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Ultramicroscopy 110 (2010) 881–890

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Ultramicroscopy

0304-39

doi:10.1

n Corr

E-m

(J. Had

journal homepage: www.elsevier.com/locate/ultramic

Direct space structure solution from precession electron diffraction data:Resolving heavy and light scatterers in Pb13Mn9O25

Joke Hadermann a,n, Artem M. Abakumov a,b, Alexander A. Tsirlin c, Vladimir P. Filonenko d,Julie Gonnissen a, Haiyan Tan a, Johan Verbeeck a, Mauro Gemmi e, Evgeny V. Antipov b, Helge Rosner c

a EMAT, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgiumb Department of Chemistry, Moscow State University, 119992 Moscow, Russiac Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germanyd Vereshchagin Institute of High-Pressure Physics, Russian Academy of Sciences, Troitsk 142092, Russiae Dipartimento di Scienze della Terra ‘‘A. Desio’’, Universit�a degli Studi di Milano, via Boticelli 23, 20133 Milano, Italy

a r t i c l e i n f o

Article history:

Received 27 November 2009

Received in revised form

1 March 2010

Accepted 26 March 2010

Keywords:

Lead manganese oxide

Precession electron diffraction

Structure solution

91/$ - see front matter & 2010 Elsevier B.V. A

016/j.ultramic.2010.03.012

esponding author. Tel.: +32 3 2653245; fax:

ail addresses: joke.hadermann@ua.ac.be, j.had

ermann).

a b s t r a c t

The crystal structure of a novel compound Pb13Mn9O25 has been determined through a direct space

structure solution with a Monte-Carlo-based global optimization using precession electron diffraction

data (a¼14.177(3) A, c¼3.9320(7) A, SG P4/m, RF¼0.239) and compositional information obtained

from energy dispersive X-ray analysis and electron energy loss spectroscopy. This allowed to obtain a

reliable structural model even despite the simultaneous presence of both heavy (Pb) and light (O)

scattering elements and to validate the accuracy of the electron diffraction-based structure refinement.

This provides an important benchmark for further studies of complex structural problems with electron

diffraction techniques. Pb13Mn9O25 has an anion- and cation-deficient perovskite-based structure with

the A-positions filled by the Pb atoms and 9/13 of the B positions filled by the Mn atoms in an ordered

manner. MnO6 octahedra and MnO5 tetragonal pyramids form a network by sharing common corners.

Tunnels are formed in the network due to an ordered arrangement of vacancies at the B-sublattice.

These tunnels provide sufficient space for localization of the lone 6s2 electron pairs of the Pb2 + cations,

suggested as the driving force for the structural difference between Pb13Mn9O25 and the manganites of

alkali-earth elements with similar compositions.

& 2010 Elsevier B.V. All rights reserved.

1. Introduction

Structure analysis lies at the heart of solid state science,because the structural information is an essential input for anystudy of crystalline solids. Crystal structures are usually deter-mined by diffraction techniques that continuously develop andaddress new challenges, such as structure solution from powderdiffraction data or structural analysis of imperfect solids. Anotherbranch of the development deals with the structure analysis onmicro- and nanoscale using transmission electron microscopyimaging and diffraction techniques. Recent advances in precessionelectron diffraction (PED) demonstrated that this technique isable to overcome to some degree intrinsic limitations imposed bythe dynamical nature of electron diffraction and produce reliablestructural models for a row of inorganic structures [1–4]. In orderto get a diffraction image of certain reciprocal space section of acrystal in PED mode, the crystal is first oriented along the required

ll rights reserved.

+32 3 2653257.

ermann@ua.ac.be

zone axis and then the electron beam is tilted with respect to thezone axis and precessed on a cone surface having the vertex fixedon the sample. At the same time the precession of the diffractedelectrons is compensated in order to obtain a stationary pattern.Due to the relatively high precession frequency, the recordedpattern is an integration over all the diffraction conditionsobtained during an entire precession cycle. In each of theseconditions, due to the beam tilt, the intersection of the reciprocallattice plane with the Ewald sphere forms an arc, therefore onlyfew reflections are in Bragg condition and the multiple diffractioneffects are strongly reduced [5]. Thus the obtained PED patternshave a quasi-kinematical character that makes them moresuitable for structure solution than conventional selected areaelectron diffraction patterns taken with the electron beam parallelto the crystal zone axis [6].

However, many structures of complex metal oxides stillrepresent a great challenge for the PED technique [7,8] because(i) the presence of heavy scatterers, such as alkali-earth, rare-earth or 6s2 lone electron pair cations (Pb2 +, Bi3 +) makes thedynamical scattering really severe even for thin crystallites and(ii) these structures comprise heavy and light elements with ahuge difference in the scattering power (like metal cations and

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J. Hadermann et al. / Ultramicroscopy 110 (2010) 881–890882

oxygen anions). In these compounds the oxygen positions couldnot yet be determined from PED data. However, the properinterpretation of the material’s properties requires exact knowl-edge on the metal–oxygen interatomic distances, which meansthat both types of elements must be accurately located within thestructure.

Lead–manganese oxides are an interesting group of inorganiccompounds. The Pb–Mn–O system, when investigated underambient pressure, includes materials with diverse structures, suchas the hollandite-type structure of Pb1 + xMn8O16 [9], close packedPb3Mn7O15 [10–12] and Pb4Mn9O20 structures [13], and thePb2MnO4 structure with infinite chains of edge-sharing MnO6

octahedra [14]. The current interest in finding multiferroicity inperovskite-like compounds with lone-pair A-cations (e.g., BiFeO3

and BiMnO3 [15]) inspires the search for new perovskitesamong complex oxides of transition metals and Pb2 +. However,preparations under ambient pressure did not evidence anyperovskite-type compounds in the Pb–Mn–O system. Utilizing ahigh pressure high temperature technique seems to be fruitfulfor the preparation of new perovskites and already led to aperovskite-based structure with crystallographic shear planes in‘‘PbMnO2.75’’ [16] and to a tetragonal perovskite PbMnO3 [17].

