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.
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
2001 Jana2000
Support for powder data and multiphase refinement. Graphical interface for Win32 and UNIX X11.
2008 Jana2006
Combination of data sources, magnetic structures, TOF data. Dynamical allocation of memory. Only for
Windows.
Data repository
X-rays OR synchrotron OR neutrons
Powder data of
multiphases
OR
Domains of
raw single crystal data
OR
Domains of
reduced single crystal data
Import Wizard
Data Repository
Format conversion, cell transformation,
sorting reflections to twin domains
Program Scheme
M95 + M50
Determining symmetry, merging symmetry equivalent reflections, absorption correction
M90
Solution
M40, M41
Refinement
Transformation
Introduction of twinning
Change of symmetry
M95
M90
M50
Plotting, geometry parameters, Fourier maps ….
M40
data repository
refinement reflection
file
basic crystal
information, form
factors, program
options
structure model
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
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.
Group-subgroup transformation
Twinning (non-merohedric three-fold twin)
Twinning matrices
for data indexed in
hexagonal cell:
0
1

 0  12
 0
3
2

0

1
2
1 
2
0
0
1


1
1
0


2
2

 0 3
1 
2
2

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 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
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 .
Anharmonic description of ADP (ionic conductor Ag8TiSe6)
Plot: Jana calculates
electron density map
and calls Marching
Cube.
Local symmetry
Local icosahedral
symmetry for atom C of C60
Powder data, (J.Appl.Cryst.
(2001). 34, 398-404)
Single crystal multiphase systems
View along a
◄Lindströmite
View along a
Krupkaite ►
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
Harmonic modulation from arbitrary displacements
Basic
position
e=A4
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
m
n 1
n 1
u  x4    A s ,n sin  2 nx4    A c ,n cos  2 nx4 
Checking results in
Fourier:
Ai-A4 Fourier sections
Charge Flipping (Superflip of Lukas Palatinus)
Special modulation functions
Cr2P2O7, incommensurately modulated phase at room temperature
Palatinus, L., Dusek, M., Glaum, R. & El Bali, B. (2006). Acta Cryst. (2006). B62, 556–566
O2
O2
Average structure
Modulated structure
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
Special modulation functions
Indication of crenel (O2) and sawtooth (O3) function
O2
O3
Parameters of crenel function
0.50
0.25
0.00
-0.07
+0.07
Parameters of sawtooth function
1.25
0.75
0.25
0.50
0.56
-0.06
0.00
Combination of crenel and sawtooth function with additional position modulation
O2
O3
The additional modulation is expressed by Legendre polynomials
1
1
2  2  n 1
Pn  z  
 1  2tz  t  t dt
2i
P0  x   1
P1  x   x
P2  x   12 3 x 2  1
P3  x   12 5 x 3  3 x 
P4  x   18 35 x 4  30 x 2  3
P5  x   18 63 x 5  70 x 3  15 x 
P6  x   161 231x 6  315 x 4  105 x 2  5
r  r , 0   Usn sin 2nx4   Ucn cos2nx4 
with harmonic waves
n
r  r , 0   Son Pno 2 x4  x40    Sen Pne 2 x4  x40  
with Legendre polynomials
n
“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.
Modulation parameters as
function of t
t=0
t=1
x4  t  r  q
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.
Plotting of modulated structures in an external program
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/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
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
incommensurate
structure
commensurate
structure
R3
The set of
superspace
symmetry
operators realized
in the supercell
depends on t
coordinate of the
R3 section.
Superspace
description,
superspace
symmetry
operators
basic cell
For given t
Jana2006 can
transform
commensurate
structure from
superspace to a
supercell.
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 M2P2O7 diphosphates are derived from the same superspace
symmetry.
Typical Fourier
section ►
Composite structures
Hexagonal perovskites
Two hexagonal subsystems with common a,b but
incommensurate c.
q is closely
related with
composition
q  0 , 0 ,  
  c2 c1
c1
c2
1

0
W 
0

0
0
1
0
0
0
0
0
1
0

0
1
2
,
H

H
W
1

0
Modulated structure of Sr14/11CoO3
q = 0.63646(11) ≈ 7/11
Acta Cryst. (1999). B55, 841-848
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*.
A B C
1

0
W  0

0
1

1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1

1
0  or

0
0 
1

0
0

0
0

1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1

1
0

0
0 
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.
Magnetic structure factor :


F h   p  f h T h S exp2ih  r 
M
f
i
T

S
i
i
i
i
i
magnetic form factor
temperature factor
i
i
r
i
mmm mmm ' m' mm m' m' m m' m' m'
Pnma Pn' ma Pnm' a Pnma '
Pn' m' a Pn' ma ' Pnm' a ' Pn' m' a '
magnetic moment
atomic position
Intensity of magnetic diffraction :


I h   F h   h h  F h 
2
M
M

Total intensity :
I h   I h   I h 
N
M

2
M
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 P6 3 mmc
Diffraction pattern of magnetic structure described with P63 mmc '
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:
N
S i  x4   S i 0   S ins sin 2nx4   S ikc cos2nx4 
n 1
The structure factor of modulated magnetic structures is similar to that for nonmodulated 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.
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.
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