Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS),...
-
Upload
brian-wade -
Category
Documents
-
view
217 -
download
0
Transcript of Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS),...
![Page 1: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/1.jpg)
Barcelona, September 2005, MULTIMAT
Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France
Neutron Powder Diffraction: a powerful technique for studying structural and
magnetic phase transitions
A-site ordered perovskite YBaMn2O6: atomic versus larger scales charge ordering
![Page 2: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/2.jpg)
Barcelona, September 2005, MULTIMAT
Content of the talk
• Generalities about the properties and use of neutrons for condensed matter research
• Neutron powder diffraction. Data treatment. Introduction to the programs of the FullProf Suite
• Study of the phase transitions in YBaMn2O6. Charge/orbital/spin ordering.
![Page 3: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/3.jpg)
Barcelona, September 2005, MULTIMAT
Chadwick1932
Neutrons as constituents of matter
![Page 4: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/4.jpg)
Barcelona, September 2005, MULTIMAT
Properties of neutrons
![Page 5: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/5.jpg)
Barcelona, September 2005, MULTIMAT
• The reactor geometry is optimized to produce the maximum number of neutrons.
• The fission of a 235U nucleus produce in average 2.5 neutrons. 1.5 are used to keep the chain reaction, only 1 is used for making neutron beams.Main research reactors in Europe:
France, ILL (57 MW) in Grenoble Orpheé (14 MW) in Saclay
GermanyFRJ-2 (23 MW) in Julich (closed)BER-2 (10 MW) in BerlinFRM-II (24 MW) in Munich (new)
Neutron production: nuclear reactors
![Page 6: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/6.jpg)
Barcelona, September 2005, MULTIMAT
• H+ accelerated to 1 GeV • Targets of W, Pb, Hg, U • 20 to 25 neutrons by H+ • Pulses of 50 Hz • Flux of 3.7 1016 ns-1 (ISIS) • Pulse length of µs• Relatively small average
flux
Switzerland, SINQ quasi-continuous ( 10 MW)
United Kingdom, ISIS (1.5 MW) SNS, Oak Ridge (USA) – in construction
Neutron production: spallation sources
![Page 7: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/7.jpg)
Barcelona, September 2005, MULTIMAT
Neutron reactors: ILL
![Page 8: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/8.jpg)
Barcelona, September 2005, MULTIMAT
Neutron reactors: ILL
![Page 9: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/9.jpg)
Barcelona, September 2005, MULTIMAT
kinetic energy (E) velocity (v) temperature (T).
k= 2/= mnv/ħ
E= mnv2/2= kB T = p2/2mn= (ħk)2/2mn=(h/2/2mn
wavevector (k)
wavelength ()
Particle-wave properties
momentum (p)
ħ=h/2
p= mnv = ħ k
![Page 10: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/10.jpg)
Barcelona, September 2005, MULTIMAT
E = mn v 2 /2 = kB T = (ħk)2/2mn ; k = 2/ = mnv/ħ
Also cold moderating source, liquid deuterium at 25K (Cold neutrons)
And hot moderating source, graphite at ~2000K
Neutrons moderated by heavy water at 300K (Thermal neutrons)
Particle-wave properties (moderators)
![Page 11: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/11.jpg)
Barcelona, September 2005, MULTIMAT
E = mnv2/2 = kB T = (ħk)2/2mn ; k = 2/ = mnv/ħ
Energy (meV) Temp (K) Wavelength (Å)
Cold 0.1 – 10 1 – 120 4 – 30
Thermal 5 – 100 60 – 1000 1 – 4
Hot 100 – 500 1000 – 6000 0.4 – 1
Cold Sources
COLDTHERMAL
HOT
Particle-wave properties (Energy-Temperature-Wavelength)
![Page 12: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/12.jpg)
Barcelona, September 2005, MULTIMAT
q
k
Direction
,
r
dS
z
k’
Target
d
',''
2
,
2
2
2
'''2
'
'
EEkVkppm
k
k
dEd
d
= number of incident neutrons /cm2 / second
= total number of neutrons scattered/second/
Fermi’s golden rule gives the neutron-scattering Cross-section number of neutrons of a given energy scattered per second in a given solid angle
(the effective area presented by a nucleus to an incident neutron)
Interaction neutron-nucleus
![Page 13: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/13.jpg)
Barcelona, September 2005, MULTIMAT
•Fermi Pseudo potential of a nucleus in rj