In the following, we will show that PED is able to propose areliable and complete structural model for the complex transitionmetal oxide Pb13Mn9O25 where nearly one third of the atoms areheavy Pb scatterers. This new compound was identified in apolyphasic mixture prepared using a high pressure high tempera-ture technique. Precession electron diffraction data were used forthe structure solution. For the first time, a direct space method ofMonte-Carlo based global optimization with the application ofchemically sensible constraints was implemented with PED data.The PED structure solution is assisted by other transmissionelectron microscopy methods and by ab initio band structurecalculations that justify the structural model and evaluate theaccuracy of the structure refinement. Pb13Mn9O25 represents a newstructure type, and its structure is discussed along with thestructures of oxygen-deficient perovskites having frameworks ofcorner-sharing BO5 pyramids and BO6 octahedra [18,19].

2. Material and methods

A mixture of PbO and Mn2O3 (Reakhim, ‘‘pure for analysis’’purity grade) with the Pb2Mn2O5 bulk composition was used as astarting material. This powder was pressed into pellets of 3 mm inheight and 5 mm in diameter. The pellets were placed in goldcapsules to avoid a chemical reaction between the specimen andthe surrounding material. Thermobaric synthesis was carried outby using the high pressure chambers of toroid-type consisting oftwo hard metal anvils with special profile [20]. The pressure wasgenerated in a lithographic limestone cell placed between theanvils. The pressure values were calibrated at room temperatureby measuring the electric conductivity and fixing the phasetransition of Bi I–II (2.55 GPa) and Bi IV–V(7.7 GPa). Thetemperature was measured by chromel–alumel thermocouples.The high-pressure treatment was carried out under the followingexperimental conditions: pressure of �7.0 GPa, temperaturerange of 800–1000 1C. After stabilization of the applied pressure,the samples were heated up to the desired temperature, whichwas held for 5 min. Then, the samples were quenched to roomtemperature before the pressure was released.

X-ray powder diffraction (XRPD) patterns were collected on aHuber G670 Guinier diffractometer (CuKa1 radiation, curved Gemonochromator, transmission mode, image plate).

The samples for electron microscopy investigations wereprepared by crushing the powder in ethanol and depositing it

on a holey carbon grid. Selected area electron diffraction (ED)patterns were recorded using Philips CM20 and JEOL 4000EXmicroscopes. High resolution transmission electron microscopy(HRTEM) images were recorded on a JEOL 4000EX microscope.Energy dispersive X-ray (EDX) spectra were obtained on thePhilips CM20 with an Oxford INCA system. The HRTEM imageswere simulated by means of the MacTempas software. High angleannular dark field scanning transmission electron microscopy(HAADF-STEM) images were recorded on a Tecnai G2 microscope.

Precession electron diffraction (PED) data for structuredetermination were recorded on Ditabis image plates, using aPhillips CM20 with a precession module (Spinning Star—Nano-megas).

All patterns were recorded at the maximal precession angle forthis setup, which is 2.51. The intensities were extracted using theprogram ELD [21] by integrating the intensity within a circulararea around each reflection. Two-dimensional data from the PEDpatterns were merged into a three dimensional set using thesoftware Triple. Overlap of reflections of the higher order Lauezones with the reflections of the zero order Laue zone waschecked by simulations using JEMS software. SIR2008 [22],FOX [23] and JANA2006 [24] program packages were used forstructure solution and refinement.

Electron energy loss spectroscopy (EELS) data were acquiredusing a Gatan GIF200 system on a Philips CM30 microscopewith an acceleration voltage of 300 kV and an energy resolutionof 0.8 eV. All spectra were recorded in diffraction mode with acollection angle of 4.01 mrad and a convergence angle of1.0 mrad. EELSMODEL [25–29] was used to extract the excitationedge fine structures of the recorded spectra.

For the computational structure relaxation, we used theinternal procedure of the Vienna ab initio simulation package(VASP) [30]. Band structure calculations utilized the projectoraugmented wave basis set [31] and the Perdew–Burke–Ernzerhofexchange-correlation potential [32] that corresponds to general-ized gradient approximation (GGA) of density functional theory.All the calculations were performed with the ‘‘High’’ accuracysetting of VASP, which implies 400 eV energy cutoff for the basisset. Reference calculations with the lower energy cutoff led tosimilar results and indicated the convergence with respect tothe basis set. The k mesh included 128 points within the firstBrillouin zone.

Several structural models resulting from the analysis of theexperimental data were relaxed within GGA. For all the models,we found similar energy spectra comprising lead states below�8 eV, oxygen valence bands below �2 eV and manganese bandsnear the Fermi level. The spectra were gapless suggesting metallicbehavior. Since the Pb13Mn9O25 compound has not been preparedin a pure form, there is no reference experimental information tocontrol the accuracy of the computational results. In particular, itis presently unclear whether Pb13Mn9O25 should be metallic. Tocheck for different possibilities, we also performed GGA+U

calculations (fully-localized-limit double-counting correction[33]) for the energy-favorable structural model. The U correctionaccounts for correlation effects in Mn d shell and leads to aformation of the band gap. Indeed, we were able to obtain gappedsolutions. However, the value of the band gap and the resultinggeometry were strongly dependent on the initial spin configura-tion. In our calculations, we applied U¼5 eV (on-site Coulombrepulsion) and J¼1 eV (on-site exchange) which should bereasonable parameters for Mn2 +–Mn3 + [34]. The relaxed geome-tries roughly matched the GGA solution with a difference inindividual interatomic distances below 0.15 A.

