Institute of Physics, Prague 6, Cukrovarnická street

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1 Jana2006

2 Institute of Physics, Prague 6, Cukrovarnická street

3 Jana2006 Program for structure analysis of crystals periodic in three or more dimensions from diffraction data Václav Petříček, Michal Dušek & Lukáš Palatinus Institute of Physics, Prague, Czech Republic

4 Which part of the cake you can have with Jana? Magnetic structures Microcrystals by electron diffraction Quasicrystals Modulated and composite structures Locally ordered structures (diffuse scattering) Proteins Thin layers Nanomaterials Minerals Small molecules in service crystallography

5 History 1980 SDS Program for solution and refinement of 3d structures 1984 Jana Refinement program for modulated structures 1994 SDS94 and Jana94 Set of programs for 3d (SDS) and modulated (Jana) structures running in text mode Jana96 Modulated and 3d structures in one program. Graphical interface for DOS and UNIX X Jana98 Improved Jana96. First widely used version. Graphical interface for DOS, DOS emulation and UNIX X Jana2000 Support for powder data and multiphase refinement. Graphical interface for Win32 and UNIX X Jana2006 Combination of data sources, magnetic structures, TOF data. Dynamical allocation of memory. Only for Windows.

6 Where to start?

7 Data input X-rays OR neutrons OR electrons Powder data of one or more phases OR Single crystal data of one or more domains Import Wizard Format conversion, cell transformation, sorting reflections to twin domains Data Repository

8 Program Scheme M95 + M50 Reading of one or more data sets. Powders must be indexed by an external program. M90 Single crystals: determination of symmetry, merging symmetry equivalent reflections, absorption correction Extraction of intensities, determination of symmetry M41 Powders: Le Bail refinement of profile parameters Solution (by calling external programs) M40 Refinement or Rietveld refinement Transformation Introduction of twinning Change of symmetry Plotting, geometry parameters, Fourier maps. M95 M90 M50 M40 data repository refinement reflection file basic crystal information, form factors, program options structure model

9 Reading of data: M95 + M50 Determination of symmetry: M50

10 Merging of symmetry equivalent reflections, application of extinction rules: M90 Le Bail refinement of powder profile: M41 Structure solution: M40

11 Structure refinement: M40 Transformations Structure plots

12 Charge flipping

13 Topics Basic crystallography Advanced tools Incommensurate structures Commensurate structures Composite structures Magnetic structures Jana2006 is old fashioned: written in Fortran; not using external libraries (except basic graphics); not written by a team of programmers flexibility NOT included in Jana2006: Phase problem solution: calls SIR97,2000,2004; EXPO, EXPO2004, Superflip Plotting: calls Diamond, Vesta, MC (marching cube) and other plotting software Validations and geometry analysis: relies on Platon

hydrogen atoms Constrains, Restrains Fourier calculation Plotting (by an external

14 Basic crystallography Wizards for symmetry determination External calls to Charge flipping and Direct methods Tools for editing structure parameters Tools for adding hydrogen atoms Constrains, Restrains Fourier calculation Plotting (by an external program) CIF output Under development: graphical tools for atomic parameters, CIF editor

15 Advanced tools common for 3d and modulated structures Fourier methods Transformation tools, group-subgroup relations Twinning (merohedric or general), treating of overlapped reflections User equations and restrictions Disorder and Rigid body approach Anharmonic ADP Multiphases for both powder and single crystal data Multipole refinement Powder data: Anisotropic strain broadening (generalized to satellites) Fundamental approach TOF data Local symmetry

Twinning (pseudo-merohedric three-fold twin) 2 1 2 3 2 1 2 1 2 1 2 3 2 1 2

16 Twinning (pseudo-merohedric three-fold twin) Twinning matrices for data indexed in hexagonal cell:

17 Disorder and rigid bodies Disorder of tert-butyl groups in N-(3-nitrobenzoyl)-N', N"-bis (tert-butyl) phosphoric triamide. The groups were described like split rigid bodies. One of rigid body rotation axis was selected along C-N bond in order to estimate importance of rotation along C-N for description of disorder.

