European Powder Diffraction Conference; August 2010, Darmstadt, Germany 9783486991321, 9783486989403

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EPDIC 12 Proceedings of the Twelfth European Powder Diffraction Conference held August 2 7 - 3 0 , 2010 in Darmstadt, Germany Editors 2 1 Hartmut Fuess , Paolo Scardi and Udo Welzel 1

o

Institute of Materials Science, University of Technology, Darmstadt, Germany 2 Department of Materials Engineering and Industrial Technologies, University of Trento, Italy 3 Max Planck Institute for Intelligent Systems (formerly Max Planck Institute of Metals Research), Stuttgart, Germany

Proceedings No. 1 of Zeitschrift für Kristallographie Oldenbourg Verlag

EPDIC 12 Twelfth European Powder Diffraction Conference Darmstadt, Germany, August 27 - 30, 2010 Conference location:

Darmstadtium Conference Center, Darmstadt, Germany

Conference chairman:

Hartmut Fuess

Organising committee:

Barbara Albert Wolfgang Donner Helmut Ehrenberg Hartmut Fuess Achim Kleebe Ralf Riedel Christina Roth Ingrid Svoboda

Scientific programme committee: Paolo Scardi, Trento, Italy (Chair) Robert J. Cernik, Dares bury, UK (Co-chair) Udo Welzel, Stuttgart, Germany (Co-chair) Nathalie Audebrand, Rennes, France Pierre Bordet, Grenoble, France Radovan Cerny, Genève, Switzerland William I.F. David, Oxon, UK Andrew Fitch, Grenoble, France Hartmut Fuess, Darmstadt, Germany Antonella Guagliardi, Bari, Italy Torbjörn Gustafsson, Uppsala, Sweden Sergey A. Ivanov, Moscow, Russia Jens Erik Jorgesen, Aarhus, Denmark Arnt Kern, Karlsruhe, Germany Radomir Kuzel, Prague, Czech Republic Christian Lengauer, Vienna, Austria Irene Margiolaki, Patras, Greece Anton Meden, Ijubljana, Slovenia Bogdan Palosz, Warsaw, Poland David Rafaja, Freiberg, Germany Jordi Rius, Barcelona, Spain Arnold Vermeulen, Almelo, The Netherlands

EPDIC12 has been supported by: • • • • • • • • • • • • • • • • • • • • • •

AJK Analytical Services (Bergen op Zoom/The Netherlands) ¡analytic consulti GmbH & Co. KG (Roth/Germany) Anton Paar GmbH (Graz/Austria) Bruker AXS GmbH (Karlsruhe/Germany) Crystal Impact GbR (Bonn/Germany) GE Sensing & Inspection Technologies GmbH (Hürth/Germany) Hecus X-Ray Systems (Graz/Austria) HUBER Diffraktionstechnik GmbH & Co. KG (Rimsting/Germany) INCOATEC GmbH (Geesthacht/Germany) INEL (Artenay/France) International Centre for Diffraction Data ICDD(Newtown Square/USA) International Union of Crystallography IUCr (Chester, UK) Marresearch GmbH (Norderstedt/Germany) MaTeck GmbH (Juelich/Germany) Oldenbourg Wissenschaftsverlag GmbH (München/Germany) Panalytical GmbH (Kassel/Germany) Rayonix LLC (Evanston/USA) Rigaku Röntgenlabor Dr. Ermrich (Reinheim/Germany) Sietronics Pty Limited (Canberra/Australia) Stoe & Cie GmbH (Darmstadt/Germany) Xenocs SA (Sassenage/France)

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PREFACE The 12th edition of the European Powder Diffraction Conference EPDIC12 has been organized at Darmstadt from the 27th to the 30th of August, 2010. As the European Crystallographic Meeting ECM26 gathered scientists from the 29th of August to the 2nd of September an almost complete representation of Crystallography in Europe was achieved. More than 1300 participants came to Darmstadt to present their latest results in plenary and keynote lectures, in microsymposia, poster shows or in the commercial exhibition. The city of Darmstadt is situated in the centre of the Federal Republic of Germany and access is easy by rail, motorways and Frankfurt International Airport. Former capital of the Grand-Duché of Hessen until 1918 and the Land Hessen from 1918 to 1945, the town is now known as the "City of Sciences" (Stadt der Wissenschaft) with important institutions like the Gesellschaft für Schwerionenforschung GSI and the European Space Agencies ESA and ESOC. The Technische Universität Darmstadt, founded in 1836, is a well known centre of education for engineers and scientists. The University is linked through many channels with the GSI, ESOC, several Fraunhofer Institutes or the local MERCK company (pharmacy and chemistry). Therefore it was quite normal that the University together with EPDIC and EC A committees invited scientists to join at the newly constructed congress centre named after the chemical element 110 DARMSTADTIUM, detected in nuclear fusion processes at GSI. The EPDIC conference itself started on Friday the 28th of August by an opening speech of Paolo Scardi, the chairman of the EPDIC committee. During the opening the EPDIC-Prize for senior scientists has been awarded to Hugo Rietveld. This is a name well-known in crystallography, especially powder diffraction. The "Rietveld method" has been introduced about 45 years ago to refine neutron powder diffraction patterns by using the entire profile of the scattered intensities, not only the integrated intensities. Rietveld was at that time working at Petten at the neutron research centre in the Netherlands. The method has been extended in the following years to X-ray patterns and proved its full potential with the many powder stations at synchrotron facilities. The EPDIC-Prize for young scientists was awarded the following day to Pavol Juhas (East Lansing, USA) acknowledging his achievements in the development of new algorithms for the structure investigation of nanomaterials, especially based on synchrotron data. A special note by Robert Cernik was commemorating the late Lachlan Cranswick whose untimely death became known during the conference. Whereas about 250 participants were registered for EPDIC, additionally about 100 scientists profited from both events. The state of the art in powder diffraction was represented by six invited plenary talks. The subjects covered were on one side new developments in instrumentation and methods and on the other new materials and their properties as studied by powder diffraction. The organizers gave place to present many aspects of research at large facilities (neutrons and synchrotron) in the program. The trend to harder and harder x-rays

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European Powder Diffraction Conference, EPDIC 12

was covered by Harald Reichert from the ESRF (Grenoble, France) who explained the upgrade of existing facilities and the move to more and more microfocus beam-lines. Neutrons were presented by the director of the European Spallation Source (ESS) Colin Carlile who described the present state of the facility that is going to be built in Lund (Sweden). An overview of the instrumentation of the Japanese Spallation Source in Tokaimura (KEK, Ibaraki, Japan) was given by Takashi Kamiyama. The combination of powder diffraction with electron microscopy was demonstrated by Ute Kolb. New materials for hydrogen storage based on borohydrides and metal organic frameworks were the subject of talks by Torben Jensen (Aarhus, Denmark) and Nathalie Guillou (Versailles, France). The treatment of nanocrystalline materials by Bogdan Palosz (Warsaw, Poland) was both methodological and materials oriented. A talk by Helena van Swygenhoven-Moens (Villingen, Switzerland) was dedicated to the investigation of deformation mechanisms by in situ X-ray diffraction investigations. The great variety of contributed papers in the microsymposia and posters is well represented in the Proceedings. A first collection of the results of the conference was published in a special issue of Zeitschrift für Kristallographie devoted to the plenary contributions and selected keynotes from microsymposia (see Z. Kristallogr. 225 [12] (2010); open access). All participants with active contributions to the conference (i.e. oral or poster presentations) were invited to submit articles for the Proceedings. The editors Hartmut Fuess, Paolo Scardi and Udo Welzel received 79 contributions. After peer-review and corrections a few papers were finally not accepted, but 74 accepted articles give an excellent overview of the broad field of powder diffraction from the study of stress/strain to the solution of the structure of biological macromolecules. The editors would like to thank Mrs Maritta Dudek from the Max Planck Institute for Intelligent Systems (formerly Max Planck Institute for Metals Research) who organized the technical aspects of editing and printing in close collaboration with Kristin Berber-Nerlinger from the publisher. We are grateful to all participants of EPDIC 12 and to all contributors to the Proceedings and we are looking forward to EPDIC 13 in Grenoble in 2012.

Hartmut Fuess, May 2011, Darmstadt Paolo Scardi, May 2011, Trento Udo Welzel, May 2011, Stuttgart

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Editorial Notes The number of papers in these Proceedings is 74. The total number of papers published in the Proceedings of the preceding EPDIC conferences ranges from 73 to about 190. The subdivision of the papers over the sections has been largely maintained as for preceding EPDIC proceedings. Only very minor adjustments, to adapt the subsections to the submitted papers, have been performed. Reviewing the twelve editions of the EPDIC Proceedings, the ratios of the numbers of papers on developments in the methods and techniques of powder diffraction and those on applications of powder diffraction methods to specific classes of materials are found to be 1.0, 0.7, 0.5, 1.0, 0.9, 0.5, 0.7, 0.7, 0.8, 0.5, 0.8 and, for the current proceedings, 0.7. As for the EPDIC 11 Proceedings, a strict refereeing procedure was adopted for the Proceedings of EPDIC12. Each contribution was considered by at least one referee. The referees were, to a large extent, participants of EPDIC 12. A few (in this sense) external referees were contacted as well. We thank all referees for their efforts and time spent on the manuscripts. We did not correct the English used, apart from minor corrections in a few papers. We also thank Mrs Maritta Dudek (Max Planck Institute for Intelligent Systems, formerly Max Planck Institute for Metals Research, Dept of Prof. Dr Ir. E.J. Mittemeijer, Stuttgart, Germany) for final technical corrections and invaluable help during editing and preparation of the required material for the publisher. We sincerely hope that these Proceedings will be a useful collection of papers outlining the newest developments in the field of Powder Diffraction.

H. Fuess Darmstadt

P. Scardi Trento

U. Welzel Stuttgart May 2011

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European Powder Diffraction Conference Award for Young Scientists Sponsored by PANalytical B.V. (Almelo, The Netherlands) The EPDIC Award for Young Scientists is assigned at each EPDIC Conference and honours outstanding scientific achievement by young scientists in the field of powder diffraction. The award winner is invited to present a plenary talk at the next European Powder Diffraction Conference. The EPDIC Committee of each EPDIC Conference selects the awardee. Short proposals of candidates containing descriptions of the scientific contributions to be assessed should be addressed to any member of the EPDIC Committee who is asked to make names public within this committee. As a rule, an age limit of 35 applies to the candidates.

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European Powder Diffraction Conference Award for Distinguished Powder Diffractionists Sponsored by Bruker AXS (Karlsruhe, Germany) The EPDIC Award for Distinguished Powder Diffractionists is assigned at each EPDIC Conference for outstanding results and/or continued, important contributions to the field of powder diffraction. The award winner is invited to present a plenary talk at the next European Powder Diffraction Conference. The EPDIC Committee of each EPDIC Conference selects the awardee. Short proposals of candidates containing descriptions of the scientific contributions to be assessed should be addressed to any member of the EPDIC Committee who is asked to make names public within this committee.

Table of Contents Preface Editorial Notes EPDIC award for Young Scientists EPDIC award for Distinguished Powder Diffractionists

ix xi xiii xv

VOLUME I I.

METHOD DEVELOPMENT AND APPLICATION

1.1

Determination of Crystal Structure

U. Kolb, E. Mugnaioli Complementarities between precession electron and X-ray powder diffraction M. Allieta, M. Bruneiii, M. Coduri, M. Scavini, C. Ferrerò Differential Pair Distribution Function applied to Cei-xGdxC>2-x/2 system

1.2

1

15

Qualitative and Quantitative Phase Analysis

S. Dittrich, J. Neubauer, F. Goetz-Neunhoeffer A suitable method for quantitative phase analysis of samples with high amorphous content

23

A. Bonnin, H. Palancher, V. Honkimäki, R. Tucoulou, Y. Calzavara, C. V. Colin, J-F. Bérar, Ν. Boudet, H. Rouquette, J. Raynal, C. Valot, J. Rodríguez-Carvajal UMo/Al nuclear fuel quantitative analysis via high energy X-ray diffraction

29

1.3

Microstructure and Line Broadening Analysis

A. Leonardi, Κ. Beyerlein, T. Xu, M. Li, M. Leoni, P. Scardi Microstrain in nanocrystalline samples from atomistic simulation

37

Κ. R. Beyer lein, M. Leoni, R. L. Snyder, M. Li, P. Scardi Simulating the temperature effect in a powder diffraction pattern with molecular dynamics

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Romain Gautier, E. Furet, Régis Gautier, N. Audebrand, E. Le Fur A new combined approach to investigate stacking faults in lamellar compounds

49

S. Popovic, Z. Skoko, G. Stefanie Factors affecting diffraction broadening analysis

55

P. Pardo, F. Javier Huertas, M. A. Kojdecki, J. Bastida Crystallite size evolution in hydrothermal formation of kaolinite

63

T. Ida, T. Goto, H. Hibino Particle statistics in synchrotron powder diffractometry

69

D. Dodoo-Arhin, G. Vettori, M. D 'Incau, M. Leoni, P. Scardi High energy milling of Cu 2 0 powders

75

M. Müller, M. Leoni, R. Di Maggio, P. Scardi Defects in nanocrystalline ceria xerogel

81

Z. Matéj, L. Matéjovà, F. Novotny, J. Drahokoupil, R. Kuzel Determination of crystallite size distribution histogram in nanocrystalline anatase powders by XRD

87

J. V. Clausell, J. Bastida, M. A. Kojdecki, P. Pardo Crystal growth mechanism of kaolinites deduced from crystallite size distribution

93

M. Herrmann, P. B. Kempa, U. Förter-Barth, S. Doyle Diffraction peak broadening of energetic materials

99

A. Zuev, R. Dinnebier, W. Depmeier Calculation of a line profile for the diffractometer with a primary monochromator 1.4

105

Texture

L. Kalvoda, S. Vratislav, J. Hladil, M. Machek Characterization of weakly deformed limestone from Chotee, Bohemia by neutron transmission

113

J. Palacios-Gómez, T. Kryshtab, C. Vega-Rasgado Multiple scattering from textured polycrystals

119

II.

INSTRUMENTAL

A. Huq, J. P. Hodges, O. Gourdon, L. Heroux Powgen: A third-generation high-resolution high-throughput powder diffraction instrument at the Spallation Neutron Source

127

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M. Knapp, I. Peral, L. Nikitina, M. Quispe, S. Ferrer Technical concept of the materials science beamline at ALBA

137

X. Alcobe, J. M. Bassas, M. A. Cuevas-Diarte Instrumental calibration of laboratory X-ray powder diffractometers

143

N. S. P. Bhuvanesh, J. H. Reibenspies, W. Seward, T. Pehl New anti-air-scatter screen for powder XRD with linear position sensitive detectors

149

M. C. Dalconi, M. Favero, G. Artioli In-situ XRPD of hydrating cement with lab instrument: reflection vs. transmission measurements

155

C. G. Hartmann, P. Harris, K. Stähl In-house characterization of protein powder

163

P. Mikula, M. Vrána, J. Saroun, B. S. Seong, V. Em Multiple reflections accompanying allowed and forbidden single reflections in bent Si-crystals

169

S. Sulyanov, H. Boysen, C. Paulmann, E. Sulyanova, A. Rusakov 29-scanning 2D-area detector for high quality powder data collection using synchrotron radiation

175

III.

SOFTWARE

J. Bergmann, Κ. Ufer, R. Kleeberg Adaption of a Rietveld code towards clay structure description

183

L. Gelisio, C. L. Azanza Ricardo, M. Leoni, P. Scardi Real-space powder diffraction computing on clusters of Graphics Processing Units

189

K. Momma, F. Izumi Evaluation of algorithms and weighting methods for MEM analysis from powder diffraction data

195

M. Ende, G. Kloess YAYLA, a program for handling area detector data of glasses

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VOLUME II IV.

MATERIALS

IV. 1

Thin Layers

M. J. Heikkilä, J. Hämäläinen, M. Rítala, M. Leskelä HTXRD study of atomic layer deposited noble metal thin films heat treated in oxygen

209

J. Riha, P. Sutta, J. Siegel, Ζ. Kolskà, V. Svorcík XRD real structure characterization of sputtered Au films different in thickness

215

K. Yusenko, D. Zacher, R. A. Fischer Liquid-phase self-terminated growth of MOF thin films: An X-ray diffraction study

IV.2

221

Nanocrystalline and Amorphous Materials

T. Brunátová, S. Danis, R. Kuzel, D. Králová, M. Slouf X-ray study of structure of the Ti02 nanotubes and nanowires 229 E. Grzanka, S. Stelmakh, B. F. Palosz, S. Gierlotka, Th. Profferì, M. Drygas, J. F. Janik Core-Shell structure of nanocrystalline A1N in real and reciprocal spaces 235 S. Stelmakh, E. Grzanka, S. Gierlotka, J. F. Janik, M. Drygas, C. Lathe, B. Palosz Compression and thermal expansion of nanocrystalline TiN

241

G. K. Rane, D. Apel, U. Welzel, E. J. Mittemeijer Diffraction analysis of grain growth in nanocrystalline Ni-W powders prepared by mechanical milling

247

M. Petrik, B. Harbrecht Orientational degeneracy of antiferromagnetic exchange striction in anisotropic ultrafine NiO nanocrystals

253

IV.3

Metals and Alloys

IV.3.1

General

J. Garin, R. Mannheim, M. Camus X-ray diffraction analysis of phases in weldments of super duplex stainless steels

261

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V.E. Danilchenko, R.M. Delidon X-ray studies of martensitic transformation in the Fe-Ni alloys rapid quenched from melt

267

V. Danilchenko, V. Iakovlev γ-α-γ-martensitic transitions influence on the martensite decomposition of quenched steel

273

IV.3.2

Microstructure, Stress and Texture

S. Gierlotka, E. Grzanka, A. Krawczynska, S. Stelmakh, B. Palosz, M. Lewandowska, Ch. Lathe, K. J. Kurzydlowski Strain relaxation and grain growth in 316LVM stainless steel annealed under pressure

281

M. A. Abdalslam, J. Brötz, W. Ensinger, FL. Fuess Influence of elastic stress on stainless steel corrosion

287

A. Leineweber, F. Lienert, S. Glock, T. Woehrle, P. Schaaf, M. Wilke, E. J. Mittemeijer X-ray diffraction investigations on gas nitrided nickel and cobalt

293

S. Starenchenko Study of the ordering kinetics in Au4V alloy

299

IV.4

Minerals and Inorganics

IV.4.1

Structural Changes, In-situ and Non-Ambient

Investigations

D. Stürmer, L. Giebeler, H. Fuess Structural characterisation of lanthanum manganese perovskite catalysts by in-situ X-ray powder diffraction

307

M. Lvanov, A. Shmakov, O. Podyacheva, Z. Lsmagilov Structural aspects of oxygen stoichiometry in SrCo0.6-xFe0.2NbxO3-z perovskites

313

T. Basyuk, V. Berezovets, D. Trots, S. Hoffmann, R. Niewa, L. Vasylechko Phase diagram of the PrA10 3 -GdA10 3 system

319

O. Bulavchenko, S. Tsybulya, E. Gerasimov, S. Cherepanova, T. Afonasenko, P. Tsyrulnikov High-temperature XRD investigation of spinel Μη1.5Α11.5θ4 decomposition

325

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S. Cherepanova, O. Bulavchenko, I. Simentsova, E. Gerasimov, A. Khassin Influence of AL ions on the reduction of CO3.XA1x04: in situ XRD investigation

331

A. M. T. Bell, C. M. B. Henderson CS2CUSÌ5O12 phase transition?

337

J. Darul, W. Nowicki, P. Piszora, C. Lathe Hydrotalcite-like materials under high pressure

343

B. Raab, H. Pöllmann "C 2 AH 8 " - 2CaOAl 2 0 3 -(8±n)H 2 0 - main hydration products of CAC

349

W. Nowicki, J. Darul, A. Bell Low temperature structural studies of zinc substituted copper ferrite using synchrotron X-ray powder diffraction

355

Z. Amghouz, S. Khainakov, J. R. Garcia, S. Garcia-Granda Phase transformation on mixed yttrium/sodium-MOFs, X-ray thermodiffractometry and structural modelling

361

O. Schulz, Ν. Eisenreich, H. Fietzek, Β. Eickershoff, M. Schneider, E. Kondratenko Structural changes during the oxidation of micrometer-sized Al particles up to 1523 Κ in air

367

W. Paszkowicz, P. Piszora, R. Minikayev, M. Knapp, D. Trots, F. Firszt, R. Bacewicz Evolution of CuInSe 2 lattice parameters in a broad temperature range

373

IV.4.2

Determination

of Crystal Structure; Structure

Refinement

E. Harju, I. Hyppänen, J. Hölsä, J. Kankare, M. Lahtinen, M. Lastusaari, L. Pihlgren, T. Soukka Polymorphism of NaYF4: Yb 3+ , Er 3+ up-conversion luminescence materials

381

W. Oueslati, M. Meftah, R. Chalghaf, H. Ben Rhaiem, A. Ben Haj Amara XRD investigation of selective exchange process for di-octahedral smectite: Case of solution saturated by Cu 2+ and Co 2+ cation

389

P. Tzvetkov, D. Kovacheva, D. Nihtianova, T. Ruskov Synthesis of cation substituted A 2 B 2 0 5 perovskites with crystallographic shear planes

397

E. Fernández-Zapico, J. Montejo-Bernardo, S. Garcia-Granda, J. R. Garcia, G. R. Castro, F. Y. Liu, J. Rocha New lanthanide phosphonates structures obtained using XRPD data

403

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R. Chalghaf, S. Jebali, W. Oueslati, H. Ben Rhaiem, A. Ben Haj Amara Structural formula determination of 2:1 Tunisian clay using XRD investigation

IV.4.3

Determination of Magnetic Structure, Magnetic

409

Materials

M. Bakr Mohamed, A. Senyshyn, H. Fuess

Neutron diffraction and magnetic properties of GaFei. x Mn x 03 with x= 0.05 and 0.10

IV.4.4

417

Microstructure, Phase Analysis

A. Sanz, J. Bastida, M. A. Kojdecki, A. Caballero, F. J. Serrano Influence of quartz particle size of triaxial compositions on mullite formation in the obtained porcelains Ν. V. Tarakina, R. B. Neder, L. G. Maksimova, I. R. Shein, Y. V. Baklanova, T. M. A. Denis ovastructure ofS.TiO(OH) Defect crystal salt Li 2 Ti0 3 2 and related J. Montejo-Bernardo, García-Granda, A. lithium Fernández-González Quantification of Ammonium Sulphate Nitrate (ASN) fertilizers

431 437

B. Peplinski, C. Adam, H. Reuther, C. Vogel, Β. Adamczyk, M. Menzel, F. Emmerling, F.-G. Simon First identification of the tridymite form of A1P0 4 in municipal sewage sludge ash

443

ST. Bergold, M. Göbbels Combined study of phase relations by X-ray diffractometry/Rietveld & ΕΡΜΑ in the system Mn0 x -Al 2 0 3 -Si0 2 -Mg0

449

G. Kimmel, J. Zabicky, R. Shneck, A. Tsinman, Z. Shalle, J. D. Fidelus, S. Gierlotka, W. Lojkowski XRPD study of phase transformations accompanied with grain growth in the aluminazirconia system

455

M. A. Kojdecki, A. M. López-Buendía, J. Bastida, M. M. Urquiola X-ray diffraction microstructural analysis in pyrites of peats from Moncófar marsh (Castellón, Spain)

461

M. Meftah, W. Oueslati, A. Ben Haj Amara XRD and MAS-NMR investigation of synthesized zeolite from 2:1 Tunisian clays: Effect of concentration o f N a O H solution on the final product nature

467

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IV.5

Organic Materials

J. Hasek, J. Labsky, T. Skàlovà, P. Kolenko, J. Dohnâlek, J. Duskovà, A. Stépánková, T. Koval Polymer structure database and protein-polymer interactions

475

P. B. Kempa, M. Herrmann Phase transitions of FOX-7 investigated by temperature resolved X-ray diffraction

481

D. Jehnichen, D. Pospiech, P. Friedel, S. S. Funari Semifluorinated PMMA / PSFMA diblock copolymers with multiple phase separation

487

Author Index

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I.

METHOD DEVELOPMENT AND APPLICATION

1.1

Determination of Crystal Structure

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Complementarities between precession electron and X-ray powder diffraction U. Kolb*, E. M u g n a i o l i Institut for Physical Chemistry, Johannes Gutenberg-University, Weiderweg 11, 55099 Mainz, Germany Contact author; e-mail: [email protected] Keywords: electron diffraction, structure determination, X-ray powder diffraction, reciprocal space tomography Abstract. The choice of the appropriate method for structural characterization of crystalline material is strongly dependent on the achievable crystal size. Single crystal X-ray diffraction is already developed into a standard method for crystal structure solution, followed by X-ray powder diffraction. Electron radiation provides several advantages in comparison to X-ray radiation but structure solution from electron diffraction data is a difficult task mainly due to dynamical scattering effects. In fact the application of electron diffraction is still an expert's task and is at the moment only performed within a small community. Recent developments such as electron beam precession and reciprocal space tomography turned structure analysis by electron diffraction into an approach which can be learned and performed in a reasonable time scale. Both, X-ray powder and electron diffraction are strongly complementary and provide in combination an exceptional strong tool for structure solution of nano crystalline material.

1. Introduction In times of increasing interest in production and application of nano crystalline materials with new and highly applicable physical properties the development of techniques suitable to investigate the atomic structure of nano particles is one of the most important frontiers of crystallography. Single crystal X-ray structure solution, already a routinely applied technique, can be performed only on crystals down to about one micron. In order to obtain crystal structure solution of smaller particles X-ray powder diffraction (XRPD) is applied successfully. This widespread technique, for which well consolidated structure analysis routines exist, utilizes the diffraction of X-rays on samples consisting of many small crystallites. Exactly this circumstance provides one of the strongest advantages of XRPD, namely that the data is collected from the bulk sample and not from a selected crystal which may not be representative for the material. On the other hand the simultaneous measurement of many crystallites leads to the information reduction from three to one dimension. The resulting reflection overlap, apart from the mere multiplicity, can happen systematically in the case of high symmetric space groups (e.g. cubic case (511)/(333) ) or accidentally dependent on cell dimensions and space group. This prevents the direct analysis of many peaks and enforces an

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estimation of the underlying intensities. Additionally, peak profile shapes may be strongly biased by broadening due to small crystallite size in the nano regime and by asymmetry due to strain effects, which both may appear even in an anisotropic manner. The uncertainties in intensity determination hamper structure solution significantly. Even cell parameter determination and thus indexation of the diffraction pattern can be problematic or impossible and is enhanced for samples consisting of multiple phases or containing impurities.

2. Application of electron diffraction - historic overview The advantage of using electron beams is that structural information can be collected from areas of a few tens of nanometres [1], This is possible because charged electrons undergo coulombic interaction and have therefore a stronger interaction with matter. The electron beam can be focused down to a size of 0.1 nm for convergent illumination and to about 20 nm for parallel illumination of the sample, allowing the investigation of single nano particles even if they are slightly agglomerated. High resolution transmission electron microscopy (HRTEM), one of the best established techniques for nano particle characterization, provides direct space structural information down to 0.8-0.5 Â resolution [2, 3], Additionally, elemental analysis methods such as energy dispersive X-ray spectroscopy (EDX) or electron energy loss spectroscopy (EELS) can be applied. Nevertheless, these methods require a relatively strong illumination and thus a large electron dose on the sample. Under these conditions, nearly all organic and most of inorganic materials suffer a fast deterioration due to beam damage. This leads to a modification of the crystalline structure or to complete amorphization or sublimation of the sample [4-6], Electron diffraction in comparison to HRTEM can deliver structural information at a comparable resolution but demands a significantly lower radiation level on the sample. Due to the small wavelength of the electron radiation the simultaneous detection of several reflections, comparable to a planar cut through reciprocal space referred to as zones, is possible. Using electron diffraction cell parameters, presence of centre of symmetry (by convergent beam electron diffraction CBED [7-9], space group (if extinctions are not violated by dynamical effects), and even crystallographic specialities such as superstructure, disorder or defects (best in combination with direct space information) can be determined. The possibility to achieve a nano size probe allows to measure single nano particles and thus to analyse properly multiphasic systems. The application of electron diffraction data for structure solution dates back to 1936 [10], but for a long time electron diffraction data on its own was considered to be of little use because the presence of dynamic effects in the data [11, 12], Thus attempts of structure solution, performed often through a combination of diffraction and imaging data, focused on weak scatterer such as organic [13, 14] or biological samples [15-17] which were expected to deliver nearly kinematical diffraction data. A second approach to reduce dynamical effects was the use of very thin crystals so that the assumption that intensities are proportional to F 2 is sufficient for structure solution [18-20], Parallel to these attempts, excellent results were achieved solving structures from data sets collected by the electron diffraction camera realized by Pinsker and Vainshtein in Moskow during 1950' [21- 23], The technique developed by these authors, named oblique-textured electron diffraction (OTED), is based on the illumination of a large amount of textured nano-

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crystals collected at high angle, where families of hkn rings are sampled as reflection arcs. Thus dynamic effects, which are maximized in oriented zones, are significantly reduced and a number of organic and inorganic phases were solved, up to the localization of Η atoms in the structure [24, 25], Unfortunately, OTED demands a highly sophisticated sample preparation procedure and is therefore rarely used. The idea of collecting diffraction data from slightly misoriented zones in order to reduce dynamic effects is as well the basic idea of precession electron diffraction (PED) [26], In this technique, the beam is precessed around an axis comprising a conical path so that the sample is never oriented along a zone axis. Reflections have always a certain three dimensional shape and in principle the full reflection volume should be considered to collect correct intensities. A reflection is cut by the Ewald sphere at some distance from the reflection centre (excitation error) and an interpolation of the correct value is only possible if reflection centre, position and shape are known. In contrast to electron diffraction experiments where single cuts through the reciprocal space are collected the problem does not exist for X-ray powder diffraction since the reflection intensities are integrated statistically. Thus a second very important effect of the beam precession is the integration of reflections by the precessing Ewald sphere (see figure 1) that eliminates or at least reduces drastically the uncertainty in intensity determination caused by the excitation error. An increasing number of structure solutions achieved by PED data are reported in literature, even for relatively thick samples [27, 28], α 1

g

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Figure 1. Sketch of the electron beam precession (precession angle a) and the resulting movement of the Ewald sphere integrating the reciprocal space in the precession wedge (grey area).

Electron diffraction has been frequently used in combination with X-ray powder data with different emphasis on one or the other approach. As an example, zeolite ITQ-37 may be mentioned. This material crystallizes in the cubic space group P4¡32 or P4¡¡2 with a=26.52 A. Although the X-ray powder pattern could be indexed the severe peak overlap and peak broadening caused by particle sizes of 200-70nm hindered the structure solution. Medium resolution electron diffraction intensities derived from four oriented zones taken by selected area electron diffraction were used to support XRPD intensity integration of the overlapping peaks, in order to obtain structure solution by charge flipping algorithms [29]. Another recent structure solution of nano crystalline materials combines precessed electron diffraction with a priori crystallochemical information, HRTEM and XRPD data [30], This method was successfully used for the solution of complicated zeolite structures.

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Figure 2. Example of oriented (in-zone) electron diffraction patterns (left: [100], middle: [210], right: [110]) selected from a tilt series around c* axis (indicated by white dotted line).

b' Figtre 3. Sketch of the reciprocal net viewed down the tilt axis c*. Collected zones are marked as linear cuts (grey lines). The non reacheable area, the missing cone, is indicated in black. Collected reflections (black spots): missed reflections (grey spots). Top: Traditional tilt collecting prominent zones: Bottom: Scan of the reciprocal space with fixed tilt steps.

HRTEM images as well as electron diffraction patterns are collected two dimensionally and only the combination of several images or diffraction patterns from different orientations of the sample can deliver the three dimensional information necessary for a complete structure solution. If the cell metric is known it is possible to collect, index and extract intensities from a set of single oriented zones [28, 31, 32], Another possibility is to combine electron diffraction patterns of prominent oriented zones collected in a three dimensional net by tilting the crystal around a special crystallographic axis (figures 2 and 3 top) [33, 34], The use of oriented zones has several drawbacks. 1 : the time necessary to adequately orient the crystal increases the total exposure time and thus the beam damage. This may prevent the analysis of several classes of materials, like organic or water-containing inorganic materials.