In the following, we discuss the GGA solution only and do notmention any of the GGA+U results, because the lack of experi-mental information prevents a reliable choice of the spin

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J. Hadermann et al. / Ultramicroscopy 110 (2010) 881–890 883

configuration and of the orbital state (which should be relevantfor the local environment of the Jahn-Teller Mn3 + cation). Wesuppose that the GGA geometry is sufficiently accurate. Previousexperience in structure relaxation for transition metal compoundssuggests that the GGA+U corrections will mainly affect the localenvironment of the Mn cations [35], while general structuralfeatures and the local environment of lead should be properlyreproduced within GGA or even within local density approxima-tion (LDA) [36].

After relaxing the crystal structure, we used the resultinggeometry to analyze bonding features via electron localizationfunction (ELF) calculation [37]. ELF was computed after a self-consistent procedure within the TB-LMTO-ASA code [38]. TheLMTO calculation was performed for the spin-nonpolarizedconfiguration and employed Perdew–Wang exchange-correlationpotential [39]. ELF is known to be robust with respect to theeffects of spin polarization and electronic correlations [37], hencethe LDA calculation should be sufficient for a reliable analysis.

3. Results

3.1. Unit cell, space symmetry and chemical composition

The multiphase ‘‘Pb2Mn2O5’’ sample was investigated usingtransmission electron microscopy, which showed two majorphases with a perovskite-based structure, coexisting in thesample. The crystallites of these phases can be easily distin-guished because of a significant difference in their electrondiffraction patterns and in the Pb:Mn atomic ratio. The presentmanuscript is focused on a complete characterization of one ofthese phases, whereas the structure solution for the second phase(with the Pb2Mn2O5 composition and aEO2ap, bEap, cE4O2ap

(ap—the parameter of the perovskite subcell)) is still in progress.The precession electron diffraction (PED) patterns of the main

zones of the target phase are shown in Fig. 1. The PED patterns canbe indexed using a tetragonal cell with a¼3ap�2bp, b¼2ap+3bp,c¼cp (where subscript p stands for the perovskite subcell), givingthe approximate cell parameters aEO13apE14.2 A, cEapE3.9 A. The relation between the subcell and the supercell isclarified in the two schemes (reciprocal and direct space relations)at the bottom of Fig. 1. The absence of systematic extinctionsresults in 8 possible tetragonal space groups. However, the

Fig. 1. Top: PED patterns of the main zones of Pb13Mn9O25. Bottom: scheme of the

relation between the perovskite parent structure and the supercell in reciprocal

space (left) and in direct space (right).

absence of a mirror plane perpendicular to /1 0 0S or /1 1 0Sand also the absence of 2-fold rotation axes along /1 0 0S and/1 1 0S is obvious from the [0 0 1] ED pattern: there is noequivalence of the intensity of the reflections hk0 with hk0 or hk 0(required for m perpendicular to /1 0 0S and for a 2-fold axisalong /1 0 0S), nor with kh0 or kh0 (required for m perpendicularto /1 1 0S or 2-fold axis along /1 1 0S). This can be most clearlyseen by tracking the intensity of the reflection 150. Alternatively,the absence of these symmetry elements can also be seen in directspace on the HAADF-STEM and HREM images along the [0 0 1]direction (discussed later and shown in Figs. 5 and 6 respectively).Therefore, the only possible space groups are P4, P4 and P4/m.To decide between these three space groups, convergent beamelectron diffraction (CBED) was performed. If the space group isP4/m, a mirror plane should be present perpendicular to the cn-axis in all [u v 0] CBED whole patterns, while for both P4 and P4this mirror plane should be absent. Fig. 2 shows the presence ofthe mirror plane perpendicular to the cn-axis, for the [3 2 0] zone,therefore P4/m is the correct space group. The [3 2 0] zone waschosen because, due to the large unit cell parameters, thereflections are too close together in such main zones as [1 0 0]and [1 1 0] to allow to take CBED discs large enough to observeany intensity variation inside the discs.

The EDX analysis on 20 crystals with ED patterns which wereverified to belong to the target phase, shows a compositionPb3Mn2.0(1)Ox. The volume of the tetragonal supercell is 13 timeslarger than the volume of the perovskite subcell. Therefore thecation content of the tetragonal supercell is Pb13Mn8.7(4) orPb13Mn9.

The formal Mn valence (VMn) was determined from EELS, bymeasuring the distance of the energy onset between the O K edgeand the Mn L2,3 edge (Fig. 3), and comparing this to a linearcalibration curve obtained from measuring standards aspublished in [40]. We corrected for nonlinear dispersion in thespectrometer to obtain a better reproducibility and obtain arelation DE¼a+bnVMn with a¼103.0270.18 eV and b¼2.2670.06 eV/Valence. From the analysis of five crystallites and 100spectra for each, it was found that the edge onset difference of O K

Fig. 2. SAED and CBED patterns of the [3 2 0] zone of Pb13Mn9O25 SAED pattern

with indices using the supercell parameters (left), CBED whole pattern at high

camera length (middle), the same CBED whole pattern at low camera length

(right). The intersection of the mirror plane perpendicular to the cn-axis is

indicated by a white line.

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Fig. 3. Parts of the EEL spectrum of Pb13Mn9O25 showing the O K and Mn L2,3

edges.

Table 1Rsym

a for the patterns in space group P4/m and number of resulting unique

reflections to be used.

Pattern Extracted

intensities

Rsym Unique

reflections

[0 0 1] 617 0.054 155

[1 0 2] 30 0.094 14

[1 0 3] 30 0.066 14

[1 0 4] 115 0.069 56

[1 0 5] 101 0.056 50

[1 0 0] 30 0.019 15

a Rsym¼S(jo Int(h k l)4� Int(h k l)j)/S Int(h k l) [21].

