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