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2: the collection of only prominent zones ignores a vast number of high indexed reflections inside the scanned reciprocal space and reduces therefore the total number of collected reflections (figure 3 top). 3: the manual orientation of a zone is never perfect and it is not assured that intensities originate from a cut through the centre of the reflection (excitation error).

3. Automated diffraction tomography In order to collect improved three dimensional electron diffraction data sets suitable for ab initio structure solution, quantity and quality of collected intensities had to be enhanced drastically. This demand recently led to the development of the Automated Diffraction Tomography (ADT) method [35, 36] including two major novelties. First, the tilt axis is an arbitrary crystallographic axis rather than a special direction. Secondly, the reciprocal space is sliced homogenously in fixed tilt steps. Thus allowing the collection of a larger amount of reflections, reducing the exposure time and, most important, providing reflections from nonoriented cuts through the reciprocal space (off-zone data), which reduces dynamical effects significantly (figure 4). It is especially important to avoid the tilt around a special crystallographic axis since in this case oriented zones are collected accidentally and a high number of symmetrically dependent reflections are measured (see figure 3 bottom). The idea is closely related to routines used nowadays in single crystal X-ray diffraction with two-dimensional CCD detectors. Nevertheless, a direct application of the X-ray concepts to electron diffraction is not possible due to significant differences in acquisition geometry and special effects which need to be taken into account.

Figure 4. Top: Sketch of the reciprocal space tomography procedure Bottom: Two dimensional o f f zone diffraction patterns at different tilt angles selected from an ADT tilt series.

The crystal position can be tracked by high angular annular dark field scanning transmission electron microscopy (HAADF-STEM) and diffraction patterns are acquired in nano electron diffraction (NED) mode, using a small condenser aperture (C2) of 10 μηι to obtain a beam size < 50 nm on the sample with almost parallel illumination. With these settings the illumination, and thus the electron dose on the sample, can be significantly reduced down to an

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electron dose rate of 0.2-15 ë A"2 s"1 [35], A sequential tilt of a crystal can in principle be performed manually but automation of the procedure is not only convenient for increasing the feasibility of the experiment, but more important for reducing the overall exposure time so that three-dimensional data acquisitions can be performed even on beam sensitive samples [6], Assuming an exposure time of 1 sec per diffraction pattern, it is possible to collect a full tilt series with a total exposure time of 2 min. Beam damage can be further reduced using cooling conditions or by slightly moving the beam around the crystal during the acquisition.

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Figure 5. Reconstructed three dimensional reciprocal space showing diffraction information up to 0.6 A resolution (top left); showing two intergrown individuals (top right); showing disorder with sequence 'Δ unit cell indicated by red arrows (bottom left); showing superstructure reflections (bottom right).

After the acquisition, a stack of two dimensional non-zonal diffraction patterns is stored. The tilt series is analyzed by the software package ADT-3D [37]. The three dimensional reciprocal space can be reconstructed and used for direct visualization of disorder, twinning and polycrystallinity as it is shown in figure 5. Cell vectors (cell parameters + orientation matrix) are defined by automated routines based on clustering in difference vector space [36], The approach allows the determination of unit cell parameters even for triclinic cells with a cell

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axis accuracy of about 2-5% and can be successful even for sparse data sets or small tilt ranges. Finally, reflections are indexed and intensities integrated. Because nearly all reflections inside the available tilt range are sampled, ADT intensity data sets have a significantly higher coverage of reciprocal space than those obtained by conventional electron diffraction in-zone acquisition. Depending on the crystal family, completeness ranges from 60% for triclinic, to 7 0 - 9 0 % ) for monoclinic, 90%o for orthorhombic and 100%o for cubic lattices. Reflection intensities integrated by ADT approach are expected to be more kinematic than those measured in oriented patterns, as they are collected off-zone and dynamic effects are therefore drastically reduced. Nevertheless a significant deviation from expected values is still present, mainly due to the excitation error, i.e. the distance the Ewald sphere cuts the reflection from the centre [38], In order to take the excitation error better into account by an integration of the full reflection intensity, PED can be coupled with ADT [39, 40], The resulting data sets proved to be of extremely high quality and in the last two years several complicate inorganic and organic structures have been solved ab initio by direct methods with a fully kinematic a p p r o a c h [6, 41-43],

4. Complementarities between ADT and X-ray powder approach The following section introduces a few examples of structure solutions obtained using a varying ratio of information gained from X-ray (figure 6) powder and three-dimensional electron diffraction. The structures were solved by ADT (electron diffraction) data with direct methods implemented in SIR2008 [44] and refined by SHELX [45], A fully kinematic approximation was used (I proportional to F2). No correction for absorption or geometry was applied. MUF41ong and NaHTi 3 07-2H 2 0 were respectively solved and refined by XRPD data, confirming electron diffraction results. For charoite the structure is composed by a network of fully connected Si-tetrahedra and Ca-octahedra as expected for this kind of material, the interatomic distances are reasonable and the composition fits the expected composition, as extensively described in Rozhdestvenskaya et al. 2010. The only R taken into account is Ri, as defined in SIR2008 and SHELX. The first exemplary structure is a metal-organic framework (MFU-41ong: [Zn5Cl4(BTDD)3]; Fh-BTDD = (bis-1//-1,2,3 -triazolo-[4,5-b],[4',5 ' -i])dibenzo-[ 1,4]-dioxin) which crystallizes in the cubic space group Fm-3m (a sketch of the structure is in the inset of figure 6). Cell parameter is 31.057Â when measured by XRPD, and 32.0 Â when measured by ADT [41], In spite of the big unit cell volume (~30.000 Â 3 ) the centring reduces peak overlap so that the structure could be solved directly from X-ray powder lab data with R p = 4 . 6 3 / R ^ T . 16, GoF = 1.34. The structure solution was performed as well with ADT data taken at liquid N 2 temperature with a resolution up to 1.3 Â and 100%o completeness of the reciprocal space. The amount and quality of the data obtained by ADT is remarkably superior to any previous electron diffraction experiment performed on a MOF, where cell parameters were determined from single oriented projections [46-51],

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European Powder Diffraction Conference, EPDIC 12

Figure 6. Lab X-ray powder pattern of MFU4-long using CitKa radiation. In the inset the same pattern after excluding the first strong peak and the structure solved by both X-ray powder diffraction and electron diffraction. Black arrow indicates the position of the strongest distortion of the bezene ring: the carbon atom was found initially directly on the mirror plane (=shift of 0.6 A).

"Ab initio" structure solution did deliver directly the complete structure. The structure was refined imposing a rigid benzene ring, which showed distortions in the original solution, and using soft bond restraints. The final residual R¡ was 32.1%, which is in an acceptable range for electron diffraction data. The maximum deviation in atom positions from X-ray powder diffraction solution is 0.2 A. The second example is NaHTi 3 0 7 -2H20, [52] appearing as an intermediate material in the production of dye-synthesized solar cells, which was available only in small, strongly disordered nanowires. Peak broadening and disorder did prevent indexing as well as structure solution by X-ray powder diffraction. The cell parameters could be determined only from ADT data and was subsequently refined against X-ray powder lab data. (Space group C2/m, cell parameters: ADT: a = 21.53 A, b = 3.79 A, c = 11.92 Α, ß = 136.3°, V= 672 A 3 ; XRPD refinement (graphite monochromatized CuKa): a = 21.555(7) A, b = 3.758(1) A, c = 11.925(5) Α, ß = 136.16(2)°, V = 669 A 3 ). Several ADT tilt series were taken from selected crystals which exhibited different amount of disorder along the c axis (figure 7 top). Structure solution was performed using the ADT data set with the lowest amount of disorder. 628 independent reflections were collected (out of 1749 total reflections sampled), comprising 79% completeness up to 0.8 A resolution. All the 13 non-Η atoms of the asymmetric unit were directly detected ab-initio and the structure was refined down to Ri = 27% (figure 7 bottom). A subsequent refinement against X-ray powder data delivered: Rwp = 20.3%, GoF = 1.45.

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Figure 7. NaHTii0f2H20: three dimensional reconstruction of the reciprocal space using two different ADT data sets along (100) projection (c* axis is oriented vertical). Left hand side: taken from a crystal with a high amount of disorder; right hand side: taken from a crystal with a low amount of disorder. Bottom: Stnicture solved ab initio on the basis of the ADT data set shown on the top-right.

The third example is charoite [42], a highly appreciated semi-precious stone found originally in the alkali-rich intrusion of the Murun massif in Yakutiya (Sakha Republic, Sibiria, Russia), which has resisted structure solution attempts by other methods since long. The idealized compositions of Charoite is (K, Sr, Ba, Mn)15.16 (Ca, Na), 2 [SÍ7o(0,OH)1So](OH,F)4 •HOG. The main problem in this case is caused by the asbestos-like fiber shape of the crystals, typically around 200 nm in diameter. The c direction is always oriented parallel to the fiber axis, while a and b are arbitrarily oriented. Fibers are laterally separated by an amorphous phase. Additionally, two modifications co-exist in the sample exhibiting similar cell parameters which differ only by about 5° in the monoclinic angle β. The presence of these geometrically related polymorphs result in a strong peak overlap in XRPD, and therefore hampers the unambiguous determination of the cell parameters and thus structure solution from this data. Both modifications (charoite-90/charoite-96) could be solved only by ADT data using 2878/3353 independent reflections out of 8508/10271 total sampled reflections, equivalent to a completeness of 97/96% up to 1.1 A resolution. The structures consist both of 90 atoms in the asymmetric unit. Refinement for charoite-90 using SHELX delivered a final residual of R! = 17%.

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European Powder Diffraction Conference, EPDIC 12

5. Conclusions The two structural methods - single crystal electron diffraction and powder X-ray diffraction - can often be applied to the same systems and therefore the combination of them can reinforce structure solution. Lattice parameter determination from powder diffraction data is not straight forward due to one dimensional information reduction. It is an especially severe problem for polyphasic samples which show a superposition of powder diffraction profiles. This is not the case for single crystal electron diffraction - the unit cell vectors are determined in 3d reciprocal space for each selected crystal separately. On the other hand distances derived from electron diffraction data show some inaccuracy due to excitation error, lens hysteresis and other effects which cause a distortion of the reciprocal space. Therefore, refinement of lattice parameters against X-ray powder profile deliver more reliable cell metric. Besides, only few crystals are usually selected to be studied by electron diffraction. So, testing the received cell metrics consistency with bulk powder data is necessary to ensure that the phase (in possibly polyphase systems) is representative. Lattice symmetry in terms of reflection extinctions can be determined both from electron diffraction and X-ray powder data. Nevertheless, problems may appear for both methods: electron diffraction, where dynamical effects may cause reflection extinction violations, and X-ray powder where peak overlap hampers the identification of extinction. Both methods - single crystal electron diffraction and X-ray powder diffraction are nowadays established techniques for structure solution, demonstrated by numerous examples. Nevertheless, when problematic systems are met, the structure solution can benefit by combining the two kinds of data. Intensity data sets extracted from X-ray powder data may have problems due to peak overlap and peak broadening causing an uncertainty in partitioning the intensities. In this case an initial estimation of intensity ratio obtained from electron diffraction data can facilitate the solution. An initial structural model build from a combination of high-resolution imaging and electron diffraction can also help a structure solution from Xray powder data. Electron diffraction intensities data sets are always influenced by dynamical effects more or less pronounced. In the case of CBED dynamical effects support structural investigation, especially when absolute symmetry needs to be determined, but usually these effects hinder structure determination. ADT approach and electron precession allow minimizing dynamic effects in the data and therefore the direct use of electron diffraction data for ab-initio structure solution. ADT data sets allow structure solution of phase mixtures and relatively complex structures. Intensity data sets are suitable for the localization of all non-H atoms within the structure, also oxygen in the vicinity of heavy atoms (or carbon in organic or hybrid organic-inorganic materials). Structure solution can be performed with routines and software developed for X-ray crystallography. The whole procedure, from data acquisition to structure solution, is now close to the time scale of single crystal X-ray structure analysis. Still, the strong deviation of electron diffraction reflection intensities from kinematical expected values, resulting in the high final residual of the solution (20-30%), is problematic for structure refinement. Different kinds of deviation from kinematic values affect intensity data, as residual dynamic effects, lack of geometrical correction, a need for better recording systems, more acurate background modelling, more elaborated intensity determination (e.g. 3-

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dimensional shape fitting of reflections). Therefore, the final refinement of the structure against the X-ray powder data (if the data quality allows) is still an important step. When compared to X-ray powder diffraction, single crystal electron diffraction is a young structural method still strongly under development. Nevertheless both approaches can be applied to the same system and benefit from data combined at different levels - reflection indexing, symmetry determination, structure solution and refinement.

References 1.

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14, 78.

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10. Rigamonti, R., 1936, Gazz. Chim. Ital., 66, 174. 11. Cowley, J.M., 1956, Acta Crystallogr.,

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12. Lipson, H. & Cochran, W., 1966, The Determination of Crystal Structures, and enlarged edition (Ithaca NY: Cornell University Press). 13. Dorset, D.L. & Hauptman, H.A., 1976, Ultramicroscopy, 14. Dorset, D.L., 1995, Structural Electron Crystallography

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15. Dorset, D.L., 1995, Proc. Natl. Acad. Sci., 92, (22), 10074. 16. Kühlbrandt, W „ Wang, D.N. & Fujiyoshi, Y „ 1997, Nature, 367, 614. 17. Unwin, P.N.T. & Henderson, R„ 1976, J. Mol. Biol., 94, 425. 18. Nicolopoulos, S., González-Calbet, J.M., Vallet-Regi, M., Corma, Α., Corell, C., Guil, J.M. & Pérez-Pariente, J., 1995, J. Am. Chem. Soc., 117, 8947.

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European Powder Diffraction Conference, EPDIC 12 19. Weirich, T.E., Ramlau, R„ Simon, Α., Hovmöller, S. & Zou, Χ., 1996, Nature, 382, 144. 20. Wagner, P., Terasaki, O., Ritsch, S., Nery, J.G., Zones, S.I., Davis, M.E. & Hiraga, K„ 1999, J. Phys. Chem., B103, 8245. 21. Pinsker, Z.G., 1953, Electron Diffraction (London: Butterworth). 22. Vainshtein, B.K., 1956, Soviet Physics - Crystallography, 1, 117. 23. Vainshtein, B.K., 1964, Structure analysis by electron diffraction (Oxford: Pergamon Press). 24. Zhukhlistov, A.P. & Zvyagin, B.B., 1998, Crystallogr. Rep., 43, 950. 25. Zhukhlistov, A.P., Avilov, A.S., Ferraris, D., Zvyagin, B.B. & Plotnikov, V.P., 1997, Crystallogr. Rep., 42, IIA. 26. Vincent, R. & Midgley, P.A., 1994, Ultramicroscopy, 53, 271. 27. Weirich, T.E., Portillo, J., Cox, G„ Hibst, H. & Nicolopoulos, S„ 2006, Ultramicroscopy, 106, 164. 28. Dorset, D.L., Gilmore, C.J., Jorda, J.L. & Nicolopoulos, S., 2007, Ultramicroscopy, 107, 462. 29. Sun, J., Bonneau, Ch., Cantin, Α., Corma, Α., Díaz-Cabañas, M., Moliner, M., Zhang, D„ Li, M. & Zou, X., 2009, Nature, 458, 1154. 30. Baerlocher, Ch., Gramm, F., Massüger, L., McCusker, L.B., He, Z., Hovmöller, S. & Zou, X., 2007, Science, 315, 1113. 31. Dorset, D.L., Roth, W.J. & Gilmore, C.J., 2005, Acta. Crystallogr. A, 61, 516. 32. Gemmi, M., Klein, H., Rageau, Α., Strobel, P. & Le Cras, F., 2010, Acta Crystallogr. B, 66, 60. 33. Voigt-Martin, I.G., Yan, D.H., Yakimansky, Α., Schollmeyer, D., Gilmore, C.J. & Bricogne, G., 1995, Acta Crystallogr. A, 51, 849. 34. Voigt-Martin, I.G., Zhang, Z.X., Kolb, U. & Gilmore, C., 1997, Ultramicroscopy, 68, 43. 35. Kolb, U„ Gorelik, T., Kübel, C„ Otten, M.T. & Hubert, D„ 2007, Ultramicroscopy, 107, 507. 36. Kolb, U„ Gorelik, T. & Otten, M.T., 2008, Ultramicroscopy, 108, 763. 37. Schömer, E„ Heil, U„ Schlitt, S„ Kolb, U„ Gorelik, T.E. & Mugnaioli, E„ 2009, ADT-3D - a software package for ADT data visualizing and processing, in cooperation with the Institute of Computer Science. Johannes Gutenberg-University, Mainz, http://www.adt.chemie.uni-mainz.de. 38. Williams, D.B. & Carter, C.B., 1996, Transmission Electron Microscopy (New York: Plenum Press). 39. Mugnaioli, E„ Gorelik, T. & Kolb, U„ 2009, Ultramicroscopy, 109, 758. 40. Kolb, U„ Gorelik, T. & Mugnaioli, E„ 2009, Mater. Res. Soc. Symp. Proc., 1184GG01-05.

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41. Denysenko, D., Grzywa, M., Tonigold, M., Schmitz, Β., Krkljus, I., Hirscher, M., Mugnaioli, E., Kolb, U., Hanns, J. & Volkmer, D., 2010, Chem. Eur. J.. accepted. 42. Rozhdestvenskaya, I., Mugnaioli, E., Czank, M., Depmeier, W., Kolb, U., Reinholdt, A. & Weirich, T., 2010, Minerai Mag., 74, 159. 43. Schade, Ch.S., Mugnaioli, E„ Gorelik, T., Kolb, U., Panthöfer, M. & Tremel, W„ 2010,J.A.C.S., 132,(28), 9881. 44. Burla, M.C., Caliandro, R., Camalli, M., Carrozzini, Β., Cascarano, G. L., De Caro, L., Giacovazzo, C., Polidori, G., Siliqi, D. & Spagna, R., 2007, J. Appi. Crystallogr.. 40, 609. 45. Sheldrick, G.M., 2008, Acta Crystallogr. A. 64, 112-122. 46. Lebedev, O.I., Millange, F., Serre, C„ Van Tendeloo, G. & Férey, G., 2005, Chem. Mater.. 17, 6525. 47. Chandra, D., Kastore, M.W. & Bhaumik, Α., 2008, Micropor. Mesopor. Mat.. 116, 204. 48. Jiang, D., Mallat, T., Krumeich, F. & Baiker, T.A., 2008, J. Catal.lSl,

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49. Turner, S., Lebedev, O.I., Schröder, F., Esken, D., Fischer, R.A. & Van Tendeloo, G„ 2008, Chem. Mater..20, 5622. 50. Schröder, F., Esken, D., Cokoja, M., van den Berg, M.W.E., Lebedev, O.I., Van Tendeloo, G., Walaszek, B., Buntkowsky, G., Limbach, H.-H., Chaudret, B. & Fischer, R.A., 2008,/. Am. Chem. Soc., 130, 6119. 51. Yang, S.J., Choi, J.Y., Chae, H.K., Clio, J.H., Nahm, K S . & Park, C.R., 2009, Chem. Mater., 21, 1893. 52. Andrusenko, I., Mugnaioli, E., Gorelik, T.E., Koll, D., Panthöfer, M., Tremel, W., Kolb, U., 2010, Acta Cryst. B, submitted. Acknowledgements. The authors thank Dr Tatiana E. Gorelik and Dr Andrew Stewart for fruitful discussions and the Deutsche Forschungsgemeinschaft for supporting the project in the Sonderforschungsbereich 625.

Ζ. Kristallogr. Proc. 1 (2011) 15-20/DOI 10.1524/zkpr.2011.0002 © by Oldenbourg Wissenschaftsverlag, München

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Differential Pair Distribution Function applied to Cei_xGdx02-x/2 system M. Allieta1, M. Bruneiii2'*, M. Coduri1, M. Scavini1, C. Ferrerò3 1

Dipartimento di Chimica Fisica ed Elettrochimica dell'Università di Milano, 20133 Milano, Italy 2 Institut Laue Langevin, 6 av. J. Horowitz, BP 156, 38042 Grenoble Cedex 9, France 3 European Synchrotron Radiation Facility, 6 av. J. Horowitz, BP 220, 38043 Grenoble Cedex 9, France Contact author; e-mail: [email protected] Keywords: Pair Distribution Function, anomalous dispersion; doped ceria Abstract. The Pair Distribution Function technique based upon X-ray diffraction data is a powerful tool to unveil disorder on the nanometric scale, which is however element insensitive. To overcome this problem, Differential Pair Distribution Functions (DPDF) can be obtained by exploiting the anomalous dispersion of X-rays near the absorption edge of a certain element. In this paper the DPDF method is briefly reviewed and applied to the case of gadolinium doped ceria electrolytes XRPD data have been collected at the Ce-K edge on the ID31 beamline of the European Synchrotron Radiation Facility (ESRF). The validity of this approach to extract chemical specific information is also briefly discussed.

Introduction Cei_xGdxC>2-x/2 (CGO) compounds have been intensively studied in the last years as conducting electrolytes for electrochemical cells [1], The ionic conductivity in CGO is due to oxygen diffusion via the vacancy mechanism. Actually, half oxygen vacancy is introduced into the structure when a Ce 4+ ion is substituted by a Gd , + one. At increasing Gd , + concentration .τ, the conductivity o¡(.t) reaches a maximum (at fixed T) and then decreases for higher .τ values [2], This behaviour has been attributed to the formation of defect clusters. Accordingly, EXAFS measurements have detected the presence of Gd , + -V 0 -Gd , + defect clusters in CGO materials [3], However, the EXAFS technique can be successfully employed to explore only the local structure of Ce 4+ and Gd , + ions, and cannot provide further information in case of more extended defects (e.g. on the nanometric scale). In contrast, the Pair Distribution Function (PDF) G(r), i.e. the real space analysis of diffraction data, is a unique tool to determine the local and medium range deviations with respect to an ideally periodic structure within the same X-ray powder diffraction (XRPD) experiment. However, unlike EXAFS, this technique is not element sensitive, therefore it can be difficult to discriminate the contributions of Ce 4+ and Gd , + ions since their ionic radii are similar.

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European Powder Diffraction Conference, EPDIC 12

This problem can be overcome by applying the anomalous X-ray diffraction (AXD) technique [4] to a total scattering method in order to obtain the so-called Differential Pair Distribution Function (DPDF) [5]. As a part of a wider study on the local and medium range structure in CGO compounds, we discuss the applicability of the DPDF technique to these systems. For this purpose the DPDF principle is reviewed and its basic equations are reported. Finally, the DPDF application to XRPD data collected close to the Ce K-edge is shown. The validity of this approach to obtain chemical specific information is briefly discussed.

Experimental A micro-crystalline CGO sample with Gd concentration χ =0.25 was prepared with the Pechini sol-gel method and fired at 900°C for 72 hours. XRPD patterns were collected at the ID31 beamline of the ESRF in the diffraction range 0). The values of Lhkl were 15% bigger t h a n ( l ) W A , but

similar for various hkl. The values of ß's obtained by (8) were used to construct the plot according to equation (5) for Mg0 60 o, shown in figure 4. A straight line through the origin was obtained; this meaning that no strains were present in the sample. A crystallite size Lhki of 10.0(5) nm was obtained from the slope of the straight line. As the calcination temperature of MgO increased from 600 to 1000° C, the crystallite size increased from 10 to 44 nm, while the specific surface area decreased from 50 to 16 m 2 /g.

.

200

/

c m 3

V , 220 - · — 222 422 - -

420

/ a )

γ I sin2 θ„ Figure 4. The application of equation (5) on five profiles ofMgOeoo: Lhkl = 10.0(5) nm.

Conclusion The combined truncation-background level error, for points where the profile falls to 1/100 of its maximum intensity, was calculated for several functions usually used in diffraction broadening analysis and in structure refinement in general. In line with well known qualitative facts in literature, the error is the biggest for C(f) (12.7 %), the smallest for Ο(ε) (2.7 %), while the errors for V{s) and Vp(¿) (8.6 %) are in between of those of C(f) and G(,î).This should be kept in mind in case of overlapping of diffraction line profiles due to large strains and small crystallites or due to a wide size distribution, all resulting in long profile tails. Precautions, which should be undertaken in diffraction analysis in order to minimize the combined error, were shown through a simple example of MgO, exhibiting only small crystallite size broadening.

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References 1. 2. 3. 4. 5. 6. 7.

Warren, B.E., 1969, X-ray Diffraction (Reading: Addison-Wesley). Ruland, W„ 1968, J. Appi. Crystallogr., 1, 90. Balzar, D. & Popovic, S„ 1996, J. Appi. Crystallogr., 29, 16. Langford, J.I., 1978, J. Appi. Crystallogr., 11, 10. Halder, N.C. & Wagner, C.N.J., 1966, Acta Crystallogr., 20, 312. Young, R.A., Gerdes, R.J. & Wilson, A.J.C., 1967, Acta Crystallogr., 22, 155. Delhez, R„ De Keijser, Th.H. & Mittemeijer, E.J., 1986, J. Appi. Crystallogr., 19, 459. 8. Delhez, R., De Keijser, Th.H. & Mittemeijer, E.J., 1980, in Accuracy in Powder Diffraction, edited by S. Block & C.R. Hubbard (Washington: NBS Spec. Pubi. 567), pp. 213-253. 9. Honkimäki, V. & Suortti, P., 1999, in Defect and Microstructure Analysis by Diffraction, edited by R.L. Snyder, J. Fiala & H.J. Bunge (Oxford: University Press), pp. 41-58. 10. Thomson, P., Cox, D.E. & Hastings, J.B., 1987, J. Appi. Crystallogr., 20, 79. 11. Langford, J.I., 1999, in Defect and Microstructure Analysis by Diffraction, edited by R.L. Snyder, J. Fiala & H.J. Bunge (Oxford: University Press), pp. 59-81.

Ζ. Kristallogr. Proc. 1 (2011) 63-68/DOI 10.1524/zkpr.2011.0009 © by Oldenbourg Wissenschaftsverlag, München

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Crystallite size evolution in hydrothermal formation of kaolinite P. Pardo1'*, F. Javier Huertas2, M. A. Kojdecki3, J. Bastida4 1 2 3 4

Interdisciplinary Nanoscience Center, Aarhus Universitet, Denmark Instituto Andaluz de Ciencias de la Tierra, CSIC-Universidad de Granada, Spain Wojskowa Akademia Techniczna, Warszawa, Poland Departamento de Geología, Universidad de Valencia, Spain Contact author; e-mail: [email protected]

Keywords: hydrothermal, kaolinite, cristallite size, growth mechanism Abstract. In the present work, kaolinite was hydrothermally precipitated from solutions of amorphous aluminosilicates, with different weight fractions of AI2O3, at two temperatures (200 and 250°C) and at different aging times. X-ray Diffraction (XRD) micro structural analysis was applied to the obtained materials. Crystallite size was studied applying the WarrenAverbach method to 001 and 002 kaolinite reflections using "XPowder" software, and the Voigt function method was also applied to the 001 reflection. Results from both methods were strongly correlated. For a given chemical composition, kaolinite crystallite size increases with temperature or aging time. The volume-weighted average crystallite sizes are in the range: 17.2-39.1 nm. Symmetry of crystallite size distributions (CSDs) also increases with time and temperature, due to the growth of part of the crystallites obtained in the first stage of formation. The study of the shape of CSDs allows the deduction of the crystallite growth mechanism.

1. Introduction and aim Synthesis of kaolinite at room temperature yields low amounts of poorly crystalline kaolinite due to its low precipitation rate [1], Better results are obtained under hydrothermal conditions from amorphous aluminosilicates in solutions with different pH at temperatures between 175 and 230°C [2], In neutral or acidic conditions boehmite crystallizes, whereas under alkaline conditions smectites and zeolites were intermediate phases in the formation of kaolinite [3-6], The influence of temperature and starting material composition on kaolinite morphology was pointed out; aluminosilicate gels produced platy crystals at relatively high temperatures (>200°C) with low or high Si/Al ratio. This work is focused in the microstructural evaluation of two sets of synthetic kaolinites produced under hydrothermal conditions at 200 or 250°C, from two starting materials with different Si/Al ratio and with different aging times. Under these conditions, differences in structural order were previously observed [1],

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2. Materials and methods Hydrothermal aging of amorphous precursors was carried out under different conditions and XRD micro structural analysis was applied to the resulting materials. 2.1 Hydrothermal synthesis Starting materials were prepared according to the procedure described in [4], Amorphous aluminosilicates were precipitated by co-hydrolysis of tetraethyl orthosilicate and aluminium tri-isopropoxide Merck reagents, dried at 60°C and ground. Gel compositions and aging conditions are resumed in table 1. Table 1. Starting gel compositions (% by weight), temperatures and aging times for synthesis ofkaolinites.

GEL

Si0 2

A1 2 0 3

CaO N a 2 0

LOI

A1 2 0 3 / Si0 2 +Al 2 0 3

hydrothermal

Aging time (hours)

T(°C) Si/Al a

b

c

d

BK21 56.250 26.040 0.010 0.010 17.670

0.214

1.840 200 250 12 24 48 96

BK34 43.880 37.750 0.000 0.020 18.240

0.336

0.990 200

96 191 361

2.2 XRD microstructural analysis XRD data were collected in a PANalytical X'Pert Pro system operating at 45 kV and 40 mA with an X'Celerator detector, CuK a radiation, Ni filter and 0.25° divergence slit; step size of 0.02 °2Θ and 1 s. counting time, for the whole pattern in the range 2-65 °2Θ. Data evaluation and phase identification was performed with Diffrac Plus Eva (Bruker) program, and only kaolinite was identified. CSDs were obtained applying the Warren-Averbach method [7] with XPowder software [8] to 001 and 002 experimental kaolinite peaks, using the corresponding instrumental profiles calculated from reflections of LaB 6 (NIST 660 a) standard. The Voigt function method of microstructural analysis [9] as presented in [10] was also applied fitting the abovementioned experimental and instrumental reflections to pseudo-Voigt functions with the Profile (Diffract - AT) software.

3. Results and discussion Figure 1 presents ranges of the obtained XRD patterns including the 001 and 002 kaolinite reflections. In figure 1 left, profile definition increases noticeably from a to d samples, with slight differences in broadening of 001 peaks; i.e. BK21_250_b (24 hours) shows higher order (see the higher definition of peaks in the 20-25° range) than BK21_200_b (191 hours), without producing significant differences in the crystallite size. Figure 1 right shows clear differences in structural order for kaolinites of BK21 and BK34 compositions, without clear differences in mean crystallite size for 001 reflections.

Ζ. Kristallogr. Proc. 1 (2011)

65

2-Theta - Scale

2-The1a - Scale

Figure 1. XRD patterns normalized at the same heightfor 001 kaolinite peaks for BK21 composition at 200°C and 250°C (left) and BK21 and BK34 compositions (right) with increasing aging time.

A ίΚ

m MS • ftSS •

PS* ^ftW .«»S VfB

893 I»

«i» ffi» liyruKdíy AUAw

Figure 2. CSDs (Warren-Averbach method) for samples BK 21 200 a, b &c (respectively, up to down, left side) and samples BK 34 200 a, b &c (respectively, up to down, right side).

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European Powder Diffraction Conference, EPDIC 12 «sä MG 6S5 WB CÜÍ «Β

a» (L«3

sœ «ai cej ) and /¿{ψ) about the deviation angles along the equatorial and axial directions, respectively. The skewness of the observed intensity distribution, defined by 8^{{Μ)%Μ)γ\ (6) is expressed by the following equations,

Ζ. Kristallogr. Proc. 1 (2011)

5 =

71

[ > t f ΔΩΔψ]" 2 (V])(Vj)a(3MR,Θ)Α(UR,θ) 2

[^«¿•ΔΩ'ΔΨ']"

ΔΩ Ξ

' {-Ι

2 2

(ν, ) [Λ (2μϋ,

Β' d ® } { - Ι

(7) 2

θ)]

Β' d ® ' J '

Further details of the theory about particle statistics for capillary transmission mode measurements will be described elsewhere [4],

3. Experimental 3.1 Sample preparation Three samples (#1, #2, #3) of quartz powder with similar average but different variance in particle size distribution were prepared by mixing fractions of pulverised Brazilian quartz crystal separated by a sedimentation method. The nominal Stokes diameters of the component fractions were 3-7, 8-12 and 18-22 μηι. The crystallite size distributions of the fractions were evaluated by analysis of scanning electron microscope (SEM) images, assuming approximately spherical particle shape and log-normal size distribution [3], The density function of the log-normal distribution is given by fiN(D)=~f^exΡ Λ/2πω

1 2ω\

In

ínV D_

(H)

The characteristic parameters, Dm and tu, for the optimised log-normal distributions of the component fractions are listed in table 1. The effective diameter Deff is calculated by Deff = (6v ef J%) lß from the effective particle volume veff, defined and calculated by

The degree of dispersion of the particle size distribution is measured by a parameter defined by

the calculated values of which are also listed in table 1. The mixing ratios, the effective particle diameters Deg a n d dispersion parameters Keff calculated from the component fractions of the three samples #1, #2, #3 for diffraction measurements are listed in table 2.

