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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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