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

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.

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

M95 + M50 M90 M40, M41 Determining symmetry, merging symmetry equivalent reflections, absorption correction Solution Refinement Transformation Introduction of twinning Change of symmetry M95data repository M90refinement reflection file M50basic crystal information, form factors, program options M40structure model Plotting, geometry parameters, Fourier maps …. Program Scheme

Topics Basic crystallography Advanced tools Incommensurate structures Commensurate structures Composite structures Magnetic 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.

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

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

M40 M50 M90 M80M81RefinementContourFourier 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. Fourier maps

Group-subgroup transformation

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

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.

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 C H1c3 keep ADP riding C3 1.2 H1c3 keep hydro tetrahed C C8x 0.96 H1c13 H2c13 H3c13 keep ADP riding C H1c13 H2c13 H3c13

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, 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: mm Secondary radius of goniometer: 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 Fundamental approach for powder profile parameters With fundamental approach profile parameters (particle size and strain) have clear physical meaning because they are separated of instrumental parameters.

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

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

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

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

Symmetry Wizard for (3+1)d modulated strucure

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. e=A 4 Basic position Harmonic modulation from arbitrary displacements

Checking results in Fourier: A i -A 4 Fourier sections

Charge Flipping (Superflip of Lukas Palatinus)

Average structure Modulated structure O2O2 O2O2 Special modulation functions Cr 2 P 2 O 7, incommensurately modulated phase at room temperature Palatinus, L., Dusek, M., Glaum, R. & El Bali, B. (2006). Acta Cryst. (2006). B62, 556–566

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

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

Parameters of crenel function

Parameters of sawtooth function

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

The additional modulation is expressed by Legendre polynomials “o” and “e” indicate odd and even member. The first polynom, i.e. P 1 o, defines a line. The three coefficients of P 1x o, P 1y o and P 1z o are refined either to crenel or sawtooth shape.

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. Modulation parameters as function of t

Plotting of modulated structures in an external program

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. Twinning of modulated structures

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 incommensurate structure commensurate structure

Superspace description, superspace symmetry operators basic cell The set of superspace symmetry operators realized in the supercell depends on t coordinate of the R 3 section. For given t Jana2006 can transform commensurate structure from superspace to a supercell. R3

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.

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

Composite structures Hexagonal perovskites Two hexagonal subsystems with common a, b but incommensurate c. c2c2 c1c1 q is closely related with composition Typical Fourier section ►

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

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

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.

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

Diffraction pattern described without magnetic moments

Diffraction pattern of magnetic structure described with

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)

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.

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. R3

Future of Jana system Development: magnetic structures, electron diffraction …. Polishing: wizards, graphical tools … Better support for simple structures Jana2006 is available in www-xray.fzu.cz/jana