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Table 1. Parameters of size distribution evaluated by SEM image analysis of three fractions of quartz powder separated by a sedimentation method. Dm is the median diameter, ω the logarithmic standard deviation, Deff the effective diameter, and Keff is a dispersion parameter of the crystallite size distribution (see text).

Stokes diameter (μιη)

3-7

8 - 12

18-22

Dm (μιη)

4.831(6)

9.239(18)

21.03(2)

ω

0.2836(11)

0.2400(12)

0.1937(11)

7.0

12.0

28

2.06

1.68

1.40

Deff(\xm) Keff

Table 2. Mixing ratio, effective particle diameter and dispersion parameter of the controlled mixture (#1, #2, #3) of quartz powder. The weight fractions of the 3-7, 8-12, 18-22 μm source powder are shown as w(3-7), w(8-12), w(18-22), respectively. The diameters and absorption coefficients of the capillary specimens are also listed as 2R and μ.

Sample

#1

#2

#3

w(3-7) (%)

0

54.2

92.6

w(8-12) (%)

100

42.2

0

w(18-22) (%)

0

3.6

7.4

Deff(\xm)

12.0

11.3

11.3

K

1.68

6.67

11.3

0.575(1)

0.547(1)

0.508(1)

17.11(9)

17.34(8)

15.50(8)

eff

2R (mm) 1

μ (cm" )

The radiuses R and linear absorption coefficients μ of the Lindemann-glass capillary specimens filled with powder samples #1, #2, #3, were evaluated by analysing the transmission intensity profile on scanning the vertical positions of the capillary specimens crossing the attenuated direct beam, the cross section of which was restricted by a couple of slits with 0.05 mm in height and 2.5 mm in width. The intensity profile was modelled by the convolution of the transmission profile of a cylinder and a rectangular slit function. The values of parameters optimised to fit the observed profiles are also listed in table 2. The filling factor of each powder specimen is calculated b y / = μ / μ0 from the observed absorption coefficient μ and the bulk absorption coefficient μ0 calculated from the chemical composition.

Ζ. Kristallogr. Proc. 1 (2011)

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3.2 Capillary spinner-scan measurement The mechanism and driver software for the capillary rotating attachment of a high-resolution synchrotron powder diffractometer on the bending-magnet beamline BL-4B2 at the Photon Factory in Tsukuba [5] was temporarily modified to enable stepwise rotation at the interval of 0.072° and also synchronous acquisition of diffracted beam intensity for 0.5 s per each step. The analyser/detector angles were fixed at the diffraction peak position of the quartz 101/011-reflection during the measurement. Five thousand diffraction intensity data were collected for each of the capillary specimens.

4. Results The observed spinner-scan intensity profiles of the 101/011-reflection of the quartz powder capillary specimens #1, #2, and #3 are shown in figure 1. Difference in distributions of the observed intensities can certainly be detected even in the raw intensity profiles. As has been expected, the collection of crystallites with broader size distribution clearly shows more skewed distribution in diffraction intensities.

60000 2·

I

4000020000 -

0

5 tiDOOO

% g

(il) Sample #1

(b) Sample #2

40000 —

S·

I

20000

1

0

Io,

40000

1

0

Τ (c) Sample #3

Λ3 Λ « 20000 I 90

180

270

360

Spinner angle Π Figure 1. Spinner-scan

profiles of 101/011-reflection

of quartz powder samples #1, #2 and #3.

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Table 3. Characteristics of spinner -scan data. The effective particle diameter D¡ffof sample #1 is treated as a fixed parameter. Sample

#1

#2

#3

(I)

28370(50)

25430(42)

22380(42)

M)

1.29(4) χ 107

8.7(4) xlO 6

8.8(5) χ 106

» . ^ c y / M )

62(3)

74(5)

56(6)

H(A/)3}/HT

0.56(9)

1.22(19)

2.9(5)

Deff{\xm)

12.0(fix)

11.0(7)

11.1(1.2)

2.8(5)

6.7(1.0)

14(2)

Keff

The statistical properties of the observed spinner-scan intensity data are listed in table 3. The effective crystallite diameter of sample #1, D e ff= 12.0 μηι, is treated as the reference value to calibrate an instrumental constantAQ. The value of ΔΩ is estimated at 0.061(2)°, assuming Neff = 62(3), Deff= 12.0 μηι, meff= 10.272, μ = 17.34 cm"1, μ0 = 48.49 cm"1, 2R = 0.575(1) mm, L = 10 mm, 2Θ = 20.6255°, [A(jiR, 0)f!A^R, θ) = 0.956, and ΔΨ = 1.5°. The values of crystallite diameter Deff = 11.0(7) and 11.1(1.2) μηι estimatd for samples #2 and #3 are coincided with the calculated values 11.3 μηι listed in table 2 within the estimated experimental errors. The dispersion parameter Keg listed in table 3 are also evaluated from the effective number of diffracting crystallites Λ ^ and the skewness S of the intensity distributions. The values of Keff in table 3 are also well corresponded with the values listed in table 2. It is suggested that the difference in the values of for the sample #1 can partly be caused by the neglect of anisotropic shape of the crystallites in the SEM image analysis. It is concluded that this method can show statistical trends in well controlled samples.

References 1.

Alexander, L„ Klug, H. P. & Kummer E., 1948, J. Appi. Phys., 19, 742.

2.

De Wolff, P.M., 1958, Appi. Sci. Res., 7, 102.

3.

Ida, T., Goto, T. & Hibino, H., 2009, J. Appi. Crystallogr., 42, 597.

4.

Ida, T., in preparation.

5.

Toraya, H., Hibino, H. & Ohsumi, K., 1996, J. Synchrotron Rad., 3, 75.

Acknowledgements. This work has been performed under the approval of the Photon Factory Program Advisory Committee (Proposal No. 2009G131).

Ζ. Kristallogr. Proc. 1 (2011) 75-80/DOI 10.1524/zkpr.2011.0011 © by Oldenbourg Wissenschaftsverlag, München

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High energy milling of C112O powders D. Dodoo-Arhin, G. Vettori, M. D'Incau, M. Leoni*, P. Scardi University of Trento, Department of Material Engineering, Trento, Italy * Contact author; e-mail: [email protected] Keywords: high energy milling, Whole Powder Pattern Modelling Abstract. Whole Powder Pattern Modelling was employed to investigate the microstructure changes in Cu 2 0 powders milled in a vibrating cup mill. The reduction in the average size of coherently scattering domains - and simultaneous narrowing of the size distribution - occurs in the first minutes. An asymptotic limit of ca. 10 nm is obtained. The reduction in size is obtained at the expenses of introducing a massive quantity of dislocations in the system, reaching a limit of ca. 4*10"16 m"2. A proper nanocrystalline microstructure can be obtained with an effective milling time of ca. 20 min.

Introduction Nano-sized particles keep attracting the attention of the scientific community because of their peculiar properties arising both from the high surface/volume ratio and from the possible quantum confinement effects. Several methods have been proposed for the synthesis of nanostructured materials. Among them, high energy milling has an undoubted technological importance as it allows producing large quantities of powder in short time and at competitive prices [1]. The microstructure of the nanostructured materials resulting from milling can be conveniently investigated by microscopy and by X-ray diffraction (XRD). XRD of nanocrystalline powders guarantees a better statistical significance of the result, as the information is collected on a much larger quantity of grains (millions versus tens analyzed under the microscope). Line Profile Analysis (LPA) is the group of techniques employed for microstructure analysis from diffraction data, as they are based on the analysis of the broadening of the diffraction peaks [2], It should be recalled that the broadening of the X-ray diffraction line profiles is determined by instrumental features but also by the small size of the coherently scattering domains (aka crystallites) and by lattice distortions (dislocations, stacking faults, etc). The most widespread techniques for microstructure analysis based on XRD data are certainly the Scherrer formula [3] and the Williamson-Hall plot [4], that are quite often used without care on the underlying theory or hypotheses, and imposing an arbitrary shape to the peaks. The state of the art alternative is offered by full pattern methods, like, e.g., the Whole Powder Pattern Modelling (WPPM) [5], that provides for an interpretation of the whole diffraction pattern in terms of physical models for the broadening sources. Cuprite Cu 2 0 is a wide bandgap (2.0-2.2eV) p-type semiconductor that finds important technological applications e.g. in solar cells, gas sensors chemical refinement catalysis and

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water splitting [6-9]. The possibility of producing nanostructured Cu 2 0 could led to an increased activity of the material [10], We report here the successful reduction in size of a commercial cuprite powder and its micro structural analysis via XRD and microscopy.

Methods Commercial Cu 2 0 (99.99+%, Aldrich) was employed as starting material. A high contamination from Cu and CuO was found. The powder was thus subjected to thermal oxidation at 850 °C and 9.5 mbar for 1 h and subsequently stored in sealed containers under Ar atmosphere. The heat treated powder was milled in a Fristch Pulverisette 9 Vibromill (-20°C) using a customised ferritic steel grinding set [11], A cup of 120ml (nominal volume) and a 662.20 g crushing cylinder were used. Approximately 3.0 g of Cu 2 0 were milled with 4 %wt ethanol for 1, 5, 7.5, 10, 20 and 40 min, respectively (specimens named P9-1 through P9-40). The given time represents the actual milling time: the process time, however was much longer. In fact, to limit possible effects of heating - leading e.g. to recrystallization - milling was done in batch cycles consisting of a 1 minute milling followed by 5 minutes pause. X-ray diffraction data were collected on the ID31 high-resolution powder diffraction beamline at the European Synchrotron Radiation Facility (ESRF) in Grenoble - France. The information collected every 15ms from the nine detectors installed on the ID31 goniometer, was suitably mixed and re-binned to provide diffraction patterns in the 2.0° - 65.0° 2Θ range with an angular increment of 0.005°. A wavelength of 0.3999284 Â was chosen, calibrated with the NIST SRM 640b Si standard. In order to obtain the best pattern quality (no specimen holder effects), the powder was mounted free standing in a 5x5 mm silicon frame (500 μηι thickness) and measured in Θ/2Θ scanning mode (parallel-beam transmission geometry). The diffraction pattern of the NIST SRM 660a LaB 6 line profile standard was also collected under the same experimental conditions, as to characterize the instrumental effects on the diffraction line profiles. A set of 20 evenly spaced peaks was simultaneously fitted with symmetrical pseudo-Voigt functions whose width and shape was constrained according to the Caglioti et al. formulae [12], The PM2K software [13] was used. Qualitative phase analysis was done using the PANAlytical X'pert Highscore software and the ICDD PDF-4+ database. Quantification was then obtained via the Rietveld method [14] using the TOPAS software [15].The WPPM method [5] implemented in PM2K [13] was employed for the microstructure analysis. An FEI XL30 Environmental Scanning Electron Microscope (ESEM) was employed for microscopy analysis. Specimens were metalized and analyzed at 30 kV, 93 μΑ and 0.7 Torr (water pressure). HRTEM was carried out on a JEOL 2100 URP microscope equipped with a Gatan "Ultrascan" 2k χ 2k CCD camera operated at 200 kV with a point and line resolution of 0.19 nm and 0.14 nm respectively, scaled with Au(100).

Results and discussion Quantitative Phase Analysis Pattern matching reveals that only Cu 2 0, CuO (tenorite) and Cu are present in all powders in different proportions: quantification done via Rietveld method is proposed in Table 1. As the starting (heat treated) powder is pure Cu 2 0 (within the limits of detection of XRD), the près-

Ζ. Kristallogr. Proc. 1 (2011)

77

enee of the extra phases, and in particular of CuO, has to be attributed to the milling process. In all cases the Rietveld fit is good but not perfect: there is still a certain degree of anisotropic broadening not completely taken into account by our isotropic model, but this should be within the errors presented in Table 1. Table 1. Quantitative Phase Analysis results obtained from synchrotron data. Specimen

Milling time (min)

wt% Cu 2 0

wt% CuO

wt% Cu

P9-1 P9-5 P9-7.5 P9-10 P9-20 P9-40

1.0 5.0 7.5 10.0 20.0 40.0

93.5(1) 89.4(3) 90.2(1) 92.5(1) 88.0(1) 86.7(1)

3.9(1) 6.9(5) 5.1(1) 1.7(5) 6.0(3) 6.5(1)

2.6(9) 3.7(4) 4.7(2) 5.8(8) 6.0(4) 6.8(3)

It can be seen a clear increase in the content of Cu with the milling time; it cannot be excluded that this phase is actually a mixed Cu/Fe phase. Contamination from the mill is certainly possible and some deposition of a metallic copper film has been observed on the surface of the cup and cylinder. Part of the metallic copper can come from the cuprite - tenorite - copper transformation. Assuming that the transformation occurs in the absence of oxygen, we can see that up to 7wt% Cu could be produced if all present CuO comes from Cu 2 0. Microstructure analysis via WPPM Synchrotron radiation X-ray diffraction data were analysed by means of the WPPM algorithm assuming the presence of a lognormal distribution of spherical domains. Dislocations were identified as the main cause of strain broadening. Table 2 summarises the main results of the WPPM analysis. Table 2. WPPM results: unit cell parameter a0, average domain size , lognormal variance σ, dislocation density p, effective outer cut-off radius Re and Wilkens' parameter W = Re pI/2. Specimen P9-1 P9-5 P9-7.5 P9-10 P9-20 P9-40

Milling Time (min) 1.0 5.0 7.5 10.0 20.0 40.0

a o (nm)

(nm)

4.2673(1) 4.2682(6) 4.2709(5) 4.2744(1) 4.2736(2) 4.2736(2)

45(1) 20 (1) 16(1) 11.9(9) 9.3(4) 9.8(5)

σ (nm)

67(7) 42(13) 21 (3) 10(1) 11(1)

Ρ (IO15 m"2)

Re (nm)

Wilkens parameter

GoF

0.3(2) 7(1) 21 (1) 30(1) 39(1) 42(1)

11(1) 9.0(6) 5.0(2) 3.0(1) 2.3(1) 2.4(1)

0.1(1) 0.74(1) 0.72(1) 0.52(2) 0.45(2) 0.48(3)

2.23 1.26 1.20 1.24 1.18 1.10

All specimens but P9-1 gave an excellent fit, as shown e.g. in Figure 1 for the P9-40 specimen. The reason for the poor modelling of P9-1 has to be found in the high grain size inhomogeneity, which in turn is caused by a too short milling time; larger grains (large scattering power) tend to hide the smaller ones (smaller volume, i.e. smaller overall scattering power), thereby leading to incorrect grain statistics evaluation when a wide distribution is present.

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As expected, milling causes a reduction in the average size of the coherently diffracting domains and a corresponding increase in the quantity of defects (dislocation density).

2θ (degrees) Figure 1. WPPM of the synchrotron X-ray diffraction data for the P9-40 specimen. Data (circle), model (line) and difference between the two (residual, line below). The inset shows the data in log scale to evidence the modelling quality of the tails.

It can be observed a steep variation of those parameters for short milling times, with a levelling (saturation) of the values starting at 20 min effective milling time. It is plausible that the observed phenomenon for shorter milling times corresponds to the formation of dislocation cells [16] as it happens during conventional plastic deformation. The corresponding increase in the cell parameter suggests a pumping of excess volume inside the structure, whereas the levelling after 20 min milling is a clear indicator that a proper nanostructure has been reached. More informative than the mere average size is certainly the size distribution, shown in figure 3 for the whole set of analysed powder.

D (nm)

Figure 2. Domain size distribution obtained from WPPM for the specimens analysed in this work. Curves for P9-5 (triangles), P9-7.5 (circles), P9-10 (dots), P9-20 (squares), and P9-40 (diamonds).

It can be observed a progressive narrowing of the distribution, the variation again saturating

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at 20 min. It is also interesting to note the trend of Wilkens parameter W= Re p" 2 , related to the interaction and dipole character of dislocations. The higher the W, the weaker the dipole character and the screening of the displacement field of the dislocations. Lower W values (below unity) indicate enhanced interactions of a high density of dislocations at the grain boundaries leading to nanocrystallinity conditions [17]. In our case, W saturates for P9-20, further validating the hypothesis that after 20 min milling time the nanostructure is reached in the powder. Scanning and transition electron microscopy A clear evolution of the powder morphology can be observed by ESEM. The initial powder is characterized by the presence of sharp fragments of various shapes and sizes. After a short milling time (e.g., 1 min) it can be clearly observed the coexistence of fine and coarse particles (figure 3a).

Figure 3. (a) ESEM micrograph for the P9-1 powder and (b) TEM micrograph for the P9-5 specimen.

This can explain the impossibility of getting a proper fit of the XRD data for the P9-1 powder. It is possible that some of the large particles are monocrystalline or composed of a small number of very large domains. Already after 5 minutes of milling, the sharp edges disappear and the small particles start agglomerating over the larger ones. For increasing milling time, a progressive homogenisation of the size and shape of the small particles is observed, with the larger aggregates progressively being formed by large sets of small particles. All morphological observations are compatible with the XRD results. A direct comparison is however not possible, and in any case the observed particle size of the order of 100 nm or more is far larger than the domain size estimated via XRD. This is a clear indication that most of the particles are made of several domains: the milling process contributes to reduce the size of the particles, but also the domain size, with possible introduction of internal grain boundaries. A possible validation for the XRD results comes from the TEM investigation even if the high density of defects and the extensive agglomeration of domains hinders a possible estimation of a size distribution from TEM. HRTEM, on the other hand, allows observing the presence of defects, quantitatively measured by WPPM of the XRD data. Figure 3 b shows, for instance, a HRTEM micrograph of the P9-5 specimen: distortion of the lattice planes as well as traces of the presence of dislocations (causing local deformation of the lattice), and possible presence of small angle grain boundary, are evident. All those defects can be caused

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by the pileup of a large number of dislocations, and this can justify the large value of the dislocation density observed for this material. As an Energy Dispersive X-ray Spectroscopy gives unphysical results here (the absolute determination of oxygen in heterogeneous powders like those proposed here is really challenging), it is not possible to identify where CuO and Cu (possibly contaminated by Fe from the milling set) are located.

References 1.

Suryanarayana, C., 2001, Prog. Mater. Sci., 46, 1.

2.

Mittemeijer, E.J & Scardi, P. (Editors), 2004, Diffraction Analysis of the Microstructure of Materials (Berlin: Springer).

3.

Scherrer, P., 1918, Math.-Phys., Kl., 2, 98.

4.

Williamson, G.K. & Hall, W.H., 1953, Acta Metall., 1, 22.

5.

Scardi, P. & Leoni, M., 2002, Acta Crystallogr., Sect. A, 58, 190-200.

6.

Mittiga, Α., Salza, E., Sarto, F., Tucci, M. & Vasanthi, R., 2006, Appi. Phys. Lett., 88, 163502.

7.

Shishiyanu, S.T., Shishiyanu, T.S. & Lupan, O.I., 2006, Sensors & Actuators B, 113, 468.

8.

Hara, M., Kondo, T., Komoda, M., Ikeda, S., Shinohara K., Tanaka, Α., Kondo, J.N. & Domen, K„ 1998, Chem. Commun., 357-358.

9.

De Jongh, P.E., Vanmaekelbergh, D. & Kelly, J.J., 1999, Chem. Commun., 1069.

10. Rothenberger, G., Moser, J., Grätzel, M., Serpone, Ν. & Sharma, D.K., 1985, J. Am. Chem. Soc., 107, (26), 8054. 11. D'Incau, M., 2008, High Energy Milling in Nanomaterials Technologies: Process modelling and optimization, PhD thesis. Università degli Studi di Trento - Italy. 12. Caglioti, G., Paoletti, A. &Ricci, F.P., 1958, Nucl. Instr. Meth., 3, 223. 13. Leoni, M., Coniente, T. & Scardi P., 2006, Ζ. Kristallogr. Suppl, 23, 249. 14. Young, R. Α., (Editor), 1993, The Rietveld method, International Union of Crystallography (Oxford University Press). 15. Bruker AXS. TOPAS Users Manual. 2008 (Karlsruhe, Germany). 16. Xu, Y., Liu, Ζ. G., Umemoto, M. & Tsuchiya, Κ., 2002, Met. Mater. Trans. A, 33, 2195. 17. Wilkens, M., 1970, Phys. Status Solidi (A), 2, 359. Acknowledgements. Authors wish to acknowledge the European Synchrotron Radiation Facility (ESRF) - Grenoble (France) for the provision of beamtime on the ID31 beamline. Dr A. Fitch is acknowledged for the support on the beamline. Prof. E. Gamier (Univ. Poitiers France) is acknowledged for the TEM analyses.

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Defects in nanocrystalline ceria xerogel M . Müller 1 ' 2 '*, M . Leoni 1 , R. D i Maggio 1 , P. Scardi 1 1 University of Trento, Department of Materials Engineering and Industriai Technologies, via Mesiano 77, 38123 Trento, Italy 2 Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany Contact author; e-mail: [email protected]

Keywords: nanocrystalline materials, ceria, line profile analysis, WPPM Abstract. Nanocrystalline ceria was produced via sol-gel from Ce alkoxides with and without the addition of water and a chelating agent (acetylacetone). Microstructure analysis of the resulting powder was conducted on laboratory and synchrotron radiation data using the Whole Powder Pattern Modelling algorithm. It is shown that the synthesis with water leads to smaller and more defective particles and that aggregation of the crystalline domains occurs at temperatures as low as 80°C. The route to the formation of the ceria nanograms is explained in terms of balance of competing condensation reactions.

Introduction Most properties of nanocrystalline systems are related to the shape and size distribution of the grains. Those, in turn, are strongly dependent on the preparation method and on kinetic conditions of the growth process. Among the analytical techniques available for the study of the microstructure, X-ray diffraction Line Profile Analysis is ideally suited in the size interval ranging from a few hundreds down to about one nanometre [1, 2], In the recent years, Whole Powder Pattern Modelling (WPPM [3]) has been proposed as a robust and flexible technique to deal with nanodomains and a variety of lattice defects simultaneously, thus allowing an assessment of the main features of a nanocrystalline material. This method is based on a physical model for the microstructure of a material, without using arbitrary profile functions for fitting the data; parameters used in WPPM include crystallite shape and size distribution, as well as density of various defects, like dislocations and stacking faults, frequently observed in real materials [1-3], The present study reports recent WPPM results on nanocrystalline cerium oxide produced by sol-gel under different conditions. In particular, comparison is made between a traditional preparation with a chelating agent (acetylacetone) [4, 5] and a simpler preparation involving the use of the pure alkoxide eventually added with water. Effects on the resulting ceria nanocrystals are observed and discussed and a possible mechanism is proposed for the formation of the nanoparticles, based on the balance of the reactions involved in the synthesis.

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Experimental For all preparations, a starting solution of 5 g of Ce(IV)isopropoxide (Gelest AB CR, 80% cerium isopropoxide, 20% isopropyl alcohol) in 20 ml of isopropyl alcohol (2-propanol Carlo Erba RPH 99.5%, H 2 0 < 0.5%) was employed. A first specimen (named CE) was produced from the pure solution. The two other specimens were obtained by adding to the starting solution, respectively, 2.41 ml of distilled water (specimen CEW) or 0.67 ml of acetylacetone (2,4-pentanedione, Carlo Erba RPE 99%, H 2 0 ~ 0.2%) (specimen CEacac). All solutions were boiled under reflux for 24 h. In order to produce a xerogel (dry gel) powder, the specimens were left in a rotary evaporator at 40°C for 2 h (to extract the solvent) and subsequently dried in air at 80°C for 16 h. X-ray powder diffraction data were collected on a laboratory Rigaku PMG-VH horizontal diffractometer with Cu radiation (40 kV, 30 mA). The setup of the machine includes narrow Soller slits (2° both on the primary and diffracted side) and a secondary monochromator that guarantee a narrow, clean and symmetrical instrumental profile down to ca. 15° 2Θ. Patterns were collected in the 18 - 100° 2Θ range with a step of 0.05° and a counting time of 30 s per point. Synchrotron radiation powder diffraction data were recorded on the MCX beamline at the ELETTRA synchrotron (Trieste, Italy) using a wavelength of 0.09991 nm calibrated with the NIST SRM 640a silicon standard. A fiat-plate setup and a secondary monochromator were employed. Data were collected in the 8 - 92° 2Θ range with a step of 0.05° and a total counting time of 20 s per point. The pattern of the NIST SRM 660a (LaB 6 ) standard was collected on both instruments in order to characterise the instrumental contribution to the line profile.

Results and discussion All recorded data were analysed by Whole Powder Pattern Modelling [3] using the PM2K software [6], Particles were assumed being spherical, with a lognormal distribution of diameters. Lattice distortions were effectively considered under the form of dislocations on the primary !/2{111} slip system of ceria; the dislocation contrast factor was calculated using the procedure proposed in [7]. For each specimen, the same set of parameters was simultaneously refined on both laboratory and synchrotron patterns. Even if the quality of the synchrotron data is not excellent, the extra information it brings (in terms of larger extension in reciprocal space) allows a stabilisation of the minimisation algorithm and a reduction of the errors on the estimation of the anisotropic effects (dislocation density). The results of the modelling are shown in figure 1, whereas key parameters are reported in table 1. The quality of the modelling is rather good for all specimens, as already observed in ceria [4, 5], Differences in the refined parameters are however clearly present in table 1. A large dispersion in the mean domain sizes exists: better information is however provided by the actual domain size distribution shown in figure 2 and compared with the distribution of a ceria xerogel similar to CEacac and analysed in [8] (CEOLD specimen). Independently of the preparation, all distributions are wider than that of CEOLD; the differences may be due to the fact that CEOLD was just heat treated in the vacuum evaporator and did not undergo any subsequent heat treatment. The bland treatment at 80°C applied to the powders analysed

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here is thus sufficient to start aggregation of the d o m a i n s a n d to w i d e n the distribution.

Figure 1. WPPM modelling of laboratory (left column) and synchrotron (right column) powder diffraction patterns. Data refer to specimens CE (a)-(b), CEW (c)-(d) and CEacac (e). Raw data (dots), modelled pattern (line) and difference cim>e (line below) are shown in each plot.

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Table 1. WPPM results: lattice parameter aa mean domain size , variance of the lognormal distribution, dislocation density p, effective outer cutoff radius Re. Comparison with literature data (taken from [8]) is proposed. Errors are given in parentheses, referred to the last significant digit.

Specimen

CEOLD [8]

CEacac

CE

CEW

a0

(nm)

0.543809(8)

0.543296(8)

0.543313(7)

0.54296(9)

(nm)

2.28(2)

2.19(3)

2.34(2)

1.78(3)

Variance (nm)

0.22(1)

0.33(1)

0.43(1)

0.40(2)

ρ

(IO16 m"2)

0.1(1)

1.6(5)

1.4(2)

3.0(6)

Re

(nm)

4.3(6)

2.5(4)

2.5(5)

2.7(4)

D (nm) Figure 2. Comparison of the domain size distributions CEW (dash), CEacac (dot) and CEOLD (dash-dot).

obtained

by PM2K for specimens

CE (line),

The wide distributions of the specimens are also compatible with the results relative to the defects present in the powders. We observe in fact much larger strains (in the form of dislocation density) than those previously observed for CEOLD. As pointed out in [5], aggregation of domains in a xerogel may occur by small movements of the domains, with no intervention of diffusion: local steps on the surface may therefore be trapped in the larger grain under the form of edge dislocation [5], The quantity of dislocations in the CEacac specimen is compatible with the literature data on heat treated xerogels [4]; in fact as shown in figure 3a (presenting a comparison between new and literature data), the CEacac specimen follows on the trend line of a set of analogous specimens heat treated at increasing temperature [4], The variance of the distribution, apparently quite small, well correlates with the one observed on literature data at increasing temperature (see figure 3b).

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(a)

(b)

1o ofH ¿' i 0.4

Temperature (°C)

Temperature (°C)

Figure 3. Trend of (a) dislocation density and (b) variance of the distribution versus heat temperature. Data at 80°C from this work; data at increasing temperature taken from [4],

treatment

(nm)

Figtre

4. Stoichiometiy

of CeO2 and variation in lattice constant with respect to 0.54 nm [9],

According to model 1 in [9], the cell parameter data (figure 4) suggest that peroxide 20 2 2 " species are present on the surface of the nanoparticles: the condition is certainly met here as we work in low acidity conditions and resonant oxygen bonds are expected on the surface of the particles (coming either from coupled acac oxygens or vicinal hydroxyls). The resulting estimated stoichiometiy of the powder is CeOi.92, not far from the ideal 1:2 ratio. Remarkable in figure 2 is the behaviour of CEW, yielding smaller crystalline domains with respect to the other specimens. In isopropyl alcohol, Ce(IV)isopropoxide (CeiOPr 1 ^) forms mainly (CeiiOPr'Js^HOPr 1 ) dimers [10], with trimers and monomers also being possible. In general, hydrolysis goes to almost completion when sufficient water is added, but it is partial when only moisture of air is present. The structure and the size of condensed products depend on the relative rates of the three condensation reactions: M-OR + M-OH M - O - M + R-OH M-OH + M-OH M - O - M + H-OH M-OX + M-(OH 2 ) M-0(X)-M + H20

Alcolation Oxolation Olation

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When hydrolysis is promoted (e.g. by the addition of water), oxolation is competitive with alcolation and highly condensed products are favoured: oxo-hydroxides form by aggregation of much smaller oligomeric building blocks, wrapped in OH groups, which act as spacers. Further condensation can take place when materials are treated thermally at higher temperature. When hydrolysis is carefully reduced (only moisture of air present), the most likely condensation reaction between partially hydrolysed and coordinatively saturated ceria precursors seems to be alcolation, which releases isopropanol and results in oxo-alkoxide products. Cerium acquires its maximum coordination number also via olation, which is even favoured because of its size. The oxo-alkoxide products are still able to condense again, resulting in more extended and less branched polymers. A smaller particle size is therefore expected if a larger quantity of water is present.

Conclusions A set of ceria specimens was produced via sol-gel from cerium isopropoxide with and without the addition of water and of acetylacetone as chelating agent. X-ray line profile analysis evidenced the nanocrystalline nature of the domains and the presence of a large quantity of defects. The bland heat treatment applied to the present specimens to guarantee the removal of all solvent is sufficient to start agglomeration and thus incorporation of defects in the growing domains. The addition of water in place of the chelant favors the formation of smaller domains. Further work is in progress to validate the results using complementary techniques.

References 1.

Mittemeijer, E.J. & Scardi, P. (Editors), 2004, Diffraction Analysis of the Microstructure of Materials (Berlin: Springer).

2.

Warren, B.E., 1990, X-ray Diffraction (New York: Dover).

3.

Scardi, P. & Leoni, M., 2002, Acta Crystallogr. A, 58, 190.

4.

Leoni, M., Di Maggio, R., Polizzi, S. & Scardi, P., 2004, J. Am. Ceram. Soc., 87, 1133.

5.

Scardi, P., Leoni, M„ Müller, M. & Di Maggio, R„ 2010, Mater. Sci. Eng. Α., DOI: 10.1016/j.msea.2010.03.077.

6.

Leoni, M., Coniente, T. & Scardi, P., 2006, Ζ. Kristallogr. Suppl., 23, 249.

7.

Martinez-Garcia, J., Leoni, M. & Scardi P., 2009, Acta Crystallogr. A, 65, 109.

8.

Scardi, P. & Leoni, M., 2006, ECS Transactions, 3, (9) 125.

9.

Tsunekawa, S., Sahara, R., Kawazoe, Y. & Ishikawa, K., 1999, Appi. Surf. Sci., 152,53.

10. Ribot, F., Tolédano, P. & Sanchez, C„ 1991, Chem. Mater., 3, 759. Acknowledgements. We acknowledge Sincrotrone Trieste s.c.p.a (ELETTRA synchrotron) for the provision of beamtime on the MCX beamline. We acknowledge also Dr M. D'Incau, Mr K. Beyerlein and Mr L. Gelisio for help in data collection.

