Structure determination of Pb13Mn9O25 by direct methods on PED data

Structure determination of complex oxides from PED data : 

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

Overview : 

Overview Context of the research Precession electron diffraction Direct methods Monte Carlo based global optimization of the structure in direct space Structure refinement

Context : 

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 : 

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)

Overview : 

Overview Context of the research Acquiring the diffraction data Direct methods Monte Carlo based global optimization of the structure in direct space Refinement of the structure

Precession : 

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 : 

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 Merging only patterns with good R factor: 100 unique reflections

Overview : 

Overview Context of the research Acquiring the diffraction data Direct methods Monte Carlo based global optimization of the structure in direct space Refinement of the structure

Direct Methods : 

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° *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

Solution from direct methods : 

Solution from direct methods Result: R=0.34 Pb and Mn positions Oxygen dummies Pb Mn Mn vacancy

STEM: indeed Mn-vacancies at those positions : 

STEM: indeed Mn-vacancies at those positions

Cation positions : 

Cation positions

Overview : 

Overview Context of the research Precession Direct methods give cations Monte Carlo based global optimization of the structure in direct space Refinement of the structure

Slide 14: 

V. Favre-Nicolin et al, J. Appl. Cryst. 35 (2002) 734-743 Metropolis Algorithm Random configuration: evaluate cost function evaluate cost function better keep configuration worse keep configuration with probability Random move of atoms

Cost function : 

Cost function Weigthed sum of cost functions: R: correspondence calculated and experimental diffraction antibump: high cost for short distances BVS: high cost for disagreement between valence and bond lengths according to V. Favre-Nicolin et al, J. Appl. Cryst. 35 (2002) 734-743

Global optimisation with parallel tempering : 

Global optimisation with parallel tempering Multiparameter optimisation: #pars to optimize = # crystal parameters Simulated annealing: high to low temperature can overjump global minimum at high T can get stuck in local minimum at low T Parallel tempering: parallel Monte Carlo runs at high and low temperatures Dynamical occupancy corrections (V. Favre-Nicolin et al, J. Appl. Cryst. 35 (2002) 734-743)

Structure solution with global optimization in direct space : 

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 : 

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

Overview : 

Overview Context of the research Precession Direct methods give cations Monte Carlo based global optimization in direct space finds all atom positions Refinement of the structure

Structure refinement : 

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

Refinement in JANA : 

Refinement in JANA

Final refined solved structure : 

Final refined solved structure c b

Final refined solved structure : 

Final refined solved structure

Structure optimization : 

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)

In support of the correctness of the model : 

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!)

Electron localization function : 

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

Refined model : 

Refined model

Conclusion : 

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