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"

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. 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. 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. 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. 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. 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. Solution from direct methods
• Result:
– R=0.34
– Pb and Mn positions
– Oxygen dummies
PbMn
Mn vacancy
Perovskite subcell

8. STEM: indeed Mn-vacancies at
those positions

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. 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. Monte Carlo based methods give
also the oxygen positions
R=0.28 R=0.33

12. Structure refinement
diverges during the
refinement
converges to R=0.239
using Jana 2006

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. Final refined solved structure
c
b

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. 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. 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. 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. Refined model

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