J. Hadermann et al. / Ultramicroscopy 110 (2010) 881–890884

and Mn L2,3 edges is 108.8170.14 eV. From the relation above,the Mn valence can be estimated as VMn¼ +2.56(6). This gives anoxygen content corresponding to Pb13Mn9O24.5(6) or Pb13Mn9O25,assuming that Pb atoms keep their oxidation state +2.

For the second phase the composition was also determinedwith the same procedure, giving Pb0.98(6)Mn1.02(6)O2.53(14) orPb2Mn2O5, that is clearly different from the target phase.

3.2. Structure solution

Both phases found in the ‘‘Pb2Mn2O5’’ sample are perovskitebased, resulting in the overlap of many reflections on the powderXRD pattern, that hinder the structure solution. However, theanalysis of the reflections corresponding to the perovskite subcellon the powder XRD pattern revealed that the tetragonal distortionof the perovskite subcell is very small and does not causenoticeable splitting of the reflections. The perovskite subcellparameter was refined as a¼3.9320(7) A. Using the subcell-to-supercell transformation matrix, the supercell lattice parameterscan be calculated as a¼14.177(3) A, c¼3.9320(7) A.

The precession electron diffraction patterns obtained alongdifferent zone axes were verified for the lack of overlap of Lauezones using simulations calculated with JEMS for the determinedspace group and cell parameters and a precession angle of 2.51, asexperimentally used. The [1 1 0] PED pattern had an overlap ofzero order and first order Laue zones up to dE2.5 A and wasexcluded from further use, as too few reflections were useable. Forthe [1 0 2], [1 0 3] and [1 0 0] zones only the reflections down tod42.28 A were used to avoid overlap. The [0 0 1], [1 0 4] and[1 0 5] zones were free of overlap and the reflections down tod¼1.0 A were used. For all data sets, the upper d-value limit wasset to 7 A to exclude the reflections close to the transmitted beam.All intensities were then multiplied with the geometrical correc-tion factor Cðg,RÞ ¼ gð1�ðg=2RÞ2Þ1=2 (g is the reciprocal vector, R isthe radius of the Laue circle) [41], which corrects for the intensitydifference introduced by the circular motion of the beam itself, asit leads to a longer excitation of reflections closer to thetransmitted beam. (The effect of the geometrical correction onthe data set can be found in the Supplementary Information inFigure S1.) The data sets from the different zones were firstsymmetry averaged using the TRIPLE software into sets of uniquereflections using the P4/m space group. The agreement with thissymmetry, expressed in Rsym-values (see Table 1), and the numberof unique reflections in each pattern are shown in Table 1. Withthe same software TRIPLE, a 3D set of intensities was obtainedfrom the separate 2D data sets by calculating the scaling factorbetween the sets using the common reflections. The consistency

of these common reflections is expressed by Rmerge. The Rmerge andnumber of common and resulting reflections can be found inTable 2. The data from the [0 0 1] pattern were not included in thefinal 3D data set because the Rmerge gave a too high value around0.40. Possibly, this main zone had still too much dynamicalscattering due to the presence of many strong reflectionsbelonging to the perovskite subcell, which causes a badagreement with the other zones containing only few brightreflections and less influence of dynamical effects. Mosttrustworthy will be the zones with least dynamical effects, so[0 0 1] was excluded from further calculations. Again compactingthe combined list using P4/m symmetry gave a value Rsym¼0.061,and left a total of 100 unique reflections to be used.

The data list with extracted intensities from the PED patterns,the determined composition Pb13Mn9O25, refined cell parameters(a¼14.177(3) A, c¼3.9320(7) A) and space group P4/m were usedas input for the structure determination.

The strategy of the structure solution in this particular case isnot obvious. Using the PED technique can significantly diminishthe dynamical scattering, but residual dynamical effects remain,which makes the kinematical treatment of the diffractedintensities (9Fhkl9

2� Ihkl) a poor approximation. A complete

structure solution implies finding the positions of oxygen atoms(Z¼8) in a unit cell where the main impact into the scatteringdensity is made by such heavy scatterers as Pb (Z¼82). Due to thepoor diffraction data compared to the single crystal X-raydiffraction data normally used for direct methods and therelatively low scattering power of oxygen atoms one can expectthat a reciprocal space approach including direct methods forassigning phases of the structure factors and subsequent Fouriermapping for completing the structure model will fail. Never-theless, an attempt was made to use direct methods withSIR2008. Both the dynamical (jFhklj� Ihkl) [42] and the kinematical(jFhklj

2� I) approximations were tried. In the case of the dynamical

approximation, the obtained solution (R¼0.34) has Pb and Mnatoms at perovskite type positions (Fig. 4a), whereas thekinematical approximation has a distribution of the Pb and Mnatoms in a non-perovskite related manner (SupplementaryInformation Figure S2). To decide between these solutions,HAADF-STEM images along [0 0 1] were obtained, a repre-sentative image is shown in Fig. 5. On these images, the atomiccolumns are represented by dots with a brightness proportional toZn (1ono2), where Z is the average atomic number in thecolumn. Thus the brighter dots in the image can be interpreted asthe columns of lead atoms, the faint dots between the brighterones can be assigned to the Mn–O columns, whereas pure oxygencolumns are not seen as separate dots. The HAADF-STEM imagessupport the solution using the dynamical approximation: thebrightest dots form a perfect square lattice, in agreement with thePb sublattice in the solution with the dynamical approximation.The ordered arrangement of the Mn vacancies is also clearly seen:it corresponds to the pattern of dark spots.