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Determination of crystallite size distribution histogram in nanocrystalline anatase powders by XRD Z. Matëj1'*, L. Matëjovà2, F. Novotny3, J. Drahokoupil4, R. Kuzel1 1

Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, 121 16 Praha 2, Czech Republic 2 Department of Catalysis and Reaction Engineering, Institute of Chemical Process Fundamentals, Academy of Sciences, Rozvojová 135, 165 02 Praha 6, Czech Republic 3 Department of Physical Electronics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Brehová 7, 115 19 Praha 1, Czech Republic 4 Institute of Physics, Academy of Sciences, Na Slovance 2, 182 21 Praha 8, Czech Republic Contact author; e-mail: [email protected] Keywords: titanium dioxide, crystallite size, crystallite size distribution, sol-gel method Abstract. The whole powder pattern modelling (WPPM) method developed by Scardi & Leoni (2002) is used for determination of a crystallite size distribution in Ti0 2 nanocrystalline powders. The distribution is represented by a histogram. The histogram frequencies are refined from X-ray diffraction (XRD) data. The method is slightly modified by introduction of the distribution régularisation. It is applied on (i) two reference Ti0 2 samples synthesized by a sol-gel process at different temperatures (ii) and on a series of well defined mixtures of these reference samples. The refined size distributions of both reference samples can be well approximated by a log-normal distribution. The volume fractions of the reference samples in the mixtures are derived from the determined crystallite size histograms. The difficulties with an uncertainty of the distribution shape in the case of small volume fractions of small crystallites at the presence of majority of large crystallites are discussed.

1. Introduction The WPPM method (Scardi & Leoni [1]) and the methods based on the Debye formula [2] belong to the most recently developed approaches of the diffraction line profile analysis (LPA). They are based on modelling of whole diffraction patterns in reciprocal and/or real spaces by using of physically relevant models. They profit from explicit meaning of the model parameters and straightforward interpretation of their results. The WPPM method is computationally less demanding than the latter procedure and it was demonstrated to be a suitable LPA tool for the determination of the crystallites size. Many of its extensive appli-

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cations to ceramic and mineral materials and fine grained metals can be found in the literature (e.g. Ce0 2 [3-6], Ti0 2 [7,8], highly deformed metals [1,9]). Usually some analytical functions such as a log-normal distribution [10] are utilized for the description of the crystallite size distribution. Leoni & Scardi introduced another method in [3], An electron microscopy (EM) histogram like representation of the crystallite size distribution was applied and the histogram frequencies were refined from XRD data [3-6], In this work, the WPPM method with the size distribution histogram model [3] is employed for the analysis of nanocrystalline Ti0 2 powders. The method is slightly modified; it is applied to the well defined samples; and pros and cons of the method are examined.

2. Experimental 2.1 Samples preparation Ti0 2 nanocrystallites were prepared by calcination of titania organogels synthesized by solgel process controlled in reverse micellar environment of nonionic surfactant Triton X-100. The molar ratio of chemical components in the liquid mixture - cyclohexane: Triton X-100: water: Titanium (IV) isopropoxide - was 11: 1: 1: 1. After 24 hours ageing on the air the sol converted into the rigid organogel. The organogel was calcined in a muffle furnace 003LP-P Svoboda at (i) 400°C (4 hours, l°C/min) and (ii) 550°C (12 hours, 2°C/min). 2.2 XRD and EM measurements Powder XRD patterns were measured in the Bragg-Brentano geometry with PANalytical X'Pert MPD diffractometer, Οίκα radiation, variable slits and PSD. The sample for EM imaging was prepared by dispersing the nano-powder in ethanol solution by sonication; and by subsequent dropcasting the solution onto the carbon coated TEM grid. EM images were acquired by JEOL JSM-7500f FE-SEM (field emission scanning electron microscope) in the bright field STEM mode.

3. Model description The WPPM [1] method is based on a Rietveld-like fitting of the whole diffraction pattern with a special care to modelling of diffraction lines shapes. The broadening effects due to the small crystallite size and the presence of the crystal structure defects are described by Fourier coefficients. The instrumental effects are included by convolution with an instrumental function. The method is described in detail in [1], it is implemented in the PM2k software [11] and in some other projects as the CMWP-fit [9], or MSTRUCT [12], An implementation of the models described below can be found also for the TOPAS software, e.g. in [6], The size broadening is described as in [3], Crystallites are assumed to have a spherical shape with diameter (D). Two models of statistical distributions of the diameter (D) are used: (i) a "reference" model of the log-normal size distribution [1] and (ii) a "histogram" model [3], The instrumental function is represented by the pseudo-Voigt function with parameters obtained from the fitting of the pattern of the NIST LaB 6 standard sample. The influence of crystal structure defects is accounted phenomenologically using the pseudoVoigt function with two refineable parameters, which are converted [12] to phenomenological microstrain (e), characterizing the defects effect strength.

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More physical models of micro-structural defects (dislocations, stacking faults) [8] were not considered in the present study since the microstrain in the studied samples was quite weak and phenomenological approach found to be satisfactory.

4. XRD data analysis 4.1 Reference samples - the log-normal distribution XRD patterns of both samples, calcinated at 400°C and 550°C, were fitted using the lognormal size distribution model first. The relevant refined parameters are listed in table 1. Quality of the fit was essentially the same as for all the patterns analysed here (GoF ~ 1.5). Results indicate clearly different crystallite size for these samples. The sample calcinated at 400°C had anatase crystallites of about 6 um in diameter; the second sample had crystallites of about 22 um large. Crystallite sizes correspond roughly to EM images (figure 1). Table 1. Reference samples — the log-normal distribution model. M, S — size distribution parameters - mean crystallites size: M exp(S"/2); e — microstrain; f— crystal phase fraction.

Sample

M

(phase)

(nm)

400°C (anatase)

6.2 ±0.1

0.384 ±0.003

550°C (anatase)

20.7 ±0.3

0.398 ±0.005

0.068 ±0.004

93.2

550°C (rutile)

33 ±1

0.3 fixed

S

e

/

(%)

(wt.%)

0.15 ±0.04

99.6

6.8 Figure 1. EM image of the large crystallites reference sample (calcinated at 550°C).

For crystals of a tetragonal symmetry, like anatase, non-spherical particles are often expected. In fact this is also visible in the EM micrograph (figure 1). In contrary there was no anisotropy observed in the diffraction line broadening and the fits were good enough with the simplified spherical crystallite model. Hence the simplest model was used with aware of the risk that it can result in the slightly bigger crystallite size dispersion. 4.2 Histogram model An implementation of the model here differs a little from the original one of Leoni & Scardi [3], The bins in the histogram do not have equal widths (figure 2). The histogram has 20 bins logarithmically spaced in the range (D) 1—100 nm. This is more similar to what has been used in [6] than in [3], Each bin is described by the lower (Dim) a n d the upper limit ( D J I Ì I ) of the crystallites size. The crystallites size within the bin has an equal probability density P{ii. Since the crystallites contribute to the integrated intensity proportionally to their volume it is useful to introduce in addition an auxiliary volume weighted distribution Fw(i) = Ρ(ί)*Ό(ί)3, where D (il = (ΰ1(ί)+ΰ2(ί))/2 is an arithmetic mean crystallite size in the z'-th bin (figure 2d-f). Beside the reference - small and larger crystallites - samples the histogram model was also tested on their mixtures. Six mixed samples were prepared with the following weight fractions (r) of the first - small crystallites - component in the mixtures: 0.05, two samples with

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0.15, 0.30, 0.60, and 0.80. The pattern fitting of each sample was started from a wide bell shaped distribution settled in the middle of the histogram. Each refinement converged to the solution having a very good agreement with the measured data, as good as in the case of the log-normal model for the reference samples. Whereas the refined volume weighted distributions PW(D) looked reasonable (figure 2d-f), the crystallite distributions P(D) had no physical validity, except for the case of the pure small crystallites reference sample. A typical distribution with the extremely high, noisy low bins is depicted in figure 2a. Compared to the large crystallites, the very small ones contribute to the diffracted intensity very weakly. Moreover the diffracted intensity is spread in tails of the peaks and difficult to separate. [11.1511 -o [111411 I β " su um il 2» i¡i (.i) ao h i d ο 211 (¡i (.ι m mo i) 2i)

L

D (lilil í

S

!

0,030

T y3 i^ 0.020 g) Q üU.ÏS. 0 , 0 1 0 >

) .111111

(J.I K M

i

E? I [111])

A\ .M

I) 21) 40 60 Sil 100 II 211 Jo 611 so loi) H -ι) 411 ni KU Ilio Γ> (imi) D Iran} Diurni

Figure 2. Refined histograms for the large crystallites reference sample, (a, d) - no regilarisation is used; (b, e) - only the ciystallite size distribution P(D) regularised; (c,f) - only the volume weighted distribution P"(D) regilarised. (b, e) - solid line - the log-normal distribution (table 1).

4.3 Histogram model - régularisation The problem of the crystallite size distribution determination here is similar to a problem of deconvolution, where filtering and régularisation methods [13,14] are utilized. Basically, the size distribution can be assumed to be smooth. As a measure of the distribution smoothness an integral of square of the distribution derivative P { i(D) was taken. The same régularisation condition can be applied also to the volume weighted distribution Pv{i(D). In addition, it was assumed that the maximum model crystallite size Dlnax was chosen large enough that there are no crystallites larger. The same was also required for the crystallites smaller than Amn· If the régularisation for the size distribution P ^ D ) was employed, an erroneous and noisy distribution obtained in the previous step converted to a smoother peak-like distribution (figure 2b). Unfortunately, the refined histogram distribution of the large crystallites reference sample was different from the expected log-normal (table 1, figure 2b). The histogram distribution revealed larger fraction of small crystallites (< 10 nm). If the volume weighted size distribution Pw{¡> was regularised, especially in the case of the large crystallites reference sample, it resulted in an extremely asymmetric inverse-exponential-like size distribution P(ii(D) (figure 2c), where a huge number of the smallest crystallites arise from the requirement of the smoothness of the volume weighted distribution (figure 21). The volume

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weighted distributions did not depend much on the régularisation scheme (figures 2d-l). The best results were obtained for the reference sample with small crystallites. The crystallite size distribution P{i(D) had a well defined peak shape independently of the régularisation type. If both régularisation conditions were applied simultaneously, well defined smooth distribution appeared (figure 4b, d). It is worth noting that the power of the régularisation was always chosen to be low enough to not affect significantly XRD data agreement of final solutions. Unfortunately different crystallite size distributions could be obtained with almost the same goodness of fit for the same sample depending on the régularisation condition involved. The most difficult problem consisted in the characterization of small crystallites in the presence of large ones. If the large crystallites (~ 25 nm) were present in the sample and constitute the major contribution to the integrated diffracted intensity, it was difficult to distinguish the smaller (~ 5-10 nm) ones. Similar limitations of the method were reported also in [2], 0.200

LU

Í.IJ

D(itm)

Figure 3. Final size distributions for the reference samples, (a, c) - the sample calcinated at 400°C; (b, d) - the sample calcinated at 550°C. Solid lines — the log-normal model (table 1).

4.4 Histogram model - samples mixtures - final results The method was tuned on the large crystallites reference sample and the same procedure was applied to all other samples. The size distribution of the reference samples was in a good agreement with the log-normal distribution refined earlier (figure 3). Reasonable distributions were obtained also for the mixed samples. In the mixture of a dominant fraction (~ 0.8) of small crystallites with a small volume fraction of large ones the large crystallites (~ 30 nm) could be identified as a small peak in the volume distribution histogram. Small volume fractions (~ 0.1) of small crystallites could be resolved in the majority of larger ones. Finally the refined histograms of volume weighted distributions of the mixed samples were fitted (figure 4) by a linear combination of the histograms of the reference samples. The volume fractions (xLPA) of the small crystallites reference sample in the mixtures were determined. Complementary to the LPA, the rutile, present mainly in the large crystallites reference sample, was used as an internal standard. The fractions (.TW&QPA) of the reference samples in the mixtures were deduced from the samples weight ratios and from the quantitative phase analysis (QPA). Very good correlation (figure 5) between the values obtained by the two methods was obtained.

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ii c -Ξ "3 'C S < Ν 4Λ ú >

0.06 0.05 11.04 il I 'ι Ο.02 O.DI o

nn

41) 6U SI) 101) D (ran)

Figure 4. The refined histogram of the mixed sample (χ ~ 0.30) fitted by a linear combination of the reference samples histograms.

D 0 55 0 50 0-75 1-00 Sniyli Ciy&allUcs Volume Fraction from Weights&QPA Dal« Figure 5. The small crystallites volume fraction (alpa) as obtained from LP A results plotted against the volume fraction (a'w&qpa^ as obtained from the sample weights and QPA analysis.

The logarithmic sampling of a size distribution makes it possible to treat small and large crystallites simultaneously and determine their volume fractions. Unfortunately, the problem studied here reveals that the determination of the crystallite size distribution of small crystallites in the presence of large ones is an ill-posed problem, as also indicated in [2,6], Then the choice of the logarithmic sampling is rather unsteady and the régularisation is needed.

References 1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11. 12. 13. 14.

Scardi, P. & Leoni, M., 2002, Acta Crystallogr. A, 58, 190. Beyerlein, K„ Cervellino, Α., Leoni, M., Snyder, R.L. & Scardi, P., 2009, Ζ Kristallogr. Suppl., 30, 85. Leoni, M. & Scardi, P., 2004, J. Appi. Crystallogr., 37, 629. Scardi, P.& Leoni, M., 2006, J. Appi. Crystallogr., 39, 24. Scardi, P., Leoni, M., Lamas, D.G. & Cabanillas, E.D., 2005, Powder Diffr., 20, 353. David, W.I.F., Leoni, M. & Scardi, P., 2010, Mater. Sci. Forum, 651, 187. Vives, S. & Meunier, C„ 2009, Powder Diffr., 24, 205. Spadavecchia, F., Cappelletti, G., Ardizzone, S., Bianchi, C.L., Cappelli, S., Oliva, C., Scardi, P., Leoni, M. & Fermo, P., 2010,ΑρρΙ. Catal. Β: Environ., 96, 314. Balogh, L„ Ribárik, G. & Ungár, T., 2006, J. Appi. Phys., 100, 023512. Langford, J.I., Louer, D. & Scardi, P., 2000, J. Appi. Crystallogr., 33, 964. Leoni, M., Coniente, T. & Scardi, P., 2006, Ζ Kristallogr. Suppl., 23, 249. Matëj, Z„ Kuzel, R. &Nichtová, L„ 2010, Powder Diffr., 25, 125. www.xray.cz/mstruct Kojdecki, M.A., 2001, Mater. Sci. Forum, 378-381, 12. Cerñansky, M., 1999, in Defect and Microstructure Analysis by Diffraction, edited by R.L. Snyder, J. Fiala & H.J. Bunge (New York: Oxford University Press), pp. 611-651.

Acknowledgements. This work was supported by the research program MSM0021620834 of the Ministry of Education of the Czech Republic and by the project KAN400720701 of the Czech Academy of Sciences.

Ζ. Kristallogr. Proc. 1 (2011) 93-98/DOI 10.1524/zkpr.2011.0014 © by Oldenbourg Wissenschaftsverlag, München

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Crystal growth mechanism of kaolinites deduced from crystallite size distribution J. V. Clausell1, J. Bastida1'*, M. A. Kojdecki2, P. Pardo1 1 2

Departamento de Geología, Universidad de Valencia, Spain Instytut Matematyki i Kryptologii, Wojskowa Akademia Techniczna, Warszawa, Poland Contact author; e-mail: [email protected]

Keywords: kaolinite, micro structural analysis, crystal growth mechanism Abstract. The influence of hydrothermal and meteoric alteration processes on the formation of kaolins in deposits in the Iberian Massif was studied. X-ray diffraction microstructural analysis of kaolinite was performed by the Mudmaster program, based on the BertautWarren-Averbach method. The evolution of the lognormal parameters of crystallite size distributions are interpreted as resulting from two different growth mechanism of hydrothermal and meteoric kaolinites.

1. Introduction and aim There are several kaolin deposits in the Iberian Massif developed over palaeozoic granites and slates. The influence of hydrothermal and meteoric alteration processes on the formation of these kaolins is not always clear. Genetic environment is the principal factor influencing kaolinite crystallinity and particle size [1], The aim of this paper is to show different mechanisms of crystallite growth of kaolinite in hydrothermal and meteoric kaolins by means of crystallite size distributions.

2. Materials and methods Two sets of samples collected, respectively, from hydrothermal kaolin developed on granite (Granito del Barquero) and from an alteration surface (altered slates of Horcajo de los Montes [2]) were investigated. Samples for microstructural analysis of kaolinites were prepared as untreated orientated aggregates (dried in air oven at 45°C during 24 hours) of clay fraction with particle of diameter less than 2μηι. The X-ray diffraction (XRD) patterns in range from 2° to 32° 2Θ were recorded using a Siemens D500 system with a diffracted beam nickel monochromator, Cu Κα radiation from a tube working at 30 mA and 40 kV, equipped with a scintillation counter, I o divergence slit, I o antiscatter slit, I o receiving slit and 0.15° Söller slits, with step of 0.02° 2Θ and count time of 3 s per step. Random powder patterns were registered in range from 2° to 62° 2Θ to identify minerals other than clay minerals. The XRD patterns are shown in figures 1 and 2. The effects of preferred orientation was reduced by back-loading the powder [5], Although in this way that problem probably was not com-

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pletely eliminated, it seemed to be enough to distinguish principal mineral components of the analysed samples. Semi-quantitative estimation of mineral contents in a whole sample was determined by the option S-Q of the Eva V.9 program [3] based on the reference intensity method [4], Results are shown in table 1; an error estimated for each phase contents follows from standard deviation for counting statistics [6], It must be noted that chlorite, smectites and mixed layers illite-smectite were not identified with usual methods [7, 8] in the analysed mineral assemblages, using the Search utility of Eva program [3], Thus a contribution from interlayered phases to XRD patterns are not significant, particularly for kaolinite being the principal subject of this study.

Barquero Set

2-Theta - Scale

Horcajo Profile Set

2-Theta - Scale

Figure 1 (up) and 2 (low). X-ray diffraction patterns of the studied samples. Labels K001, K002, 1001 and 1002 correspond to lines used for XRD microstructural analysis of kaolinite and illite respectively.

Ζ. Kristallogr. Proc. 1 (2011)

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Microstructural analysis of kaolinite was performed by the MudMaster programme [9] (based on the Bertaut-Warren-Averbach method [10, 11]) exploiting peaks extracted from XRD patterns from orientated aggregates and using corresponding instrumental profiles computed from XRD pattern from lanthanum hexaboride (NIST SRM 660a). Table 1. Mineral contents estimations of the studied kaolins with error estimates from standard deviation for counting statistics.

Quartz Sample

[%]

JVC130

Kaolinite

[%]

Other

Illite

[%]

67.2

[±%] 2.5

58.8

1.3

41.2

5.0

JVC132

50.7

0.8

49.3

6.0

JVC267

33.7

1.7

15.7

1.9

49.8

2.5

0.8

Horcajo 24.8 • de los Montes ~ 16.6 JVC270 profile 27.0 JVS271

1.3

14.1

1.5

60.6

6.7

0.5

0.9

21.9

2.3

60.3

6.9

1.2

1.4

11.9

1.3

60.0

6.7

1.1

JVC131

JVC268

Barquero

[±%]

[%]

31.7

[±%] 0.7

1.1

3. Results Mean area-weighted apparent crystallite size and crystallite size distributions (CSD) were computed by the Bertaut-Warren-Averbach method, with using the MudMaster programme (without correction for strain). The same programme was used to calculating a logarithmicnormal approximation to each CSD, characterised fully by mean value a and variance β 2 of the logarithm of size ln(s): g(s) = (ζβ)-ι(2πΥ112 e x p { - ( i / r 2 ) [ l n * - a]2} . Both parameters were computed as empirical moments for ln(s) with using CSD obtained before from XRD patterns. The values of both parameters and crystallite mean sizes M calculated from the CSD are collected in table 2. The results are presented as obtained; the estimations of errors are impossible in practice, due to complexity of an inverse problem solved. In general, the inverse problems of X-ray crystallography are ill-posed and reliable error estimation would be possible only in very specific cases. Moreover, the MudMaster programme realises the Bertaut-Warren-Averbach analysis (as usually it is performed) in a one-way mode: the crystalline microstructure characteristics are computed on the basis of X-ray diffraction data, but without backward analysis to controlling the quality of approximating simulated XRD line profiles to experimental ones. Such analysis will be a subject of more detailed study. According to Bertaut's and Warren's assumptions [10,11] both mean crystallite size and CSD must be treated only as apparent characteristics, with no immediate physical interpretations. For all these reasons the results of this work are rather semi-quantitative, but worth of noting for remarkable tendencies in CSD (as illustrated in figures 2, 3, 4).

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Table 2. Microstnictural parameters ofkaolinites from Horcajo ele los Montes slates (HM) and kaolinites from Barquero granite (BG) calculated for logarithmic-normal ciystallite size distributions approximating the distributions found by the Bertaut- Warren-Averbach method using MudMaster.

Samples

M [À]

a

ß2

Samples HM

M [À]

a

ß1

BG JVC130

228

2.67

0.55

JVC267

118

2.37

0.18

JVC131

76

1.83

0.39

JVC268

91

2.09

0.23

JVC132

18

0.65

0.06

JVC270

114

2.31

0.21

JVS271

120

2.41

0.16

The trend in a versus β 2 of the hydrothermal kaolinites shows that β 2 increases linearly with increase in a (figure 2), in agreement with the plots of reduced CSD (frequency/maximum frequency plotted versus size/mean size) of kaolinites, showing an evolution towards a steady-state shape (coincidence of reduced distributions) with maximum at smaller relative size (figure 4). On the other hand, in the edaphic profile, β 2 decreases with increase in a (figure 2); in this case the plots of reduced CSD during crystal growth show a shift of frequency maximum towards greater relative sizes, and a decrease of reduced distribution asymmetry, without reaching the steady-state shape (figure 3).

GROWTH MECHANISMS BASED ON LOGNORIMAL PARAMETERS

CI

C .5

I

1.5 Alpha

i

J.5

3

Figure 2. Trend ofβ' versus a ofkaolinites from Barquero granite and Horcajo de los Montes profile.

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R e t r a c e d C S D s of kaolìnites from B a r q u e r o granite

G

D,5

1

1,5

2

2.5

3

3.5

SizeJMean s i z e

R e d u c e d C S D s of kaolin Itss from Horcajo da Ioê Montas

0

0,5

1

1.5

2

2.5

3

3.5

StzeíMean s i z e

Figure 3 (up) and 4 (low). Crystallite size distributions ofkaolinites from Barquero granite and Horcajo de los Montes; in brackets mean apparent crystallite sizes are given.

4. Conclusions The lognormal parameters evolution of the studied hydrothermal kaolinites from the Barquero granite can be interpreted [12] as produced by crystal growth mechanism of nucleation and growth with decaying nucleation rate in an open system or surface-controlled growth in an open system, while the evolution of the Horcajo de los Montes meteoric kaolinite is related to an Ostwald ripening (supply controlled) in a closed system. Full contact details: Dr José Vicente Clausell. Departamento de Geología, Universidad de Valencia, 46100 Burjassot (Valencia). Tel. 34-963544393, 34-635139392, fax 34-963544600

References 1.

Galán, E., Matías, P. & Galván, J., 1977, Proc. 8 o Intern. Kaolin Symp. and meeting on Alunite. Madrid, Rome, K-8, 8 pp.

2.

Vicente, M.A., Molina, E. & Espejo, R„ 1991, Clay Miner., 26, 81-90.

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European Powder Diffraction Conference, EPDIC 12 3.

Bruker AXS, 2003, Diffrac Plus. Evaluation Package. Eva v.9. 219 pp.

4.

Hubbard, C.R. & Snyder R„ 1988, Powder Diffr., 2, 74-77.

5.

Niskanen, E„ 1964, Amer. Min., 49, 705-714.

6.

Klug. H.P. & Alexander L.E, 1974, X-ray Diffraction Procedures (New York: J. Wiley & Sons), 503 pp

7.

Warshaw, C. & Roy, R„ 1961, Geol. Soc. Am. Bull.,12, 1455-1492.

8.

Thorez, J., 1976, Practical identification of clay minerals, G. Lelotte editions (Belgique: Dison), 90 pp.

9.

Eberl, D.D., Drits, V., Srodoú, J. & Nüesch, R„ 1996, U.S. Geological Survey Open File Report, 96-171, 55 pp.

10. Bertaut, E.F., 1950, Acta Crystallogr., 3, 14-19. 11. Warren, B.E. & Averbach, B.L., 1950, J. Appi. Phys., 21, 595-599. 12. Eberl, D. D„ Drits, V. & Srodoú, J., 1998, Am. J. Sci., 298, 499-533. Acknowledgements. CCEC, Generalitat Valenciana (Ph. D. These 1495-2000, University of Valencia) and integrated CEE project NMP2-CT-2006-026661.

Ζ. Kristallogr. Proc. 1 (2011) 99-104/DOI 10.1524/zkpr.2011.0015 © by Oldenbourg Wissenschaftsverlag, München

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Diffraction peak broadening of energetic materials 1 2 M. Herrmann 1, P. B. Kempa 1, U. Förter-Barth , S. Doyle 1 2

Fraunhofer Institut für Chemische Technologie ICT, Pfinztal, Germany Institut für Synchrotronstrahlung ISS, Eggenstein-Leopoldshafen, Germany Contact author; e-mail: [email protected]

Keywords: peak profile analysis, Williamson-Hall-plot, energetic materials Abstract. The peak broadening of a series of energetic materials was measured at the synchrotron ANKA, and the results were evaluated by means of Williamson-Hall-plot and the double Voigt approach yielding mean crystallite size and micro strain. The investigations revealed characteristic anisotropic peak broadening which is discussed in relation to prevailing twin and dislocation slip systems. Besides, the concentration of amorphous H M X impurities was found to correlate with the peak broadening of RDX.

Introduction The investigation of the crystal structure of solid energetic materials is an established tool in research and quality assessment of propellants and explosives. In recent years microstructure investigations shifted into the scope of actual research, as it was shown that a careful crystallization of the solid load of a plastic bonded explosive (PBX) reduces their shock sensitivity. Subsequently, so called reduced sensitivity (RS) varieties of high explosives were proposed for use in insensitive munitions (IM) and voids, inclusions, impurities, dislocations and twins are discussed to influence the mechanical sensitivity and the creation of hot spots during shock loading. In this context investigations revealed anisotropic diffraction peak broadening and correlate size/strain broadening with particle processing and shock sensitivities [1-3],

Experimental and evaluation X-ray diffraction patterns of fine powders of RDX, H M X and FOX-12 and the standard reference material lanthanum hexaboride (SRM 660a) were measured at the diffraction beamline at A N K A on a Bragg-Brentano diffractometer equipped with a germanium analyzer crystal and rotating sample holder at monochrome synchrotron radiation with wavelengths of 1.1479 and 1.2997 Â. Selected 29-ranges were measured with a step width of 0.0025°. Two evaluation techniques for size/strain broadening of X-ray diffraction peaks are used, the Double-Voigt approach [4] and the Williamson-Hall plot [5], In the Double-Voigt approach crystallite size (domain size) and microstrain comprise Lorentzian and Gaussian component convolutions of diffraction peaks varying in the diffraction angle 2Θ as a function of 1/cos θ

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and tan Θ, respectively. Implemented into a whole pattern fit of the program TOPAS of Bruker AXS, the evaluation yields volume weighted mean crystallite sizes LVoi-œ a n d the mean strain value eg (=Ad/d). For the method after Williamson and Hall, diffraction peaks were indexed and fitted using the split-Pearson VII analytical function of program TOPAS. The peak widths of the energetic materials (FWHM) were reduced by the geometric widths, and reciprocal peak widths β*=β/λ cos θ are plotted versus reciprocal lattice distances d*=2//1 sin Θ, where ß, d, 2Θ and λ are the diffraction peak width, lattice distance, diffraction angle and wavelength. In addition, the concentrations of HMX-impurities were determined using Rietveld analysis and by HPLC [6], The results are summarized in table 1. Table 1. Median particle size, ciystallite size, microstrain and concentrations of impurities.

Material

Part. Size [μηι]

Cry.-Size Lvoi-m [nm]

Strain ε0

(hkO)-trace non-(hkO) all peaks

353 125 4490

0.0122 0.0533 0.0500

(hOl) trace (hkO)trace all peaks HMX impurity

160 311 244 243

0.041 0.046 0.045 0.017

4.7

6.5

FOX-12

HMX [%] XRD HPLC

RDX(l)

5

RDX(2)

17.6

>3000

0.52

9.7

>3000

0.029 0.021

0.44

RS-RDX

2.6

2.6

I-RDX

10.5

>3000

0.023

0

0.01

2673 202 224 123 244

0.0219 0.0427 0.0506 0.0642 0.0494

HMX HMX(l) HMX(2) HMX(3) HMX(4) FOX-12

~ 100 ~ 10 ~ 10 ~1

Original Rotor/Stator Rotor/Stator Gap Mill 0.5% RDX

(C2H7N705)

FOX-12 is used as a gas generator for airbags. It crystallizes in space group Pna2! [7]. The Williamson-Hall plot in figure 1 depicts a horizontal trace below 0.01 A"1 and a widespread belt above 0.02 A"1. Indexing revealed that (hkO)-peaks build the trace but (hkl; 1^0)-peaks the belt. The crystal structure in figure 2 explains the extremely anisotropic peak broadening. The planar molecules crystallize in a layered structure, with strong interactions inside the layers represented by the (hkO)-peaks, but weak between. In this model layer slippage releases mechanical stress, while the layers themselves keep undisturbed. Therefore layer structured energetic materials such as FOX-12, FOX-7 and TATB show low mechanical sensitivities, and consequently are considered for desensitizing high explosives e.g. by coating or co-crystallization. For FOX-12 partial whole pattern fits were applied to (hkO)- and non(hkO)-peaks, yielding a domain size of 350 nm and a micro strain value of 0.012 for directions in the layers and 125 nm and 0.053 crossing the layers (table 1). An overall "blackbox"-evaluation would yield 4490 nm, and thus fail for the highly anisotropic structure.

Ζ. Kristallogr. Proc. 1 (2011)

101

0.06

FOX-12

_(412>

0.05 .-(221}.--'**" • •••'Α δ > · ' '

'0.04

(011) Δ' Δ'"'* οιυ

"σ > 0.03 ro φ

> (hkl) peaks

A

A (002)

A

A

¿0.02 o φ L_

(hkO) peaks

(040)

0.01 Δ

4

(110) (210)

0.00 0.1

0.2

(420)

(220) 0.3

0.4

A (440) 0.5

0.6

0.7

recipr. lattice distance d* [1/Â] Figure 1. Williamson-Hall plot ofFOX-12 with strong anisotropic broadening.

'•m

*

Figure 2. Layered crystal structure ofFOX-12, based on the crystal data reported by Bemm [7],

RDX (C3H6N606) The situation is different with the ring structured RDX [8], which is probably the most important high explosive. Figure 3 shows an indexed Williamson-Hall plot of a sample containing significant HMX impurities. The significant fluctuations result in a belt-like distribution confined by (h01)- and (hkO)-peaks as upper and lower rims; except (004) due to peak overlap. Thus, the indexed plot shows a characteristic anisotropic peak broadening which most likely is attributed to incorporation of HMX molecules into the RDX lattice. The size/strain analysis revealed low microstrain of 0.021 and 0.023 for the reduced sensitivity variants RSand I-RDX compared to 0.029 and 0.045 for the conventional RDX(2) and RDX(l), and a reduced crystallite size of 250 nm in RDX(l), which differs between 160 and 311 nm for the (h01)- and (hkO)-peaks, respectively.

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(104)

RDX (1) *

4

*Ά A

*

(122) ,' (202) V (odf^ A (102), Δ' A ( 0 40) (002) . A A (11

ϋ

*

χ

A

Λ

' (420)

(^pr (220)

Δ (020) (200)

0.0

0.1

0.2

0.3

0.4

0.5

0.7

0.6

Reciprocal lattice distance d* [1/A] Figure 3. Williamson-Hall plot of the RDX(l); belt-like distribution between (hkO)- and (hOD-peaks.

2.00 φ RDX(1) ¿1.50

3 1.00

·2' 13 g

0.8

g 0.6.

