Structure determination of
complex oxides from PED data
Joke Hadermann, Artem M. Abakumov,
Alexander A. Tsirlin, Mauro Gem...
Context
• ED:multiple phases Pb-
Mn-O, all with the
perovskite based
structures -> overlap
• ED-HREM allow to
determine ce...
Problems expected for
direct methods
• Have to find positions for oxygen (Z=8) while
main impact is from heavy scatterers ...
Precession
• Beam is precessed on a cone
• Descan by lower scan coils for
stationary pattern
• Recorded pattern = integrat...
Obtained ED
• Tilt series around b*
axis: [100], [102],
[103], [104], [105]
+ [001]
• Checked overlap with
FOLZ using SG a...
Direct Methods
• Dynamical approximation used *
• Input: 100 unique reflections, P4/m, a=b=
14.2 Å, c=3.9 Å
• Composition?...
Solution from direct methods
• Result:
– R=0.34
– Pb and Mn positions
– Oxygen dummies
PbMn
Mn vacancy
Perovskite subcell
STEM: indeed Mn-vacancies at
those positions
Cation positions
Atom Position x/a y/b z/c
Pb(1)
Pb(2)
Pb(3)
Pb(4)
Mn(1)
Mn(2)
Mn(3)
O???
4j
4j
1c
4j
4k
4k
1b
0.0269
0.57...
Structure solution with global
optimization in direct space
• Implementation: software FOX *
• Input:
– PED data
– Space g...
Monte Carlo based methods give
also the oxygen positions
R=0.28 R=0.33
Structure refinement
diverges during the
refinement
converges to R=0.239
using Jana 2006
Refinement in JANA
Formula Pb13Mn9O25
Space group P4/m
a, Å 14.177(3)
c, Å 3.9320(7)
Z 1
Cell volume, Å3 790.3(1)
Calculat...
Final refined solved structure
c
b
Atom Position x/a y/b z/c
Pb(1)
Pb(2)
Pb(3)
Pb(4)
Mn(1)
Mn(2)
Mn(3)
O(1)
O(2)
O(3)
O(4)
O(5)
O(6)
O(7)
4j
4j
1c
4j
4k
4k
1...
Structure optimization
Discarded model
E = 0 E = 0.48 eV E = +3.13 eV
Relaxing atomic positions
(VASP, PAW method, PBE)
E...
In support of the correctness
of the model
A5B5O13 compounds
e.g. Sr5Mn5O13
Pb13Mn9O25
•The structure has a link with know...
Electron localization function
h = 0.85
Three Pb positions show
localized 6s2 lone pairs
inside the channels
The Pb(3) pos...
Refined model
Conclusion
• Structure solution of a complex oxide with
oxygen atoms in presence of heavy scatterers
(Pb, 82):
– Cation po...
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Determining a structure with electron crystallography - Overview of the paper "Solving the Structure of Li Ion Battery Materials with Precession Electron Diffraction: Application to Li2CoPO4F"

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The route to a solved structure (in this case Pb13Mn9O25) on the basis of precession electron diffraction, combined with HAADF-STEM, HRTEM, EELS and EDX is shown.
Summary of the paper "Solving the Structure of Li Ion Battery Materials with Precession
Electron Diffraction: Application to Li2CoPO4F"

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Determining a structure with electron crystallography - Overview of the paper "Solving the Structure of Li Ion Battery Materials with Precession Electron Diffraction: Application to Li2CoPO4F"