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Fig. 4. The structure models of Pb13Mn9O25 viewed along [0 0 1]. Pb is represented by green spheres, Mn is represented by yellow spheres (a) or is at the center of the

yellow pyramids, orange octahedra or red tetrahedra (b)–(e) while oxygen is at the corners of these polyhedra. (a) Positions of the Pb and Mn atoms as obtained from direct

methods; (b) and (c), respectively, models I and II obtained from Monte-Carlo based methods; (d) 3D view of the Pb13Mn9O25 structure; (e) overview showing the

chessboard order of the two groups; (f) ordering scheme of Mn atoms (full squares) and Mn vacancies (open squares); (g) ordering scheme of the O atoms (dots) and

oxygen vacancies (open squares) in the Mn–O layer.

Fig. 5. HAADF-STEM image of Pb13Mn9O25 along the [0 0 1] zone axis. The outline

of one unit cell is indicated by a large white square. Smaller squares indicate the

positions of the Mn vacancies in the structure.

Table 3Positional parameters for the cations as obtained using direct methods with

SIR2008.

Atom Position x/a y/b z/c

Pb(1) 4j 0.0269 0.1853 0

Pb(2) 4j 0.5794 0.8834 0

Pb(3) 1c 1/2 1/2 0

Pb(4) 4j 0.6502 0.2730 0

Mn(1) 4k 0.775 0.847 1/2

Mn(2) 4k 0.6955 0.4594 1/2

Mn(3) 1b 0 0 1/2

Table 2Rmerge

a for and sequence of the merged patterns.

Merged patterns Rmerge Common refls. used Number of refls. after merging

[1 0 5]+[1 0 0] 0.043 4 57

([1 0 5]+[1 0 0])+[1 0 4] 0.097 12 97

[1 0 2]+[1 0 3] 0.055 5 19

([1 0 5]+[1 0 0]+[1 0 4])

+([1 0 2]+[1 0 3]) 0.014 4 108

n Rmerge¼S(Inta(h k l)� Intb(h k l))/S(Inta(h k l)+Intb(h k l)), where the reflection hkl belongs to both patterns a and b [21].

J. Hadermann et al. / Ultramicroscopy 110 (2010) 881–890 885

However, even though the cation positions are resolvedcorrectly, the analysis of the metal–oxygen interatomic distancesdemonstrated that the direct methods result in oxygen atomslocated at dummy positions. Subsequent difference Fourier

syntheses performed with the JANA2006 program produced mapswhere the maxima that would correspond to the oxygen positionscould not be discriminated from the noise and artifacts. Never-theless, the solution confirmed that the cations form a perovskite-like motif with ordered Mn vacancies. The atomic coordinates forthis solution are listed in Table 3.

Since the lack of accurate structure factor amplitudes did notallow solving the complete Pb13Mn9O25 structure using reciprocalspace techniques, direct space techniques were applied. Suchtechniques were initially developed to overcome the incomplete-ness and poor quality of powder diffraction data. The Monte-Carlobased global optimization with parallel tempering algorithm, asimplemented in the FOX program, was used for the structure

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Table 5Positional parameters for Pb13Mn9O25 (first row—Monte-Carlo optimization,

second row –structure refinement, third row—ab initio structure relaxation). The

last column shows the calculated bond valence sums.

Atom Position x/a y/b z/c BVS

J. Hadermann et al. / Ultramicroscopy 110 (2010) 881–890886

solution. The optimization was performed using the P4/m spacegroup and the unit cell parameters determined from powderX-ray diffraction data. Experimental information on the chemicalcomposition was included into the optimization process impli-citly via two sets of constraints:

Pb(1) 4j 0.0369 0.1794 0 1.68

�

TabCry

F

S

a

c

Z

C

C

0.035(2) 0.176(2) 0 1.84

0.0265 0.1863 0 1.75

Pb(2) 4j 0.5688 0.8869 0 1.63

0.570(2) 0.893(2) 0 1.54

antibump conditions were set, delimiting minimal cation–cation and anion–anion interatomic distances according to theknown formal oxidation states of Pb and Mn and assuming aperovskite-like structure;

0.6117 0.8432 0 1.76

�

Pb(3) 1c 1/2 1/2 0 2.04

1/2 1/2 0 5.24

1/2 ½ 0 1.98

Pb(4) 4j 0.6673 0.2946 0 1.84

0.664(2) 0.296(2) 0 1.42

0.6388 0.2241 0 1.76

Mn(1) 4k 0.7603 0.8435 1/2 2.57

0.757(4) 0.843(4) 1/2 2.90

0.7959 0.8330 1/2 3.26

Mn(2) 4k 0.7161 0.4898 1/2 2.25

0.711(4) 0.490(4) 1/2 1.78

0.6520 0.4091 1/2 3.50

Mn(3) 1b 0 0 1/2 2.48

0 0 1/2 2.06

0 0 1/2 3.54

O(1) 4k 0.1178 0.1004 1/2

0.122(10) 0.111(10) 1/2

0.1223 0.0657 1/2

O(2) 4k 0.8195 0.3712 1/2

0.825(10) 0.366(10) 1/2

0.7745 0.3367 1/2

O(3) 4j 0.5135 0.7203 0

0.507(11) 0.710(10) 0

0.6062 0.6732 0

O(4) 1a 0 0 0

0 0 0

0 0 0

O(5) 4j 0.7411 0.8879 0

0.735(10) 0.898(10) 0

0.78229 0.8358 0

O(6) 4 k 0.3082 0.8120 1/2

0.303(10) 0.821(10) 1/2

0.2893 0.8415 1/2

O(7) 4 k 0.6090 0.5789 1/2

0.553(9) 0.550(9) 1/2

0.6395 0.5347 1/2

bond valence sum (BVS) conditions were set for the cationsusing BVS coefficients for Pb2 + and Mn3 + to ensure a propercoordination of these cations by the oxygen atoms.

