Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS),...

$: Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS), Saclay, France Neutron Powder Diffraction: a powerful.$
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


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.


Chadwick1932

Neutrons as constituents of matter


Properties of neutrons


• 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


• 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


Neutron reactors: ILL


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


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)


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)


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


•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


Neutron scattering lengths


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


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


Form Factor


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


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


Content of the talk





D1B(ILL) or G41(LLB)

Diffractometers: Powder high flux


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


yi

Position “i”: Ti

Bragg position Th

yi-ycizero

Powder diffraction profile:scattering variable T: 2, TOF, Energy


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, ...


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


, ,{ }

( )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


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


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)


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)


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.


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


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.


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


( ) ( ) (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


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


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


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


• 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


Directory structure of the FullProf Suite


WinPLOTR: program to access the whole FullProf Suite


Configuration of WinPLOTR

File: winplotr.set


Indexing demo with WinPLOTR

New facility: DICVOL04

Two other indexing programs: TREOR, ITO


Other features of WinPLOTR

Access to other programs: EdPCR, Fp_Studio, DICVOL04, BasIreps

Two other indexing programs: TREOR, ITO


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


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


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


A new GUI for FullProf: EdPCR

GUI using Winteracter: http://www.winteracter.com


Content of the talk





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


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


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 …

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


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


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)


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)


Phase transitions, crystal and magnetic structures of mixed valence

YBaMn2O6


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


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


T1 500 K TCO 480 K (?)T2 560 KT3 805 K TTM 780 K (?)

Phase transitions in YBaMn2O6: resistivity vs T


Radiation: pure CuK1 spectral line (=1.5406Å)

X-ray diffraction versus temperature


T=398KT=438KT=458KT=500KT=510KT=520KT=530KT=535KT=720KT=730KT=750KT=793K

(110

)

(102

)


T=398KT=438KT=458KT=500KT=510KT=520KT=530KT=535KT=720KT=730KT=750KT=793K

(200

)

(004

)


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?

Barcelona, September 2005, MULTIMATq

q

Neutron diffraction versus temperature (D20, high resolution mode at ILL)


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


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)


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


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


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


YBaMn2O6 (298K)Combined refinement

RX - Neutrons (3T2)

(P-1 without the published constraints)


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


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


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


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


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


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

)


The magnetic propagation vector is different to disordered manganites: k=(½ 0 ½ )Instead of k=(½ 0 0 )

Magnetic scattering of YBaMn2O6


(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


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)


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


Ionic model

ZP model

Comparison of two simple models (three degrees of freedom)


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


Magnetic Structure of YBaMn2O6


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


Access to the LLB neutron beams


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

Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS),...

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Transcript of Barcelona, September 2005, MULTIMAT Juan Rodríguez-Carvajal Laboratoire Léon Brillouin (CEA-CNRS),...