Vj
22
mb j (r rj )
The range of nuclear force (~ 1fm) is much less than neutron wavelength so that scattering is “point-like”
Weak interaction with matter aids interpretation of scattering data
Potential with only one parameter
Plane wave e ik·x
SampleV(r)
k
Plane wave e ik’·r
k’
r
Detector
2k’
k
Q
Spherical wave(b/r)e ik·r
Interaction neutron-nucleus
![Page 14: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/14.jpg)
Barcelona, September 2005, MULTIMAT
Neutron scattering lengths
![Page 15: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/15.jpg)
Barcelona, September 2005, MULTIMAT
H D N Mn Fe
X-Rays
H D N FeMn
Neutrons
negative negative
Neutron scattering is a nuclear interactionNeutron scattering is a nuclear interaction
X-rays and neutron scattering lengths
![Page 16: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/16.jpg)
Barcelona, September 2005, MULTIMAT
3 2
0
(2 )( ) ( )N
coh
d NQ F Q
d v
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
For elastic scattering:
Where v0 is the unit cell volume and a reciprocal lattice vector
The coherent elastic scattering takes place only for
2 sind
'k k Q
' 2 sin( )k k Q k
Bragg Law
Elastic Scattering: Diffraction
![Page 17: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/17.jpg)
Barcelona, September 2005, MULTIMAT
Form Factor
![Page 18: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/18.jpg)
Barcelona, September 2005, MULTIMAT
Dipolar interaction (n , m): vector scattering amplitude
2
1
2
Q m Qa Q Q mM er f
Q
Q= kF - kI
kI=2/uI
kF=2/ uF
Magnetic Scattering
![Page 19: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/19.jpg)
Barcelona, September 2005, MULTIMAT
m
m
Q=Q e Only the perpendicularcomponent of m to Q contributes to scattering
- Magnetic interactions are long range and non-central
– Nuclear and magnetic scattering have similar magnitudes
– Magnetic scattering involves a form factor:
Fourier Transform of unpaired electron spatial distribution
– Magnetic scattering depends only on the component of m
perpendicular to Q
Magnetic Scattering
![Page 20: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/20.jpg)
Barcelona, September 2005, MULTIMAT
Content of the talk
• Generalities about the properties and use of neutrons for condensed matter research
• Neutron powder diffraction. Data treatment. Introduction to the programs of the FullProf Suite
• Study of the phase transitions in YBaMn2O6. Charge/orbital/spin ordering.
![Page 21: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/21.jpg)
Barcelona, September 2005, MULTIMAT
D1B(ILL) or G41(LLB)
Diffractometers: Powder high flux
![Page 22: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/22.jpg)
Barcelona, September 2005, MULTIMAT
A powder diffraction pattern can be recorded in numerical form for a discrete set of scattering angles, times of flight or
energies. We will refer to this scattering variable as : T. The experimental powder diffraction pattern is usually given as three arrays :
The profile can be modelled using the calculated counts: yci
at the ith step by summing the contribution from neighbouring Bragg reflections plus the background.
1,2,...
, ,i i i i nT y
Experimental powder pattern
![Page 23: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/23.jpg)
Barcelona, September 2005, MULTIMAT
yi
Position “i”: Ti
Bragg position Th
yi-ycizero
Powder diffraction profile:scattering variable T: 2, TOF, Energy
![Page 24: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/24.jpg)
Barcelona, September 2005, MULTIMAT
The calculated profile of powder diffraction patterns
( )h h{h}
ci i iy I T T b Contains structural information: atom positions, magnetic moments, etc h h II I
( , )h Pix Contains micro-structural information: instr. resolution, defects, crystallite size…
Bi ib b Background: noise, incoherent scatteringdiffuse scattering, ...
![Page 25: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/25.jpg)
Barcelona, September 2005, MULTIMAT
The calculated profile of powder diffraction patterns
( )h h{h}
ci i iy I T T b The symbol {h} means that the sum is extended only to those reflections contributing to the channel “i” .