0.4 0.2

¿-spacing (Â)

Figure 4. Rietveld refinement profile fior LaB6 powder (NIST SRM-660Ò). Dots indicate normalized profile, solid line is the calculated profile, tics above profile indicate the positions of all allowed reflections, and difference line is shown below the top profile (d-spacing range 0.30 — 3.0Â). The inset is expanded and shown as the bottom profile (d-spacing range 0.32 — 0.70A). Small ν mark two visible reflections from the vanadium sample holder (fitted as a 2nd phase). Note. S.G. = Pm-3m, a = 4.1575(1)Â, La: Uiso = 0.0048(2)Â2, Β: χ = 01996(2), un = 0.0023(2)Â2, "22 = "33 = 0.0040(2)Â2, Rwρ = 0.031, Äp = 0.044, χ 2 = 1.93, Ri = 0.050.

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A Rietveld refinement for a powder sample of LaB 6 NIST SRM-660b (>99% isotopically enriched 10B) is shown in Figure 4 and refined parameters are listed below the Figure caption. The data were collected in 3.3 h (2.5 mA.h) on a 0.99 g sample. The crystallographic parameters agree well with NIST certified parameters, a = 4.15689(8) Â at 22.5°C, and published neutron powder and x-ray single crystal structures [12, 13] except that no vacancy was observed on the La site whereas published structures indicate 1.7(4)% and the refined ADPs are on average - 1 7 % below the published values. This discrepancy in ADPs although significant is well within the uncertainty due to unknown 10B isotope content of the NIST SRM which is stated as 0.4 with no additives) for sample preparation. Advantages of Bragg-Brentano measurements are fast sample preparation and good intensities with short counting time, whereas main disadvantages consist in bleeding and sample segregation effects, remarkable sample displacement during hydration, strong preferred orientation for platy crystals, interferring peaks of Kapton film. The focusing transmission flat-sample geometry allow fast sample preparation, minimize sample segregation effects, yield a low background contribution and high intensities patterns with short counting time. However, several disadvantages have to be accounted for, such as strong preferred orientation and paste dehydration due to a not perfect sealing of the sample holder. With this method the hydration process is stopped in the long period, and the evolution of the system can be monitored only within the first 4-5 hours of hydration.

References 1. 2.

3. 4. 5. 6. 7. 8.

9. 10. 11. 12. 13. 14.

Taylor, H.F.W., 1997, Cement Chemistry, 2nd edition (London: Thomas Telford Publishing). Gartner, E.M., Young, J.F., Damidot, D.A., & Jawed, I., 2002, in Structure and Performance of Cements, edited by J. Bensted, P. Barnes. (London: Spon Press), pp. 57-113. Jupe, A.C., Turrillas, X., Barnes, P., Colston, S.L., Hall, C., Hausermann, D. & Hanfland M., 1996, Phys. Rev. B, 53, 697. Merlini, M., Artioli, G., Meneghini. C„ Cernili, T., Bravo, A. & Cella, F., 2007, Powder Diffr., 22, (3), 201. Christensen, A.N., Scarlett, N.V.Y., Madsen, I.C., Jensen, T.R. & Hanson, J.C., 2003,Dalton Trans., 1529. Scrivener, K.L., Fiillmann, T., Gallucci, E., Talenta, G. & Bermelo, E., 2004, Cem. Cone. Res., 34, 1541. Hesse, C., Goetz-Neunhoeffer, F., Neubauer, J., Braeu, M. & Gaeberlein, P., 2009, Powder Diffr., 24, (2), 112. Neubauer, J., Goetz-Neunhoeffer, F., Holland, U., Schmitt, D., Gaeberlein, P. & Degenkolb, M., 2007, Proceedings of the 12th International Congress on the Chemistry of Cement, Montréal, Canada. Weyer, H.J., Müller, I., Schmitt, B„ Bosbach, D. & Putois, Α., 2005, Nucí. Instr. Meth. Phys. Res. B, 238, 102. Feldman, S.B., Sandberg, P., Brown, D. & Serafín, F., 2007, Proceedings of the 12th International Congress on the Chemistry of Cement, Montréal, Canada. Coelho, A.A., TOPAS Version 3.1, 2003, Bruker AXS GmbH, Karlsruhe, Germany. Cheary, R.W. & Coelho, A.A., 1992, J. Appi. Crystallogr., 25, 109. Madsen, I.C., Scarlett, N.V.Y., 2008, in Powder diffraction theory and practice, edited by R.E. Dinnebier and S.J.L. Billinge. (RSC Publishing) pp 298-331. Mitchell, L.D., Margeson, J.C. & Whitfield, P.S., 2006, Powder Diffr., 21, (2), 111.

Acknowledgements. This study has been performed in the frame of the MAPEI-UNIPD research agreement.

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In-house characterization of protein powder C. G. Hartmann , P. Harris, K. Stähl Department of Chemistry, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark Contact author; e-mail: [email protected] Keywords: in-house powder diffraction, protein, bulk-solvent correction Abstract. Collecting protein powder diffraction data on standard in-house powder diffractometers requires careful handling of the samples. Specially designed sample holders combined with optimized collimation were found to be the key factors in improving the data quality and reducing the data collection time. For safe identification of the crystal form the experimental patterns have to be compared with patterns calculated from known crystal structures. Very good agreement with Protein Data Bank data was obtained after including corrections for background, unit cell parameters, disordered bulk-solvent, and geometric factors. The data collection and correction procedures were demonstrated by the identification of three different crystal forms of insulin.

1. Introduction Since the first protein structure was refined from X-ray powder diffraction (XRPD) data ten years ago [1], high-resolution protein powder diffraction at synchrotron sources has been developed and used for refining and even solving small protein structures [2], Furthermore, it has recently been shown that in-house XRPD can be successfully used for the identification of different crystal forms of proteins [3,4], It thereby offers a convenient and quick way to characterize crystalline protein precipitate in the laboratory. Growing suitable protein crystals of sufficient size and quality is one of the major bottlenecks in solving protein structures from single-crystal X-ray diffraction experiments. Screening for the optimal crystallization conditions is trial-and-error based and often gives many hits with precipitate. Early powder diffraction characterization of those precipitates would be valuable when optimizing the crystallization process. Protein crystals contain 30-70 % of disordered solvent and they must be prevented from drying out and are thus kept in the mother liquor. Due to the large molecules and the high solvent content, protein crystals are soft and in general poor scatterers. Combined with the non-Bragg scattering from the surrounding mother liquor and the sample holder, it results in poor peak-to-noise ratios {PIN). Minimizing the sample amount and improving the PIN requires careful design of the sample holders and collimators.

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Furthermore, the large unit cells result in Bragg peaks occurring at very low angles and at higher angles the reflections are suffering from a severe peak overlap limiting the data resolution to about 4 Â (20 = 2-20° with CiiKai-radiation in our tests). Reliable identification of crystal forms requires calculation of realistic protein powder patterns based on for example Protein Data Bank (PDB) coordinate files. Including straightforward corrections for background, unit cell parameters, disordered bulk-solvent and geometric (Lorentz) factors we have obtained very good agreements between measured and calculated patterns [3], The techniques will be demonstrated with data from three crystal forms of insulin.

2. Collection of protein powder data using in-house equipment The diffraction experiments were carried out on a standard in-house Huber G670 diffractometer with a Guinier (transmission) geometry setup using CiiKai -radiation (λ = 1.54059 À). The data were recorded on an imaging strip in the range 2-100° in 20. The diffractometer was equipped with an Oxford Cryo-cooler. Crystals were grown in batches containing 2 - 6 mg of protein and suitable powder samples were obtained by gently crushing the crystals in the mother liquor resulting in a powder slurry. As cry o-protectant glycerol was added for the sample used in sample holder model 3 (loop). The samples were mounted in specially designed sample holders. Two sample holders for room temperature measurements and a loop for cryo-cooling temperatures (100-120 K) were tested. These are shown in figure 1. The sample holder design must fulfil several requirements. In general the major challenge is to find a way to support a thin film of wet powder. Firstly, the samples must be kept in sealed sample chambers or alternatively kept cryo-cooled in order to prevent the samples from drying out. Secondly, data collections are run in transmission mode meaning that the thickness of the samples must be as low as possible and the sample chamber windows must be made of a material with low absorption and low contribution to the background. Mylar was shown to be an ideal choice. Thirdly, the crystallite packing efficiency must be high and homogeneous and collimation of the X-ray beam must ensure that it hits the homogeneous part of the sample in order to maximize the PIN.

Figure 1. Different sample holders for in-house powder diffraction on proteins. The sample holderssupport slurries of protein crystallites in mother liquor, (a) Sample holder model 1 contains 120—150 μΤ of sample, (b) Sample holder model 2 contains 10 μΣ of sample, (c) Model 3: The loop supports 1—2 μΤ of ciyo-cooled sample.

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Sample holder model 1 requires approx. 150 μ ί of sample in an O-ring between two pieces of mylar foil. The O-ring and the foil are held in place by two metal discs providing a tight fit. Rotation of the sample is possible. Model 2 consists of a polycarbonate plate with a hole with mylar windows which are glued to the plate after the sample has been loaded. The sample size is approximately 10 μ ί . The polycarbonate holder is mounted on a goniometer head with a lead pinhole placed in front to reduce the background level. It is not possible to apply rotation of the sample. The holder was easily adaptable to synchrotron beamlines for X-ray absorption spectroscopy (XAS) without the lead pinhole. Model 3 is a loop (diameter approx. 2 mm) where small sample amounts are required. A thin film of wetted powder is easily supported on the loop cut from mylar and prevented from drying out by cryo-cooling. The loop was used in combination with the lead pinhole from model 2. All the sample holders were tested with insulin to compare their performances. Data were collected for 4 h for sample holder model 1 and 2 and for 12 h for model 3 (loop). The raw powder diffraction patterns from trigonal insulin prior to background subtraction are directly compared on figure 2. The peak-to-noise ratios have been calculated for each powder pattern in figure 2 and are given as PIN = (/Bragg+^BoV^BG, evaluated at the most intense peak at 2Θ = 6.84° Resolution d (A)

Figure 2. Raw data prior to background subtraction. The patterns have been collected on trigonal insulin for 4 h for sample holder model 1 and 2 and for 12 h for model 3. Comparison with calculated pattern (bottom), where the intensities have been scaled to the pattern from model 2.

The effect of reducing the background using the lead pinhole is clearly demonstrated by comparing model 1 with model 2. Presently 10 μ ί of sample is required to collect good powder diffraction patterns within hours, but in fact the crystal form can be safely identified

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in 15 minutes. The sample volumes can be further reduced to 1-2 μ ι using the loop (model 3), but at the expense of longer data collection time and poorer PIN.

3. Data treatment The background was subtracted in the program PROTPOW [3] (available from http://www.xray.kemi.dtu.dk/Englisli/Computer%20Programs/PROTPOW.aspx) by manually picking between 10 and 20 background points, fitting to a spline function and subtracting. The manual procedure is necessary to distinguish background from overlapping signal. Optimization of the unit cell parameters was done by a full-pattern profile fit. Optimized parameters describing the peak width (FWHM) and peak shape of a pseudo-Voigt function are included in the pattern fit by PROTPOW. Resolution d (Â) 30

20

15

12

10

9

8

7

6

5

20 (°) Figure 3. Comparison of calculated and experimental powder diffraction patterns for trigonal insulin, (a) Before correction for disordered bulk-solvent, (b) After correction for disordered bulk-solvent.

Powder patterns were calculated in PROTPOW from PDB coordinate files using the optimized unit cell and peak profile parameters. In general the peak positions fit well, but without taking into account the disordered bulk-solvent, the intensities fit poorly with the measured intensities, in particular at low 20, as seen in figure 3(a). The contribution from the solvent was calculated in PHENIX [5] using the flat bulk-solvent model [6] where a constant level of electron density is assumed in the voids between the macromolecule. The bulk-

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solvent model takes two parameters ksol defining the level of electron density and Bsol defining the steepness of the border between the solvent and the macromolecular regions. The parameters are refined in today's single-crystal X-ray structure refinement software, but in case no other information is available following average values can be used ¿soι = 0.35 e Â~3 and Bsoí = 46 A2 [7]. The contribution from the solvent is added to the calculated structure factors. The improved fit from the powder pattern based on calculated structure factors is seen on figure 3(b). Applying an improved geometrical (Lorentz) factor further improves the fit [3],

4. Results and discussion The applicability of the methods has been demonstrated in a recent study where XRPD was used to verify three different conformations (T6, T 3 R/ and R6) of hexameric Zn-insulin before and after EXAFS experiments. The same samples in model 2 sample holders were used for both experiments. The differences between the crystal forms are obvious in figure 4. Resolution d (A) 30

20

15

10

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I

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J , .

( a )

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12

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8

7

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Figure 4. Position (a) and FWHM (b) along the Si 642, horizontal lines from Rieh'eld fit.

To additionally verify the quality of the method we calculated /(20) for two exposures with different detector rotation angles. Figure 5 shows the measured patterns. Only the scale factor is adjusted. It is seen that the difference curve is smooth and close to zero.

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Figure 5. 1(20) reproducibility for two measurements with different rotation angles.

Figure 6. Rietveklplots

(Si, Al20¡

mixture).

Rietveld refinement The relative count statistics error is e, = {N/k.-Ii2θ,)γ112· 100%, where kj is the averaged correction coefficient for each particular point of 7(20) which accounts for polarization, inclined incidence, absorption, etc. Taking into account that each point is averaged by a different number of pixels N¡ a data format with three columns (20,·, I¡. gI¡) was used to perform the Rietveld refinement with the program FullProf [17]. With symmetric pseudo-Voigt functions and no preferred orientation correction good fits (figure 6) and reasonable results in agreement with literature were obtained. For the Si and AI2O3 NIST powder standards Bragg Rfactors were 0.84 and 1.28 %, respectively. It was found that large inclined incidence at the beginning and end part of 7(20) in one exposure leads to slightly different peak profiles, which are not perfectly described. Thus, at a 20 range wider than that shown in figure 6, the Bragg R-factor for AI2O3 increased to 1.68 %. However, this does not affect the quality of difference Fourier maps seriously. These are smooth with residual electron densities around 0.05 e/Ä3 (figure 7). -ι I . ».>•,' . (_:' •·. fî 1 .''On

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; 1

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Figure 7. Al20¡ difference electron density maps in the (100) plane. The step ofisolines is 0.05 e/Â3. The solid and dotted lines show, respectively, the positive and negative electron densities; the dashed lines indicate zero level. a) 147 reflections, Δρ„,αχ/Δρ„ή„=0.12/-0.15, (sin9/l)max=0.93 ; b) 97 reflections, ¿IPmax/dPmm =0- 22/-0.11, (si ηθ/λ)„,α=0.85.

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3. Concluding remarks 20-scanning with 2D-area detectors is a promising approach for high quality powder data collection. Further improvements may be achieved by the use of low noise and (or) larger solid angles 2D-area detectors with smaller pixel size, precise goniometers providing the work in automatic scanning regime, using better SR sources, special focusing, etc. It should be emphasized that very high angular resolution is of course desirable, but not necessarily the demanding point, since the Rietveld method itself is capable to overcome the problem of peak overlap as long as 'good' peak profiles, which can be accurately described, are available (cf. Fig. 2b, 6). With such data registered up to high Q and having good angular resolution and very high intensities it is conceivable that powder diffraction may become comparable to single crystal diffraction allowing e.g. the determination of electron densities. In some respects it may even be better, e.g. there should be less extinction problems.

References 1.

Piltz, R.O., McMahon, M.I., Crain, J., Hatton, P.D., Nelmes, R.J., Cernik, R.J. & Bushnell-Wye, G„ 1992, Rev. Sei. Instrum., 63, 700.

2.

Shimomura, O., Takemura, Κ., Fujihisa, H., Fujii, Y., Ohishi, Y., Kikegawa, T., Amemiya, Y. & Matsushita, T. ,1992, Rev. Sci. Instrum. 63, 967.

3.

Cernik, R.J., Clark, S.M., Deacon, A.M., Hall, C.J., Pattison, P., Nelmes, R.J., Hatton, P.D. & McMahon, M.I., 1992, Phase Trans., 39, 187.

4.

Hammersley, A.P., Svensson, S.O., Hanfland, M., Fitch, A.N. & Häusermann, D., 1996, High Pres. Res., 14, 235.

5.

Bunge, H.J. & Klein, H„ 1996, Z. Metallkd., 87, (6), 465.

6.

He, B.B.P., 2003, Powder Diffr., 18, (2), 71.

7.

Sulyanov, S.N., Popov, A.N. & Kheiker, D.M., 1994, J. Appi. Cryst., 27, 934.

8.

Sulyanov, S.N., Burenkov, G.P. & Kheiker, D.M., 1995, Kristallografiya, 40, 234.

9.

Fujiwara, Α., Ishii, K., Watanuki, T., Suematsu, H., Nakao, H., Ohwada, K., Fujii, Y., Murakami, Y., Mori, T., Kawada, H., Kikegawa, T., Shimomura, O., Matsubara, T., Hanabusa, H., Daicho, S., Kitamura, S. & Katayama, C., 2000, J. Appi. Cryst., 33, 1241.

10. Bergese, P., Bontempi, E., Colombo, I. & Depero, L., 2001, J. Appi. Cryst., 34, 663. 11. Rodriguez-Navarro, A.B. ,2006, J. Appi. Cryst., 39, 905. 12. Hinrichsen, B., Dinnebier, R.E.,& Jansen, M., 2007, Ζ. Kristallogr. Suppl, 26, 215. 13. Gommes, C.J.,& Goderis, B„ 2010, J. Appi. Cryst., 43, 352. 14. Kahn, R., Fourme, R., Gadet, Α., Janin, J., Dumas, C.,& Andre, D., 1982, J. Appi. Cryst., 15, 330. 15. Bowden, M.,& Ryan, M„ 2010, J. Appi. Cryst., 43, 693. 16. Ida, T., 2010, J. Appi. Cryst., 43, 1124. 17. Rodriguez-Carvajal, J., 2010, Program FullProf, http://www.ill.eu/sites/fullprof.

III.

SOFTWARE

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Adaption of a Rietveld code towards clay structure description J. Bergmann 11*', Κ. Ufer2 '* , R. Kleeberg2 1

Ludwig-Renn-Allee 14, 01217 Dresden, Germany Institut für Mineralogie, TU Bergakademie Freiberg ,Germany * Contact author; e-mail: [email protected]

2

f Joerg Bergmann passed away just after visiting the EPDIC 12. He very much enjoyed the conference, especially the honouring of Hugo Rietveld, and he was happy to present this poster summarizing the last improvements of his program BGMN. The day before his long desired but tragic transplant operation he updated his webpage http://www.bgmn.de/ and distributed a new version of BGMNfor testing to some co-workers. The program BGMN was developed by Joerg as a private passion, without significant institutional support. Nevertheless, a growing number of scientists have recognized the power and potential of BGMN and have applied it successfully in their research. Joerg wanted to make the use of his work free for the scientific community, and we will give our best to continue the project in that sense. But we all will miss Joerg's enthusiasm, genius ideas, and his warm friendship as well. Keywords: Rietveld method, clay, stacking disorder Abstract. The Rietveld method is well established in scientific and industrial applications, mainly in the fields of quantitative phase analysis and structure refinement. Clay minerals are of special interest due to their technical importance. Typically, disordering features like (i) well defined stacking faults, (ii) turbostratic layer stacking, and (iii) mixed-layered stacking hamper the application of classic Rietveld codes. BGMN [1] comes with a full featured structure description language. That includes variables and user defined functions plus special solutions and tools for structure description, which enables description of disordered layered structures diffraction patterns. We demonstrate the principles and some exemplary applications.

1. Introduction Clay minerals are very common in fine grained sedimentary rocks such as shales, mudstones and siltstones. The quantitative mineral content of these clays as well as their structural features are important parameters in applied studies as well as in geological interpretation. In recent years, X-ray diffraction in combination with the Rietveld method became an established method for these purposes. Unfortunately clay minerals show different kinds and degrees of disorder, which prevent the fit of XRD patterns by simply calculating Bragg

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peaks. Alternative approaches for the simulation of powder patterns of disordered clay minerals exist, but these methods lack the possibility to combine the clay mineral patterns with patterns of ordered minerals [2-4] or have no option of automatic refinement [5], BGMN fills the gap of Rietveld refinement and calculation of patterns of disordered structures. The builtin structure description language enables the program to treat disorder phenomena either phenomenological or structurally based. The possibility of combined refinement allows the simultaneous refinement of the same mineral after different pre-treatments and therefore enhances the reliability and uniqueness of the results.

2. Examples In the following subsections four different examples give an overview how to use the description language for the simulation of disorder phenomena. For detailed description of the experiments, see the corresponding references. 2.1 b/3 disorder 60° and 120° rotational as well as b/3 translational disorder are common for most clay minerals, due to the pseudohexagonal symmetry of the layers. Chlorite and kaolinite may be used as examples [6], Empirically, an asymmetric broadening and partial shifting of the peaks with k unequal 3n can be observed and must be described in the structure description file. Here, the asymmetry is approximated by a splitting into two 'peaks' and by introducing hkl dependent shifting and broadening. The resulting fit of a 'medium-disordered' kaolinite (figure 1) illustrates the success. 1400

1200 ;

1000 I

tfl a. υ

800

j

G00 -

10

I

I

I

20

30

40

,:

I

I

I

50

60

70

I SO

2Θ

Figure 1. Rieh'ekl fit of a slightly disordered kaolinite by an hkl-dependent peak broadening and splitting model.

The exemplary formulation of the hkl dependency of the broadening term Β1 can be seen in the formulation below.

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Bl=cat(hklK==h*Kl3+k*K23+l*κ33,hkltau==h*taua+k*taub+l*tauc, blk==K33*sqr(hkltau), B2==k2*sqr(sk)+sqr(sqrt(sqr(sk)+ sqrt(cl2sqr)*sqr(cl[iref]*ifthenelse(mod(k,3),bll+blk,blk)))-sk) , DELTAsk==sqrt(sqr(sk)+c2*sqr(cl[iref]*ifthenelse(mod(k,3),bll+blk,blk)))-sk+ c3*cl[i r e f ] *K33*hkl K*hkl t a u / s k , b l O + c l [ i > e f ] * i f t h e n e l se(mod(k, 3) , bll+blk, blk)*abs(hkl K)/sk) 2.2 Turbostratic disorder Turbostratic disorder is defined as the completely random lateral orientation of the (identical) layers in a stack. Thus, each layer acts as a separate scattering unit, just interacting in the direction perpendicular on the layers. The reciprocal lattice consists in discrete points along 001 but continuous hk rods. A simple trick for the generation of such a diffraction pattern consists in the generation of a big number of hkl 'peaks' along c* by definition of a single layer in a c* elongated 'empty' supercell [7], approximating the continuous rods in the reciprocal lattice. The calculated 'peak' intensity must be scaled according to the degree of filling the supercell, the meaningless generated 001 reflections must be sorted out, and any separate broadening parameters for hkl and 001 reflections must be defined, as demonstrated in some lines in the structure description file: layer==10 C=c0*layer Bl=ifthenelse(and(eq(h,0),eq(k,0)),blO+bll,blO) gewicht[1]=GEWlCHT*ifthenelse(and(eq(h,0),eq(k,0)) ,

i f t h e n e l se (mod (1, l a y e r ) ,0, layer) , 1) These formulations contain user defined parameters (e.g. layer: number of layers per supercell), BGMN predefined keywords (e.g. GEWICHT: the scaling factor) and typical crystallographic parameters (C: lattice parameter). This approach can be applied to turbostratically disordered clay minerals like smectites, see figure 2.

500 -

«Û. 300-

JO

Figure 2. Rietveld fit of a

60

Ca-montmorillonite.

80

¡00

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2.3 Stacking of different layers Clay minerals may consist of different types of layers which are stacked regularly or randomly with different translation vectors. The patterns may be calculated by the recursive method [8] which may be calculated using the functions of the structure description language. Again, a supercell extended along c* is the frame for the calculation of structure factors. The different layer types and possible translation vectors must be defined as well as the probabilities of the neighbouring of layers. The formulae of the recursive calculation of intensity must be also written into the structure description file. As the generation of a big number of peaks according to the elongation of the supercell and the effort for partial structure factor calculation need for a lot of computing power, BGMN was parallelized. So it is possible to apply the method routinely on recent desktop computers. The example below (figure 3) shows a fit of a disordered layered double hydroxide [9]. The x=2/3 plus y=l/3 and x=0 plus y=0 translations stand for two polytypes, the 3R¡ stacking of hydrotalcite like minerals and the 2Hi stacking of manasseite like ordering. These two orderings form here a randomly mixed layered material.

2520

Φ 15CL

10 -

m/U uuU C . J'wv

10

20

30

Figure 3. Rietveld fit of a mixture containing a layered double

hydroxide.

2.4 Combined refinement In clay mineralogy oriented samples are used to extract structural information from 001 series, typically from different stages of interlayer occupation like special cations, hydratation, or ethylene glycol solvation. The refinement of mixed-layer structure parameters (such as site occupation factors or individual basal spacings) from one basal series only has the risk of uncertainty. The combined refinement of the same ('global') parameters from different samples of the same material may add more information to the problem. In the BGMN notation, parameters that are used in several structural models of the same material may be refined globally in a control file. The example below (figure 4) shows a combined refinement of a Ca saturated illite/smectite mixed layered material from air dried powder, air dried oriented, and ethylene glycol solvated oriented samples.

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29

29

26

Figure 4. Rietveld fit of a combined refinement of a R3 illite/smectite mixed-layered mineral from three preparations. From top to bottom: air dried oriented, ethylene glycol oriented, air dried powder.

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Besides of a big number of individual parameters in the three structure models, the percentage of illite layers wl and the occupation of the interlayer position by potassium pK have been refined globally to obtain more accurate results. This is performed by using a user defined parameter "pKconnected" in the refinement controlling file. This file defines the measured data and calls the refineable structure files. In these structure files, the global parameter is passed to the structure specific parameters by formulations like pK=pKconnected.

3. Conclusion The phenomenological as well as the structure-based refinement of the diffraction patterns of disordered clay minerals is a useful tool for the investigation of these materials. Quantitative phases contents and structural parameters are achievable. The combined refinement of multiple measurements increases the quality of the results.

References 1.

Bergmann, J., Friedel, P. & Kleeberg, R., 1998, CPD Newsletter (Commission of Powder Diffraction, International Union of Crystallography), 20, 5-8.

2.

Leoni, M., Gualtieri, A.F. & Roveri, Ν., 2004, J. Appi. Cryst., 37, 166-173.

3.

Casas-Cabanas, M., Rodríguez-Carvajal, J. & Palacin, M.R., 2006, Ζ. Kristallogr. SuppL, 23, 243-248.

4.

Aplin, A.C., Matenaar, I.F., McCarty, D.K. & van Der Pluijm, B.A., 2006, Clays Clay Miner., 54, 500-514.

5.

Reynolds, R.C., 1993, in CMS Workshop Lectures, Volume 5, edited by R.C. Reynolds & J.R. Walker (Boulder: The Clay Mineral Society), pp. 43-77.

6.

Bergmann, J. & Kleeberg, R„ 1998, Mater. Sci. Forum, 278-281, 300-305.

7.

Ufer, K„ Roth, G„ Kleeberg, R„ Stanjek, H. & Dohrmann, R„ 2004, Z. Kristallogr., 219,519-527.

8.

Treacy, M.M.J., Newsam, J.M. & Deem, M.W., 1991, Proc. Roy. Soc. Lond., A433, 499-520.

9.

Ufer, K„ Kleeberg, R„ Bergmann, J., Curtius, Η. & Dohrmann, R„ 2008, Ζ. Kristallogr. SuppL, 27, 151-158.

Acknowledgement. We are grateful to Annegret Bergmann for deciding to make the program BGMN available for free distribution. After clarifying some formal and organisational issues, the BGMN webpage will be updated by a link for download of the last version of the program.

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Real-space powder diffraction computing on clusters of Graphics Processing Units L. Gelisio*, C. L. Azanza Ricardo, M. Leoni, P. Scardi Department of Materials Engineering and Industrial Technologies, University of Trento, 38123 via Mesiano, 77, Trento, Italy Contact author; e-mail: [email protected] Keywords: Debye scattering equation, Graphics Processing Units, Message Passing Interface Abstract. The Debye scattering equation was implemented in a brute-force massively parallel calculation using Graphics Processing Units (GPUs). Computing tasks can also be distributed among several computers thus further reducing the elaboration time. Graphite oxide in water is considered as a test case of study.

Introduction In the traditional reciprocal-space approach to diffraction, a crystal is assumed being perfect and infinitely extended in space: lattice defects are accounted for as a perturbation to the perfect crystalline order. At the nanoscale, however, the materials strongly deviate from these assumptions: problems arise due to the finiteness of the body and to the presence of a variety of defects and non-crystallographic features, like fivefold axes. Furthermore, below a few nanometres, nanocrystals do not show translational symmetry and should be better considered as large molecules than the usual stacking of unit cells. The most rigorous way to deal with the diffraction pattern of these imperfect materials is offered by real-space methods based on the Debye scattering equation [1], thus on the calculation of the interference of all atoms forming the particles. A widespread use of this equation is limited by the computational cost: the complexity of the formula scales with N2 being Ν the number of atoms in the system. The present work explores the most effective implementation of this approach on commercially available, relatively inexpensive GPUs [2],

The Debye scattering equation The Debye scattering equation (1) describes the intensity scattered from a given particle made of Ν atoms, under the hypothesis that it can take with equal probability every orientation with respect to the incoming beam. This is equivalent, if the kinematical approximation applies, to the evaluation of the intensity scattered from an ideal powder of the given particle. The Debye equation only takes into account the distances between two atoms (r¡j) and their scattering factors (f¡ and f¡). The arguments of the function are the wavevector transfer

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modulus ( ζ ) = Αττ ύΐί[Θ^Ι

λ^

and the energy of the incoming photons i^E = tico),

since

atomic scattering factors also depends on this quantity. / ( ß . M ^ Z Z / ' i ß ' ^ i ß ' M s m c f ^ ) . /=i j=ι

(1)

As the double sum runs over all atoms in the particle, its computational complexity increases with N 2 : historically this has been the major limitation to a widespread use of equation (1). Although some smart solutions can be exploited [3-6], they are not convenient or do not apply to particles significantly deviating from ideal geometrical bodies. For highly defected particles, equation (1) is conveniently mapped on GPUs on single hosts [2] or distributed on clusters of video cards, in order to further decrease the elaboration time.

The algorithm The basic algorithm is just outlined in the following (details can be found in [2]). Since thousands of threads can run concurrently on a GPU, we associate every atom with a thread. While GPU computes interference of all atoms, CPU calculates additional terms (e.g., polarization factor, atomic scattering factor, aberration corrections). No assumptions or approximations are made, apart from those inherent in the use of floating-point numbers. On a computer hosting several video cards, the Portable Operating System Interface (POSIX) Threads standard [7] is used to distribute the work. As each GPU computes a given region of the powder diffraction pattern, scaling with respect to the number of GPUs is linear.

node 1

2

\

GPU 1

GPU 1 2

1

4 5 6 7 8 9 10 11 12 13 Q[*-'|

node 2 i i f l l

node 1

f

4 5 6 7 8 9 10 11 12 13 α μ'j

GPU 2 2 3 4 S 6 7 8 9 10 11 12 13 0 [Α Ί

s f

node 2 GPU 2 2 3 4 S 6 7 8 9 10 11 12 13 Q[A'|

Figure 1. Powder pattern from a nanoparticle cluster: Schematic of the algorithm

workflow.

By using the Message Passing Interface specification (MPI) [8], the same algorithm can run concurrently on the GPUs hosted on different computers. Atomic coordinates are sent to the various nodes of the cluster, where POSIX Threads invoke GPUs. Again, each video card computes a given Q-region of the powder pattern. These concepts are summarized in figure 1, where we portrait an ideal architecture based on a cluster with two nodes, each hosting

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two GPUs. This solution limits the number of communications which could really be a bottleneck, especially if the computer cluster does not rely on high-performance (and expensive) data-transmission lines.

A case of study: Graphite oxide in water GO is a nonstoichiometric layered material consisting of graphene sheets bearing epoxy and hydroxyl groups on their basal planes and edges [10], This causes GO to be hydrophilic and the interlayer separation to increase when increasing the water content [11], The phenomenon is summarized in figure 2, where the trend of the position of the diffraction peak associated to the interlayer distance of a GO sample (produced by the Hummers method [12]) versus humidity content is shown. Data were collected on the MCX beamline diffractometer at

relative humidity [%]

Q = 4π sin(Ö) / λ [A"1]

Figure 2. Evolution of the GO interlayer separation, peak position versus relative humidity (left) and typical XRD patterns, flat plate geometry, λ = 1.23984 Â (right). The peak associated to the interlayer

Q = 4π sin(O) / λ [Á1]

Q = 4π sin((ì) / λ [Λ ]

Figure 3. Powder diffraction pattern of a glass capillary containing GO and water (left); simulated GO - water system, see text for details (right).

