1. 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
72085 LE MANS Cedex 9, France
Tel: (33)
Fax: (33)
WWW:

2. 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

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(?))
Slide 3
Using diffraction methods to solve the problems of the world
Lachlan M. D. Cranswick

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

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

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

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

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

9. 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

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
Ga2(HPO3)3.4H2O 29 independent atoms, 86 coordinates refined
J. Solid State Chem. 103, CONVENTIONAL X-RAY
A. Le Bail
-Ba3AlF9 29 independent atoms, 74 coordinates refined
J. Solid State Chem. 111, SYNCHROTRON + NEUTRON
R.E. Morris, J.J. Owen, J.K. Stalick & A.K. Cheetham
La3Ti5Al15O independent atoms, 178 coordinates refined
Slide 10
Using diffraction methods to solve the problems of the world
Lachlan M. D. Cranswick

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)
Slide 11
Using diffraction methods to solve the problems of the world
Lachlan M. D. Cranswick

12. 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

13. 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

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 - 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

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

16. Using diffraction methods to solve the problems of the world
Energy Dispersive Diffraction E(keV) = / (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

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

18. 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

19. 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

20. 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

21. 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

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

23. 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

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

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

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

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
Slide 27
Using diffraction methods to solve the problems of the world
Lachlan M. D. Cranswick

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

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
Slide 39
Using diffraction methods to solve the problems of the world
Lachlan M. D. Cranswick

40. 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

41. 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

42. 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

43. 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 and
Slide 43
Using diffraction methods to solve the problems of the world
Lachlan M. D. Cranswick

44. 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

45. 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

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

47. 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

48. 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

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