Determining a structure with electron crystallography
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Transcript of Determining a structure with electron crystallography
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
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
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)
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)
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
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. Siliqiand R. Spagna, J. Appl. Cryst. (2007). 40, 609-613
Solution from direct methods
• Result: – R=0.34– Pb and Mn positions– Oxygen dummies
PbMn
Mn vacancyPerovskite 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???
4j4j1c4j4k4k1b
0.02690.57941/20.65020.7750.69550
0.18530.88341/20.27300.8470.45940
00001/21/21/2
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
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)
Calculated density, g/cm3 7.536
Reflections used 100
Parameters refined 23
RF 0.239
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)
4j4j1c4j4k4k1b4k4k4j1a4j4k4k
0.035(2)0.570(2)1/20.664(2)0.757(4)0.711(4)00.122(10)0.825(10)0.507(11)00.735(10)0.303(10)0.553(9)
0.176(2)0.893(2)1/20.296(2)0.843(4)0.490(4)00.111(10)0.366(10)0.710(10)00.898(10)0.821(10)0.550(9)
00001/21/21/21/21/20001/21/2
Final refined solved structure
Structure optimizationDiscarded 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)
In support of the correctness of the model
A5B5O13 compoundse.g. Sr5Mn5O13
Pb13Mn9O25
• The structure has a link with known structures (except for the missing Mn!)
Electron localization function
h = 0.85
Three Pb positions showlocalized 6s2 lone pairs
inside the channels
The Pb(3) position hassymmetric environment
(no Mn vacancies around),hence the lone pair remains delocalized
Refined model
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