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We want to speculate here qualitatively (i.e. without trying to actually model the data) on the interpretation of the diffraction pattern of graphite oxide (GO) and water [9, 10] that could hardly be interpreted by a traditional reciprocal-space approach. In particular, we neglect instrumental aberrations, incoherent scattering and other phenomena not directly related to the sample. Moreover, as a first order approximation, we neglect the presence of oxygen and hydrogen on the layers. Figure 3 shows the X-ray Powder Diffraction (XRPD) pattern of a system composed of 0.050 g of GO and 150 μ ι of distilled water, loaded in a glass capillary after ultrasonic bath for one hour.

Three main features can be distinguished in the pattern of figure 3 : (i) the two peaks at Q ~ 5.1 Ä"1 and Q ~ 2.9 Ä"1 belong respectively to graphene in-plane distances of 1.23 Â and 2.13 Ä. Figure 4 shows a simulation for a powder of perfect graphene layers, where those two peaks are clearly visible; (ii) the broad peak about Q ~ 2 Ä"1 is the superposition of the main signal of water and the contribution of the glass capillary; (iii) the peak at Q ~ 0.5 Ä"1, corresponding to an interplanar distance of about 11.38 Ä, as a result of the stacking of GO layers. As mentioned above GO is hydrophilic, and increases the interlayer separation with the water uptake. We can describe this system as made of small graphite-like clusters with the appropriate layer separation (here we refer to graphite as we do not account for the presence of oxygen and hydrogen). The simulated pattern for a five-layer system having the interlayer separation of the experimental data (11.38 Ä), and layer diameter D = 500 À is shown in figure 5. In more detail, figure 5a is the XRPD pattern of a graphite-like system, i.e. a perfect stacking, of five layers, which clearly differs from the observed data (cf. figure 3a). Rotation of each graphene layer by a random quantity about the stacking axis (figure 5 b) affects only the in-plane scattering: (100) and (110) peaks (see the inset) assume the typical asymmetry of 2D systems, clearly visible in the experimental pattern. A different type of disorder is responsible for the suppression of the higher orders reflections

Ζ. Kristallogr. Proc. 1 (2011)

193

of the Q ~ 0.5 Â"1 peak, mostly visible in figure 5a as satellite lines in the Q range 0.5 h- 3.0 Â"1. By adding a random fluctuation (< 1 Â) of the interlayer distance, several features tend to disappear (figure 5c). The most intense effect is produced by a random tilt about the stacking direction: as shown in figure 5d, even a small tilt (< 5 χ IO"3 deg) removes most features apart from the fundamental modulation of the stacking (Q ~ 0.5 Â"1) and the in-plane reflections.

(a)

25

3 0

3.5

4.0

4.5

5.0

5.5

5 0

(b)

2 5

^

3.0

3.5

4,0

4.5

5.0

5.5

6 0

Í Q = 4π sin(O) / λ [Á1]

Q = 4π sin(O) I λ [Λ1]

(C)

2.5

^IaAv-^

30

3.5

4.0

4.5

5.0

5.5

0 0 Ü2

(d)

2.5

30

3.5

4.0

4.5

5Ό

5.5

6 0

kQ = 4rt sin((i) / λ [A"1]

Q = 4π sin(o) / λ [Λ ]

Figure 5. Simulated pattern for a system offive graphite-like layers: See text for details.

A further smoothing of the powder pattern results from the effect of the dispersion of shapes and extension of the coherent domains, either along the stacking direction (i.e., number of stacked layers) and in-plane. As shown in figure 4b, a plausible simulation can be produced by considering a distribution of domains, with a stacking of two to ten layers and an in-plane extension between 1000 and 2000 Â, and the disorder types described above. The Debye scattering equation was also used to simulate the contribution of water, as obtained by Molecular Dynamics considering a large cluster of molecules (~ 6.4 χ 107 Â 3 ) [13],

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Conclusions Modern GPUs have shown rapid increase in computational performances in the last few years. As video cards are embedded in almost every desktop computer, we have developed an algorithm which allows the use of GPUs on different hosts for a brute-force computation of the Debye scattering equation. This approach, which operates in direct space, is the most natural one for nano-sized objects and amorphous systems since the interference of all the atoms forming the system is considered. The executable, tested on various Linux-based operating systems, is freely available on request and the source will be soon available under GPL licence.

References 1.

Debye, P., 1915, Ann. Phys., 351, 809.

2.

Gelisio, L., Azanza Ricardo, C.L., Leoni, M. & Scardi, P., 2010, J. Appi. Crystallogr., 43, 647.

3.

Germer, L.H. & White, A.H., 1941, Phys. Rev., 60, 447.

4.

Glatter, O., 1980, Acta Phys. Austríaca, 52, 243.

5.

Hall, B.D. & Monot, R„ 1991, Comput. Phys., 5, 414.

6.

Cervellino, Α., Giannini, C. & Guagliardi, Α., 2006, J. Comput. Chem., 27, 995.

7.

IEEE and The Open Group, IEEE Std 1003.1, Technical report, 2004.

8.

M.P.I. Forum, MPI: A Message-Passing report, 2009.

9.

Dreyer, D.R., Park, S., Bielawski, C.W. & Ruoff, R.S., 2010, Chem. Soc. Rev., 39, 228.

Interface Standard Version 2.2, Technical

10. Gao, W„ Alemany, L.B., Ci, L. & Ajayan, P.M., 2009, Nat. Chem., 1, 403. 11. Lerf, Α., Buchsteiner, Α., Pieper, J., Schöttl, S., Dekany, I., Szabo, T. & Bohem, H.P., 2006, J. Phys. Chem. Sol, 67, 1106. 12. Hummers, W.S. & Offeman, R.E., 1958, J. Am. Chem. Soc., 80, 1339. 13. Kohlmeyer, Α., 2010. Private communication. Acknowledgements. The authors wish to thank Dr S. Bunch (University of Colorado at Boulder, USA) and Dr A. Kohlmeyer (Temple University, USA) for providing us, respectively, graphite oxide samples and some water clusters obtained by the means of Molecular Dynamics. Moreover we appreciated the support provided by the MCX beamline staff, Dr A. Lausi, Dr J. Plaisier, and G. Zerauschek.

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Evaluation of algorithms and weighting methods for MEM analysis from powder diffraction data K. M o m m a * , F. Izumi Quantum Beam Center, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan Contact author; e-mail: [email protected] Keywords: maximum-entropy method, electron density, MEM-based pattern fitting Abstract. Two different algorithms of the maximum-entropy method (MEM), i.e., 0th order single pixel approximation (ZSPA) and a variant of the Cambridge algorithm, were evaluated for MEM analysis from X-ray powder diffraction data. The Cambridge algorithm generally gave slightly better estimates of structure factors than the ZSPA algorithm. However, both algorithms tend to overestimate normalized residuals of some low-angle reflections. A weighting method on the basis of «-th power of the lattice-plane spacing, d, was effective in reducing such a tendency. The effect of the weighting on results of MEM analysis is discussed, and yet another weighting method, i.e., prior-derived weighting, is proposed.

1. Introduction In the maximum-entropy method (MEM) [1-3] for X-ray and neutron diffraction, the normalized electron or nuclear densities, pk (k: voxel number), in the unit cell are determined by maximizing the information entropy S: (1) where i k is the normalized density derived from prior information. The solution is iteratively reached by maximizing (2) containing two Lagrange multipliers, λ and μ, under the constraint C. The so-called F constraint, CF, is generally used as C. Let F0(hj) and F(hj) be the observed and calculated structure factors of reflection hj, a{hj) the standard uncertainty (s.u.) of \F0(hj)\, and NP the total number of observed reflections, then CF is formulated as (3)

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A problem in application of the MEM to powder diffraction data is that both \F0(hj)|'s and phases are biased toward the structural model in Rietveld analysis. This bias can be minimized by MEM-based pattern fitting (MPF), where MEM analysis and whole-pattern fitting are alternately repeated [4], Here, we report evaluation of two different MEM algorithms and weighting methods, exemplifying MPF analysis from powder X-ray diffraction (XRD) data o f N a V 6 0 „ [5], Our results basically confirm the results of earlier works for single-crystal XRD data [6-9]. We also propose yet another weighting method: prior-derived weighting.

2. Analytical procedures RIETAN-FP [10] was used for Rietveld refinements and whole-pattern fitting. During these processes, o(A;)'s were estimated on the basis of counting statistics: Fn M 1 , σ(,0 (4) σ(Α,) = 2 EI 0 where £ is a parameter to adjust a(hj), I0 is the observed integrated intensity, s is the scale factor, and o(s·) is the s.u. of s. The optimal value of £ was determined by close examination of results of MPF analyses with several different E values. Two algorithms are mainly used for determining the maximum-entropy (MaxEnt) distribution of electron or nuclear densities. One is Oth-order single pixel approximation (ZSPA) [11], and the other is the Cambridge algorithm [12], Electron densities calculated by the two algorithms are mostly consistent with each other. However, the normalized residuals of the structure factors, AFj, obtained by the ZSPA algorithm do not satisfy the exact MaxEnt conditions whereas the Cambridge algorithm always affords solutions close to the real MaxEnt ones [8], In this study, we have developed a new MEM analysis program, Dysnomia, where both the ZSPA algorithm and a variant of the Cambridge one are implemented. The convergence of the Cambridge algorithm was judged by the gradient of equation (2) : 1 «F -L^(dQ/dPkY072'

1

2,068· — Yield Strength

0,0

Elastic Modulus

(RpO.1 %) MPa GPa 304SS

1,0840A ^ 1,0832· t I . « ^ 1,0824·

175.45

293 Poisson's rado (y)= 0.3

0.000

0,005

0,010

0,015

0,020

0,025

0,030

0,035

0,040

Strain

Figure 1. Tensile Testing.

1,08160,0

-ι

1

*

1

:

.

1—

0,2 0,4 0,6 0,8 Applied Stress Zero MPa PlaneUl * ά(·Ψ) Φ =180 ® ά(+Ψ) Ψ (-65 to +65) • * * Λ 0,2

0,4

*

0,6

0,8

*

Figure 2. "d" \ 's. si if φ plot at zero applied stress of planes (111) and (311), ÄCa = 1.5415À.

Electrochemical measurements In order to gain information about the influence of tensile stress on the corrosion rate, breakdown potential, corrosion potential (E corr ), and corrosion current (Icorr), at 0.02M NaCl pH2 solution, several electrochemical measurements are required. Potentiodynamic curves of 304SS samples were measured on the unstressed and stressed sample (85% of Rp0.2) in 0.02M NaCl pH2 at a potential scanning rate 0.5 mVs"1, starting at -600 mV vs. SCE up to +700 mV vs. SCE as a final potential. Prior to determining the Mott-Schottky plots, samples (unstressed and tensile samples, respectively) were immersed at open circuit potential (OCP) for 3 h in order to reach a steady state (after 16 h alternative voltage passivation process (AVPP) in 0.02M NaCl pH2), then the polarization was applied in the anodic direction, by successive steps of 50 mV, and the electrochemical impedance was measured at 1.5 kHz. The polarization time before each measurement was 1 min. For the capacitance measurements, the concept of electrochemical double layer capacitance developed in the passive oxide near the film/electrolyte interface is

Ζ. Kristallogr. Proc. 1 (2011)

289

generally introduced and the measured capacitance corresponds to the space charge region developed at this interface. The values of interfacial double layer capacitance were calculated by the system software using the relation, ¡ m ( z \=

1

where Ζ is the imaginary part of

2.π/ C

the impedance and f is the frequency. The EC-Lab (VMP2) potentiostat from BioLogic science instruments was used for all the electrochemical experiments. The relationship between capacitance and applied potential is given by the Mott-Schottky equation. — = Γ

1

2

RR

_ P.N 2

1 —y = C

.

( e - ε ,. - — ) for η-type semiconductor J"

kT

{E - E r,

ss eN

3

0 a

e

) for p-type semiconductor

e

where ε is the dielectric constant of the passive film, ε 0 is the permittivity of the free space (8.85xl0" 14 F/cm); e is electron charge (1.602xl0" 19 C), N d and N a are the donor and acceptor densities, respectively. E f t is the flat band potential, k is the Boltzmann constant (1.38xl0" 23 J/K), and Τ is the absolute temperature. N d and N a can be determined form the slope of the experimental 1/C2 vs. applied potential (E) assuming the dielectric constant of the passive film on the stainless steel as 15.6 [6],

Residual stress measurements The determination of the residual stress using X-rays is based on the measurement of the angular shift of diffraction peaks caused by a small homogeneous variation of the lattice plane spacing, Ad, in the sampling volume with respect to the stress-free lattice plane spacing, do. In the case of a biaxial stress state(σ 1 3 = σ 2 3 = σ 3 3 = o), the micro-strain ε φψ{ΗΜ)stress related to (hkl) diffracting plane can be expressed as follows: ε

φψ (hkl)

=

2(-hkl')\_cr

Where -S2(hkl)

\

= (l + v ) / £

φ +σ an

u

sin 2φ + σ

d S^(hkl) = -vlE

22

sin 2 φ J sin 2 ψ + S j ( A ¿ / ) [ c t η + σ

22]

with ν and E are the Poisson ratio and

Young's modulus, respectively. ε a so w r φψ(ΚΗ) c a n ^ i t t e n using the Bragg's law in the form: ε φψ (hkl) ,MJ, =

Ad d

= -0.5cot an(0~),, , Α2Θ,, , v 0 '[hkl} (hkl)

6>0 and 2Θ are the angles corresponding to the position of the diffraction peak in a stress-free state and the Bragg angle, respectively[l-2], A Seifert 3003 X-ray diffractometer has been used to measure the surface stresses in the direction of loading by applying various constant loading (step 50 MPa) up to Rpo.2· The measurements were performed in the theta/2theta configuration, where the sample has been tilted by changing the ψ angle from -65 to +65 with a step of 10.8°, and φ measured for

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three different angles (145=325), (180=0), and (215=35). These measurements have been done for (111) and (311) planes of 304SS. Figure 2 shows the "d" vs. sin2\|/ plot at zero applied stress for the two studied planes.

Results and discussion Using a Seifert 3003 X-ray diffractometer system software and the mechanical elastic constants, the numerical values of the surface stress (on 304SS) in the direction of loading by applying various constant loading (step 50 MPa) were calculated. Below an applied stress of 190 MPa (corresponding to 65% of Rpo.2), the passive film is formed with a compressive stressed surface (see table (1)). On the other hand, tensile surface stresses are measured above 190 MPa. The residual stress measured on the (111) plane shows higher values than for the (311) plane. The reason for that might be attributed to the different penetration depths for (111) plane (τ 0 =0.75 μηι) and (311) plane (τ 0 = 1.43 μηι), and the assumption that the compressive stress at the surface is higher than under the surface. The results for the (311) plane have been used to describe the Mott-Schottky results as shown in figure 4. Table 1. Surface stress in the direction of loading from XRD experiments and stress applied during static loading tests of304 stainless steel for different planes of diffraction.

Grade

Plane

(311) 304 SS

(111)

Surface Stress (MPa)

Applied Stress (MPa)

Percentage of

-218

0

0

0

190

65%

115

293

100%

-340

0

0

-158

293

100%

Rpo.2%

Figure 3 shows a difference in the passive current density and the breakdown potential between the unloaded and the 85% Rp0.2 loading condition. The unloaded sample has higher value of breakdown potential. The decrease in the breakdown potential in the stressed sample could be due to passivity breakdown, localized dissolution, and modification of the tensile stress in the structure and conductivity of the passive film [7]. This is an indication that the material under stress is more sensitive to pitting corrosion.

Ζ. Kristallogr. Proc. 1 (2011)

291

Log I (m.4/cm2) Figure 3. Polarization cun'es of (a) Unstressed 304SS Specimen, (b) Stressed 304SS specimen in 0.02MNaCl, andpH2.

The results obtained from the Mott-Schottky analysis in the presence of an applied stress were discussed with respect to figure 4 and table 2. The zero applied stress can be considered as the reference trend. Although the passive film is heavily doped, this plot reveals two linear parts corresponding to Mott-Schottky-type behavior. In the cathodic region (E < - 100 mV vs. SCE), the capacitance describes the behavior of a p-type semiconductor which can be related to the inner oxide layer whereas in the anodic region (E > 250 mV vs. SCE), the capacitance represents the behavior of a η-type semiconductor which can be used to characterize the outer hydroxide layer. The results show that, by increasing the applied stress the slopes of the p-type and η-type semiconducting behavior decrease, resulting in increasing the doping of the inner oxide (associated to the p-type semiconducting behavior) and the outer hydroxide (associated to the η-type semiconducting behavior).

304SS —O—(a) Zero stress of Rp0.2 —m—(b)25% stress ofRp0.2 —φ—(ο)85% stress of Rp0.2

1,2x10'-

V

i

\ν

%

V.

/ f 1«! a•

/ /

j r j

χ

?

"...

Ewe(V) vs SCE Figure 4. Mott-Schottky·plots obtained on tensile specimen after using theAVPPfor OCP immersion in 0.02MNaCl pH2 in the presence of various applied stresses: («» σappi =0MPa c

σ

("surfa = "218·°

( > αρρ1 = -49.0 MPa

MPa

^

^

= 65.2 MPa)

σ

appi = 733

MPa

«>sUrfa = "134

MPa

>
0.25. Continuous phase transitions from the rhombohedral to a cubic structure in Pri^Gd.vAlOj solid solutions are predicted to take place at higher temperatures than the transformation in pure PrAlOq (1760 Κ [5,8]). Unfortunately, the limitations of the used equipment didn't allow the experimental determination of the Pm3im->R3c transition temperature. The temperatures of the continuous transition R3c*->Pm3m were estimated from the extrapolation of the c/a parameter ratios of the rhombohedral phase. As an example, the temperature dependencies of the normalized lattice parameters and the cell volume (fig. 3 a) and DSC graph (fig. 3, b) of Pr07Gd0.3AlOq are shown in figure 3. It was found that the transition temperatures of both HT transformation increase linearly with increasing Gd content. ^ 53.5 ^ 53.03,783.7(3 3.74 400

600

030

i 000

Temperature, Κ

1200

350

400

450

500

Temperature, Κ

Figure 3. Temperature dependencies of normalised lattice parameters and cell volume (a) and DSC graph (b) of Pr07Gd0¡A10¡, representing a first-order phase transitions R3 c*-*Pbmn.

Examination of LT powder diffraction patterns revealed a sequence of phase transition in Pri^Gd.vAlOj solid solutions with χ < 0.2, whereas samples with χ > 0.25 remain orthorhombic (Pbmn) down to 12 K. Analysis of the obtained diffraction data showed the following sequence of the phase transitions: i?3c/mmaC2/m (figure 4). Substitution of praseodymium in the pseudo-binary system PrAlOrGdAlO, leads to the opposite dependence of transition temperature versus composition of solid solution. The temperature of the orthorhombicto-monoclinic structure transition decrease linearly with decreasing Pr content, whereas for the rhombohedral-to-orthorhombic transformation a slight increase of the transition temperature is observed. Based on the results of in situ synchrotron powder diffraction examinations and DTA/DSC measurements as well as available literature data, the phase diagram of the pseudo-binary system PrAlOrGdAlO, has been constructed (figure 5). Five kinds of solid solutions with different perovskite-type crystal structures exist in the system, depending on composition and temperature. On cooling Pri^Gd.vAlOj samples with χ < 0.45 crystallize in the cubic perovskite structure and transform to the rhombohedral structure with decreasing temperature. The solid solution with the cubic structure exists only in a narrow temperature range between the liquidus (solidus) lines and the cubic-to-rhombohedral transition temperature.

Ζ. Kristallogr. Proc. 1 (2011)

323 90.60

—Η

90.55 90.50

\

ri) 90.45

α) ca

I2lm

90.40 90.35

\

Ε

90.30 90.25 50

90.20

100 150 200 Temperature, Κ

b) 20

40 60 80 Temperature, Κ

100

Figure 4. Thermal dependencies of normalised lattice parameters and cell volumes (a) and beta angels of the monoclinic phase (b) of Pr09Gd01AlO3. Lattice parameters are normalized to the perovskite ones as follows: ap=a,/^2, cp=c,Hl2, Vp=V/6: ap=a0/^¡2, bp=bJ2: cp=cJ~Í2, VP=VJ4; ap=a„/^2, bp=bm/2, cp=cmÑ2, Vp=Vm/4. The error bars (typically ±(1-3)-IO'4 A and ±(l-2)-10~} deg) are smaller than symbols in the graphs.

The mixed praseodymium-gadolinium aluminates Pr^Gd^AlOi with χ > 0.45 crystallize in the rhombohedral structure. For this composition the temperature of the rhombohedral-tocubic phase transition is predicted to occur above the melting point of the compound. The range of existence of the rhombohedral phase is largest in the phase diagram. The orthorhombic structure (Pbmn) appears in Gd-rich samples below 1970 K. This phase field shrinks with decreasing temperature and Gd-content until .v > 0.25. Solid solutions with orthorhombic (Imma) and monoclinic structures have very limited concentration and temperature existence ranges: They occur only for compositions with .v < 0.25 and below 290 Κ and 150 K, respectively.

Figure 5. Phase diagram of the pseudobinary system PrAlO¡-GdAlO¡. The letters L, C, Rh, Ol, 02 and M designate liquid, cubic, rhombohedral, orthorhombic Imma, orthorhombic Pbmn and monoclinic phase fields, respectively.

PrAI03

0.2

0.4

0.6

0.8

GdAI03

Gd content, at. fractions

4. Concluding remarks The crystal structures of solid solutions Pr^Gd^AlO, and their thermal behaviour in a wide temperature range 12-1773 Κ have been investigated by using in situ X-ray powder diffraction and DTA/DSC techniques. It was established that five kinds of solid solutions with

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different types of perovskite structures exist in the PrA10 3 -GdA10 3 system, depending on composition and temperature. At elevated temperatures, two phase transitions occur in Pri-^GdtAlOj: a continuous transformation R3c^Pm3m and a first-order transition Pbnm^R3 c. Two LT structural transformations R 3 c/mma and ImmaC2/m observed in the P r ^ G d j A l O j compounds with x < 0.2 below RT. The phase diagram of the PrA10 3 GdAlC>3 pseudo-binary system has been constructed based on the results of powder diffraction examinations and DTA/DSC measurements as well as available literature data.

References 1.

Geller, S. & Bala, V.B., 1956, Acta Crystallogr., 9, 1019.

2.

Vasylechko, L., Matkovskii, Α., Senyshyn, Α., Savytskii, D., Knapp, M. & Baehtz, C„ 2003, HASYLAB Ann. Rep., 1, 251.

3.

Vasylechko, L„ Senyshyn, A. & Trots, D.M., 2007, HASYLAB Ann. Rep., 1, 469.

4.

Coutures, J. & Coutures, J.P., 1984, J. Solid State Chem., 52, 95.

5.

Howard, C.J., Kennedy, Β.J. & Chakoumakos, B.C., 2000, J. Phys.: Condens. Matter, 12, 349.

6.

Vasylechko, L., Senyshyn, A. & Bismayer, U., 2009, in Handbook on the Physics and Chemistry of Rare Earths, Vol. 39, edited by K.A. Gschneidner, Jr., J.-C.G. Bünzli & V.K. Pecharsky (Netherlands: North-Holland), pp. 113-295.

7.

Cohen, E., Riseberg, L.A., Norland, W.A., Burbank, R.D., Sherwood, R.C. & Van Uitert, L.G., 1969, Phys. Rev., 186, 476.

8.

Harley, R.T., Hayes, W„ Perry, A.M. & Smith, S.R.P., 1973, J. Phys. C: Solid State Phys., 6, 2382.

9.

Birgeneau, R.J., Kjems, J.K., Shirane, G. & Van Uitert, L.G., 1974, Phys. Rev. B, 10, 2512.

10. Lyons, K.B., Birgeneau, R.J., Blount, E.I. & Van Uitert, L.G., 1975, Phys. Rev. B, 11,891. 11. Young, A.P., 1975, J. Phys. C: Solid State Phys., 8, 3158. 12. Fleury, P.A, Lazay, P.D. & Van Uitert, L.G., 1974, Phys. Rev. Lett., 33, 492. 13. Harley, R.T., 1977, J. Phys. C: Solid State Phys., 10, 205. 14. D'Iorio, M., Berlinger, W„ Bednorz, J.G. & Müller, K.A., 1984, J. Phys. C: Solid State Phys., 17, 2293. 15. Moussa, S.M., Kennedy, B.J., Hunter, B.A., Howard, C.J. & Vogt, T., 2001, J. Phys.: Condens. Matter, 13, 203. 16. Fujii, H., Hidaka, M. & Wanklyn, B.M., 1999, Phase Transition, 70, 115. 17. Watanabe, S., Hidaka, M., Yoshizawa, H. & Wanklyn, B.M., 2006, Phys. Solidi B, 243, 424.

Status

18. Akselrud, G.L., Zavalij, P.Yu., Grin, Yu., Pecharsky, V.K., Baumgartner, Β. & Woelfel, E., 1993, Mater. Sci. Forum, 133, 335.

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High-temperature XRD investigation of spinel Mn1.5Al1.5O4 decomposition 12 *

12

12

0 . Bulavchenko ' ' , S. Tsybulya ' , E. Gerasimov ' , 12 3 3 S. Cherepanova ' , T. Afonasenko , P. Tsyrulnikov 1

Boreskov Institute of Catalysis, pr. Akad. Lavrentieva 5, Novosibirsk 630090, Russian Federation 2 Novosibirsk State University, Pirogova 2, Novosibirsk 630090, Russian Federation Institute of Hydrocarbons Processing, st. Neftezavodskaya 5, 644040, Russian Federation Contact author; e-mail: [email protected] Keywords: high-temperature XRD, spinel, catalyst structure Abstract. This article describes a study of behaviour of cubic Mn1.5Al1.5O4 spinel during heating and cooling under air. High-temperature XRD and TEM were used to investigate structure transformations and sample micro structure. XRD data show spinel decomposition during cooling and heating under air at 500-700°C. The products of decomposition consist of nanocrystalline tetragonal phase (with particle size of 20 nm) and cubic spinel (50 nm). Cubic spinel composition changes by various ways on the initial step during the heating and cooling. Thus, the structure mechanisms of decomposition are different. But the final decomposition products are the same.

1. Introduction Manganese-aluminum oxides are often used as catalysts of deep oxidation. The Μη0*/Αΐ20 3 catalyst is formed during the high-temperature synthesis at 950°C. An active component of the catalyst consists of nano-sized particles of tetragonal β-Μη 3 0 4 spinel containing up to 15% at. of aluminium ions [1]. In literature [2, 3] it is reported that at the synthesis temperature (950°C) the catalyst consists of cubic spinel with composition of M n 1 . 5 A l 1 . 5 O 4 and corundum. During slow cooling in the furnace the cubic spinel decomposes into β-Μη 3 0 4 spinel and amorphous phase containing aluminium ions. However, phase composition and structure of the catalyst aren't fully understood under real conditions. In this work we investigated the model Mn1.5Al1.5O4 system during cooling and heating under air.

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2. Experimental 2.1 Preparation A sample with a ratio of Mn:Al =1:1 was prepared by simultaneous deposition of manganese and aluminium hydroxides with ammonia from A1(N0 3 ) 3 and Mn(N0 3 ) 2 solutions under stirring with a rate of 550 rpm until reaching pH 10. Then the residue was aged at 7080°C for 1 h. Further it was filtered, washed out with distilled water to pH 6 and dried at 120 C. The dried residue was ground in a mortar and calcined at 300°C for 4 h. From previous investigations [4] it was known that single phase cubic Mn1.5Al1.5O4 spinel can't be obtained during calcination at 950°C under air. Cubic spinel of Mn1.5Al1.5O4 is formed under low oxygen partial pressure (vacuum conditions of ~10~3 Torr or inert gas atmosphere), and is stable during cooling under these condition. Therefore, the sample was further calcined under air at 700°C for 4 h and under argon at 1050°C for 4 h. 2.2 Experimental High-temperature diffraction studies were carried out using a D8 diffractometer (Bruker, Germany) equipped with a high temperature X-ray chamber (Anton Paar, Austria) and a Goebel mirror. The X-ray diffraction (XRD) patterns were recorded using CuKa. The crystallite size was estimated using the Scherrer equation. Samples were quenched by cooling with a rate of 10 C/sec. Thermogravimetric analysis was carried out on NETZSCH STA 449C (Germany). Weight loss of the sample (50 mg) was studied in a temperature range from 25 to 1000°C (heating rate 5°C/min) under air. Transmission electron microscopy (TEM) images were obtained on a JEM_2010 microscope (JEOL, Japan) with a resolution of 1.4Â. Energy dispersive X-ray analysis (EDX) was carried out on an energy dispersive spectrometer with a Si (Li) detector and an energy resolution of 130 eV.

3. Results and discussion 3.1 High-temperature XRD investigation Figure 1 shows XRD data obtained under the stepwise sample heating from ambient temperature to 950°C and cooling from 950 to 25°C under air. As the temperature was raised, the diffraction lines of the initial spinel decreased in intensity and completely disappeared at 700°C. At the same time broad peaks of the new phases appeared in the XRD pattern. With increasing temperature to 950°C broad peaks disappeared and narrow peaks of cubic spinel with composition close to Mn1.5Al1.5O4 are formed again. During cooling from 950°C week broad lines of new phase started to appear at the temperature of 800°C. Further decrease in temperature up to 700°C led to Mn1.5Al1.5O4 disappearance (figure 1). At the temperature lower than 700°C no considerable change is seen in the diffraction pattern. As one can see in figure 1 at the temperature range of 600—700°C the diffraction patterns of samples obtained by heating and cooling are similar. In both cases the XRD patterns contain broad peaks, which can be ascribed to two phases: tetragonal spinel-type β-Μη 3 0 4 with particle size of 20 nm and cubic spinel with particle size of 50 nm.

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Figure 1. High-temperature XRD patterns under heating from 25 to 950PC and cooling from 950 to 25°C under air. At each temperature, the catalyst was held for 30 min. Asterisks point at the peaks of β-Μη3θ4, V — cubic spinel, circles — Μη¡ Ά1¡ ¡Οφ

3.2 Thermogravimetric (TG) analysis Thermogravimetric analysis was used to characterize the behaviour of Mn1.5Al1.5O4 during the heating under air. Figure 2 shows that an increase in the weight of sample is observed during heating from 300°C to 650 °C, and then heating to 1000 °C leads to weight loss. In addition the amount of added weight is equal to loss one.

Temperature (°C)

Figure 2. Thermogravimetric

analysis of the Mn I¡A1IÍ04 during heating to 1000°C.

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We assume that the change in the weight indicates a change in the oxygen content in the sample. There is a correlation between change in sample weight and its phase composition. It is interpreted that during heating from 300°C to 650 °C the initial spinel adds oxygen and decompose. The oxygen addition is accompanied by partial oxidation of Mir to Mn , + . On further heating from 650 °C to 1000°C Mn , + is reduced to Mn 2+ and the sample regenerates to cubic spinel structure. 3.3 TEM analysis TEM data obtained for the initial spinel and sample calcined at 700°C shows that the sample microstructures are rather changed. Initial sample consists of agglomerates of particles with crystal size higher than 100 nm (figure 3a). Particles are seen to be well-crystalline (figure 3b). Figure 3c displays TEM images of the sample calcined at 700°C. As seen in figure 3c along with large particles of cubic spinel small species of tetragonal phase are observed. EDX analysis was made approximately from the highlighted area. The area contains tetragonal phase and also is intersected with cubic one. So EDX data indicates that atomic ratio of Mn:Al in the selected region is approximately equal to 80:20, i.e. particle mainly contains manganese atoms.

Figure 3. TEM image of a,b) initial sample of cubic Mn¡ ¡A1L¡04 spinel, c) sample calcined at 700", d) EDX analysis of selected region (Signal of Cu is observed on the EDX data due to sample holder consisted of the copper).

