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 PbZn 1/3 Nb 2/3 O 3, (PZN) PZN

Relaxor ferroelectrics PbMg 1/3 Nb 2/3 O 3 (PMN) PbZn 1/3 Nb 2/3 O 3 (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 computer disks

Perovskite structure important to see oxygens  use neutron scattering [110] PbOZn/Nb [001]

Neutrons vs X-rays neutron flux on SXD at ISIS ~ 6-7  10 4 neutrons per sec per mm 2. neutron flux on SXD at ISIS ~ 6-7  10 4 neutrons per sec per mm 2. is it possible to do neutron diffuse scattering at all? X-ray flux at 1-ID beamline at APS ~ 1  photons per sec per mm 2. X-ray flux at 1-ID beamline at APS ~ 1  photons per sec per mm 2.

11 detectors 64  64 pixels per detector SXD instrument at ISIS complete t.o.f. spectrum per pixel

angle subtended by 90  detector 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 settings 8 detectors (h k 0.5) apply m3m symmetry nb. full 3D volume PZN diffuse scattering

h k 0h k 1h k diffuse lines are in fact rods not planes azimuthal variation of intensity - displacement along 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 theory a rod of scattering in reciprocal space a plane in real-space (normal to the rod) corresponds to rods are parallel to the six directions planes are normal to hence in this case: azimuthal variation of intensity means: atomic displacements are within these planes and parallel to another direction atomic displacements are within these planes and parallel to another direction

Planar defect normal to [1 -1 0] cation displacements in planar defect are parallel to [1 1 0] Planar defects in PZN

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 model Simple MC model h k 0h k 1h k 0.5 Observed patterns Calculated patterns even odd

Bond valence

12 1 2,3 4,5 8,9 10, ,3 4,5 8,9 10,11 6 Pb atoms are grossly under-bonded in average polyhedron Pb shift along [110] achieves correct valence

Cations displaced from centre of coordination polyhedra PZN lone-pair electrons

Bond valence - Nb/Zn order NbO 6 octahedron Bond valence requires a = 3.955Å for Nb valence of 5.0 ZnO 6 octahedron Bond valence requires a = 4.218Å for Zn valence of 2.0 PZN measured cell a = 4.073Å Weighted mean (2* )/ a = 4.043Å Weighted mean ( )/ a = 4.087Å Strong tendency to alternate but because of 2/3 : 1/3 stoichiometry cannot be perfect alternation

SRO of Nb/Zn B-site occupancy is 2 / 3 Nb and 1 / 3 Zn 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/Zn0 maximal Nb/Zn ordering (h k 0.5) layer Peaks due to cation displacements Extra peaks due to Nb/Zn ordering

Planar defects random variables to represent cation displacements cation displacements in planar defect are parallel to [1 1 0]

modeling 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 orientations Displacements refer to cation displacements in a single plane

displacement models Model 1 O 1 moves in phase with Pb’s Model 2 O 1 moves out of phase with Pb’s Model 1 O 1 moves in phase with Pb’s

comparison of models 1 and

random variable model obs v. calc h k 0h k 1h k 0.5 Observed patterns Calculated patterns

Summary of Gaussian Variable models 1. planar nanodomains normal to 2. atomic displacements parallel to 3. atomic displacements within domains correlated 4. Pb & Nb/Zn displacements in phase 5. O 1 displacements out of phase with Pb 1. planar nanodomains normal to 2. atomic displacements parallel to 3. atomic displacements within domains correlated 4. Pb & Nb/Zn displacements in phase 5. O 1 displacements out of phase with Pb can we construct an atomistic model satisfying these criteria?

atomistic model E1E1 E2E2 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 energy

development of atomistic model E1E1 E2E2 Note scattering around Bragg peaks as well as diffuse rods [001] Polar nanodomains 12 different orientations [110] Single layer normal to [1 -1 0] diffraction Pb only

[001] Polar nanodomains 12 different orientations [110] development of atomistic model two successive planes normal to [1 -1 0] domains do not persist in successive layers

[100] [010] Linear features do persist in successive layers development of atomistic model view down [0 0 1]

[100] [010] Linear features do persist in successive layers neighbours attract or repel each other according to their mutual orientation development of atomistic model

size-effect relaxation [110]. [110] = 2 [110]. [1 -1 0] = 0 [110]. [101] = 1 [110]. [ ] =-2 [110]. [ ] =-1 P E = (d - d 0 (1 - P   size-effect parameter smaller than average bigger than average average

Size-effect relaxation  = 0  =  = observed (h k 0)

Other models thick domains i.e. 3D double layer 2D 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} Acknowledgements

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