diffuse scattering and disorder in relaxor ferroelectrics. t.r.welberry, d.j.goossens diffuse...

Diffuse scattering and disorder in relaxor ferroelectrics.

T.R.Welberry, D.J.Goossens

Diffuse scattering and disorder in relaxor ferroelectrics.

T.R.Welberry, D.J.Goossens

PbZn1/3Nb2/3O3, (PZN)

PZN

Relaxor ferroelectricsPbMg1/3Nb2/3O3 (PMN)

PbZn1/3Nb2/3O3 (PZN)

Relaxor ferroelectricsPbMg1/3Nb2/3O3 (PMN)

PbZn1/3Nb2/3O3 (PZN)

• high dielectric constant• dispersion over broad range of frequencies • and wide temperature range

• high dielectric constant• dispersion over broad range of frequencies • and wide temperature range

• evidence of polar nanostructure• plays essential role in piezo-electric properties

• evidence of polar nanostructure• plays essential role in piezo-electric properties

• no consensus on exact nature of polar nanostructure• no consensus on exact nature of polar nanostructure

computer diskscomputer disks

Perovskite structurePerovskite structure

important to see oxygens use neutron scatteringimportant to see oxygens use neutron scattering

[110]

Pb O Zn/Nb

[001]

Neutrons vs X-raysNeutrons vs X-rays

• neutron flux on SXD at ISIS ~ 6-7 104 neutrons per sec per mm2.• neutron flux on SXD at ISIS ~ 6-7 104 neutrons per sec per mm2.

• is it possible to do neutron diffuse scattering at all?• is it possible to do neutron diffuse scattering at all?

• X-ray flux at 1-ID beamline at APS ~ 1 1012 photons per sec per mm2.• X-ray flux at 1-ID beamline at APS ~ 1 1012 photons per sec per mm2.

11 detectors

6464 pixels per detector

SXD instrument at ISISSXD instrument at ISIS

complete t.o.f. spectrum per pixel

angle subtended by 90detector bank

A-A’ and B-B’ given by detector bank

B-A and B’-A’ given by time-of-flight

volume of reciprocal space recorded simultaneously with

one detector bank.

neutron time of flight geometry

(h k 1)

(h k 0)

10 crystal settings8 detectors

(h k 0.5)

apply m3m

symmetry

nb. full 3Dvolume

PZN diffuse scattering

h k 0 h k 1 h k 0.5

12

3 4 5

1

35

• diffuse lines are in fact rods not planes

• azimuthal variation of intensity - displacement along <1 1 0>

• all rods present in hk0 but only odd numbered rods in hk1

• only half of spots in h k 0.5 explained by intersection of rods

diffraction features

Fourier transform theoryFourier transform theory

a rod of scattering in reciprocal spacea rod of scattering in reciprocal space

a plane in real-space (normal to the rod)a plane in real-space (normal to the rod)corresponds tocorresponds to

rods are parallel to the six <110> directionsrods are parallel to the six <110> directions

planes are normal to <110>planes are normal to <110>hencehence

in this case:in this case:

azimuthal variation azimuthal variation of intensity means:of intensity means:

atomic displacements are within these planesand parallel to another <110> direction

atomic displacements are within these planesand parallel to another <110> direction

Planar defect normal to [1 -1 0]Planar defect normal to [1 -1 0]cation displacements in planar

defect are parallel to [1 1 0]

Planar defects in PZNPlanar defects in PZN

Simple MC modelSimple MC model

atoms connected by springs and allowed to vibrate at given kT

most successful model had force constants in ratios:-

Pb-O : Nb-O : O-O : Pb-Nb5 : 5 : 2 : 80

Simple MC modelSimple MC model

h k 0 h k 1 h k 0.5

Observed patterns

Calculated patterns

even odd

Bond valenceBond valence

Bond valenceBond valence

121

2,3

4,5

8,9

10,11

6121

2,3

4,5

8,9

10,11

6

Pb atoms are grossly under-bonded in average polyhedronPb atoms are grossly under-bonded in average polyhedron

Pb shift along [110] achieves correct valencePb shift along [110] achieves correct valence