Thus, the overall optimization cost included the impact ofthe agreement with the PED data, and of the fulfillment of theantibump and BVS conditions. The cation positions from thedirect method solution were used as the starting model. Oxygenatoms were randomly placed in the structure. Dynamicaloccupancy correction was used, which automatically reducesthe occupancy factor for special atomic positions. When theassignment of the oxygen atoms to general and special positionsbecame clear, the optimization was repeated with the amount ofoxygen atoms fulfilling the chemical composition and with fixedatomic coordinates for the oxygen atoms at special positions. Thefull set of measured intensities (as used for the structure solutionwith SIR2008) (0.12osin y/lo0.72) was used. Multiple trialsrevealed two solutions with an acceptable agreement betweenthe calculated and experimental PED intensities and similarreliability factors. Solution I (RI¼0.28) contains the Mn atomslocated in corner sharing tetrahedra, tetragonal pyramids, andoctahedra of oxygen atoms (Fig. 4b). Solution II (RI¼0.33)represents the structure based on a framework formed by cornersharing MnO6 octahedra and MnO5 tetragonal pyramids (Fig. 4c).

In the final step of the structure solution, both models wererefined with JANA2006 using the kinematical approximation forthe intensities and without any additional restrictions imposed onthe atomic coordinates, using the same set of reflections as for thestructure solution with SIR2008. The refinement of model Idiverged. The refinement of model II readily converged toRF¼0.239. Model II was accepted as a final solution. The choiceof the model II was additionally supported by ab initio structurerelaxation (see below). Crystallographic data are listed in Table 4.Atomic positions and interatomic distances obtained after Monte-Carlo optimization and structure refinement are given in the firstand second rows of Tables 5 and 6, respectively.

Complementary HRTEM images were taken. HRTEM imagesalong the [0 0 1] zone axis are shown in Fig. 6, a highmagnification image at the top, a low magnification overviewimage at the bottom. An image calculated with the atomiccoordinates for model II from Monte-Carlo optimization (Table 5)is set on top of the experimental image and indicated by a thinblack border. An excellent agreement between the calculated andthe experimental images was obtained at the focus value

le 4stallographic parameters for Pb13Mn9O25.

ormula Pb13Mn9O25

pace group P4/m

(A) 14.177(3)

(A) 3.9320(7)

1

ell volume (A3) 790.3(1)

alculated density (g/cm3) 7.536

f¼�250 A and the thickness t¼24 A. On this image, the blackdots are the projections of the cation columns, while the darkestdots correspond to the Pb columns. The square network of darkdots is interrupted by a pattern corresponding to the missingMn–O columns. The difference between the simulations of theHRTEM images using models I and II are minimal, and neitherHRTEM nor HAADF-STEM by themselves would allow discardingone of the two models. Therefore, apart from the refinement ofthe model, also ab initio structure relaxation was performed onboth models to decide between them.

3.3. Ab initio structure relaxation

For structure relaxation, we used models I and II from theMonte-Carlo optimization. We also relaxed the refined structuralmodel, as obtained from model II. The lattice parameters and thecrystal symmetry were fixed according to the experimentalinformation. The initial geometries showed an energy preferencefor model II with EI�EII�3.6 eV/f.u. (E stands for the total energy).The refined structure is also less favorable compared to thestarting model: Eref�EII�0.5 eV/f.u. This energy difference is stillsignificant (about 6000 K) and exceeds typical thermal energiesfor more than an order of magnitude.

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Table 6Selected interatomic distances for Pb13Mn9O25 (first row—Monte-Carlo optimiza-

tion, second row—structure refinement, third row—ab initio structure relaxation).

Pb(1)–O(1) 2.537�2+2.901�2

2.50(9)�2+2.95(11)�2

2.53�2+2.94�2

Pb(1)–O(4) 2.597�1

2.54(3)�1

2.67�1

Pb(1)–O(5) 2.394�1

2.32(15)�1

2.73�1+2.74�1

Pb(2)–O(2) 2.346�2

2.37(8)�2

2.32�2

Pb(2)–O(3) 2.489�1

2.74(14)�1

2.41�1

Pb(2)–O(5) 2.443�1

2.34(14)�1

2.42�1

Pb(3)–O(3) 3.129�4

2.98(14)�4

2.88�4

Pb(3)–O(7) 2.739�8

2.22(6)�8

2.83�8

Pb(4)–O(2) 3.115�2

3.17(11)�2

3.18�2

Pb(4)–O(3) 2.572�1+2.822�1

2.43(15)�1+ 2.87(15)�1

2.45�1

Pb(4)–O(5) 3.168�1

3.34(12)�1

2.79�1

Pb(4)–O(6) 2.504�2

2.62(10)�2

2.40�2

Pb(4)–O(7) 2.703�2

3.32(11)�2

3.13�2

Mn(1)–O(1) 1.902�1

1.83(15)�1

1.85�1

Mn(1)–O(2) 1.895�1

1.77(15)�1

2.05�1

Mn(1)–O(5) 2.082�2

2.14(6)�2

1.98�2

Mn(1)–O(6) 2.272�1

2.25(15)�1

1.85�1

Mn(2)–O(2) 2.231�1

2.39(15)�1

2.02�1

Mn(2)–O(3) 1.967�2

1.966(3)�2

2.00�2

Mn(2)–O(7) 1.975�1

2.38(14)�1

1.79�1

Mn(2)–O(7) 2.397�1

2.36(13)�1

1.80�1

Mn(3)–O(1) 2.194�4

2.34(14)�4

1.97�4

Mn(3)–O(4) 1.966�2

1.9660(3)�2

1.97�2

Fig. 6. HRTEM images of Pb13Mn9O25 along the [0 0 1] zone axis. One unit cell is

indicated by a white rectangle. The top image is a high magnification image, the

bottom image is a low magnification overview image. The calculated image is

indicated by a black border in the top image.