18 Anharmonic description of ADP (ionic conductor Ag 8 TiSe 6 ) Plot: Jana calculates electron density map and calls Marching Cube.

19 Local symmetry Local icosahedral symmetry for atom C of C 60 Powder data, (J.Appl.Cryst. (2001). 34, )

20 Single crystal multiphase systems View along a Lindströmite View along a Krupkaite

21 Modulated structures very short explanation what does it mean

22 Sodium carbonate View along c z from 0 to 1

23 Sodium carbonate View along c z from 1 to 2

24 Sodium carbonate View along c z from 2 to 3

$Probably yes because the diffraction pattern looks$

25 Is there some translation periodicity? Probably yes because the diffraction pattern looks like usually

26 c* a*. but we cannot describe all peak positions with a lattice

27 a* c*

c* a* q= q a + q b + q c * * * 1 2 3 The remaining spots can be

28 c* a* q= q a + q b + q c * * * The remaining spots can be described with q- vector, which has irrational components. Indices h k l m

29 Four-dimensional reciprocal lattice Modulated and composite crystals can be described in a (3+d) dimensional superspace. The theory has developed by P.M.DeWolff, A.Janner and T.Janssen (Aminoff prize 1998). The basic idea: real diffraction pattern is a projection from the (3+d) dimensional superspace. The basic assumption: all satellites are clearly separated. (the intensities diminish for large satellite index). e q * A 4 * R 3 * a * 3 = A3

30 Modulation function incommensurate Basic position e=a 4 The atom is displaced from its basic position by a periodic modulation function that can be expressed as a Fourier expansion. In the first approximation intensities of satellites reflections up to order m are determined by modulation waves of the same order. r= r + u m ( x ) = sin( 2πnx ) + cos( 2πnx ) 4 sn, 4 cn, 4 n= 1 n= 1 m u A A

31 Incommensurate structures Modulation of occupation, position and ADP Traditional way of solving from arbitrary displacements Solving by charge flipping Modulation of anharmonic ADP Modulation of Rigid bodies including TLS parameters Special functions Fourier sections Plotting of modulated parameters as a function of t Plotting of modulated structures Calculation of geometric parameters

32 Natural melilite from San Venanzo, Umbria, Italy Formula: (Ca 1.89 Sr 0.01 Na 0.08 K 0.02 )(Mg 0.92 Al 0.08 )(Si 1.98 Al 0.02 )O 7

33 Charge Flipping (Superflip of Lukas Palatinus)

34 Twinning of modulated structures The twinning matrix is 3x3 matrix regardless to dimension. Twinning may decrease dimension of the problem. Example: La 2 Co 1.7, Acta Cryst. (2000). B56, Average structure: , P6 3 /mmc Modulated structure: modulated composite structure, C2/m(α0β), 6-fold twinning around the hexagonal c Reconstruction of (h,k,1.835) from CCD measurement.

Disorder in modulated structures Cr 2 P 2 O 7, incommensurately modulated phase at room temperature Cr1 (0.500000-0.187875 0.000000) Δ[Cr1] = 1 New atom: Cr1a (0.47, -0.187875 0.03) t40[cr1a] = t40[cr]+0.

35 Disorder in modulated structures Cr 2 P 2 O 7, incommensurately modulated phase at room temperature Cr1 ( ) Δ[Cr1] = 1 New atom: Cr1a (0.47, ) t40[cr1a] = t40[cr]+0.5* Δ[Cr1] Δ'[Cr1] = Δ[Cr1] - x Δ[Cr1a] = x New parameters for refinement: x and position of Cr1a Temperature parameters of Cr1a can be put equal to Cr1. No modulation can be refined for Cr1a. Analogically one can split positions of P1, O2 and O3. Refinement is very difficult, the changes should be done simultaneously.

