley method - –"Unit-cell refinement from powder diffraction scans", (G.S. Pawley J. Appl. Cryst. 14 (1981) ) 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(?))

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 4 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.”

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 5 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...."

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 6 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) –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) "

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 7 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.

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 8 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 9 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 10 Some of the most complex structures solved from Le Bail method data Nature 359, SYNCHROTRON + NEUTRON R.E. Morris, W.T.A. Harrison, J.M. Nicol, A.P. Wilkinson & A.K. Cheetham Ga 2 (HPO 3 ) 3.4H 2 O29 independent atoms, 86 coordinates refined J. Solid State Chem. 103, CONVENTIONAL X-RAY A. Le Bail  -Ba 3 AlF 9 29 independent atoms, 74 coordinates refined J. Solid State Chem. 111, 52-57SYNCHROTRON + NEUTRON R.E. Morris, J.J. Owen, J.K. Stalick & A.K. Cheetham La 3 Ti 5 Al 15 O independent atoms, 178 coordinates refined

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 11 Some organic structures solved from Le Bail method data Fluorescein Diacetate K. D. Knudsen, P. Pattison, A. N. Fitch, R. J. Cernik Angew. Chem. Int. Ed. 37 (1998) C24H16O7 Solved by direct methods (EXTRA/Sirpow) 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) Solved by simulated annealing (PSSP)

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 12 Recent example 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) (Mg,Fe 2+ ) 3 (Al,Fe 3+ ) 4 (PO 4 ) 4 (OH) 6  2H 2 O A. Le Bail, P.W. Stephens, F. Hubert, European Journal of Mineralogy, in press

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 13 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 14 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 - RbClO 4  B2-RbCl + 2O 2 4 R-KClO3 = 3 O-KClO4 + B2-KCl O-KClO4 = B2-KCl + 2 O2 O 2 from the differences in the unit cell volumes Thus use powder diffraction

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 15 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.

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 16 Energy Dispersive Diffraction E(keV) = / (d_space * sin(theta_angle of Energy Dispersive detector)) Schematic Diagram

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 17 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 18 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.

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 19 Energy Dispersive Diffraction : Example of High pressure/temp. sample assembly for the multi-anvil Walker Cell

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 20 Energy Dispersive Diffraction : Example datasets at high pressure and high temperature

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 21 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!)

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 22 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)

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 23 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)

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 24 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 25 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 26 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 27 Performing the Le Bail fit Rietica Rietveld for Windows by Brett Hunter – –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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 28 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 29 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 30 Rietica Rietveld for Mass Le Bail fitting 1 of 10 Before the phase transition - only Potassium Chlorate is present

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 31 Rietica Rietveld for Mass Le Bail fitting 2 of 10 In the phase transition No completely freestanding peak for KCl

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 32 Rietica Rietveld for Mass Le Bail fitting 3 of 10 Repeat as required No completely freestanding peak for KCl

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 33 Rietica Rietveld for Mass Le Bail fitting 4 of 10 Repeat as required No completely freestanding peak for KCl

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 34 Rietica Rietveld for Mass Le Bail fitting 5 of 10 Repeat as required Still no completely freestanding peak for KCl

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 35 Rietica Rietveld for Mass Le Bail fitting 6 of 10 Repeat as required

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 36 Rietica Rietveld for Mass Le Bail fitting 7 of 10 Repeat as required

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 37 Rietica Rietveld for Mass Le Bail fitting 8 of 10 Repeat as required

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 38 Rietica Rietveld for Mass Le Bail fitting 9 of 10 Repeat as required

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 39 Rietica Rietveld for Mass Le Bail fitting 10 of 10 Done!!! Just have to repeat for a few more 100 to few 1000 datasets

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 40 Rietica Rietveld for Mass Le Bail : Graphing up “some” results Using Le Bail fittingUsing Traditional Methods

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 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?

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 43 Using XFIT and UNITCELL for traditional Unit-cell refinement and EOS using unit weighting of HKLs and

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 44 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)

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 45 Volume of Oxygen as a function of Pressure Energy Dispersive XRD: vol O 2 ~10 cc/mol Established vol O 2 from shockwave experiments: ~15 cc/mol (50% difference)

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 46 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 47 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 (G 3 ) Vol 2, October "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 (G 3 ), (in press)

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 48 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

Using diffraction methods to solve the problems of the world Lachlan M. D. Cranswick Slide 49 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: Other information about the Le Bail method at: Thanks: –Brett Hunter - Rietica Rietveld