This should be taken into account (resolution function of the diffractometer and sample broadening) before doing the actual calculation of the profile intensity.
This is the reason why some Rietveld programs are run in two steps
![Page 26: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/26.jpg)
Barcelona, September 2005, MULTIMAT
, ,{ }
( )h hh
ci i iy s I T T b
, ,{ }
( )h h
h
p p p p pci i iy s I T T b
Several phases ( = 1,n) contributing to several (p=1,np) diffraction patterns
Several phases ( = 1,n) contributing to the diffraction pattern
![Page 27: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/27.jpg)
Barcelona, September 2005, MULTIMAT
2h h
I S L pO ACFIntegrated intensities are proportional to the square of the structure factor F. The factors are: Scale Factor (S), Lorentz-polarization (Lp), preferred orientation (O), absorption (A), other “corrections” (C) ...
( )h h{h}
ci i iy I T T b
![Page 28: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/28.jpg)
Barcelona, September 2005, MULTIMAT
1
2h h t rn
j j j jsj s
F O f h T exp i S
( , , ) ( 1,2,... )rj j j jx y z j n
sinexp( )j jT B
The Structure Factor contains the structural parameters
(isotropic case)
![Page 29: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/29.jpg)
Barcelona, September 2005, MULTIMAT
Structural Parameters(simplest case)
( , , )rj j j jx y z Atom positions (up to 3n parameters)
jO Occupation factors (up to n-1 parameters)
jBIsotropic displacement (temperature) factors (up to n parameters)
![Page 30: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/30.jpg)
Barcelona, September 2005, MULTIMAT
Structural Parameters(complex cases)
As in the simplest case plus additional (or alternative) parameters:
• Anisotropic temperature (displacement) factors
• Anharmonic temperature factors
• Special form-factors (Symmetry adapted spherical harmonics ), TLS for rigid molecules, etc.
• Magnetic moments, coefficients of Fourier components of magnetic moments , basis functions, etc.
![Page 31: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/31.jpg)
Barcelona, September 2005, MULTIMAT
1
( ) 2h h h t rn
j j j j s jsj s
F O f h T g exp i S
( )hj sgComplex form factor of object jAnisotropic DPsAnharmonic DPs
1,2,...h Ts s G
s
h h
k S k s N
l l
The Structure Factor in complex cases
![Page 32: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/32.jpg)
Barcelona, September 2005, MULTIMAT
The approximation of the peak shape profile function and microstructural effects
Precise refinements can be done with confidence only if the intrinsic and instrumental peak shapes are properly approximated.
At present The approximation of the intrinsic profile is mostly based in the Voigt (or pseudo-Voigt) function
The approximation of the instrumental profile is also based in the Voigt function for constant wavelength instruments For TOF the instrumental+intrinsic profile is approximated by the convolution of a Voigt function with back-to-back exponentials or with the Ikeda-Carpenter function.
![Page 33: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/33.jpg)
Barcelona, September 2005, MULTIMAT
The peak shape function of powder diffraction patterns contains the Profile
Parameters
( , ) ( , )h P h Pi ix T T
( ) 1x dx
( ) ( ) ( )x g x f x instrumental intrinsic profile
( ) ( ) ( ) ( )x L x G x V x
In most cases the observed peak shape is approximated by a linear combination of Voigt (or pseudo-Voigt) functions
![Page 34: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/34.jpg)
Barcelona, September 2005, MULTIMAT
( ) ( ) (1 ) ( )pV x L x G x The pseudo-Voigt function
( ) ( ) ( ) ( ) ( )V x L x G x L x u G u du
( ) ( , , ) ( , , )L G L GV x V x H H V x
( ) ( , , )pV x pV x H
The Voigt function
![Page 35: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/35.jpg)
Barcelona, September 2005, MULTIMAT
The Rietveld Method consist of refining a crystal (and/or magnetic) structure by minimising the weighted squared difference between the observed and the calculated pattern against the parameter vector:
22
1
( )n
i i cii
w y y
21
iiw
2i : is the variance of the "observation" yi
The Rietveld Method
![Page 36: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/36.jpg)
Barcelona, September 2005, MULTIMAT
Minimum necessary condition:
A Taylor expansion of around allows the application of an iterative process. The shifts to be applied to the parameters at each cycle for improving 2 are obtained by solving a linear system of equations (normal equations)
2
0
( )icy 0
Least squares: Gauss-Newton (1)
0
0 0
0
( ) ( )
( )( )
A b
ic ickl i
i k l
ick i i ic
i k
y yA w
yb w y y
![Page 37: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/37.jpg)
Barcelona, September 2005, MULTIMAT
Least squares: Gauss-Newton (2)
The new parameters are considered as the starting ones in the next cycle and the process is repeated until a convergence criterion is satisfied. The variances of the adjusted parameters are calculated by the expression:
The shifts of the parameters obtained by solving the normal equations are added to the starting parameters giving rise to a new set
01 0
1( ) ( )Ak kk
N - P+C
![Page 38: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/38.jpg)
Barcelona, September 2005, MULTIMAT
• Constant scattering length. Contrast.