  1. 1. Structure determination of complex oxides from PED data Joke Hadermann, Artem M. Abakumov, Alexander A. Tsirlin, Mauro Gemmi, Hans D’Hondt, VladimirP.Filonenko, Julie Gonnissen, HaiyanTan, JohanVerbeeck, HelgeRosner, EvgenyV.Antipov The contents of this lecture were published in: Ultramicroscopy 110 (2010) 881–890
  2. 2. Context • ED:multiple phases Pb- Mn-O, all with the perovskite based structures -> overlap • ED-HREM allow to determine cell pars and SG • ED-HREM allow many different models!! – approximately a=b=14.2 Å=ap√13, c=3.9 Å=ap – P4/m
  3. 3. Problems expected for direct methods • Have to find positions for oxygen (Z=8) while main impact is from heavy scatterers Pb(Z=82) • Poor diffraction data compared to single crystal X-ray data normally used (few reflections, not really kinematic intensities) • using DM on PED data: O (Z=8) in presence of Cr 24 (Z=24)
  4. 4. Precession • Beam is precessed on a cone • Descan by lower scan coils for stationary pattern • Recorded pattern = integration – Each pattern out of zone axis – Only few reflections in Bragg cond. – Dynamical effects strongly reduced • PED more suitable for structure solution than normal ED patterns Vincent, R. & Midgley, P. A. Ultramicroscopy 53 (1994) , 271-282. Proceedings of the Electron Crystallography School 2005, ELCRYST 2005: New Frontiers in Electron Crystallography, Ultramicroscopy 107, 431-558 (2007)
  5. 5. Obtained ED • Tilt series around b* axis: [100], [102], [103], [104], [105] + [001] • Checked overlap with FOLZ using SG and cell parameters • Overlap<d<central beam • Geo.corr. • compacting in P4/m 2/12 ))R2/g(1(g)R,g(C  Merging only patterns with good R factor: 100 unique reflections
  6. 6. Direct Methods • Dynamical approximation used * • Input: 100 unique reflections, P4/m, a=b= 14.2 Å, c=3.9 Å • Composition? – EDX: Pb3Mn2.0(1)Ox – EELS: VMn = +2.56(6) – Composition: Pb3Mn2.0(1)O5.56(6) or Pb13Mn9O25 • SIR 2008° hklhkl I~F *Vainshtein, B.K. (1964) Structure analysis by electron diffraction. New York: Pergamon Press °M. C. Burla, R. Caliandro, M. Camalli, B. Carrozzini, G. L. Cascarano, L. De Caro, C. Giacovazzo, G. Polidori, D. Siliqi and R. Spagna, J. Appl. Cryst. (2007). 40, 609-613
  7. 7. Solution from direct methods • Result: – R=0.34 – Pb and Mn positions – Oxygen dummies PbMn Mn vacancy Perovskite subcell
  8. 8. STEM: indeed Mn-vacancies at those positions
  9. 9. Cation positions Atom Position x/a y/b z/c Pb(1) Pb(2) Pb(3) Pb(4) Mn(1) Mn(2) Mn(3) O??? 4j 4j 1c 4j 4k 4k 1b 0.0269 0.5794 1/2 0.6502 0.775 0.6955 0 0.1853 0.8834 1/2 0.2730 0.847 0.4594 0 0 0 0 0 1/2 1/2 1/2
  10. 10. Structure solution with global optimization in direct space • Implementation: software FOX * • Input: – PED data – Space group and cell parameters – Cation positions from direct methods solution – Randomly distributed oxygen atoms, amount according to composition • Overall cost to optimize – Agreement with the PED data – Fulfillment of the antibump conditions – Fulfillment of the BVS conditions * Fox, Free Objects for Crystallography: V. Favre-Nicolin et al, J. Appl. Cryst. 35 (2002) 734-743
  11. 11. Monte Carlo based methods give also the oxygen positions R=0.28 R=0.33
  12. 12. Structure refinement diverges during the refinement converges to R=0.239 using Jana 2006
  13. 13. Refinement in JANA Formula Pb13Mn9O25 Space group P4/m a, Å 14.177(3) c, Å 3.9320(7) Z 1 Cell volume, Å3 790.3(1) Calculated density, g/cm3 7.536 Reflections used 100 Parameters refined 23 RF 0.239
  14. 14. Final refined solved structure c b
  15. 15. Atom Position x/a y/b z/c Pb(1) Pb(2) Pb(3) Pb(4) Mn(1) Mn(2) Mn(3) O(1) O(2) O(3) O(4) O(5) O(6) O(7) 4j 4j 1c 4j 4k 4k 1b 4k 4k 4j 1a 4j 4k 4k 0.035(2) 0.570(2) 1/2 0.664(2) 0.757(4) 0.711(4) 0 0.122(10) 0.825(10) 0.507(11) 0 0.735(10) 0.303(10) 0.553(9) 0.176(2) 0.893(2) 1/2 0.296(2) 0.843(4) 0.490(4) 0 0.111(10) 0.366(10) 0.710(10) 0 0.898(10) 0.821(10) 0.550(9) 0 0 0 0 1/2 1/2 1/2 1/2 1/2 0 0 0 1/2 1/2 Final refined solved structure
  16. 16. Structure optimization Discarded model E = 0 E = 0.48 eV E = +3.13 eV Relaxing atomic positions (VASP, PAW method, PBE) E = 11.1 eV E = 11.1 eV E = 7.42 eV Accepted model Refined Initial by A. A. Tsirlin and H. Rosner (MPI CPfS)
  17. 17. In support of the correctness of the model A5B5O13 compounds e.g. Sr5Mn5O13 Pb13Mn9O25 •The structure has a link with known structures (except for the missing Mn!)
  18. 18. Electron localization function h = 0.85 Three Pb positions show localized 6s2 lone pairs inside the channels The Pb(3) position has symmetric environment (no Mn vacancies around), hence the lone pair remains delocalized
  19. 19. Refined model
  20. 20. Conclusion • Structure solution of a complex oxide with oxygen atoms in presence of heavy scatterers (Pb, 82): – Cation positions solved using direct methods, only dummy oxygens – Oxygen positions solved using direct-space methods with a Monte-Carlo based global optimization with chemically sensible constraints

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