Cations displacedfrom centre ofcoordination

polyhedra

PZNPZN

lone-pair electronslone-pair electrons

Bond valence - Nb/Zn orderBond valence - Nb/Zn order

NbO6 octahedron

Bond valence requiresa = 3.9553.955Å

for Nb valence of 5.0

ZnO6 octahedron

Bond valence requiresa = 4.2184.218Å

for Zn valence of 2.0

PZN measured cella = 4.0734.073Å

Weighted mean(2*3.955+4.218)/3

a = 4.0434.043Å

Weighted mean(3.955+4.218)/2

a = 4.0874.087Å

Strong tendency to

alternate

but because of 2/3 : 1/3 stoichiometry

cannot be perfect alternation

SRO of Nb/ZnSRO of Nb/Zn

B-site occupancy is 2/3Nb and 1/3Zn complete alternation not possible - max corr. = -0.5

• Nb certainly follows Zn but• after Nb sometimes Zn sometimes Nb

Two models tested:-1. random occupancy of Nb and Zn ?2. tendency to alternate?

random Nb/Zn0maximal Nb/Zn ordering

(h k 0.5) layer

Peaks due to cation

displacements

Extra peaks due to Nb/Zn

ordering

Planar defectsPlanar defects

random variables to represent cation displacements

cation displacements in planar defect are parallel to [1 1 0]

modeling cation displacementsmodeling cation displacements

random variables to represent cation displacements

Monte Carlo energy

Total model consists of cation displacements obtained from summing

the variables from the six different <110> orientations

Displacements refer to cation displacements in a single <110> plane

displacement modelsdisplacement models

Model 1O1 moves in phase with Pb’s

Model 2O1 moves out of phase with Pb’s

Model 1O1 moves in phase with Pb’s

comparison of models 1 and 2comparison of models 1 and 2

1

2

12

3 4 5

1

35

random variable model obs v. calcrandom variable model obs v. calc

h k 0 h k 1 h k 0.5

Observed patterns

Calculated patterns

Summary of Gaussian Variable modelsSummary of Gaussian Variable models

1. planar nanodomains normal to <110>

2. atomic displacements parallel to <110>

3. atomic displacements within domains correlated

4. Pb & Nb/Zn displacements in phase

5. O1 displacements out of phase with Pb

1. planar nanodomains normal to <110>

2. atomic displacements parallel to <110>

3. atomic displacements within domains correlated

4. Pb & Nb/Zn displacements in phase

5. O1 displacements out of phase with Pb

can we construct an atomistic model satisfying these criteria?can we construct an atomistic model satisfying these criteria?

atomistic modelatomistic model

E1

E2

• assume all Pb’s displaced in 1 of 12 different ways• assume in any {110} plane Pb displacements correlated

• assume no correlation with planes above and below

• assume all Pb’s displaced in 1 of 12 different ways• assume in any {110} plane Pb displacements correlated

• assume no correlation with planes above and below

MC energyMC energy

development of atomistic modeldevelopment of atomistic model

E1

E2

Note scattering around Bragg peaks as well as diffuse rods

[001]

Polar nanodomains12 different orientations[110]

Single layer normal to [1 -1 0]Single layer normal to [1 -1 0] diffraction Pb onlydiffraction Pb only

[001]

Polar nanodomains12 different orientations

[110]

development of atomistic modeldevelopment of atomistic model

two successive planes normal to [1 -1 0]two successive planes normal to [1 -1 0]

domains do not persist in successive layers

domains do not persist in successive layers

[100]

[010]Linear features do persist

in successive layers

development of atomistic modeldevelopment of atomistic model

view down [0 0 1]view down [0 0 1]

[100]

[010]Linear features do persist

in successive layersneighbours attract or repel each other according to their mutual orientation

development of atomistic modeldevelopment of atomistic model

size-effect relaxationsize-effect relaxation

[110].[110] = 2

[110].[1 -1 0] = 0

[110].[101] = 1

[110].[-1 -1 0] =-2

[110].[-1 0 -1] =-1

P

E = (d - d0(1 - P

size-effect parameter

smaller than average

bigger than average

average

Size-effect relaxationSize-effect relaxation

= = 00 = = -0.02-0.02 = = +0.020+0.020

observed(h k 0)

Other modelsOther models

thick domainsi.e. 3D

double layer2D domains

M.J.Gutmann (ISIS, UK) A.P.Heerdegen(RSC, ANU)

H. Woo (Brookhaven N.L.) G. Xu (Brookhaven N.L.)

C. Stock (Toronto)

Z-G. Ye (Simon Fraser University)

AINSE

{ Crystal growth}

AcknowledgementsAcknowledgements

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