• Low absorption: easy sample environment
• Magnetic structures
• High precision in structure refinement
• Moderate resolution
• Extremely high resolution
• Subtle distortions• Indexing and
Structure determination
• Anomalous scattering
• Texture effects
Neutrons Synchrotron X-rays
Neutron and synchrotron powder diffraction
![Page 39: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/39.jpg)
Barcelona, September 2005, MULTIMAT
![Page 40: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/40.jpg)
Barcelona, September 2005, MULTIMAT
![Page 41: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/41.jpg)
Barcelona, September 2005, MULTIMAT
![Page 42: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/42.jpg)
Barcelona, September 2005, MULTIMAT
Directory structure of the FullProf Suite
![Page 43: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/43.jpg)
Barcelona, September 2005, MULTIMAT
WinPLOTR: program to access the whole FullProf Suite
![Page 44: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/44.jpg)
Barcelona, September 2005, MULTIMAT
Configuration of WinPLOTR
File: winplotr.set
![Page 45: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/45.jpg)
Barcelona, September 2005, MULTIMAT
Indexing demo with WinPLOTR
New facility: DICVOL04
Two other indexing programs: TREOR, ITO
![Page 46: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/46.jpg)
Barcelona, September 2005, MULTIMAT
Other features of WinPLOTR
Access to other programs: EdPCR, Fp_Studio, DICVOL04, BasIreps
Two other indexing programs: TREOR, ITO
![Page 47: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/47.jpg)
Barcelona, September 2005, MULTIMAT
A program for analysis of diffraction patterns: FullProf
• A program for : Simulation of powder diffraction patterns Pattern decomposition integrated intensities Structure refinement Powder and single crystal data• Crystal and magnetic structures • Multiple data sets: simultaneous treatment of several powder diffraction patterns (CW X-rays & neutrons, Energy dispersive X-rays, TOF neutron diffraction)• Combined treatment of single crystal and powder data• Crystal and magnetic Structure determination capabilities: simulated annealing on integrated intensity data
![Page 48: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/48.jpg)
Barcelona, September 2005, MULTIMAT
FullProf
Outputfiles,Plot
diffr. patterns
Minimal input: Input control file (extension ‘ .pcr ’): PCR-file Model, crystallographic/magnetic information
PCR file
DAT file(s)Eventually, experimental data
How works FullProf
![Page 49: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/49.jpg)
Barcelona, September 2005, MULTIMAT
Many variables and options Complex to handlePCR file
Format depending on the instrument, usually simple
DAT file(s)
Hint: copy an existing (working) PCR-file and modify it for the user case, or... USE the new GUI: EdPCR
The PCR file: steep learning curve
![Page 50: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/50.jpg)
Barcelona, September 2005, MULTIMAT
A new GUI for FullProf: EdPCR
GUI using Winteracter: http://www.winteracter.com
![Page 51: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/51.jpg)
Barcelona, September 2005, MULTIMAT
Content of the talk
• Generalities about the properties and use of neutrons for condensed matter research
• Neutron powder diffraction. Data treatment. Introduction to the programs of the FullProf Suite
• Study of the phase transitions in YBaMn2O6. Charge/orbital/spin ordering.
