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PZN. Diffuse scattering and disorder in relaxor ferroelectrics. T.R.Welberry, D.J.Goossens. PbZn 1/3 Nb 2/3 O 3 , (PZN). computer disks. Relaxor ferroelectrics PbMg 1/3 Nb 2/3 O 3 (PMN) PbZn 1/3 Nb 2/3 O 3 (PZN). high dielectric constant

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Pzn

PZN

Diffuse scattering and disorder in relaxor ferroelectrics.

T.R.Welberry, D.J.Goossens

PbZn1/3Nb2/3O3, (PZN)


Relaxor ferroelectrics pbmg 1 3 nb 2 3 o 3 pmn pbzn 1 3 nb 2 3 o 3 pzn

computer disks

Relaxor ferroelectricsPbMg1/3Nb2/3O3 (PMN) PbZn1/3Nb2/3O3 (PZN)

  • high dielectric constant

  • dispersion over broad range of frequencies

  • and wide temperature range

  • evidence of polar nanostructure

  • plays essential role in piezo-electric properties

  • no consensus on exact nature of polar nanostructure


Perovskite structure

[001]

[110]

Pb

O

Zn/Nb

Perovskite structure

important to seeoxygens use neutron scattering


Neutrons vs x rays

Neutrons vs X-rays

  • neutron flux on SXD at ISIS

  • ~ 6-7  104 neutrons per sec per mm2.

  • X-ray flux at 1-ID beamline at APS

  • ~ 1  1012 photons per sec per mm2.

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


Sxd instrument at isis

complete t.o.f. spectrum per pixel

SXD instrument at ISIS

11 detectors

6464 pixels per detector


Neutron time of flight geometry

angle subtended by 90detector bank

volume of reciprocal space recorded simultaneously with one detector bank.

neutron time of flight geometry

A-A’ and B-B’ given by detector bank

B-A and B’-A’ given by time-of-flight


Pzn diffuse scattering

(h k 0)

apply m3m

symmetry

10 crystal settings

8 detectors

(h k 0.5)

(h k 1)

PZN diffuse scattering

nb. full 3D

volume


Diffraction features

5

5

4

3

3

2

1

1

h k 0

h k 1

h k 0.5

diffraction features

  • diffuse lines are in fact rods not planes

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

  • all rods present in hk0 but only oddnumbered rods in hk1

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


Fourier transform theory

a rod of scattering in reciprocal space

corresponds to

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

rods are parallel to the six <110> directions

hence

planes are normal to <110>

Fourier transform theory

in this case:

azimuthal variation

of intensity means:

atomic displacements are within these planes

and parallel to another <110> direction


Planar defects in pzn

Planar defects in PZN

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

Planar defect normal to [1 -1 0]


Simple mc model

Simple 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-Nb

5 : 5 : 2 : 80


Simple mc model1

h k 0

h k 1

h k 0.5

odd

even

Simple MC model

Observed patterns

Calculated patterns


Bond valence

Bond valence


Bond valence1

8,9

8,9

2,3

2,3

6

6

12

12

1

1

4,5

4,5

10,11

10,11

Bond valence

Pb atoms are grossly under-bonded in average polyhedron

Pb shift along [110] achieves correct valence


Lone pair electrons

lone-pair electrons

PZN

Cations displaced

from centre of

coordination

polyhedra


Bond valence nb zn order

NbO6 octahedron

Bond valence requires

a = 3.955Å

for Nb valence of 5.0

ZnO6 octahedron

Bond valence requires

a = 4.218Å

for Zn valence of 2.0

Bond valence - Nb/Zn order

PZN measured cell

a = 4.073Å

Weighted mean

(2*3.955+4.218)/3

a = 4.043Å

Weighted mean

(3.955+4.218)/2

a = 4.087Å

Strong tendency to

alternate

but because of 2/3 : 1/3 stoichiometry

cannot be perfect alternation


Sro of nb zn

Peaks due

to cation displacements

maximal Nb/Zn ordering

random Nb/Zn0

(h k 0.5) layer

Extra peaks due to Nb/Zn ordering

SRO of Nb/Zn

  • Two models tested:-

    • random occupancy of Nb and Zn ?

    • tendency to alternate?

  • 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


Planar defects

Planar defects

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

random variables to represent cation displacements


Modeling cation displacements

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

modeling cation displacements

Monte Carlo energy

random variables to represent cation displacements

Total model consists of cation displacements obtained from summing the variables from the six different <110> orientations


Displacement models

Model 1

O1 moves in phase with Pb’s

Model 1

O1 moves in phase with Pb’s

Model 2

O1 moves out of phase with Pb’s

displacement models


Comparison of models 1 and 2

5

5

4

3

3

2

1

1

comparison of models 1 and 2

1

2


Random variable model obs v calc

h k 0

h k 1

h k 0.5

random variable model obs v. calc

Observed patterns

Calculated patterns


Summary of gaussian variable models

Summary of Gaussian Variable models

planar nanodomains normal to <110>

atomic displacements parallel to <110>

atomic displacements within domains correlated

Pb & Nb/Zn displacements in phase

O1 displacements out of phase with Pb

can we construct an atomistic model satisfying these criteria?


Atomistic model

E1

E2

atomistic model

  • 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 energy


Development of atomistic model

[001]

Polar nanodomains

12 different orientations

[110]

E1

E2

development of atomistic model

Single layer normal to [1 -1 0]

diffraction Pb only

Note scattering around Bragg peaks as well as diffuse rods


Development of atomistic model1

development of atomistic model

two successive planes normal to [1 -1 0]

Polar nanodomains

12 different orientations

[001]

domains do not persist in successive layers

[110]


Development of atomistic model2

development of atomistic model

view down [0 0 1]

[100]

Linear features do persist in successive layers

[010]


Development of atomistic model3

neighbours attract or repel each other according to their mutual orientation

development of atomistic model

[100]

Linear features do persist in successive layers

[010]


Size effect relaxation

P

[110].[110] = 2

smaller than average

E = (d - d0(1 - P e))2

[110].[101] = 1

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

size-effect parameter

average

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

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

bigger than average

size-effect relaxation


Size effect relaxation1

Size-effect relaxation

e = 0

e = -0.02

e = +0.020

observed

(h k 0)


Other models

thick domains

i.e. 3D

double layer

2D domains

Other models


Acknowledgements

Acknowledgements

  • 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}


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