Jana2006 Program for structure analysis of crystals periodic in three or more dimensions from diffraction data

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

2. History 1980 SDSProgram for solution and refinement of 3d structures 1984 JanaRefinement program for modulated structures 1994 SDS94 and Jana94Set of programs for 3d (SDS) and modulated (Jana) structures running in text mode. 1996 Jana96Modulated and 3d structures in one program. Graphical interface for DOS and UNIX X11. 1998 Jana98Improved Jana96. First widely used version. Graphical interface for DOS, DOS emulation and UNIX X11 2001 Jana2000Support for powder data and multiphase refinement. Graphical interface for Win32 and UNIX X11. 2008 Jana2006Combination of data sources, magnetic structures, TOF data. Dynamical allocation of memory. Only for Windows.

3. Datarepository X-rays OR synchrotron OR neutrons Powder data of multiphases Domains of raw single crystal data Domains of reduced single crystal data OR OR Import Wizard Format conversion, cell transformation, sorting reflections to twin domains Data Repository

4. ProgramScheme M95 + M50 Determining symmetry, merging symmetry equivalent reflections, absorption correction M90 Solution M40, M41 Refinement TransformationIntroduction of twinningChange of symmetry M95 data repositoryM90 refinement reflection fileM50 basic crystal information, form factors, program optionsM40 structure model Plotting, geometry parameters, Fourier maps ….

5. Topics Basic crystallographyAdvanced tools Incommensurate structuresCommensurate structures Composite structuresMagnetic structures Jana2006 is single piece of code. This allows for development of universal tools working by the same way for various dimensions (3d, (3+1)d …) and for different data types (single crystals, powders). both 3d and modulated structures. Jana2006 also works as an interface for some external programs: SIR97,2000,2004; EXPO, EXPO2004, Superflip, MC (marching cube) and software for plotting of crystal structures.

6. Basic crystallography Wizards for symmetry determinationExternal 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

7. Advanced tools Fourier sections Transformation tools, group-subgroup relations Twinning (merohedric or general), treating of overlapped reflections User equations Disorder “Rigid body” approach Multiphase refinement for powder data Multiphase refinement for single crystals Multipole refinement Powder data: Anisotropic strain broadening (generalized to satellites) Fundamental approach TOF data Local symmetry

8. Fourier maps M40 M50 Refinement M80 Fourier M81 Contour M90 General section Predefined sections M81 Contour can plot predefined section or it can calculate and plot general sections. For arbitrary general sections the predefined section must cover at least asymmetric unit of the elementary cell.

10. Group-subgroup transformation

11. Twinning (non-merohedric three-fold twin) Twinning matrices for data indexed in hexagonal cell:

12. 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.

13. Restraints, Constraints, User Equations restric C39a 2 C39b restric C9a 2 C9b . . . . equation : x[c8x]=x[c8] equation : y[c8x]=y[c8] equation : z[c8x]=z[c8] equation : x[n3x]=x[n3] equation : y[n3x]=y[n3] equation : z[n3x]=z[n3] . . . . equation : aimol[mol1#2]=1-aimol[mol1#1] equation : aimol[mol2#2]=1-aimol[mol2#1] equation : aimol[mol4#2]=1-aimol[mol4#1] equation : aimol[mol5#2]=1-aimol[mol5#1] equation : aimol[mol6#2]=1-aimol[mol6#1] . . . . keep hydro triang C3 2 1 C2 C4 0.96 H1c3 keep ADP riding C3 1.2 H1c3 keep hydro tetrahed C13 1 3 C8x 0.96 H1c13 H2c13 H3c13 keep ADP riding C13 1.2 H1c13 H2c13 H3c13

14. Fundamental approach for powder profile parameters The fundamental approach allows for separation of instrumental parameters and sample-dependent parameters (size and strain). It is based on a general model for the axial divergence aberration function as described by R.W.Cheary and A.A.Coelho in J.Appl.Cryst. (1998), 31, 851-861. It has been developed for a conventional X-ray diffractometer with Soller slits in incident and/or diffracted beam and it has been already incorporated in program TOPAS. Example of instrumental parameters: Primary radius of goniometer: 217.5 mm Secondary radius of goniometer: 217.5 mm Receiving slits: 0.2mm Fixed divergence slits: 0.5 deg Source length: 12mm Sample length: 15mm Receiving slit length: 12mm Primary soller: 5 deg Secondary soller: 5 deg With fundamental approach profile parameters (particle size and strain) have clear physical meaning because they are separated of instrumental parameters .

15. Anharmonic description of ADP (ionic conductor Ag8TiSe6) Plot: Jana calculates electron density map and calls Marching Cube.

16. Local symmetry Local icosahedral symmetry for atom C of C60Powder data, (J.Appl.Cryst. (2001). 34, 398-404)

17. Single crystal multiphase systems View along a ◄Lindströmite View along a Krupkaite ►

18. 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 functions of t Plotting of modulated structures Calculation of geometric parameters

19. Symmetry Wizard for (3+1)d modulated strucure

20. Basic position e=A4 Harmonic modulation from arbitrary displacements 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.