Commensurate structures Exact intersection Example of six-fold commensurate structure Superspace description: 4d cell, atomic position + modulation function, superspace symmetry Supercell

36 Commensurate structures Exact intersection Example of six-fold commensurate structure Superspace description: 4d cell, atomic position + modulation function, superspace symmetry Supercell description: 3d six-fold supercell, atomic positions in six cells, 3d symmetry Both description are equivalent. Jana2006 can automatically transform commensurate structure to 3d structure in a supercell This angle follows from q-vector Origin of R3 section may influence symmetry in the supercell. Jana2006 can automatically find all possible supercell symmetries. Superspace Supercell

37 Commensurate families In this example known M 2 P 2 O 7 diphosphates are derived from the same superspace symmetry.

38 Composite structures Typical Fourier section Hexagonal perovskites Two hexagonal subsystems with common a,b but incommensurate c. q is closely related with composition q = γ = c ( 0,0, γ ) 2 c 1 c 1 c 2 W 1 0 = , H 1 = H 2 W

39 Modulated structure of Sr 14/11 CoO 3 q = (11) 7/11 Acta Cryst. (1999). B55,

$+ I ( h) N M i temperature of intensity : i M i form moment position magnetic i factor M factor diffraction: The distribution of the magnetic moments over the nuclear structure can be described by a$

40 Magnetic structures Magnetic structure factor : F f Ti S r I i M i i M ( h) = p f ( h) T ( h) S exp( 2πih r ) Intensity I 2 [ ] 2 ( h) = F ( h) h h F ( h) Total magnetic magnetic atomic ( h) = I ( h) + I ( h) N M i temperature of intensity : i M i form moment position magnetic i factor M factor diffraction: The distribution of the magnetic moments over the nuclear structure can be described by a modulation wave: S i N ( x4 ) = Si0 + [ Sins sin( 2πnx4 ) + Sikc cos( 2πnx4 )] n= 1 i

41 Future development (Jana2012?) Electron diffraction Interface Documentation (hard to believe) Input of data Solution Editing of structure model Transformations Fourier calculation and interpretation External plotting Calculation of geometry CIF output Plotting of modulated parameters Refinement

42 User support jana.fzu.cz KAsF 4 (OH) 2

46 Still freeware. (the driving force are citations) Jana2006 is continuously supported by Academy of Sciences of the Czech Republic and (occasionally) by (unpredictable) Grant agency of the CR

47 SHELX or Jana2006? SHELX: + Everything written in SHELX is automatically accepted by IUCr and included in Platon. Therefore publication of structures is easier. + Many other programmers write tools for SHELX + Well developed geometry constraints for small molecules - Unfriendly, old fashioned, no real development (excluding proteins), no communication with ordinary users, weak support for complicated structures Jana2006: + much more possibilities for difficult structures + many methods supported by the same program + fast development, intensive and friendly communication with every user - See + od SHELX

48 Jana2006 Tutorial in Uberlandia Session 1 Simple structure from single crystal data Disordered structure from single crystal data Session 2 Simple structure from powder data Simple structure from powder data with asymmetric profiles Session 3 Pseudomerohedric twin Twin with partial overlaps of diffraction spots Session 4-5 Three-fold twin modulated structure powder structure described with rigid body

49 Simple structure from single crystal data Data import Determination of symmetry Charge flipping Anisotropic ADP Hydrogens to carbon Hydrogens to nitrogen

50 Disordered structure from single crystal data statistical disorder: no structured diffuse scattering partial ordering -> structured diffuse scattering 2-fold supercell 3-fold supercell

51 splitting positions with large ADP

52 Refined occupancies and distances to copper indicate that C4 and C6 are probably nitrogen, C6 is probably carbon and in the position of C2 two atoms are coinciding

53 R=1.8%

54 Your flash disks

Rigid body Rigid body approach

Rigid body Rigid body approach Model molecule is a fragment, which is placed arbitrarily and does not contribute to structure factors Model molecule is transformed to Actual positions by translation vector