Jana2006

Institute of Physics, Prague 6, Cukrovarnická street

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

Which part of the cake you can have with Jana?

Small molecules in service crystallography

Minerals

Proteins

Locally ordered structures (diffuse scattering) Modulated and composite structures

Quasicrystals

Magnetic structures

Microcrystals by electron diffraction Nanomaterials

Thin layers

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.

1996 Jana96 Modulated and 3d structures in one program. Graphical interface for DOS and UNIX X11.

1998 Jana98 Improved Jana96. First widely used version. Graphical interface for DOS, DOS emulation and UNIX X11

2000 Jana2000 Support for powder data and multiphase refinement. Graphical interface for Win32 and UNIX X11.

2006 Jana2006 Combination of data sources, magnetic structures, TOF data. Dynamical allocation of memory. Only for Windows.

Where to start?

Data input

Single crystal data of one or more domains OR

X-rays OR neutrons OR electrons

Powder data of one or more phases

Import Wizard

Data Repository

Format conversion, cell transformation, sorting reflections to twin domains

M95 + M50

M90

M40

Single crystals: determination of symmetry, merging symmetry equivalent reflections, absorption correction

Solution (by calling external programs)

Refinement or Rietveld refinement Transformation Introduction of twinning Change of symmetry

M95 data repository M90 refinement reflection file M50 basic crystal information, form factors, program options M40 structure model

Plotting, geometry parameters, Fourier maps ….

Program Scheme Reading of one or more data sets. Powders must be indexed by an external program.

Powders: Le Bail refinement of profile parameters

M41 Extraction of intensities, determination of symmetry

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

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

Structure refinement: M40 Transformations Structure plots

Charge flipping

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

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 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)

−−−

−

−

−

21

23

21

21

21

23

21

21

00

001

00

001

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.

Anharmonic description of ADP (ionic conductor Ag8TiSe6)

Plot: Jana calculates electron density map and calls Marching Cube.

Local icosahedral symmetry for atom C of C60 Powder data, (J.Appl.Cryst. (2001). 34, 398-404)

Local symmetry

View along a ◄Lindströmite

View along a Krupkaite ►

Single crystal multiphase systems

Modulated structures very short explanation what does it mean

Sodium carbonate View along c z from 0 to 1

Sodium carbonate View along c z from 1 to 2

Sodium carbonate View along c z from 2 to 3

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

c*

a*

…. but we cannot describe all peak positions with a lattice

c*

a*

c*

a*

* * *1 2 3q q q= + +q a b c

The remaining spots can be described with q-vector, which has irrational components. Indices h k l m

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

*4A

*3

*3 Aa =*3a

*3R

Modulation function

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.

( ) ( ) ( )4 , 4 , 41 1

sin 2 cos 2m m

s n c nn n

x nx nxπ π= =

= +

= +∑ ∑

r r u

u A A

e=A4

Basic position

incommensurate

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

Natural melilite from San Venanzo, Umbria, Italy Formula: (Ca1.89Sr0.01Na0.08K0.02)(Mg0.92Al0.08)(Si1.98Al0.02)O7

Charge Flipping (Superflip of Lukas Palatinus)

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/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 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] - 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

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 Origin of R3 section may influence symmetry in the supercell. Jana2006 can automatically find all possible supercell symmetries.

Superspace Supercell

This angle follows from q-vector

Exact intersection

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

Composite structures

Hexagonal perovskites Two hexagonal subsystems with common a,b but incommensurate c.

c2

c1

( )

WHH

q

2=

=

==

1

12

,

0100100000100001

,0,0

W

ccγγ

q is closely related with composition

Typical Fourier section ►

Modulated structure of Sr14/11CoO3 q = 0.63646(11) ≈ 7/11 Acta Cryst. (1999). B55, 841-848

Magnetic structures

( ) ( ) ( ) ( )

( ) ( ) ( )[ ]

( ) ( ) ( )hhh

hFhhFh

rS

rhShhF

MN

MMM

i

i

i

i

iiiiiM

III

hI

Tf

iThfp

+=

⋅−=

∑ ⋅=

:intensity Total

:ndiffractiomagnetic of Intensity positionatomic

momentmagnetic

factor etemperaturfactor formmagnetic

:factor structureMagnetic

22

2exp

π

The distribution of the magnetic moments over the nuclear structure can be described by a modulation wave:

( ) ( ) ( )[ ]∑=

++=N

nikcinsii nxnxx

14404 2cos2sin ππ SSSS

Future development (Jana2012?) Electron diffraction Interface Documentation (hard to believe) Input of data

Solution

Refinement

Editing of structure model

Transformations

Fourier calculation and interpretation

External plotting

Calculation of geometry

CIF output

Plotting of modulated parameters

User support jana.fzu.cz

KAsF4(OH)2

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

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

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

Data import Determination of symmetry Charge flipping Anisotropic ADP Hydrogens to carbon Hydrogens to nitrogen

Simple structure from single crystal data

2-fold supercell

3-fold supercell

statistical disorder: no structured diffuse scattering partial ordering -> structured diffuse scattering

Disordered structure from single crystal data

splitting positions with large ADP

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

R=1.8%

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