![Page 52: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/52.jpg)
Barcelona, September 2005, MULTIMAT
Example: Study of A-site ordered manganite YBaMn2O6
• Introduction to the half-doped (Mn3+/Mn4+) manganites
• Phase transitions, crystal and magnetic structures of mixed valence YBaMn2O6
![Page 53: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/53.jpg)
Barcelona, September 2005, MULTIMAT
Charge ordering: In the charge ordered state, is the charge localization at atomic level? What does the conventional ionic states Mn3+/Mn4+ mean? … CDW, charge disproportionation, polarons, …
Orbital ordering: Is that concept really relevant for explaining the electronic/structural transitions in manganites? Is there any difference with respect to a MO6 distorting structural transition?
Our team started few years ago to answer someimportant questions!
Colossal Magnetoresistance Regain of interest in electronic properties of (semi)-conducting magnetic oxides
![Page 54: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/54.jpg)
Barcelona, September 2005, MULTIMAT
Magnetic exchange interactions: Are the Goodenough-Kanamori-Anderson rules still applicable? How to explain the canted magnetic structures?
Are there other magnetic structures compatible with the observed magnetic powder diffraction patterns?
Is the CE structure really collinear?
Electronic transitions and phase separation: Role of the chemistry and the disorder. Homogeneous/inhomogeneous states: what is a phase? Role of the defects and microstrains …
![Page 55: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/55.jpg)
Barcelona, September 2005, MULTIMAT q
The single Mn-site in the HT phase breaks up into two sublattices in the CO-low temperature phase, having very similar characteristics concerning the average Mn-O distances. The observed distortions are different of what is expected from the generally accepted picture of a concomitant charge (Mn3+-Mn4+) and orbital ordering.
Formation of “molecular” ferromagnetic Mn-O-Mn pairs stabilised by local DE and a suitable structural distortion: Zener polaron.
O2
O4
O1
O3
Mn2 Mn1
O1
O2
O4
e-
Our previous work : A new interpretation of the electronic localization in charge ordered manganites
A. Daoud-Aladine et al., Phys. Rev. Lett. 89, 097205 (2002).
Nature of the structural transition at TCO in half-doped manganites R1/2D1/2[Mn3.5+]O3
![Page 56: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/56.jpg)
Barcelona, September 2005, MULTIMAT
The temperature dependence electrical resistivity, and inverse magnetic susceptibility of the Bi1/2Sr1/2MnO3 crystal. The slope of 1/ in the charge-ordered state for 150–300 K closely approaches the value for Zener pairs with total spin S=7/2 ( exp=7.83 B , calc=7.94 B ).
J. Hejtmánek et al., J. Appl. Phys. 93, 7370 (2003)
Magnetic Susceptibility: two kinds of paramagnetic states
![Page 57: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/57.jpg)
Barcelona, September 2005, MULTIMAT
In common manganites the A-site doping induces disorder and local inhomogeneities (fluctuations of chemical composition)
Role of the A-site disorder Using Ba and a heavy rare earth, or Y, a new ordered family of half-doped manganites is obtained
Y1/2Ba1/2MnO3 YBaMn2O6
A first report on this compound was published by:
T. Nakajima et al. J. Phys. Chem. Solids 63 (2002) 913
Our previous strategy to study the structural distortions in half-doped manganites:
Minimise the size mismatch between atoms in A sites of perovskites AMnO3 (Pr, Ca)
![Page 58: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/58.jpg)
Barcelona, September 2005, MULTIMAT
Approximate phase diagram of
R1/2Ba1/2MnO3
Random Potential Effect near the Bicritical Region in Perovskite Manganites as Revealedby Comparison with the Ordered Perovskite AnalogsD. Akahoshi, M. Uchida, Y. Tomioka,1 T. Arima, Y. Matsui and Y. Tokura, Physical Review Letters 90, 177203 (2003)
![Page 59: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/59.jpg)
Barcelona, September 2005, MULTIMAT
Phase transitions, crystal and magnetic structures of mixed valence
YBaMn2O6
![Page 60: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/60.jpg)
Barcelona, September 2005, MULTIMAT
Y2O3+BaCO3
+MnCO3
1523K (purified Ar)
773K (O2)
YBaMn2O6
YBaMn2O5
1673K (air)
Y1/2Ba1/2MnO3
The Y3+ and the Ba2+ ions may be ordered or disordered depending on
the synthesis conditions
![Page 61: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/61.jpg)
Barcelona, September 2005, MULTIMAT
Nakajima et al. J. Phys. Soc. Jpn. 71, 2843-2846 (2002)
At high temperature, 3 transitions:
2 of them were reported byNakajima et al. (T1 & T2)
New transition at T3
YBaMn2O6: High temperature phases
![Page 62: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/62.jpg)
Barcelona, September 2005, MULTIMAT
T1 500 K TCO 480 K (?)T2 560 KT3 805 K TTM 780 K (?)
