1. Application of Impedance Spectroscopy to characterise grain boundary and surface layer effects in electroceramics. Derek C Sinclair Department of Engineering Materials University of Sheffield, UK

2. Outline Introduction Introduction Typical electrical microstructures for electroceramics. Background to combined Z’’, M’’ spectroscopy. Example Example La-doped BaTiO 3 ceramics Conclusions Conclusions

3. Typical Electrical Microstructures Clear indicates insulating regions Shading indicates semiconducting regions Semiconductivity either by chemical doping or oxygen loss. C = (  o  ’A)/d

4. For many electroceramics R gb >> R b and the parallel RC elements are connected in series. Brickwork layer model shows C gb >> C b Each region can be represented (to a simple approximation) as a single parallel RC element R b R gb R b R gb C b C gb C b C gb  = RC

5. Data analysis using (Z*, M*) works well for series- type equivalent circuits For a single parallel RC element Z* = Z’ - jZ’’ Z* = Z’ - jZ’’ Z’ = R Z’’ = R.  RC Z’ = R Z’’ = R.  RC 1 + [  RC] 2 1 + [  RC] 2 1 + [  RC] 2 1 + [  RC] 2 Recall : M* = j  C o Z* M’ =   C o R 2 C M’’ = C o  RC M’ =   C o R 2 C M’’ = C o  RC 1 + [  RC] 2 C 1 + [  RC] 2 1 + [  RC] 2 C 1 + [  RC] 2

6. Each RC element produces an arc in Z* and M* (or a Debye peak in Z’’ and M’’ spectroscopic plots), however:- Z* (and Z’’ spectra) are dominated by large R (gb’s) M* (and M’’ spectra) are dominated by small C (bulk) Such an approach is useful for studying ceramics with insulating grain boundaries/surface layers and semiconducting grains.

7. R b = 20 k  R gb = 1M  C b = 60 pF C gb = 1.25 nF

8. Combined Z’’, M’’ spectroscopic plot Notes: Appearance of Debye peaks in the frequency window depend on  for the various RC elements.Appearance of Debye peaks in the frequency window depend on  for the various RC elements. LimitsLimits R > 10 8  is high =>  max  max < 1 Hz R  is low =>  max > 10 MHz =>  max > 10 MHz

9. The doping mechanism in La-BaTiO 3 R min - 0.3 -0.5 atom% doping (ptcr devices) heated in air > 1350 o C followed by rapid cooling. Is there a change in doping mechanism with La-content ? Low x : donor (electronic) doping, La 3+ + e - => Ba 2+ High x : Ionic compensation, La 3+ => Ba 2+ + 1/4Ti 4+

10. Phase diagram studies showed that for samples prepared in air ionic compensation was favoured Ba 1-x La x Ti 1-x/4 O 3 where 0 ≤ x ≤ 0.25 IS showed all ceramics with x > 0 to be electrically heterogeneous when processed in air and all showed the presence of semiconducting regions. Electrical measurements are inconsistent with the phase diagram results!!

11. 2 (0.3at%) 3 (3 at%) 4 (20 at%) 2 (0.3at%) 3 (3 at%) 4 (20 at%) R T > 1 M  at 25 o C. R T = 675  at 25 o C

12. All samples processed at 1350 o C in flowing O 2 as opposed to air were insulating at room temperature. Composition 3 ( 3at%) Air (25 C) O 2 (25 C)O 2 ( 479 C) Air (25 C) O 2 (25 C)O 2 ( 479 C) C gb ~ 0.12 nF C b ~ 46 pF

13. 3 Arrhenius behaviour of R b and R gb for Ba 1-x La x Ti 1-x/4 O 3 processed in O 2

14. Is oxygen loss the source of the semiconductivity in samples processed in air? Ba 1-x La x Ti 1-x/4 O 3-  O o x => 1/2O 2 + 2V o.. + 2e ’ Samples were processed in Argon at 1350 o C and all were semiconducting at room temperature.

15. Processing in Ar at 1350 o C Composition 3 (3at%) R T ~ 522  ; R gb ~ 510  R b ~ 12  C gb ~ 2.4 nF

16. Arrhenius behaviour of R b and R gb for Ba 1-x La x Ti 1-x/4 O 3-  processed in Ar at 1350 o C. 4

17. Return to processing in air at 1350 o C. Composition 3 (3 at%): dc insulator at 25 o C Composition 4 (20 at%): dc insulator at 25 o C

18. Composition 3 R T ~ R gb > 10 7  at 25 o C R b ~ R inner + R outer < 1 k  C gb ~ 5-6 nF C outer ~ 0.2 nF, C inner < 0.2 nF At least three RC elements present. No change in response on polishing the pellets. 3 Air

19. Composition 3 processed in air at 1350 o C

20. Composition 4 Four elements present ? Z’’ : f max 2 M  f max 2 M  M’’ : f max ~ 10 2 Hz, 0.1 M  C ~ 7 nF f max ~ 10 2 Hz, 0.1 M  C ~ 7 nF f max ~ 10 4 Hz, ~ 1 k  C ~ 7 nF f max ~ 10 4 Hz, ~ 1 k  C ~ 7 nF f max > 10 7 Hz, 10 7 Hz, < 1k , C < 1 nF Dramatic change on polishing the pellet.

21. Unpolished Polished R T ~ R gb = 2.04 k  C gb = 7.5 nF Both R b and R gb obey the Arrhenius law.

22. Composition 4 (20% La) Air Air Ar Ar Ar

23. Conclusions Oxygen loss is responsible for semiconductivity in ‘Ba 1-x La x Ti 1-x/4 O 3 ’ ceramics O2O2O2O2Ar Air x = 0.03 x = 0.20

24. Conclusions IS is an invaluable tool for probing electrical heterogeneities in electroceramics. This is especially true when oxygen concentration gradients are responsible for inducing semiconductivity. IS is an invaluable tool for probing electrical heterogeneities in electroceramics. This is especially true when oxygen concentration gradients are responsible for inducing semiconductivity. Combined Z’’, M’’ spectroscopic plots are a convenient and efficient method of visually inspecting the data to allow rapid assessment of the electrical microstructure in many electroceramics. Combined Z’’, M’’ spectroscopic plots are a convenient and efficient method of visually inspecting the data to allow rapid assessment of the electrical microstructure in many electroceramics.

25. Acknowledgements Finlay Morrison Tony West EPSRC for funding.

26. Extras   ’ vs T for a range of x. 2. Arrhenius plot of R b and R gb for air (1200 C) and O 2 (1350 C) processed ceramics. 3. Analysis of composition 2.

27. Excellent dielectrics when processed in O 2

28. Arrhenius plot Arrhenius plot

29. Composition 2 R T ~ R gb R b ~ 15  ptcr effect