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### PZN

Diffuse scattering and disorder in relaxor ferroelectrics.

T.R.Welberry, D.J.Goossens

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

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

- no consensus on exact nature of polar nanostructure

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?

angle subtended by 90detector bank

volume of reciprocal space recorded simultaneously with one detector bank.

neutron time of flight geometryA-A’ and B-B’ given by detector bank

B-A and B’-A’ given by time-of-flight

(h k 0)

apply m3m

symmetry

10 crystal settings

8 detectors

(h k 0.5)

(h k 1)

PZN diffuse scatteringnb. full 3D

volume

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

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 theoryin this case:

azimuthal variation

of intensity means:

atomic displacements are within these planes

and parallel to another <110> direction

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

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

8,9

2,3

2,3

6

6

12

12

1

1

4,5

4,5

10,11

10,11

Bond valencePb atoms are grossly under-bonded in average polyhedron

Pb shift along [110] achieves correct valence

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 orderPZN 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

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

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

random variables to represent cation displacements

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

modeling cation displacementsMonte 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

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 modelsSummary 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?

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

Polar nanodomains

12 different orientations

[110]

E1

E2

development of atomistic modelSingle layer normal to [1 -1 0]

diffraction Pb only

Note scattering around Bragg peaks as well as diffuse rods

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 model

view down [0 0 1]

[100]

Linear features do persist in successive layers

[010]

neighbours attract or repel each other according to their mutual orientation

development of atomistic model[100]

Linear features do persist in successive layers

[010]

P mutual orientation

[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 relaxationAcknowledgements mutual orientation

- 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}

Go back to Disordered Materials mutual orientationGo to Home Page

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