Phase transitions in YBaMn2O6: resistivity vs T
![Page 63: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/63.jpg)
Barcelona, September 2005, MULTIMAT
Radiation: pure CuK1 spectral line (=1.5406Å)
X-ray diffraction versus temperature
![Page 64: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/64.jpg)
Barcelona, September 2005, MULTIMAT
T=398KT=438KT=458KT=500KT=510KT=520KT=530KT=535KT=720KT=730KT=750KT=793K
(110
)
(102
)
![Page 65: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/65.jpg)
Barcelona, September 2005, MULTIMAT
T=398KT=438KT=458KT=500KT=510KT=520KT=530KT=535KT=720KT=730KT=750KT=793K
(200
)
(004
)
![Page 66: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/66.jpg)
Barcelona, September 2005, MULTIMAT
T3
T2
3.80
3.82
3.84
3.86
3.88
3.90
3.92
90.00
90.10
90.20
90.30
90.40
300 400 500 600 700 800
Par
amèt
res
(Å)
beta(°)
T(K)
1.88
1.90
1.92
1.94
1.96
1.98
2.00
2.02
d Mn
-O (
Å)
Mn-O3
Mn-O1b
Mn-O2
<Mn-O1a>
Mn-O1
c/2
a
b
c/2
b/22
a/2
2.00
81.
883
2.00
21.
880
Phase transitions in YBaMn2O6 as seen by X-ray diffraction
The picture provided by X-rays is wrong!P2/m
a ~ 3.92Å
b ~ 3.85Å
c ~ 7.74Å
~90.3°
P4/mmma ~ 3.90Å
c ~ 7.78Å
Intermediate phase ?P2/m?
![Page 67: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/67.jpg)
Barcelona, September 2005, MULTIMATq
q
Neutron diffraction versus temperature (D20, high resolution mode at ILL)
![Page 68: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/68.jpg)
Barcelona, September 2005, MULTIMAT
A sigle site for Mn cations <Mn-O>=1.955(1)Å Valence Sum=3.49(1)
ILL, D20 ( =1.37 Å) YBaMn2O6: 815K P 4/nbma=5.51Å c=7.78Å (2=2.99 RB=2.40)
YBaMn2O6 high temperature phase
Wavy background due to SiO2 tube
![Page 69: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/69.jpg)
Barcelona, September 2005, MULTIMAT
ILL, D20 ( =1.37Å et 1.88 Å) YBaMn2O6: 570K
P21 /m (or C2/m)a=7.85Å b=7.69Å c=7.73Å=90.3° (2=2.69, RB=3.03)
YBaMn2O6: Intermediate phase
<Mn2-O>=1.962(7) Å <Mn1-O> =1.953 (7) ÅValence Sum=3.49(7) Valence Sum=3.58(7)
![Page 70: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/70.jpg)
Barcelona, September 2005, MULTIMAT
Williams et al. for TbBaMn2O6 (neutron diffraction pattern)The space group P21/m initially used (ap2 ap2 2ap), does not take into account few superstructure reflections, with a propagation vector q=(0,1/2,0). A good fit to the profiles was obtained by transforming the structure to a b-doubled cell with triclinic P-1 symmetry. Scarce number of observed superstructure peaks : constrained parameter refinements.