1 We primarily interpret the lone pairs in the sense of crystal chemistry, i.e.,

the lone pair is considered as a reason for the asymmetric coordination of the Pb

atom. If the coordination is symmetric, the lone pair is considered to be

delocalized. The microscopic justification for the lone pair localization comes

from the energy spectrum that shows narrow Pb 6s bands below �8 eV. The ELF

attractor serves as another justification, although the ambiguity between the lone

pair and the multi-center bond usually remains.

J. Hadermann et al. / Ultramicroscopy 110 (2010) 881–890 887

After the structure relaxation, all three energies (EI, EII, and Eref)decreased by 10.5�11.0 eV/f.u. The relaxed structures are shownin Fig. 7. The relaxed model I remained unfavorable with

EIrel�EII

rel�3.7 eV/f.u. Moreover, model I showed an unusual

triangular coordination for the Mn(2) atom. In contrast, thesolution II and the refined structure converged to the samegeometry with reasonable local environment for all the cations(see the next section for further discussion). Due to the significantenergy difference between models I and II after the relaxation,the geometry of model II can be considered as a reliable struc-tural model of Pb13Mn9O25. The residual forces did not exceed0.01 eV/A, indicating that an energy minimum has been reached.The relaxed atomic positions are listed in Table 5, while Table 6presents the resulting interatomic distances.

The Monte-Carlo optimization imposes constraints on thestructural model by setting chemically reasonable indirectconstraints on the interatomic distances. Then, the differentenergies of models I and II should be related to the arrangement ofmanganese polyhedra with respect to the lead atoms causingdifferent spatial arrangements of their lone electron pairs. Tounravel the origin of this difference, we calculated the ELF forthe relaxed structures. Lone pairs of Pb2 + are evidenced by theattractors located near the Pb atoms.1 In Fig. 7, the positions of thelone pairs are visualized by ELF isosurfaces. Model II leads tolocalized lone pairs for Pb(1), Pb(2) and Pb(4) atoms. The lonepairs are located within the large channels formed by manganesepolyhedra. Model I also allows for the lone pair localization forthree lead positions. However, the lone pairs remain uniformlydistributed throughout the structure. This feature is related to thelocation of the oxygen atoms (i.e., types of the Mn–O polyhedraand connections between them) and can also be observed for theunrelaxed structures.

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Fig. 7. Relaxed crystal structures corresponding to the solutions I and II (left and

right panels, respectively). Grey shades show ELF isosurfaces with Z¼0.75. In the

left panel, the ticks represent MnO3 triangles arranged perpendicular to the ab

plane.

Fig. 8. Coordination environment of the Pb atoms.

J. Hadermann et al. / Ultramicroscopy 110 (2010) 881–890888

The lone pairs are non-bonding moieties. Therefore, they areusually located between parts of the structure with differenttypes of chemical bonding [43]. If the bonding is similarthroughout the structure, the lone pairs should be confined tocertain non-bonding regions (usually channels or layers: see, e.g.,[11,43]). The latter case is relevant for Pb13Mn9O25 with mainlyionic bonding, as evidenced by the lack of ELF attractors in thevalence region beyond the lead lone pairs. Then, the stability ofthe structure will depend on the possibility to confine the lonepairs. Such a confinement is possible for model II and could be anexplanation for the stability of the resulting structure comparedto model I.

4. Discussion

The structural model of Pb13Mn9O25 is shown in Fig. 4d (unitcell) and 4e (overview). The positions of the Pb and Mn cationscorrespond to the A and B sites of the parent ABO3 perovskitestructure, respectively. Whereas the A sublattice is completelyfilled with Pb atoms, the B-sublattice contains a considerableamount of cation vacancies. One 4k Mn position is empty in theunit cell, therefore only 9 out of 13 Mn atoms are present in thestructure. This conclusion is in agreement with the experimen-tally determined composition Pb13Mn9O25 per unit cell, whichshould contain 13 perovskite ABO3 formula units according to the13-fold unit cell volume increase for the supercell compared tothe perovskite subcell.

The Mn cations are located at the centers of Mn(3)O6

octahedra and Mn(1)O5/Mn(2)O5 distorted tetragonal pyramids.These polyhedra form a three-dimensional network by cornersharing. The Pb13Mn9O25 structure also contains less oxygenatoms than the parent perovskite structure: oxygen vacanciesform rows along [0 0 1] with 14 vacant rows out of 39. Thisdecreases the coordination number for part of the Mn atoms from6 in the perovskite structure to 5 in Pb13Mn9O25.

The Pb(1), Pb(2) and Pb(4) cations adopt asymmetric coordi-nations (Fig. 8) leaving space for the localized lone pairs. It isreasonable to assume that the space required for localized elec-tron pairs is made at the cost of vacancies in the B-sublattice. ThePb(3) atom retains the cuboctahedral coordination characteristicfor the A-cations in the perovskite structure. The Monte-Carlooptimization suggests 8 short and 4 long, almost non-bondingPb–O distances (Fig. 8), while the ab initio relaxation keeps thesymmetric coordination environment. In both cases, there are noclear signatures of lone pair localization. The delocalization of thelone pair for Pb(3) looks somewhat unusual, because even therigid perovskite framework allows accommodating the lone pairby shifting the Pb atom away from the center of the cubocta-hedron (see, e.g., the PbCrO3 structure [44]). To test thispossibility, we reduced the symmetry down to the P4 spacegroup and shifted the Pb(3) cation along the four-fold axis. How-ever, the structure relaxation restored the starting configuration.Thus, we can conclude that the Pb(3) lone pair is indeeddelocalized. A similar effect has been observed for the PbFeO2Fperovskite structure [45].

The Pb13Mn9O25 (Fig. 4d, e) compound presents a newstructure type. The network of the MnO6 and MnO5 polyhedra isrelated to that of several oxygen-deficient perovskites. However,in contrast to those compounds, there are Mn vacancies in

ARTICLE IN PRESS

Fig. 9. Structure of the A5B5O13 anion deficient perovskites. The A-cations are

represented by orange spheres, the B cations are at the centers of the polyhedra

and oxygen atoms are at the corners.