21. Checking results in Fourier: Ai-A4 Fourier sections

22. Charge Flipping (Superflip of Lukas Palatinus)

23. Special modulation functions Cr2P2O7, incommensurately modulated phase at room temperaturePalatinus, L., Dusek, M., Glaum, R. & El Bali, B. (2006). Acta Cryst. (2006). B62, 556–566 O2 O2 Modulated structure Average structure

24. Special modulation functions Fourier map after using many harmonic modulation functions P (cyan) O1 (green) O2 (red) O3 (blue) Phosphorus and O2 are in the plane of the Fourier section

25. Special modulation functions Indication of crenel (O2) and sawtooth (O3) function O3 O2

26. 0.50 0.25 0.00 -0.07 +0.07 Parameters of crenel function

27. 1.25 0.75 0.25 0.00 -0.06 0.50 0.56 Parameters of sawtooth function

28. Combination of crenel and sawtooth function with additional position modulation O2 O3

29. The additional modulation is expressed by Legendre polynomials “o” and “e” indicate odd and even member. The first polynom, i.e. P1o, defines a line. The three coefficients of P1xo , P1yo and P1zo are refined either to crenel or sawtooth shape.

30. Modulation parameters as function of t t=0 t=1 Reason for t coordinate: modulation diplacement from the basic position is calculated in the real space, i.e. along a3, not A3. Due to translation periodicity all possible modulation displacements occur between t=0 and 1.

31. Plotting of modulated structures in an external program

32. Twinning of modulated structures The twinning matrix is 3x3 matrix regardless to dimension.Twinning may decrease dimension of the problem. Example: La2Co1.7, Acta Cryst. (2000). B56, 959-971.Average structure: 4.89 4.89 4.34 90 90 120 , P63/mmcModulated structure: modulated composite structure, C2/m(α0β),6-fold twinning around the hexagonal c Reconstruction of (h,k,1.835) from CCD measurement.

33. Disorder in modulated structures Cr2P2O7, 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]+0.5* Δ[Cr1] Δ'[Cr1] = Δ[Cr1] - xΔ[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.

34. Commensurate structures incommensurate structure commensurate structure

35. R3 The set of superspace symmetry operators realized in the supercell depends on t coordinate of the R3 section. For given t Jana2006 can transform commensurate structure from superspace to a supercell. Superspace description, superspace symmetry operators basic cell

36. Choosing commensurate model In our case we shall use symmetry operators and definition points corresponding to 3x1x2 supercell. Change of tzero should be followed by new averaging of data.

37. Commensurate families In this example known M2P2O7 diphosphates are derived from the same superspace symmetry.

38. Typical Fourier section ► Composite structures Hexagonal perovskitesTwo hexagonal subsystems with common a,b but incommensurate c. q is closely related with composition c1 c2

39. Modulated structure of Sr14/11CoO3q = 0.63646(11) ≈ 7/11Acta Cryst. (1999). B55, 841-848

40. Levyclaudite: Two triclinic composite subsystems with satellites up to the 4th order, related by 5x5 W matrix. Acta Cryst. (2006). B62, 775-789. View of the peak table along c*. ABC

42. Magnetic structures Neutrons posses a magnetic moment that enables their interaction with magnetic moments of electrons. Therefore – below the temperature of the magnetic phase transition - we can observe both magnetic and nuclear reflections. Symmetry contains time inversion which is combined with any symmetry operation. It yields magnetic point groups and magnetic space groups. Extinction rules and symmetry restrictions can be diferent for nuclear and magnetic symmetry.

43. Tool for testing magnetic symmetry “Crystallographic” approach: we are looking for magnetic symmetry that corresponds with the observed powder profile.

44. Diffraction pattern described without magnetic moments

45. Diffraction pattern of magnetic structure described with

46. Diffraction pattern of magnetic structure described with

47. Tool for representative analysis In special cases the equivalence between magnetic group and a given representation needs an additional condition, for instance that sum of magnetic moments related by a former 3-fold axis is zero (P321 -> P1)

48. Superspace approach The elementary cell of magnetic structure can be the same or different of the cell of the nuclear structure. For the same cell the magnetic reflections contribute to nuclear reflections. For a different cell part of magnetic reflections or all of them form a separate peaks. The distribution of the magnetic moments over the nuclear structure can be described by a modulation wave: The structure factor of modulated magnetic structures is similar to that for non-modulated magnetic structure. Each n-th term in the above equation will create magnetic satellites of the order n. The magnetic cell is often a simple supercell, with q vector (wave vector) having a simple rational component and the structure can be treated like a commensurate one.

49. R3 For magnetic wave the property is not position but the spin moment. This approach allows for very complicated magnetic structures and for combination of magnetic and nuclear modulation (using the same or more q vectors). Warning: this is a new tool tested with only a few magnetic structures.