• strain-relieving displacements in the TbO layer
• orbital ordering in the MnO2 layers
Conclusion of the authors: The obtained structure is characterised by a ‘‘rocksalt’’ three-dimensional Mn3+/Mn4+ charge ordering.
Nakajima et al. : Monoclinic space group P2 (ap2 ap2 2ap) with two
non-equivalent MnO6 octahedra showing a marked volume difference
Conclusion of the authors: This phase is characterised by a CO with a checkerboard pattern in the ab-plane.
YBaMn2O6:Room temperature phase
![Page 71: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/71.jpg)
Barcelona, September 2005, MULTIMAT
P-1 a ~ 5.55Å ~90°
b ~ 11.0Å ~90.3°
c ~ 7.60Å ~90°
Combined XR-N refinement of the crystal structure of YBaMn2O6 3T2 observed vs. calculated pattern
![Page 72: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/72.jpg)
Barcelona, September 2005, MULTIMAT
YBaMn2O6 (298K)Combined refinement
RX - Neutrons (3T2)
Model for TbBaMn2O6 of
J. Williams and J. P. Attfield,
Phys. Rev. B 220405R (2002)
(P-1 with constraints)
The superstructure reflections cannot be accounted with the
published model
![Page 73: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/73.jpg)
Barcelona, September 2005, MULTIMAT
YBaMn2O6 (298K)Combined refinement
RX - Neutrons (3T2)
(P-1 without the published constraints)
![Page 74: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/74.jpg)
Barcelona, September 2005, MULTIMAT
Mn1a Mn1b Mn2a Mn2b <Mn-O> : 1.940(8) <Mn-O>: 1.957(8) <Mn-O>: 1.979(8) <Mn-O>: 1.970(8)
A comparison of the Mn-O distances within each octahedron shows that the four non-equivalent MnO6 can be associated in pairs
New refinement in which we applied constraints for some coordinates and restraints for the Mn-O distances
Structure of YBaMn2O6 obtained from the combined RX-N
refinement in P-1
without constraints
![Page 75: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/75.jpg)
Barcelona, September 2005, MULTIMAT
Mn1a Mn1b Mn2a Mn2b <Mn-O> : 1.947(3) <Mn-O>: 1.949(2) <Mn-O>: 1.975(2) <Mn-O>: 1.974(3) : 17 x10-4 : 17 x10-4 : 20 x10-4 : 20 x10-4 BVS : 3.62(3) BVS: 3.61(2) BVS: 3.45(3) BVS: 3.46(3)
Structure of YBaMn2O6 obtained from the combined RX-N
refinement in P-1 with constraints/restraints
![Page 76: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/76.jpg)
Barcelona, September 2005, MULTIMAT
Mn1 =Mn3.6+ Mn2=Mn3.45+
Small separation with respect to average Mn3.5+ charge.
dz2 orbitals associated with the
longest Mn-O bonds.