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3.4 Differences in decomposition process between cooling and heating To investigate structure mechanism of spinel decomposition we compared spinel behavior during the initial steps of decomposition under cooling and heating. Figure 4 displays XRD patterns of initial Mn1.5Al1.5O4, quenched samples after heating at 400°C, 450°C, cooling from 950 to 800°C. As shown in figure 4, the diffraction lines of spinel shifted in different directions after cooling and heating due to change in cell parameter. As temperature was raised the cell parameter decreased and on the contrary it increased during the cooling. Change in cell parameter means that Mn content in spinel decreased during the cooling ( M 1 i 1 . 5 A l 1 . 5 O 4 —> Miii.5_xAli.5+x04) and increased during the heating ( M 1 i 1 . 5 A l 1 . 5 O 4 —> Mlli.5 +x Ali.5. x 0 4 ).

Along with diffraction lines shift weak broad peaks appear in XRD patterns after the temperature treatments (figure 4). In the case of heating these peaks can be ascribed to tetragonal, spinel-type β-Μη 3 0 4 and to cubic spinel at cooling.

1 30

1

1 35

1

2 0, d e g r e e s

1 40

1

1 45

Figure 4. XRD patterns of a) quenched sample after cooling from 950 to 800 °C, b) initial, c) quenched sample after heating at 400"C, d) quenched sample after heating at 450°C. Asterisks point at the peaks of β-Μη ¡Οφ V — cubic spinel, circles — Mn¡ ·Α1 ¡ ¡Ο4.

Thus different structure mechanisms of decomposition are observed during the cooling and heating. At heating, since the Al-content of the spinel increases, Mn ions rearrange to form small particles of β -Mn 3 0 4 on the surface of the host phase. During cooling the composition of cubic spinel was changed ( M 1 i 1 . 5 A l 1 . 5 O 4 —> Μιΐι.5+χΑ1ι.5.χθ4). Concentration of M n , + ions in octahedral coordination, which are the Jahn-Teller active ions, increased. As temperature decreased the concentration reached a critical value, which induced an octahedral distortion. Due to this effect spinel decomposition occurred.

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4. Conclusion High-temperature XRD and TEM analyses are demonstrated to be useful in investigation of catalyst systems. Model active component of the catalyst (cubic spinel Mn1.5Al1.5O4) is shown to decompose during the heating and cooling under air at the temperature range of 500-700°C. At these temperatures sample contains two spinel-type phases: cubic and tetragonal ones. Further heating to the temperature of 950°C regenerates its initial structure. According to TG analysis, the decomposition process is accompanied by oxygen addition and partial oxidation of Mn 2+ into Mn 3+ ions.

References 1.

Tsybulya, S.V., Krukova, G.N., Vlasov, A.A. Boldyreva, N.N., Kovalenko, O.N. & Tsyrulnikov, P.G., 1998, React. Kinet. Catal. Lett., 64,113.

2.

Kriger, T.A., Tsybulya, S.V. & Tsyrulnikov, P.G., 2002, React. Kinet. Catal. Lett., 75, 141.

3.

Tsybulya, S.V., Kryukova, G.N., Kriger, T.A. & Tsyrul'nikov, P.G., 2003, Kinet. Catal., 44, 287.

4.

Bulavchenko , O.A., Tsybulya, S.V., Cherepanova, S.V., Afonasenko, T.N. & Tsyrulnikov, P.G., 2009, J. Struc. Chem., 50, 485.

Acknowledgements. This work was supported by the integration project SB RAS N°36 and the grant under the program "Development of scientific potential of the higher school" JV°2.1.1/729.

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Influence of AL ions on the reduction of CO3.XA1x04: in situ XRD investigation 12*

12

1

S. Cherepanova ' ' , O. Bulavchenko ' , I. Simentsova , 12 1 E. Gerasimov ' , A. Khassin 1 2

Boreskov Institute of Catalysis, Lavrentieva prospect 5, Novosibirsk, 630090, Russia Novosibirsk State University, Pirogova street 2, Novosibirsk, 630090, Russia Contact author; e-mail: [email protected]

Keywords: in situ X-ray diffraction, reduction, solid solution, domain structure Abstract. The addition of small amounts of Al ions to nanocrystalline C03O4 leads to considerable changes in its reduction. In situ XRD and TPR show that Al ions affect the extent of cobalt reduction achieved in a hydrogen flow. C03O4 is fully reduced to metallic cobalt at a temperature of ca. 200°C. As for Al-modified samples ϋο 3 . Ι Α1 Ι 0 4 (χ = 0.05, 0.1, 0.2), they contain CoO even after reduction at 350°C. The higher is the Al content; the lower is the C0/C0O ratio. At 350°C, metallic particles in all cases consist of platelet domains having the hep and fee structure. In the case of metallic cobalt reduced from C03O4, the fee domains are twice thinner as compared to hep ones, their average thicknesses being ca. 0.9 nm and 1.8 nm, respectively. In metallic cobalt reduced from Co3.xA1x04 (x = 0.05, 0.1, 0.2), the fee and hep domains have almost equal average thicknesses of ca. 1.4 nm.

Introduction The reduction of nanocrystalline C03O4 modified by small amount of Al ions is not sufficiently investigated yet. The effect of Al doping on Co 3 0 4 reduction was studied in [1], It was shown that such promotion of cobalt oxide dramatically decreases its reduction rate. In contrast to ϋο 3 . Ι Α1 Ι 0 4 solid solutions, the reduction of C03O4 supported by γ-Α1 2 0 3 is widely discussed in literature. Such studies are commonly performed using temperatureprogrammed reduction (TPR) [2-7]. The TPR profiles usually contain two major peaks. Since the ratio of the first peak area to that of the second one is close to 1:3, many authors [611] assumed that this is consistent with the stoichiometry of C03O4 reduction in two stages. C03O4 is reduced to CoO at the first stage, and the second one is reduction of CoO to metallic Co. Low-temperature peak is always narrow indicating rapid exothermal process. Hightemperature peak is always wide that points at certain difficulties in the reduction of CoO to metallic cobalt. In [7] it was explained by the interaction of small oxide particles with the support leading to the formation of hard-to-reduce oxides. Another interpretation was offered in [12] where reduction of Co304/y-Al 2 03 was investigated. It was suggested that the first peak at 320°C is due to the reduction of the surface co-

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bait oxide which is not stabilized by interaction with the support and can be reduced easily, whereas the wide peak at 380-730°C corresponds to the reduction of xCoOyAl 2 0 3 mixed oxide. The similar explanation for the presence of two peaks on TPR profile was suggested in [13] where the reduction of Co 3 0 4 /y-Al 2 0 3 was studied. The first peak was attributed to the reduction of large Co 3 0 4 particles to metal and small ones to CoO. The second peak was ascribed to the reduction of small oxide particles strongly interacting with alumina support. One can't discriminate between these multiple interpretations only basing on the TPR profiles, since they only show hydrogen consumption rates, but they aren't suitable for phase and structure analysis. As for reduction of single-phase Co 3 0 4 , TPR curve consists of two narrow peaks which often are unresolved [13-15], Sometimes there is one main peak and a low-temperature shoulder [13, 15, 16], Thus, TPR data show that the reduction goes differently for Co 3 0 4 and for Co 3 0 4 /y-Al 2 0 3 . Co 3 0 4 is easily reduced to metal, while reduction of Co 3 0 4 supported by alumina meets significant hindrances at the second step. Also XRD patterns for Co/y-Al 2 0 3 contain diffraction peaks of ß-Co fee structure starting from the 350°C [8, 17] that is lower than temperature of hep-to-fee phase transition (Thcp_fcc~420 °C at normal pressure). In this paper we study by means of in-situ XRD how substantially does the promotion of nanocrystalline Co 3 0 4 oxide by small amount of Al cations change reduction behaviour of the oxide.

Experimental The samples of aluminum-promoted cobalt oxide, Co^Al^CU (x=0, 0.05, 0.1, 0.2), were prepared by calcination of the corresponding Co-Al hydroxycompounds in air at 500°C for 4 hours. These mixed compounds were obtained by the co-precipitation of Co 2+ and Al 3+ ions from 10 % wt. aqueous solutions of their nitrates at pH = 7.1-7.2 and Τ = 65-70°C. A sodium carbonate solution was used as the precipitant. The obtained precipitate was carefully washed out with distilled water and dried in air under infrared lamp at 45°C for 24 hours. According to the atomic emission spectrophotometry, the sodium content in the dried samples did not exceed 0.005% by weight. The same method was used to check the aluminum content in the samples. The X-ray diffraction (XRD) patterns were obtained using X-ray diffractometer (Siemens, CuKa radiation) featuring a home-made high-temperature camera-reactor. Samples were reduced in H 2 flow at 350°C for 1 hour; then X-ray diffraction patterns were recorded by scanning in the 2Θ angle range from 40° to 55° with step of 0.05° and acquisition time of 30 s at each point. Temperature-programmed reduction (TPR) was carried in the mixture of 10% H 2 /Ar (flow rate 40 cm 3 /min, pressure 1.0 bar). The gas was passed over the samples. The samples were heated from room temperature up to 900°C with constant temperature ramp rate (10 K/min). Before the reduction, the samples were treated at 500°C in 0 2 flow during 0.5 h and then cooled down to room temperature in 0 2 flow.

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Results Initial C03 .vAl.vO4 (λ- = 0, 0.05, 0.1, 0.2) s a m p l e s

According to XRD data, all the samples have a cubic spinel-type structure. The calculated average crystallite sizes and refined lattice constants are listed in table 1. The addition of a small amount of Al ions slightly changes the lattice constant due to formation of a C03.jAlj.O4 solid solution. A decrease in the lattice constant is related with a smaller ion radius of Al , + as compared to those of Co 2+ and Co ,+ . Table 1. Average crystallite sizes X in

CO3,JA1J04

< D > , nm a,

A

and refined lattice constants a.

0

0.05

0.10

0.20

28

26

21

22

8.084(1)

8.083(1)

8.082(1)

8.082(1)

Reduction of the C03.vAl.vO4 (λ' = 0, 0.05, 0.1, 0.2) samples in H 2 flow TPR profiles show that the addition of Al ions to C03O4 does not affect the first step — the reduction of C03O4 to CoO, but drastically hinders the second step — the reduction of CoO to metallic Co (figure 1). The reduction of C03.jAlj.O4 solid solutions with a small content of ΑΙ (.ν = 0.05, 0.1, 0.2) is similar to the reduction of C03O4 supported on y-Al^Oj. In situ XRD shows that the samples reduced at 350°C give the peaks of metallic Co and CoO phases (figure 2). The higher is the Al content, the higher is the C0O/C0 ratio. This agrees with the TPR data. In all cases, the XRD patterns of metallic cobalt have some common peculiarities (figure 2). There are the peaks of low- and high-temperature modifications of Co having the hep and fee structures, respectively. Also anisotropic peak broadening is observed. One can see that the 101 hep and 200 fee peaks are noticeably broader than the 100, 002 hep and 111 fee peaks.

ίσο

20a

30a

100 too Tempfrrslupe'C

::

as;

Figure 1. TPR profiles of nanoctystalline ( «. . 1/ (>:: α) χ = 0: b) 0.05; c) 0.1: d) 0.2.

goo

40

J5

Mi

2 Γ he! j degrses

5Í

Figure 2. XRD patterns of the samples reduced from Co; .!!():: a) χ = 0: b) 0.05; c) 0.1: d) 0.2. Squares and circles show the positions of hep and fee peaks, respectively, arrow indicates the CoO peak.

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A similar XRD pattern was observed for the metallic particles after the reduction of Coo.9Mgo.1O [18, 19], the indicated diffraction effects being explained by the formation of a microstructure with alternating hep and fee platelet domains. The domain microstructure of metallic particles was verified by a high resolution electron microscopy examination of C02.95AI0.05O4 reduced at 350°C (figure 3).

Figure 3. HREM image of metallic particle reduced from C02.95AI0.05O4 at 350 °C. Simulation of XRD patterns for metallic particles having the domain microstructure The XRD patterns were simulated by a program reported elsewhere [18, 19]. The calculations were based on the model of a one-dimensional (ID) disordered crystal [20], The model represents a statistical sequence of different type layers that can be shifted relative to each other. A Markov chain is used as a probabilistic rule for generating the sequence. One type of A B layer consisting of two close-packed A and Β layers, where Β layer is shifted on the (2/3, 1/3) vector relative to A layer, and two types of AB layer superposition were chosen to describe the fee and hep structures in the direction of close packing. So, the fee structure representing the AB-CA-BC-... sequence can be defined as a sequence where each A B layer is shifted on the (1/3, 2/3) vector relative to the previous one (below the 1 st type of AB layer superposition). In the hep structure, which is the AB-AB-AB-... sequence, AB layers follow each other without any shift (the 2 nd type). We defined the average thicknesses of fee and hep domains in the crystallites with the use of two parameters. The first parameter is the probability W¡ (i = 1 or 2) that the ¿-type of the layer superposition will appear in a pair of adjacent A B layers. It is sufficient to define one of two W¡ probabilities, for example, W¡, because W2 is dependent on W¡ ( W¡ + W2= 1). Then, a ratio of the average thicknesses of the domains with fee and hep structures is equal to WJ1 - W¡. The second parameter is the conditional probability Pu (i = 1 or 2) that a certain type of layer superposition is followed by the same type in three adjacent A B layers. Parameters P¡¡ and Ρ22 determine the average thicknesses and of fee and hep domains, respectively. The average thickness can be calculated as ΣΜ>,„/,„/ΣΜ>,„ (m = 2 , 3 , . . . ) , where vt'm = W,{P,)m-' is the probability of appearance of the domains with thickness /,„ (m is the number of A B layers). We defined P¡¡ for determination of the average thickness . The average thicknesses and are connected by the equation < I ¿ > / < I 2 > = W¡¡ 1 - W¡. Thus, varying the W¡ and Pu parameters allow us to describe the microstructure which differ by the average thicknesses of fee and hep domains and calculate the corresponding XRD patterns. Samples of the reduced C O 3 . X A 1 X 0 4 solid solutions with Χ = 0 . 0 5 , 0 . 1 and 0 . 2 have very similar microstructures as that shown below. So, we have only simulated XRD patterns

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for two of the reduced at 350°C samples: with χ = 0 (figure 4) and 0.05 (figure 5). There is a substantial difference between the experimental XRD patterns of these samples (see the ratio of 101 hep and 200 fee peaks). One can see that the experimental XRD pattern of the sample reduced from Co,0 4 corresponds to the simulated XRD patterns for the fee domains being approximately twice thinner as compared to hep ones. The average domain thicknesses of ca. 0.9 and 1.8 nm gave the best fit (figure 4). The simulations also showed that metallic particles reduced from C 0 2 . 9 5 A I 0 . 0 5 O 4 have almost equal average thicknesses of the fee and hep domains of about 1.4 nm (figure 5). It should be noted that the shape of 111 peak was not fitted well enough, however we tried to fit all the peaks simultaneously taking into account their intensity and width.

*Q

4!

η

44

45

46

¿7

4ί

49

»

>

Ξ

SI

»

»

ZTheie. d e g r e e s

Figure 4. a) Experimental XRD pattern (black) of the sample reduced from Co,O4 and simulated pattern (grey) for metallic particles having domain microstructure with the average thicknesses of 0.9 and 1.8 nm for fee and hep domains, respectively; b) the difference curve.

40

11

4Í

43

44

45

+6 4& 4 Í 2Thela. degrees

50

Si

52

65

54

55

Figure 5. a) Experimental XRD pattern (black) of the sample reduced from C02.95AI0.05O4 and simulated pattern (grey) for metallic particles having domain microstructure with the average thicknesses of 1.4 and 1.4 nm for fee and hep domains; b) the difference curve. Arrows indicate the CoO peak.

To reveal whether the Al content has an effect on the metallic particle microstructure, the XRD patterns of Al-containing samples were processed in a following manner: the background was subtracted, and the patterns were reduced by the intensity of Co0 peaks (figure 6). After that, it became clear that metallic particles have almost similar microstructures for χ = 0.05, 0.1 and 0.2. Thus, the amount of introduced Al does not affect the microstructure of metallic particles. Only the fact of absence/presence of Al ions is significant.

2Tjiela

desees

Figure 6. Comparison of XRD patterns of the samples reduced from nanocrystalline a) x=0.05 (light grey line); b) 0.1 (grey); c) 0.2 (black).

Coi_xAlx04:

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Concluding remarks Al ions have a tendency to stabilize CoO during the reduction, on the one hand, and to stimulate the formation of the high temperature fee modification of metallic cobalt, on the other hand. The latter manifests itself as an increase in the average thickness of fee domains and a decrease in that of hep domains. This can be explained as follows. Al 3+ ions can not be reduced up to oxidation state 2+ as Co ions do. Therefore they segregate to the surface of particles during first step of Co3_xA1x04 reduction. Al-enriched oxide surface forms tarnish, which inhibits the CoO reduction. Minor amount of Al 3+ ions seems to remain in the bulk of Co(II) oxide phase stabilizing the fee structure domains.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

20.

Ivanova, S.A., Dis'ko, V.A, Moroz, E.M. & Noskova, S.P., 1985, Kinetics and Catalysis, 26, 1193. Bessell, S„ 1993, Appi. Catal. A, 96, 253. Rosynek, M.P. & Polansky, C.A., 1991, Appi. Catal., 73, 97. Vob, M„ Borgmann, D. & Wedler, G„ 2002, J. Catal., 212, 10. Lin, H.-Y. & Chen, Y.-W., 2004, Mater. Chem. Phys., 58, 171. Jacobs, G., Chaney, J.A., Patterson, P.M., Das, T.K. & Davis, B.H., 2004, Appi. Catal. A, 264, 203. Jacobs, G., Das, T.K., Zhang, Y., Li, J., Racoillet, G. & Davis, B.H., 2002, Appi. Catal. A: General, 223, 263. Bechara, R., Balloy, D., Dauphin, J. & Grimblot, J., 1999, Chem. Mater., 11, 1703. Das, T.K., Jacobs, G„ Patterson, P.M., Conner, W.A., Li, J. & Davis, B.H., 2003, Fuel, 82, 805. Li, J., Zhan, X., Zhang, Y., Jacobs, G., Das, T. & Davis, B.H., 2002, Appi. Catal. A, 228, 203. Jacobs, G., Patterson, P.M., Zang, Y., Das, T., Li, J. & Davis, B.H., 2002, Appi. Catal. A, 233, 215. Lapidus, Α., Krylova, Α., Kazanskii, V., Borovkov, V., Zaitsev, Α., Rathousky, J., Zukal, A. & Jancalkova, M., 1991, Appi. Catal., 73, 65. Zhang, Y„ Wei, D„ Hammache, S. & Goodwin, J.G. 1999, J. Catal., 188, 281. Sexton, Α., Hughes, A. E. & Turney, T. W„ 1986, J. Catal., 97, 390. Solsona, B., Davies, T.E., Garcie, T., Vazquez, I., Dejoz, A. & Taylor, S.H., 2008, Appi. Catal. B, 84, 176. Okamoto, Y., Nagata, K., Adichi, T., Imanaka, T., Inamura, K. & Takya, T., 1991, J. Phys. Chem., 95, 310 Bulavchenko, O.A., Cherepanova, S.V. & Tsybulya, S.V., 2009, Z. Kristallogr. Suppl., 30, 329. Cherepanova, S.V. & Tsybulya, S.V., 2004, Materials Science Forum, 443, 87. Tsybulya, S.V., Cherepanova, S.V. & Kryukova, G.N., 2004, in Diffraction Analysis of the Microstructure of Materials, edited by Mittemeijer, E.J. & Scardi, P. (Berlin: Springer), pp. 93-124. Drits, V.A. & Tchoubar, C., 1990, X-ray Diffraction by Disordered Lamellar Structures (Berlin: Springer).

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CS2C11SÌ5O12 phase transition? A . M . T. Bell 1 '*, C. M . B. Henderson 2 1 2

HASYLAB/DESY, Notkestraße 85, 22607 Hamburg, Germany SEAES, University of Manchester, Manchester M13 9PL, UK Contact author; e-mail: [email protected]

Keywords: mineral chemistry, phase transitions, Rietveld refinement Abstract. We have recently revised the ambient temperature crystal structure of the hydrothermally synthesized leucite analogue Cs 2 CuSi 5 0i 2 [1] using high-resolution synchrotron Xray and neutron powder diffraction. This has the Pbca crystal structure with Si and Cu completely ordered over the tetrahedral T-sites (TI = Cu, T2-6 = Si). The Cs 2 CuSi 5 0i 2 lattice parameters are: - a = 13.58943(6)À, b = 13.57355(5)À and c = 13.62296(4)À. As a, b and c are so close it was thought that if this sample were to be heated the crystal structure may undergo a phase transition to a higher symmetry space group and/or to a structure with some T-site disorder. High temperature synchrotron X-ray powder diffraction measurements show a significant lattice parameter shift in the temperature range 329-335K. Above this temperature range the crystal structure becomes less distorted but the ordered Pbca structure is retained. This "phase transition" is reversible on cooling but takes place in the temperature range 319-317K.

1. Introduction Synthetic analogues of the tetrahedral silicate framework mineral leucite ( K A l S i Ä ) have the general formulae of A 2 BSi 5 0 12 or ACSi 2 0 6 (A = K + , Rb+, Cs+; Β = Mg 2+ , Mn2+, Fe2+, Co2+, Ni 2+ , Cu2+, Zn 2+ , Cd2+; and C = Al 3+ , Fe3+). A cations are extraframework, Β and C cations are incorporated into the silicate framework. By varying the synthesis conditions, stoichiometry and framework cation ordering the crystal structures of these leucite analogues can be P2¡/c monoclinic [2], Pbca orthorhombic [3], 14¡/a tetragonal [4] or laid cubic [1, 2, 5], Phase transitions from tetragonal to cubic [6, 7, 8] and monoclinic to orthorhombic [9] have also been observed on heating leucite analogues. The hydrothermally synthesized leucite analogue Cs 2 CuSi 5 0i 2 [1] has the Pbca crystal structure with Si and Cu completely ordered over the tetrahedral T-sites (TI = Cu, T2-6 = Si). The room temperature lattice parameters are: - a = 13.58943(6)Â, b = 13.57355(5)Â and c = 13.62296(4)Â. As a, b and c are so close it was thought that if this sample were to be heated the crystal structure may undergo a phase transition to a higher symmetry space group and/or to a structure with some T-site disorder.

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2. Data collection and analysis 2.1 Data collection High-temperature synchrotron X-ray powder diffraction data were collected on this sample using the STOE furnace attachment on the DORIS-III B2 beamline [10] at HASYLAB. A synchrotron X-ray wavelength of λ = 0.68806À was used. Data were collected using the OBI image-plate detector, in 2K increments approximately every 30 minutes, as the sample was heated and cooled in the temperature range 313-353K. Figure 1 shows a plot of these powder diffraction data on heating, figure 2 shows these data on cooling. On heating there is a transition from the low temperature (LT) region to the high temperature (HT) region in the temperature range 329-335K; there is a dip in maximum powder data intensity during this transition due to the presence of closely overlapped Bragg reflections for the LT and HT phases. The powder data show a shift to lower 2Θ values when moving to the HT region. This transition is reversible on cooling but takes place in the temperature range 319-317K.

Β

χ

4 K 1ú Cs2CuS¡rí012 coal

ι ' CS2CUSÌS012 heal up - 2K stspft

10

11

12

13

14

15

20

16

17

18

19

Figure 1. CsjCuSisOij powder data on heating.

down - 2K steps

20

Figure 2. CsjCuSisOu powder data on cooling.

2.2. Data analysis Rietveld [11] refinement using FULLPROF [12] showed that all data could be fitted with the ordered T-site Pbca structure [1]. Two-phase refinements were done in the transitions between the LT and HT regions. In the two-phase regions it was possible to refine lattice parameters for the LT and HT phases but it was not possible to refine atomic coordinates due to the severe peak overlap. Figure 3 shows how the unit cell volumes vary for the LT and HT regions, note the -35Â 3 volume difference between the two regions. Figure 4 shows a twophase Rietveld difference plot for the data collected on heating at 333K.

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3. Discussion Due to the presence of Cu T-sites and the extraframework Cs+ cations in this silicate framework structure, these T 0 4 tetrahedra are distorted, the O-T-O bond angles are not the ideal tetrahedral angle of 109.47°. The distortion of these tetrahedra can be expressed by the tetrahedral angle (Θ) variance [13], see equation 1.

θσ ( ω ) 2 = Σ (θ, - 109.47°)2/5. i= 1

(1)

Figures 5 (heating) and 6 (cooling) show how the tetrahedral angle variance for each TO4 unit varies with temperature. These figures show that the variance for the Si3 T-site is significantly larger than those for other T-sites in the LT region. The Si3 T-site variance decreases to (very approximately) the same value as those for other T-sites in the HT region. On cooling the Si3 T-site variance remains (very approximately) the same value as those for other Tsites in the HT region but then increases again in the LT region. Therefore in the LT region, the Si3 T-site is more distorted than all other T-sites but in the HT region the distortions of all 6 T-sites are (very approximately) the same. There are no significant changes in any of the 8 intertetrahedral (T-O-T) Si-O-Si angles over the LT and HT temperature ranges on both heating and cooling. However, there are significant changes in 2 of the 4 Cu-O-Si angles in these temperature ranges. Figures 7 (heating) and 8 (cooling) show how that the Cul-07-Si5 angle decreases on going from the LT to HT whereas the Cul-04-Si4 angle increases on going from the LT to HT. The difference between these two Cu-O-Si angles gets much smaller in the HT region. For clarity none of the other T-O-T angles are shown in these two figures. Figures 9 and 10 respectively show VESTA [14] plots of the crystal structure of Cs 2 CuSi 5 0i 2 at 313K (LT phase) and 353K (HT phase). Note the increase in distortion of the Si3 T-site and the extraframework Cs+ cation channel in the Figure 9 (LT) compared to Figure 10 (HT). At room temperature the crystal structures of the hydrothermally synthesized leucite analogues K 2 MgSi 5 0i2 [2] and Cs 2 CuSi 5 0i 2 [1] and are respectively P2¡/c monoclinic and Pbca orthorhombic, whereas at room temperature the crystal structures of dry synthesized analogues of these two leucites are both laid cubic. The cubic dry synthesized structures have complete T-site cation disorder whereas the lower symmetry hydrothermally synthesized have complete T-site cation order. For both leucite analogues the disordered cubic structures are less distorted than those of the ordered lower symmetry structures and have larger unit cell volumes (K 2 MgSi 5 0 12 :- V = 2416.33(5)À 3 - dry, V = 2348(2)À 3 - hydrothermal; Cs 2 CuSi 5 0 12 :- V = 2533.4(2)Â 3 - dry, V = 2512.847(13)Â 3 - hydrothermal). Therefore, by analogy with the K 2 MgSi 5 0i 2 and Cs 2 CuSi 5 0i 2 leucite analogues, the increase in lattice parameter in this "phase transition" is caused by the crystal structure becoming less distorted and expanding. This is due to the decrease in the Si3 Τ site distortion and the decrease in difference between the Cul-04-Si4 and Cul-07-Si5 T-O-T angles. On cooling through this transition this is reversed, the crystal structure becomes more distorted and contracts.

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healr u p LT h e a t u p HT

H

4 cool d o w n LT • cool tiov/n HT

LlUlLi.

t e m p e r a t u r e (Κ)

Figure 3. Variation of Cs2CuSisO¡2 unit cell volumes on heating up and cooling down.

!| 2h

/ V

Figure 4. Two-phase Rietveld difference Cs2CuSisO¡2 on heating to 333K.

plot

for

•

i :

iz •Ν

Figures 5a (upper left) and 5b (upper right) show the variation of the tetrahedral angle variance for C11O4 and S1O4 units on heating. Figures 6a (lower left) and 6b (lower right) show how this variance varies with cooling. Note the difference in variance for the Si3 site in the LT regions.

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/M-"1'

liiHÎnll

\

i

h y

/ \

kqaÉuN

Figures 7 (left, healing) and 8 (right, cooling) shows the variation of 2 of the 4 Si-O-Cu angles either side of the transition temperature.

T-O-T

Figures 9 (left) and 10 (right) show Cs2CuSi5O12 crystal structure plots on heating to 313K (LT phase - left) and 353K (HT phase - right). Csl cation sites are represented by light grey spheres, Cs2 cation sites by dark grey spheres and O anion sites by small black spheres. White tetrahedra represent Si3 T-site Si04 units, light grey tetrahedra represent all other Si04 units and dark grey tetrahedra represent C11O4 units. Note the greater distortion of the LT Si3 tetrahedra and the Cs cation channel in the framework structure compared to that for the HT structure.

4. Conclusions An unexpected change in the crystal structure of CS2C11SÍ5O12 is seen on heating. No changes in space group or cation ordering could be observed, the ordered Pbca crystal structure is seen in the temperature range 313-353K. However, there is a "phase transition" to a less distorted structure with a larger unit cell volume on heating in the temperature range 329335K. This less distorted structure remains on heating to 353K and is retained on cooling until in the temperature range 319-317K the structure reverts to the more distorted structure

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with a smaller unit cell volume. This change in structure is due to the Si3 T-site becoming less distorted and the difference between the Cul-04-Si4 and Cul-07-Si5 intertetrahedral angles decreasing, on heating above this "phase transition" temperature. This causes the crystal structure to become less distorted and expand.

References 1.

Bell A.M.T., Knight, K.S, Henderson, C.M.B. & Fitch, A.N., 2010, Acta Crystallogr., B66, 51-59.

2.

Bell, A.M.T., Henderson, C.M.B., Redfern, S.A.T., Cernik, R.J., Champness, P.E., Fitch, A.N. & Kohn, S.C., 1994, Acta Crystallogr., B50, 31-41.

3.

Bell, A.M.T., Redfern, S.A.T., Henderson, C.M.B. & Kohn, S.C., 1994, Acta Crystallogr., B50, 560-566.

4.

Bell, A.M.T. & Henderson, C.M.B., 1994, Acta Crystallogr., C50,1531-1536.

5.

Bell, A.M.T. & Henderson, C.M.B., 1994, Acta Crystallogr., C50, 984-986.

6.

Dove, M.T., Cool, T., Palmer, D.C., Putnis, Α., Salje, E.K.H. & Winkler, B„ 1993, Am. Mineral., 78, 486-492.

7.

Ito, Y., Kuehner, S., & Ghose, S., 1995, Solid State Ionics, 79, 120-123.

8.

Palmer, D.C., Dove, M.T., Ibberson, R.M., & Powell, B.M., 1997, Am. Mineral., 82, 16-29.

9.

Redfern, S.A.T., Henderson, C.M.B., 1996, Am. Mineral., 81, 369-374.

10. Knapp, M., Baehtz, C., Ehrenberg, H. & Fuess, H.J., 2004, J. Synchrotron. Rad., 11, 328-334. 11. Rietveld, H.M., 1969, J. Appi. Crystallogr., 2, 65-71. 12. Rodriguez-Carvajal. J., 2001, http://www.ill.eu/sites/ftillprof/. 13. Robinson, K„ Gibbs, G.V. & Ribbe, P.H., 1971, Science, 172, 567-570. 14. Momma, Κ. & Izumi, F., 2008, J. Appi. Crystallogr., 41, 653-658. Acknowledgements. AMTB wishes to thank Manuel Hinterstein and Andreas Berghäuser for help with the operation of the B2 powder diffractometer. AMTB also wishes to thank his wife, Dr. Shelley Walsh, for advice on determining error bars for the O-T-O variance.

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Hydrotalcite-like materials under high pressure 1*

1

1

2 3

J. Darul , W. Nowicki , P. Piszora , C. Lathe '

1 Faculty of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60780 Poznañ, Poland 2 HASYLAB at DESY, Notkestrasse 85, 22603 Hamburg, Germany 3 GFZ German Research Centre for Geosciences, Dept. 5, Telegraphenberg, Potsdam,

14473, Germany

Contact author; e-mail: [email protected] Keywords: synthetic LDH, high pressure, X-ray diffraction, synchrotron radiation, equation of state Abstract. The high-pressure behaviour of Zn 2 Al-N0 3 -LDH was investigated by in-situ energy dispersive synchrotron X-ray diffraction up to 6.7 GPa at room temperature, using a multianvil press (beamline F2.1., HASYLAB/DESY, Hamburg). An anisotropic compression of unit cell was found with increasing pressure. A fit of a second-order Birch-Murnaghan equation of state to the p-V data resulted in the bulk modulus K 0 = 64±3 GPa and its first derivative (Ko') of 3.4±0.6. No structural phase transformation was observed and the layered structure is stable up to 6.7 GPa.

