PZN

1. PZN Diffuse scattering and disorder in relaxor ferroelectrics. T.R.Welberry, D.J.Goossens PbZn1/3Nb2/3O3, (PZN)

2. 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

3. [001] [110] Pb O Zn/Nb Perovskite structure important to seeoxygens use neutron scattering

4. 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?

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

6. 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

7. (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

8. 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

9. 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

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

11. 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

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

13. Bond valence

14. 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

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

16. 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

17. 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

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

19. 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

20. 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

21. 5 5 4 3 3 2 1 1 comparison of models 1 and 2 1 2

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

23. 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?

24. 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

25. [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

26. 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]

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

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

29. 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

30. Size-effect relaxation e = 0 e = -0.02 e = +0.020 observed (h k 0)

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

32. 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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