First hypothesis:YBaMn2O6 with alternating Y/Ba
layers giving rise to a “rocksalt” charge
order
![Page 77: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/77.jpg)
Barcelona, September 2005, MULTIMAT
Representation showing the possible formation of Mn-Mn
pairing Elongation of the Mn-O bonds
3.9Å 4.0Å4.0Å
Second Hypothesis: formation of Zener polarons within the
ab-plane
![Page 78: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/78.jpg)
Barcelona, September 2005, MULTIMAT
Representation showing the possible formation of Mn-Mn pairing
<Mn-O-Mn>
~155°
<Mn-O-Mn>
~172°
<Mn-O-Mn>
~172°3.93Å
3.67Å
3.93Å
Widest Mn-O-Mn angle in the structure
Third hypothesis: Zener polarons
along c
![Page 79: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/79.jpg)
Barcelona, September 2005, MULTIMAT
Comparison of low-Q range neutron diffraction patterns of half-doped manganites
YBaMn2O6
Nd1/2Ca1/2MnO3
Pr1/2Ca1/2MnO3
Y1/2Ca1/2MnO3
La1/2Ca1/2MnO3
Tb1/2Ca1/2MnO3
(½,0,1)
(½,2,1)
(½,1,1) (½,3,1)
(3/2,1,1)
(½,0
,½)
(½,1
,½)
(½,2
,½)
(-½
,0,3
/2)
(½,1
,3/2
)
![Page 80: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/80.jpg)
Barcelona, September 2005, MULTIMAT
The magnetic propagation vector is different to disordered manganites: k=(½ 0 ½ )Instead of k=(½ 0 0 )
Magnetic scattering of YBaMn2O6
![Page 81: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/81.jpg)
Barcelona, September 2005, MULTIMAT
(4) 7.97eff B
(4) 13.33eff B
Paramagnetic Charge ordered
phase
AF Charge Ordered
Paramagnetic Charge
disordered
4 7.94 BMn
Spin-only effective moment for Z=4 Mn ions:
4 3( , ) 8.81 BMn Mn
2 11.23Mn ZP B
4 14.97Mn ZP B
Spin-only effective moment for Z=4 Zener Polarons:
Inverse of the magnetic susceptibility of YBaMn2O6
![Page 82: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/82.jpg)
Barcelona, September 2005, MULTIMAT
Constraints:
µ(Mn1a)= µ(Mn1b); µ(Mn2a)= µ(Mn2b)
Free rotation of the single axis within the ab-plane
Alternative non-collinear model:
A single amplitude of the magnetic moment for all Mn atoms
Two angular variables within the ab-plane
Collinear model: CE with different stacking along c(three degrees of
freedom)
![Page 83: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/83.jpg)
Barcelona, September 2005, MULTIMAT
a
b
c
d
AF?
AF
Mn3+
Mn4+
Mn3+
Mn4+2-Mn ZP
4-Mn ZP
YB
aMn
2O
6Y
1/2C
a 1/2M
nO
3Ionic ordering picture ZP ordering picture
![Page 84: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/84.jpg)
Barcelona, September 2005, MULTIMAT
Ionic model
ZP model
Comparison of two simple models (three degrees of freedom)
![Page 85: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/85.jpg)
Barcelona, September 2005, MULTIMAT
Zener polarons involving more than 2 Mn atoms?
Propagation vector (doubling c)k=(1/2,0,1/2) (+ + – – + + ..)
Susceptibility data supports the formation of ZP involving more than 2 Mn atoms
![Page 86: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/86.jpg)
Barcelona, September 2005, MULTIMAT
Magnetic Structure of YBaMn2O6
![Page 87: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/87.jpg)
Barcelona, September 2005, MULTIMAT
An image of “non-atomic” localisation, conserving the intermediate valence of Mn-ions, is more appropriate and explain most of the observed experimental facts for formally Mn3+/Mn4+ perovskites.
Extension: confinement of de-localised electron in ferromagnetic supra-atomic units, …. CO in manganites Order of Zener polarons?Implication for orbital ordering pseudo-molecular orbitalsImplication for super-exchange theory extension of GKA rules
Single crystal x-rays and neutron diffraction to obtain accurate structures Polarized neutron scattering (3D-polarimetry): magnetic structures Electron density studies Electronic structure calculations
Perspectives of research in CO transitions
![Page 88: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/88.jpg)
Barcelona, September 2005, MULTIMAT
Access to the LLB neutron beams
![Page 89: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/89.jpg)
Barcelona, September 2005, MULTIMAT
Access to the LLB neutron beams
![Page 90: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/90.jpg)
Barcelona, September 2005, MULTIMAT
![Page 91: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/91.jpg)
Barcelona, September 2005, MULTIMAT
![Page 92: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/92.jpg)
Barcelona, September 2005, MULTIMAT
![Page 93: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e535503460f94b499c3/html5/thumbnails/93.jpg)
Barcelona, September 2005, MULTIMAT
The end
Downloading of Software http://www.ccp14.ac.uk
Graphical tutorial run-through of most of this software is located via (“look before you try”):
http://www.ccp14.ac.uk/tutorial/
FullProf Suite and related programs: ftp://ftp.cea.fr/pub/llb/divers/ Set of directories with different programs, documents, tutorials and examples of powder diffraction data analysis