J. Hadermann et al. / Ultramicroscopy 110 (2010) 881–890 889

Pb13Mn9O25, which are also arranged in an ordered way. TheMn–O network consists of two building blocks, a group of fourMnO5 tetragonal pyramids in a merry-go-round and a similargroup of four MnO5 tetragonal pyramids, but centered with oneMnO6 octahedron. The first group of four tetragonal pyramidsexists also in the compounds Sr2MnO3.5 [46] and Sr3Mn2O6 [47],which are built up exclusively of this type of groups. The structureof La8�xSrxCu8O20�d [48,49] on the other hand, has only the lattergroup with four tetragonal pyramids and one octahedron in themiddle. An overview of such anion deficient perovskite structurescan be found in [18]. By having both groups, Pb13Mn9O25 bearsgreat similarity to the A5B5O13 anion deficient perovskites [50,51](Fig. 9). In these compounds, however, these groups are notseparate building blocks because they have one common tetra-gonal pyramid belonging to both groups, while in Pb13Mn9O25 notetragonal pyramids are shared between the groups, which areplaced in a chessboard manner, and they are connected only bycorner sharing.

Three sets of interatomic distances for the Pb13Mn9O25

structure are listed in Table 6. For each distance, the first lineshows the result of the Monte-Carlo optimization where atomicmovements are constrained with antibump and BVS conditions.The second line corresponds to the structure refinement withoutany constraints. Along the refinement, atomic positions areadjusted to achieve the best fit of the experimental diffractionpattern. For X-ray diffraction data, this usually leads to accuratestructural models, but the PED data are less accurate due to thepoor applicability of the kinematical approximation. This mayspoil the refined atomic positions and may reduce the accuracy ofthe structure solution. Finally, the ab initio relaxation allowsperforming an unconstrained structure optimization which isbased on the minimization of the total energy. The accuracy of theresulting crystal structure depends on the accuracy of theunderlying band structure calculation only, while the latter canbe affected by correlated electrons in the Mn d shell.

To get a rough idea about the interatomic distances, one cancalculate the BVS (see the last column of Table 5). For the leadpositions, the Monte-Carlo optimization and the ab initio

structure relaxation yield similar BVS, while the structurerefinement leads to worse results and utterly fails to reveal areasonable local environment for Pb(3). In the case of the Mnpositions, the structure refinement works better and shows BVSvalues in the range of 1.8–2.9, consistent with the experimental

average oxidation state of +2.56 for the Mn atoms. In contrast,the ab initio structure relaxation overestimates the Mn valence(the BVS values fall in the range from 3.2 to 3.6) due to theunderestimated Mn–O distances. This feature can be traced backto the band structure calculation procedure that neglects correla-tion effects in the Mn d shell. Indeed, one would expect thecorrelation effects (on-site Coulomb repulsion) to drive electronsaway from the Mn site and to reduce the Mn–O hybridization byincreasing the Mn–O distances. Still, the Monte-Carlo optimiza-tion shows a rather asymmetric local environment of the Mnatoms in contrast to the nearly regular local environment in therelaxed structure. The above discussion raises a more generalquestion about the accuracy of the structure refinement based onthe PED data. Due to the presence of the heavy lead scatterers,the positions of the light atoms are hard to determine. Indeed, oneneeds the constrained Monte-Carlo optimization to find thepositions of the oxygen atoms. The unconstrained structurerefinement keeps the structural model, but leads to unreasonablePb–O distances for one of the lead positions. The computationalapproach readily restores the realistic arrangement of oxygenaround the lead atoms but experiences certain difficulties withthe local environment of manganese. Still, the combined approachallows us to suggest to a reliable structural model for Pb13Mn9O25.

The strategy of solving this complex structural problem isdifferent from the conventional approach to structure analysis.First, we used direct methods to find the positions of the Pb andMn atoms. Then, we had to apply a constrained search (Monte-Carlo optimization) in order to find the oxygen positions. Theresults of this search left two solutions. To find the correctsolution, we had to release the constraints and to reduce theaccuracy of the solution. An independent approach of ab initio

structure relaxation confirmed our choice.

5. Conclusions

Using the example of the successful solution of thePb13Mn9O25 crystal structure we have demonstrated the powerof advanced transmission electron microscopy for the character-ization of complex oxide materials containing heavy scatteringmetal cations. The chemical composition was completely char-acterized by spectroscopic EDX and EELS techniques. The atomicpositions were retrieved from PED intensities using structuresolution with a Monte-Carlo based global optimization. Theapplication of chemically sensible constraints allowed to avoiddummy solutions and to obtain a realistic pattern of oxygenatoms and anion vacancies. The ab initio structure relaxationconfirmed the proposed model. The Pb13Mn9O25 crystal structurerepresents a new structure type within the perovskite-basedcompounds, containing ordered vacancies in both B-sublatticeand anion sublattice.

Acknowledgements

This work was supported by the Research Foundation—

Flanders (FWO G.0184.09N), BOF—University of Antwerp(23047) and the Russian Foundation of Basic Research (RFBRGrants 07-03-00664-a, 06-03-90168-a). The authors acknowledgefinancial support from the European Union under the Framework6 program under a contract for an Integrated InfrastructureInitiative. Reference 026019 ESTEEM. Haiyan Tan acknowledgesthe financial support from FWO-Vlaanderen (Project no.G.0147.06).

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J. Hadermann et al. / Ultramicroscopy 110 (2010) 881–890890

Appendix A. Supplementary material

Supplementary data associated with this article can be foundin the online version at doi:10.1016/j.ultramic.2010.03.012.

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