1. Introduction The layered double hydroxides (LDHs), also known as hydrotalcite-like materials or as anionic (more properly speaking, anion exchanging) clays, are a large group of natural and synthetic materials readily produced when suitable mixtures of metal salts are exposed to base. These materials have the general formula [MII1.xMIIIx(OH)2] (A"')x/n mH 2 0. Metal cations are located in coplanar octahedra [M(OH)6] sharing edges and forming M(OH) 2 layers with the brucite (cadmium iodide-like) structure. Partial substitution of the divalent cations by trivalent ones gives rise to a positive charge in the layers, balanced by anions (A"') located between the hydroxylated layers, where water molecules also exist. The nature of the cations in the brucite-like sheets (which is not restricted to +2/+3 combinations) and the interlayer anions together with the coefficient χ value may be varied in a broad range, giving rise to a large class of isostructural materials [1-2], Brucite-type octahedral sheets may be stacked in different ways, generating a large number of polytypes as described by Broolin and Drits [3], Stacking of the layers can be accomplished in two ways, leading to two polytypes with a rombohedral (3R symmetry) or an hexagonal cell (2H symmetry); hydrotalcite corresponds to symmetry 3R, while the 2H analogous is known as manasseite [4],

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Here, we describe X-ray diffraction measurements on ZnjAl-NOq-LDH to 6.7 GPa at room temperature. In the GPa pressure range, there are very few works concerned with high pressure applied to the aforementioned anionic clays. For instance, in this range we are only aware of a work by Parthasarathy et al. [5], who reported high-pressure electrical resistivity measurements on synthetic hydrotalcite up to 6 GPa at room temperature, using a Bridgman opposed anvil system with no pressure-transmitting medium. They observed two pressureinduced irreversible phase transitions at about 1 and 3 GPa, and their spectroscopic and structural studies on pressure-quenched samples showed that hydrotalcite transforms irreversibly to manasseite phase at 1.5 GPa. Further compression lead to pressure-induced amorphization of this phase, at pressures about 4 ^ . 5 GPa. The influence of a hydrostatic pressure (two pressure transmitting media, lead and graphite) on the crystal structure of synthetic LDH has been studied by measuring the X-ray diffraction in the pressure up to 7.7 GPa [6], It was found, that high-pressure processing have a strong influence on the memory effect of the LDH, due essencially to the reduction of the surface area and pore closing. The present work deals with the equation of state of ZnoAl-NOq-LDH at room temperature and under pressure up to 6.7 GPa, by energy dispersive X-ray diffraction technique. In this work, we performed in situ X-ray experiment in order to determine the bulk modulus of Zn^Al-NOr LDH.

2. Experimental details Preparation of LDH: The Zn 2 Al(OH) 6 (N0 3 ) 2 H 2 0 LDH (also known as Z n 2 A l - N O r L D H in short) polycrystalline powder was obtained by one-step route. A stoichiometric mixture of mixed metal (Zn 2+ and Al , + ) nitrate salts solution (with Zn 2+ :A1 ,+ equal to 2:1) was slowly added to 130 mL of aqueous NaOH solution with constant stirring under a nitrogen atmosphere to avoid contamination from atmospheric carbon dioxide. During the synthesis the pH value was kept at 8±0.2. After the addition of the mixed metal salt solution, the resulting slurry was continuously stirred at room temperature. The suspension was aged at 60°C for 6h. The solid precipitate was rinsed with deionised water and ethanol, respectively, and then dried at 60°C for 12h. The over-dried material was analysed for crystalline constituents by powder XRD (patterns were recorded on a Bruker D8 Advance diffractometer, with C u K a radiation). High pressure experiment: In-situ high-pressure X-ray diffraction experiments up to 6.7 GPa were performed at room temperature using a cubic anvil apparatus with white synchrotron radiation (F2.1 beamline) at the HASYLAB (DESY, Hamburg). Diffraction patterns were collected using energy dispersive technique with a fixed angle (theta= 4.95°) solid state Ge detector, and collecting time for each diffraction pattern of about 10 min. A 120-mg sample of LDH was mixed with 27 mg of h-BN pressure-transmitting medium, and was packed into a boron nitride container with an internal diameter of 1 mm bounded by powdered layers of NaCl on the top and bottom, which served as an internal pressure standard. Pressure was calculated from Decker's equation of state [7] using the NaCl standard. La Bail fitting procedure, implemented in FullProf program [8], was used to refine the unit cell parameters of the investigated sample. The bulk modulus (B0) as well as its pressure derivative were calculated by fitting the vol-

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urne data to the second-order Birch-Murnaghan equation of state using the EOS-FIT program [9] and a fully weighted least-squares procedure.

3. Results Synthetic LDH sample was obtained in form of white powder. The Zn 2 Al-N0 3 -LDH was compressed up to 6.7GPa, and then decompressed to ambient condition. At ambient condition apart from some closely overlapped peaks seven peaks are resolved and indexed for a hexagonal lattice (003), (006), (012), (015), (018), (110), (113) with R3m rhombohedral symmetry; polytype 3R4. At ambient pressure the cell parameters of investigated material are: a = 3.071(2) À, c = 22.729(3) À, giving a volume (V0) of 185.648(2) À3. However, the energy-dispersive X-ray data of bulk sample showed decrease in the intensity for all peaks, being more expressive for the basal d-spacing, an expected high-pressure-induced amorphization was nor observed, even in the case of sample compacted at 6.7 GPa. Figure 1 exhibits a quasi-linear behaviour of a and c lattice parameters vs. ρ and shows that the strongest lattice deformation occurs along the c-axis. Although both cell parameters a and c decrease with increasing pressure, the rate of contraction in c is much larger than that in a (figure 1) - the thickness of the octahedral layer only shows a slight decrease, whereas the interlayer spacing contracts rapidly. The anisotropic behavior in axial compression of LDHs can be explained in terms of its structure. Since the electrostatic forces between neighboring sheets (in the interlayer) are much weaker than those within the sheets themselves, the structure is more flexible along the c axis. As expected for a layer structure, the c trend is much steeper than that of a, confirming that the strain mainly tends to effect the [001] direction, by shortening the interlayer distance between octahedral sheets. Figure 2 shows the volume per formula unit cell as a function of pressure. To determine the bulk modulus K0 and its first derivative Ko\ the Birch-Murnaghan Equation of State (1) (BM EOS) [10] was applied, Ρ = 3/2K0[(V/V0)-m

- (V/Vo)-5'7 {1 + 3/4(K0' - 4) [ V/Vof3 - 1]}

(1)

where V 0 is the volume at ambient pressure, K0 is the isothermal bulk modulus, and K0* corresponds to its pressure derivative. For this pressure range we assume a linear P-V relationship. A least-squares fitting of pressure-volume data to the BM EOS was performed. A systematic pressure error of 0.1 GPa and random volume errors from the volume refinement were used in analysis. The fitting results show that the cell volume for Zn 2 Al-N03-LDH at zero pressure (K0) should be around 185 Â, and the bulk modulus at zero pressure (K0) is 64±3 GPa with a pressure first derivative of K 0 '= 3.4±0.6.

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22,7

t

22,6 ΰ

I

2 22,5 υ

i

22,4

0

1

1

1

2

3

4

5

l-H

•

22,2

22,1

tí

i

22,3

6

7

3,2

o4 ferrite is reported. Synchrotron X-ray measurements have been performed in the temperature range 300K - 15K. It was found that for Cu0.9Zn0.iFe2O4, the sample begins to transform from cubic to tetragonal at about 250K, with the coexistence of both phases down to 15K. No phase transition was observed in the CuFe 2 0 4 spinel below room temperature.

Introduction Spinel ferrites, which have vast application from microwave to radio frequencies is of great importance from both fundamental and applied research points of view [1-5], The spinel structure is based on a cubic close-packed array of oxide ions (32e), with xh of the octahedral sites (16d) and of tetrahedral sites (8a) occupied by cations. The general chemical formula is AB2O4, and there are two ideal structures with different cation ordering schemes: (A) 8a [B 2 ] 16d 0 4 (normal spinel) and (B) 8a [AB] 16d 0 4 (inverse spinel). Copper ferrite crystallizes in a tetragonal (T) or cubic (C) symmetry depending on the cation distribution among interstitial sites of spinel structure. The T-phase is an inverse spinel, with the cation distribution that can be presented by the formula: (Fe)[CuFe]0 4 . The Cu 2+ ions occur copper only octahedral B-sites and this causes the tetragonal distortion due to the cooperative Jahn-Teller effect [6-7]. The Jahn-Teller distortion in cooper ferrite has established that the critical number of octahedral site Cu 2+ ions per formula unit for a cooperative distortion to tetragonal symmetry at room temperature is 0.8 [7]. One way to reduce the Jahn-Teller effect, could be the addition of other 3d-cations to the tetragonal CuFe 2 0 4 lattice [3,7]. Since the zinc ion has a stronger tetrahedral site preference than Fe 3+ in the normal spinel Zn[Fe 2 ]0 4 , we may assume it also does so in Zn 2+ doped copper ferrite. In this work, the structural change with decreasing temperature below ambient condition polycrystalline Cu0.9Zn0.iFe2O4 compound has been compared with that of undoped copper ferrite.

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European Powder Diffraction Conference, EPDIC 12

Experimental details Powder samples having nominal composition CuFe 2 0 4 and Cu0.9Zn0.iFe2O4 were prepared by a combustion method using citrate-nitrate precursors. The stoichiometric quantities of starting materials, viz., Cu(N0 3 ) 2 -6H 2 0, Fe(N0 3 ) 3 -9H 2 0, Ζη(Ν0 3 ) 2 ·4Η 2 0 and C 6 H S 0 7 -6H 2 0 (Merck), were dissolved in distilled water. The mixed citrate-nitrate solution was heated at 120°C with continuous stirring. After evaporation of excess of water a highly viscous gel was obtained. Ultimately, the particles were sintered at different temperatures (300, 600, 900 C) for five hours and slow cooled down to room temperature. The investigations on the temperature phase transition, using high-resolution powder diffractometer, equipped with Hecryostat and Image Plate OBI detector were carried out at the Desy/Hasylab at the B2 beamline [8-9]. The wavelength applied during measurements, determined by calibration using NIST silicon standard, was 0.49342(1)A. The polycrystalline samples placed in glass capillaries of diameter 0.3 mm were cooled within a temperature range from 300K to 15K. Refinement of the diffraction data, collected as a function 2-theta were performed using the FullProf [10] and UnitCell [11-12] programs. The program WinPLOTR-2006 (version 0.5 April 2009) was used for the powder diffraction graphic representation [13],

Results and discussion Figure 1 displays the RT XRD patterns of the as-prepared samples CuFe2C>4, (A) and Cu0.9Zn0.iFe2O4, (B). The results of indexing XRD patterns has shown that the nominal composition structures with different concentrations are single phase with no additional lines corresponding to any other phase. Tetragonal structure is obtained only for copper ferrite and all of the peaks are indexed with space group IAycimd in the standard data (JCPDS no. 340425). In our communication we use the face-centred (FAy/ddrri) unit cell, with the eight CuFe 2 0 4 content, as in the spinel ( F d l m ) unit cell, allows us to demonstrate the degree of tetragonal distortion of the crystal lattice. 311,ι 311

τ

113τ

202

400,

τ

A 220

c

400

222

Β S.5

9.1

'J.7

1Ü.3

10.

11?

12.Í

12.7

I ΐ ?

I V )

14.5

2 Thêta (dog.)

Figure 1. X-ray powder diffraction patterns for A'. CuFe204 (indexing for the tetragonal F4l/ddin space group) and Β: Cu0 9Zn0 jFe:O4 (indexing for the cubic Fdim space group) at room temperature.

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The second compound (Cuo.gZno.iFeoCU), crystallizes in the cubic space group Fdim. The structure refinement by the Rietveld method was carried out to determine the cation distribution over tetrahedral and octahedral spinel sites at the room temperature (figure 2). The distribution of cations in Cuo.gZno.iFeoCU can be expressed as (Cuo.o7iZno.i25Feo.So4)Tet[Cuo.So4Fe1.196]oct04 and shows a critical number of copper ions in the octahedral spinel sublattice for the tetragonal symmetry in copper ferrospinel. Substitution with zinc ions clearly restrains Jahn-Teller effect, owing to the reduction of Cu 2+ /Fe ,+ ratio in octahedral sites in CuFejCU. The unit cell volume is found to increase with addition of zinc in copper ferrite (table 1). This is due to the fact that the ionic radius of Zn 2+ (0.83 À) is greater than that of Cu2+ (0.70 À)[14],

300Κ CuD9Zn01Fe2O4 a 31000 3 ££ 23000 S 1&QOO ζ β e

£ 700Q I

-1000

Yobs Yes le

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I IN M l Π II II IE II il II M II II

Bfagg position Yobs-Ycalc

4

IO

16

22

28

34

40

46

52

58

2 Tïieia (deg.)

64

Figure 2. Observed, calculated and difference profiles from the Rietveld analysis of X-ray powder diffraction data of the sample CuggZllg ¡FejO^ at the room temperature. Table 1. Lattice parameters and volume for samples with tetragonal and cubic unit cell at the room

Sample

c(Ä)

α (λ)

c/a

V(A3)

CuFe 2 0 4

8.7047(8)

8.2307(3)*

1.057

589.69 (0.11)*

Cuo.gZno.iFeiCU

-

8.3943(1)

1.000

591.498 (0.012)

The structure of the copper ferrite can be changed via decreasing the copper concentration, or alternatively, by temperature treatments. Annealing can modify the cationic distribution in spinel lattice - Cu2+ ions from octahedral sites migrate to the tetragonal positions. This phenomenon transforms the tetragonally distorted CuFejCU structure into a cubic lattice in the temperature range from -360 C to -420 C [15], In a previous work, we have studied the structure properties of small quantities zinc ions substituted CuFeoCU, which revealed that the

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structural transformation for Cuo.gsZno.osFeoCU from tetragonal to cubic space group occurs in the temperature range from - 5 0 C to -200 C [16], Research in the framework of Hasylab (Desy, Hamburg) project made possible the investigations on the low temperature phase transition for both samples using the high-resolution Xray diffractometer. Figure 3 shows the (113), (311) and (222) reflections for CuFejCU, from the synchrotron X-ray powder diffraction data, recorded in the temperature range from 300K to 15K. There is no phase transition effect with decreasing temperature, and the sample remains tetragonal in the whole temperature range. The volume parameter, V, of the tetragonal phase (F4,fMm) decreases with temperature from 589.69(0.11) À3 to 588,04(0.11) λ 3 .

Figure 3. Low temperature evolution of the X-ray powder diffraction patterns for

CuFe20,

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Low temperature X-ray diffraction patterns for the Cuo.gZno.iFeoCU oxide are shown in figure 4. With decreasing temperature the formation of the tetragonal polymorph was indicated at about 25 5K. The splitting of the lines and their intensity reveal clearly the tetragonal structure (space group F\xddm). The coexistence of two phases in a whole measurements range of temperature may be observed.

2-Theta [ deg ] Figure 4. Low temperature evolution of the X-ray powder diffraction patterns for C'ug gZflg ¡FejO^

Concluding remarks The CuFeoCU and Cuo.gZno.iFeoCU were synthesized by a combustion method using citratenitrate precursors. The formation of the tetragonal CuFe^CU, and the cubic Cuo.gZno.iFeoCU phases were confirmed by X-ray diffraction studies. Substitution with Zn 2+ ions reduces the total concentration of Cu2+, suppressing the Jahn-Teller effect, and stabilizes the cubic structure. The substitution of divalent zinc ions in Cui_xZnxFe204 spinel oxides increases the lat-

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tice parameters of the system. No phase transition has been observed in the CuFe 2 0 4 spinel below room temperature. The sample remains tetragonal when cooled in the range 300K 15K. On the other hand the compound with small quantities of Zn 2+ ions undergoes at 250K temperature region a structural transformation from cubic (Fdlm) to tetragonal (FAyddm) lattice, with the coexistence of both phases down to 15K. Further investigation on the structure properties of the Cui. x Zn x Fe 2 04 system are indispensable.

References 1.

Watanabe, S.C., Bamne, S.P. & Tangsali, S.P., 2007, Mater. Chem. Phys., 103, 323.

2.

Hancare, P.P., Patii, R.P., Sankpal, U.B., Jadhav, S.D., Lokhande P.D., Jadhav K.M. & Sasikala, R„ 2009, J. Solid State Chem., 182, 3217.

3.

Rana, M.U., Islam, M. & Abbas, T., 2000, Mater. Chem. Phys., 65, 345.

4.

Argentina, G.M. & Baba, P.D., 1974, IEEE Trans. Microwave Theory Tech. MTT, 22, 652.

5.

Sun, S„ Murray, C.B., Weiler, D„ Follks, L. & Morse, Α., 2000, Science, 287, 1989.

6.

Prince, E. & Treuting, R.G., 1956, Acta Cryst., 9, 1025.

7.

Tang, X.X., Manthiram, A. & Goodenough, J.B., 1989, J. Solid State Chem., 79, 250.

8.

Knapp, M., Baehtz, C., Ehrenberg, H. & Fues,s H., 2004, J. Synchrotron Rad., 11, 328.

9.

Knapp, M., Joco, V., Baehtz, C., Brecht, H.H., Berghaeuser, Α., Ehrenberg, H., Seggern, H. & Fuess, H., 2004, Nucl. Instr. Meth. Phys. Res. A, 521, 565.

10. Rodríguez-Carvajal, J., 2001, Newslett. IUCr Commission Powder Diff., 26, 12. 11. Holland, T.J.B. & Redfern, S.A.D., 1997, J. Appi. Crystallogr., 30, 84. 12. Holland, T.J.B. & Redfern, S.A.D., 1997, Mineral. Mag., 61, 65. 13. Roisnel, T. & Rodriguez-Carvajal J., 2000, Proceedings of the Seventh Powder Diffraction Conference (EPDIC 7), p.118.

European

14. Shannon, R.D. & Prewitt, C.T., 1970, Acta Crystallogr., B26, 1076. 15. Darai, J., 2009, Z. Kristallogr. Suppl., 30, 335. 16. Darul, J. & Nowicki, W„ 2009, Rad. Phys. Chem., 78, S109. Acknowledgements. This research is partially supported by the Ministry of Science and Higher Education (Poland), grant No. NN204330537. The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 226716.

Ζ. Kristallogr. Proc. 1 (2011) 361-366 / P O I 10.1524/zkpr.2011.0055 © by Oldenbourg Wissenschaftsverlag, München

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Phase transformation on mixed yttrium/sodium-MOFs, X-ray thermodiffractometry and structural modeling Z. Amghouz , S. Khainakov, J. R. Garcia, S. Garcia-Granda Departamentos de Química Física y Analítica y Química Orgánica e Inorgánica, Universidad de Oviedo - CINN, 33006 Oviedo, Spain Contact-author; e-mail: [email protected] Keywords: MOFs, X-ray thermodiffractometry, phase transformation, structural modeling Abstract. New chiral MOFs, assembled from Y(III), Na(I) and chiral flexible-achiral rigid dicarboxylate ligands, have been obtained as single phase under hydrothermal conditions and their structures were solved by single-crystal XRD. The powder X-ray thermodiffractometry study was performed, and reveals that the dehydration of both compounds is accompanied by phase transformation, while the spontaneous rehydration process is characterized by different kinetics. The crystal structures of anhydrous compounds have been modeled.

1. Introduction Metal-organic frameworks (MOFs), also known as coordination polymers, continue receiving a great attention, since they are a very attractive class of materials due to, the great deal of extended structures and to their potential applications in several fields such as gas storage [1,2], catalysis [3], magnetism [4,5], luminescence [6,7], and so on. In the last decade, large variety of bi- or multi-functional organic linkers and transition or rare earth metals units have been applied as building blocks, leading to numerous 2D and 3D structures. Nevertheless, to the best of our knowledge, only some of them exhibit interesting features, such as reversible phase transition [8-10], Previously [11] we have reported the hydrothermal synthesis and the full structural characterization of two novel chiral yttrium-based metal organic frameworks, both exhibited phase transformation corresponding to the dehydration process. In continuation of this work, and in the aim to determine the structures of the dehydrated forms, powder X-ray thermodiffraction data and the structural modelling have been performed.

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2. Experimental 2.1 Synthesis Compounds 1 and 2, formulated as NaY^F^OeXCsFUC^XH^O^ and NaY(C4H406)(Ci4H804)(H20)2, respectively, were synthesized under hydrothermal conditions, and obtained as a single phase of colorless needle crystals, as described in the ref. 11. 2.2 Powder X-ray thermodiffraction studies Powder X-ray thermodiffraction studies were performed in air. The sample was placed in an Anton Paar HTK 1200N oven-chamber, on a PANalytical XPERT-PRO diffractometer, using Cu Κα radiation, equipped with PIXcel linear detector with 255 channels. Each powder pattern was recorded in the 4-110° range (2Θ) at intervals of 25 °C up to 200 °C and cooling down to 25 °C with a step of 0.013° and a counting time of 0.424 s/channel. The temperature ramp between two consecutive temperatures was 10 °C/min. 2.3 Structural modeling The structures of 1 and 2 were used as initial models. After (i) removing the two water molecules (coordinated to sodium atoms), and (ii) using the following initial unit cell parameters, a = 6.7515(5) k,b = 28.666(6) Â, c = 7.309(1) À, and a = 6.7195(3) k,b = 37.886(4) À, c = 7.5429(6) Â, obtained from the indexation of powder XRD patterns at 200 °C corresponding, respectively, to dehydrated forms of 1 (Dl) and 2 (D2), and (iii) keeping the fractional coordinates fixed during the lattice changes. The full geometry optimizations of the resulting structures, in the space group PI, were performed in DMOL3 module implemented in Materials Studio [12], by using the local density functional (LDA) of Vosko-Wilk-Nusair (VWN) [13] with a double numerical basis set with polarization lunctions (DNP) and a "medium" lipomi set. During the optimization, the unit cell parameters were kept fixed. The structures were considered to be converged when the change in energy between two iterations was smaller than 1.10"5 hartree and gradient and displacement were, respectively, less than 2.10"3 hartree a0"' and 5.10"3 a0. Between 23 and 66 iterations were required to reach convergence. The symmetry test was performed of the models obtained in PI for D l and D2, and it was found to be higher, PI, in case of D2. Rietveld refinement of the obtained models was carried out with Reflex, a powder diffraction module implemented in Materials Studio. The PXRD profiles have been modeled as a pseudo-Voigt function in the range 2Θ = 4^-5°. The parameters refined were: the zero offset, the scale factor, 20 background terms, the U, V and W profile parameters, the unit cell parameters, Finger-Cox-Jephcoat asymmetry correction for peaks below 2Θ = 20° , global isotropic temperature factor, and the preferred orientation using March-Dollase lunction in the directions [010] (for D l ) and [001] (for D2). The unit cell parameters and the final values of figures of merit are listed in Table 1.

3. Results and discussion Compounds 1 and 2 crystallize in the orthorhombic chiral space group C222i with unit cell parameters a = 6.8854(2) À, b = 30.3859(7) À, c = 7.4741(2) À for 1, and a = 6.8531(2) À, b = 39.0426(8) À, c = 7.4976(2) À for 2. The X-ray thermodiffraction analysis indicates that 1 and 2 show a phase transformation corresponding to the dehydration process (Figure 1), by losing the two water molecules coordinated to sodium atom, which is a re-

Ζ. Kristallogr. Proc. 1 (2011)

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versible process involving a spontaneous rehydration after cooling down to room temperature, which has been seen clearly in the thermodiffractogram of 1 (blue curve at 25 °C down, Figure la), however, it is slowly reversible in the case of 2, and takes few days in air after the end of the experiment.

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Since the dehydration of 1 and 2 begins respectively at 140 °C and 150 °C, the variation of the unit cell parameters of 1 and 2 from 50 °C to 130 °C (for 1), and from 50 °C to 140 °C (for 2), obtained by Rietveld refinement using the structural models of 1 and 2 (hydrated), are illustrated in Figure 2 (a) and (b), respectively. A slight contraction of the cell volume of ca. 1% has been observed from room temperature to 130 °C. The powder XRD pattern of dehydrated compounds, 1 and 2, treated at 200 °C in air, have been indexed in the orthorhombic system with these unit cell parameters: a = 6.7515(5) À, b = 28.666(6) À, c = 7.309(1) k,V= 1414.5(4) k \ in the case of 1, and a = 6.7195(3) À, b = 37.886(4) k, c =

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7.5429(6) À, V= 1920.2(3) k\ in the case of 2, by using respectively, TREOR (M(20) = 18) and DICVOL (M(20) = 21.7). The results reveal that the structure of 1 and 2 contract of ca. 5.6 % and 3 % along the è-axis, and the cell volume of ca. 10% and 5%, respectively, maintaining the orthorhombic crystal system. •

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4. Summary and conclusions Temperature-dependent, combined WAXS and SAXS are the ideal methods to investigate both, phase separation of block copolymers and simultaneously phase separation between the methacrylate backbones and -(CH2)2-(CF2)8-F side chains of PMMA / PSFMA diblock copolymers. X-ray measurements proved the occurrence of block copolymer phase separation with lamellae spacings between 1 0 - 2 0 nm (for low Mw BCP) and > 45 nm for higher molar mass BCP, as well as the formation of SF layers with d-spacings of ~3.1 nm and distinct thermal behaviour. The d-values of the SF sub-phase and molecular modelling indicated a head-to-head arrangement of SF side chains without interdigitation and tilt. The phase separation in samples with lower M w reflects more the complicated phase behaviour of triblock copolymers (lamellar, hexagonal or mixed morphologies) as that of diblock copolymers. Detailed investigations have to be performed to clarify these peculiarities.

References 1.

(a) Friedel, P., Pospiech, D., Jehnichen, D., Bergmann, J. & Ober, C.K., 2000, J. Polym. Sci., Part B: Polym. Phys., 38, 1617. (b) Gottwald, Α., Pospiech, D., Jehnichen, D., Häußler, L., Friedel, P., Pionteck, J., Stamm, M. & Floudas, G., 2002, Macromol. Chem. Phys., 203, 5-6, 854. (c) Pospiech, D., Komber, H., Voigt, D., Jehnichen, D., Häußler, L., Gottwald, Α., Eckstein, Κ., Baier, Α. & Grundke, Κ., 2003,Macromol. Sytnp., 199, 173. (d) Pospiech, D., Jehnichen, D., Gottwald, Α., Häußler, L„ Scheler, U„ Friedel, P., Kollig, W„ Ober, C.K., Li, X., Hexemer, Α., Kramer, E.J. & Fischer, D.A., 2001, Polym. Mat.: Sci. & Eng., 84, 314.

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(a) Jehnichen, D., Pospiech, D., Häußler, L., Friedel, P., Gottwald, A. & Kummer, S., 2004, Mater. Sci. Forum, 443-444, 223. (b) Jehnichen, D., Pospiech, D., Häußler, L., Friedel, P., Funari, S.S. Tsuwi, J. & Kremer, F., 2007, Ζ. Kristallogr. Suppl, 26, 605.

3.

(a) Pospiech, D., Häußler, L., Eckstein, K., Komber, H., Voigt, D., Jehnichen, D., Friedel, P., Gottwald, Α., Kollig, W. & Kricheldorf, H.R., 2001, High Perform. Polym. 13, 275. (b) Tsuwi, J., Hartmann, L., Kremer, F., Pospiech, D., Jehnichen, D. & Häußler, L„ 2006, Polymer 47, 7189.

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(a) Keska, R., Pospiech, D., Eckstein, K., Jehnichen, D., Ptacek, S., Häußler, L., Friedel, P., Janke, A. & Voit, Β., 2006, JNPN, 2, 43. (b) Jehnichen, D., Pospiech, D., Keska, R., Ptacek, S., Janke, Α., Funari, S.S., Timmann, A. & Papadakis, C.M., 2008, JNPN, 4, 119. (c) Jehnichen, D., Pospiech, D., Ptacek, S., Eckstein, K., Friedel, P., Janke, A. & Papadakis, C.M., 2009, Z. Kristallogr. Suppl. 30, 485.

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(a) Matsen, M.W. & Bates, F.S., 1996, Macromolecules, 29, 1091. (b) Melenkevitz, J. & Muthukumar, M., 1991, Macromolecules, 24, 4199.

Acknowledgements. We thank all colleagues of IPF who contributed to synthesis and characterization of the BCP, especially Mrs. K. Eckstein for anionic polymerization and Mrs. L. Häußler for DSC measurements. We gratefully acknowledge financial support by and participation in EU NoE "NANOFUN-POLY" and by the German Science Foundation.

Author Index Volume I: pp. 1-206 Volume II: pp. 209-492 Abdalslam, M. A Adam, C Adamczyk, Β Afonasenko, Τ Alcobe, X Allieta, M Amghouz, Ζ Apel, D Artioli, G Audebrand, Ν Azanza Ricardo, C. L Bacewicz, R Baklanova, Y. V Bakr Mohamed, M Bassas, J. M Bastida, J Basyuk, Τ Bell, Α. Μ. Τ Ben Haj Amara, A Ben Rhaiem, Η Bérar, J.-F Berezovets, V Bergmann, J Bergold, S. Τ Beyerlein, Κ. R Bhuvanesh, Ν. S. Ρ Bonnin, A Boudet, Ν Boysen, H Brötz, J Brunátová, Τ Bruneiii, M Bulavchenko, O Caballero, A Calzavara, Y Camus, M Castro, G. R Chalghaf, R

287 443 443 325 143 15 361 247 155 49 189 373 431 417 143 63, 93, 425, 461 319 337, 355 389, 409, 467 389, 409 29 319 183 449 37, 43 149 29 29 175 287 229 15 325, 331 425 29 261 403 389, 409

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Cherepanova, S Clausell, J. V Coduri, M Colin, C. V Cuevas-Diarte, M. A

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Dalconi, M. C Danilchenko, V. E Danis, S Darul, J Delidon, R. M Denisova, T. A Depmeier, W Di Maggio, R D'Incau, M Dinnebier, R Dittrich, S Dodoo-Arhin, D Dohnálek, J Doyle, S Drahokoupil, J Drygas, M Dusková, J

155 267, 273 229 343, 355 267 431 105 81 75 105 23 75 475 99 87 235, 241 475

Eickershoff, Β Eisenreich, Ν Em, V Emmerling, F Ende, M Ensinger, W Favero, M Fernández-González, A Fernández-Zapico, E Ferrer, S Ferrerò, C Fidelus, J. D Fietzek, H Firszt, F Fischer, R. A Förter-Barth, U Friedel, Ρ Fuess, H l unari. S. S Furet, E

367 367 169 443 201 287 155 437 403 137 15 455 367 373 221 99 487 287, 307, 417 487 49

Ζ. Kristallogr. Proc. 1 (2011) García, J. R García-Granda, S Garin, J Gautier, Régis Gautier, Romain Gelisio, L Gerasimov, E Giebeler, L Gierlotka, S Glock, S Göbbels, M Goetz-Neunhoeffer, F Goto, Τ Gourdon, O Grzanka, E Hämäläinen, J Harbrecht, M Harju, E Harris, Ρ Hartmann, C. G Hasek, J Heikkilä, M. J Henderson, C. Μ. Β Herrmann, M Heroux, L Hibino, H Hladil, J Hodges, J. Ρ Hölsä, J Hoffmann, S Honkimäki, V Huq, A Hyppänen, 1 Iakovlev, V Ida, Τ Ismagilov, Ζ Ivanov, M Izumi, F Janik, J. F Javier Huertas, F .lobuli. S Jehnichen, D

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xxviii Kalvoda, L Kankare, J Kempa, P. Β Khainakov, S Khassin, A Kimmel, G Kleeberg, R Kloess, G Knapp, M Kojdecki, M. A Kolb, U Kolenko, Ρ Kolská, Ζ Kondratenko, E Kovacheva, D Koval, Τ Králová, D Krawczynska, A Kryshtab, Τ Kurzydlowski, K. J Kuzel, R Labsky, J Lahtinen, M Lastusaari, M Lathe, C Le Fur, E Leineweber, A Leonardi, A Leoni, M Leskelä, M Lewandowska, M Li, M Lienert, F Liu, F. Y Lojkowski, W López-Buendía, Α. M Machek, M Maksimova, L. G Mannheim, R Matëj, Ζ Matejová, L Meftah, M Menzel, M Mikula, Ρ Minikayev, R

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Palacios-Gómez, J Palancher, H Palosz, Β Pardo, Ρ Paszkowicz, W Paulmann, C Pehl, Τ Peplinski, Β Peral, 1 Petrik, M Pihlgren, L Piszora, Ρ Podyacheva, O Pöllmann, Η Popovic, S Pospiech, D Proffen, Th

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