1. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 1/36 UNIVERSITY OF OSLO Grain boundary resistance in ionic conductors Christian Kjølseth Department of Chemistry, University of Oslo Centre for Materials Science and Nanotechnology (SMN) Forskningsparken, Gaustadalléen 21, 0349 Oslo, Norway

2. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 2/36 UNIVERSITY OF OSLO Introduction Grain boundary core – space charge model Brick layer model Grain boundary resistance Grain boundaries in ionic conductors Experimental investigation Background Applications Fuel cell Membrane Challenge: Decrease the grain boundary resistance to get a high total proton conductivity + - - H + conductor e O 2 +N 2 H 2 O+N 2 H2H2 H 2 +N 2 H2H2 N2N2 H + and electronic conductor R. Haugsrud Outline Experiments - bias Experiments – electron accumulation Quantification Experiments – uniaxial pressure Some examples Short summary

3. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 3/36 UNIVERSITY OF OSLO Introduction What is a grain boundary? Structural definition: A narrow zone corresponding to one crystallographic orientation to another, thus separating one grain from another. The atom in each grain are arranged in an orderly pattern, the irregular junction of the two adjacent grains is known as the grain boundary. Electrical definition The zone between two grains which have electrical properties differing that of grain interior. The grain boundary properties is dependent on external conditions such as temperature and atmosphere.

4. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 4/36 UNIVERSITY OF OSLO Grain boundaries in ionic conductors Grain boundaries usually conduct better than grain interior → The grain boundaries acts as conducting channels e.g. protons in LaPO 4 High temperature firing of LaPO 4 leavs amorphous LaP 3 O 9 in the grain boundaries Increases conductivity over grain interior material Conductivity increases with decreasing grain size σ grain interior < σ grain boundary Harley, Yu, de Jonghe, Solid State Ionics 178 (2007) 769

5. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 5/36 UNIVERSITY OF OSLO In various functionally designed ionic conductors the grain boundary conductivity is lower than grain interior. → This may lead to significant contributions to the total resistance E.g. Oxygen ion conductors : Y-doped ZrO 2 (YSZ) [1] Gd-doped CeO 2 (CGO) [2] Mixed conductors: Fe-doped SrTiO 3 [3] Proton conductors: Ba 3 Ca 1+x Nb 2-x O 9-3x/2 [4] Gd-doped BaCeO 3 [5] Y-doped BaZrO 3 [6] Ca-doped LaNbO 4 [7] [1] X. Guo, W. Sigle, J. Fleig, J. Maier, Solid State Ionics 154-155 (2002) 555 [2] A. Tschope, E. Sommer, R. Birringer, Solid State Ionics 139 (2001) 255 [3] X. Guo, J. Fleig, J. Maier, Journal of the Electrochemical Society 148 (2001) J50 [4] H.G. Bohn, T. Schober, T. Mono, W. Schilling, Solid State Ionics 117 (1999) 219 [5] S.M. Haile, D.L. West, J. Campbell, Journal of Materials Research 13 (1998) 1576 [6] H.G. Bohn, T. Schober, Journal of the American Ceramic Society 83 (2000) 768 [7] R. Haugsrud, T. Norby, Nature Materials 5 (2006) 193 Grain boundaries in ionic conductors σ grain interior > σ grain boundary

6. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 6/36 UNIVERSITY OF OSLO Grain boundary resistance Possible contributions to grain boundary resistance Grain boundary core Space Charge Layer (SCL) Nonstoichiometry Secondary phases Impurity phases (often siliceous) Secondary phases also have boundary cores and SCLs Electrochemical reaction impedances

7. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 7/36 UNIVERSITY OF OSLO - complex impedance as a function of frequency - σ grain interior from knowledge of sample geometry - σ grain boundary challenging because of no grain boundary geometry knowledge - ”Brick layer model” - semicircles can be fit to (RQ) subcircuit elements - Brick layer model Impedance spectroscopy

8. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 8/36 UNIVERSITY OF OSLO Brick layer model G = edge length g = grain boundary thickness Grain interiors Electrode Series grain boundaries Parallel grain boundraies L = length Total length and area of all perpendicular grain boundaries (g<<G) Total length and area of all parallel grain boundaries

9. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 9/36 UNIVERSITY OF OSLO R gb ┴ Q gb ┴ Q bulk R bulk R gb || Q gb || Parallel grain boundaries Series grain boundaries R gb ┴ Q gb ┴ Q bulk+gb || Dedicated Rebecca Svensøy Assumtion: Transport in parallel and series grain boundraies occures by the same mechanism. Brick layer model

10. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 10/36 UNIVERSITY OF OSLO Brick layer model

11. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 11/36 UNIVERSITY OF OSLO Assume and because the dielectric properties of grain interior and grain boundary are often similar we combine to finally Brick layer model σ grain interior > σ grain boundary Constant phase element [5] S.M. Haile, D.L. West, J. Campbell, Journal of Materials Research 13 (1998) 1576

12. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 12/36 UNIVERSITY OF OSLO Grain boundary core – space charge model Grain boundary core x = 0 λ*λ* x δ gb log [Concentration] / Potential ++++++++++++++++++++ φ Δφ(0) Grain interior Space charge layer Δφ(0) schottky barrier height δ gb grain boundary width λ * space charge layer width [H + ] [Acceptor]

13. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 13/36 UNIVERSITY OF OSLO Grain boundary core – space charge model log Concentration ++++++++++++++++++++ Grain interior Space-charge layer Grain boundary core log Concentration ++++++++++++++++++++ Grain interior Space-charge layer Grain boundary core Gouy-Chapman Both charge carriers follows the electrical field Applicable at high temperature, where cations are sufficiently mobile Mott-Schottky One charge carrier is immobile (the dopant) while the counter majority charge carrier is depleted Consider two major charge carriers

14. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 14/36 UNIVERSITY OF OSLO Two defects; Protons and acceptors Acceptor-concentration profile frozen Electrochemical potential of protons Equilibrium: Electrical potential difference: Normalised concentration: Grain boundary core – space charge model log Concentration ++++++++++++++++++++ Grain interior Space-charge layer Grain boundary core → Δφ(x) is the electrostatic potential in relation to the grain interior x = 0x = ∞

15. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 15/36 UNIVERSITY OF OSLO Grain boundary core – space charge model Δφ(x) can be solved from the Poisson’s equation: Q(x): charge density at position x ε: dielectric constant Assume Mott-Schottky approximation Define the Debye length (L D ) and the space charge layer width (λ * ) Normalized concentration → Normalized concentration gives the concentration profile in the space charge layer log Concentration ++++++++++++++++++++ Grain interior Space-charge layer Grain boundary core x = 0x = ∞

16. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 16/36 UNIVERSITY OF OSLO Grain boundary core – space charge model Derivation of the Schottky barrier height Partial conductivity: Concentration and conductivity ratios, assuming equal mobilities: Apparent effective specific grain boundary resistivity and conductivity: Further substitution: log Concentration ++++++++++++++++++ Grain interior Space-charge layer Grain boundary core x = 0x = ∞

17. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 17/36 UNIVERSITY OF OSLO Grain boundary core – space charge model Ratio of conductivities: Activation energies: Difference between activation energies: If Schottky barrier height is temperature independent: log Concentration ++++++++++++++++++++ Grain interior Space-charge layer Grain boundary core → Δφ(0) is a measure of the magnitude of the depletion

18. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 18/36 UNIVERSITY OF OSLO Grain boundary core – space charge model Summary of mathemathics Two dominating defects Mott-Schottky: one defect is immobile with constant conc. profile up to the interface Space charge layer length Schottky barrier height (Δφ(0)) Debye length Normalized concentration ++++++++++++++++++++++++++++++++++++

19. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 19/36 UNIVERSITY OF OSLO Example: Oxygen ion conductor Grain interior Grain boundary core ++++++++++++++++++++++++ Potential,  log Concentration Space charge layer Grain boundary core – space charge model

20. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 20/36 UNIVERSITY OF OSLO Example: Proton conductor Grain interior Grain boundary core ++++++++++++++++++++++++ Potential,  log Concentration Space charge layer Grain boundary core – space charge model

21. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 21/36 UNIVERSITY OF OSLO Experimental investigation Experiments - bias Experiments – electron accumulation Experiments – uniaxial pressure Quantification

22. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 22/36 UNIVERSITY OF OSLO + Bias - log Concentration At equilibrium and zero bias state the two space charge layers are symmetrical After applying a dc bias voltage, one space charge layer is shortened, while the other is extended ++++++++++++ Grain interior Space- charge layer Grain interior ++++++++++++ Grain interior Space- charge layer Grain interior ++++++++++++ Grain interior Space- charge layer Grain interior ++++++++++++ Grain interior Space- charge layer Grain interior ++++++++++++ Grain interior Space- charge layer ++++++++++++ Grain interior Space- charge layer → Such a situation should cause nonlinear grain boundary electrical properties under dc bias voltage Grain boundary voltage drop needs to be large to derive information about a single grain boundary Experiments - bias

23. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 23/36 UNIVERSITY OF OSLO Acceptor doped ceria The current voltage relation for individual grain boundary was nonlinear → supports the space charge concept Guo, S. Mi, R. Waser, Electrochemical and Solid-State Letters 8 (2005) J1 BaZr 0.9 Y 0.1 O 3-δ Varistor behavior Protons diffuse into the space charge layer and decreases the potential → supports the space charge concept C. Kjølseth, Ø. Prytz, P.I. Dahl, R. Haugsrud, T. Norby, submitted to SSI – SSPC-14 Kyoto 2008 Experiments - bias

24. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 24/36 UNIVERSITY OF OSLO log Concentration ++++++++++++++++++ Grain interior Space-charge layer Grain boundary core pO 2 dependency for specific grain interior and grain boundary conductivity Micro and nano-crystalline ceria shows n-type contribution to the total conductivity Acceptor doped BaZrO 3 shows n-type grain boundary conduction while ionic grain interior conduction under reducing conditions X. Guo, W. Sigle, J. Maier, Journal of the American Ceramic Society 86 (2003) 77 C. Kjølseth, H. Fjeld, P.I. Dahl, C. Estournès, R. Haugsrud, T. Norby, Submitted (2008) Experiments – electron accumulation

25. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 25/36 UNIVERSITY OF OSLO Space-charge layer Grain interior TiO 2 Grain interior Space- charge layer – – – Ti 2 O 3 ++++++ ++++++++++ Addition of secondary phase Under reducing conditions electrons from the reduction of Ti 4+ to Ti 3+ accumulates in the space charge layer making the proton depletion less severe Problem: the sample becomes mixed conducting if the electrons are mobile TiO 2 in YSZ 8 mol% TiO 2 in two samples with different grain size Solute conc. at grain boundaries decreases with decreasing grain size upon reduction fewer electrons at the grain boundaries of the sample with smallest grain size Oxidizing Reducing X. Guo, R. Waser, Progress in Materials Science 51 (2006) 151 Experiments – electron accumulation

26. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 26/36 UNIVERSITY OF OSLO Experiments – uniaxial pressure Pure samples exhibit equal mechanical electrical properties Both microregions, grain interior and grain boundary are mechanically equal or similar in nature In situ impedance spectroscopy on samples subjected to uniaxial mechanical stresses Grain interior and grain boundary resistance increases upon application of stress → when Δ b = Δ gb no secondary phases exists in the grain boundaries, the grain interior and grain boundary form a unique mechanical entity → supports space charge theory J.-C. M'Peko, M. Ferreira de Souza, Applied Physics Letters 83 (2003) 737.

27. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 27/36 UNIVERSITY OF OSLO Quantitative analysis of pO 2 and T dependence of partial conductivities based on the space charge model Mott-Schottky model case: oxygen ion conductor with hole conduction in grain boundaries pO 2 dependency of oxygen vacancies Assume that λ * and Δφ(0) is independent of pO 2 pO 2 dependence of can be simplified Quantification log Concentration ++++++++++++++++++++ Grain interior Space-charge layer Grain boundary core x = 0x = ∞ In N 2 H.J. Park, S. Kim, Journal of Physical Chemistry C 111 (2007) 14903

28. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 28/36 UNIVERSITY OF OSLO Quantification pO 2 dependency of holes Simplify the pO 2 dependence of : Agrees with obtained results Temperature dependence of oxygen vacancies The temperature dependence of is given by we have The electron neutrality gives This is in agreement with measured data H.J. Park, S. Kim, Journal of Physical Chemistry C 111 (2007) 14903

29. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 29/36 UNIVERSITY OF OSLO Quantification Temperature dependency of holes its relation to oxygen vacancy dependence when values are consistent with experimental data which in terms of activation energy can be expressed (using ) Calculated values for Δφ(0) using conductivities fits with values obtained by activation energies H.J. Park, S. Kim, Journal of Physical Chemistry C 111 (2007) 14903

30. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 30/36 UNIVERSITY OF OSLO Quantification Confirm the separate analysis of holes and oxygen vacancies using the defect equation using the relation we get confirmed by and values are quantified H.J. Park, S. Kim, Journal of Physical Chemistry C 111 (2007) 14903

31. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 31/36 UNIVERSITY OF OSLO Non-linearity observed [x] Electronic contribution in samples with micro/nano grains [x]  gb increases with increasing doping level  (0) increases with decreasing doping level Schottky barrier heights at 400 °C: 1.0 mol% Y 2 O 3 -doped CeO 2 :0.47 V 10 mol% Y 2 O 3 -doped CeO 2 :0.34 V Oxygen ion conductor; Yttria-doped ceria Some examples X. Guo, R. Waser, Progress in Materials Science 51 (2006) 151

32. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 32/36 UNIVERSITY OF OSLO Oxygen ion conductor; Yttria-doped zirconia Some examples Schottky barrier height temperature dependent Schottky barrier height at 400 °C: 0.25 V X. Guo, R. Waser, Progress in Materials Science 51 (2006) 151

33. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 33/36 UNIVERSITY OF OSLO mixed conductor of oxygen vacancies and holes gi: electronic and ionic partial conductivities comparable gb conductivity mainly electronic Larger depletion of oxygen vacancies than holes in space-charge layer → Difference in charge numbers makes oxygen vacancy concentration decay more steeply than hole concentration Mixed conductor; Fe-doped SrTiO 3 Some examples X. Guo, J. Fleig, J. Maier, Journal of the Electrochemical Society 148 (2001) J50

34. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 34/36 UNIVERSITY OF OSLO Proton conductors: Y-doped BaZrO 3 Some examples Schottky barrier height at 250 °C in wet O 2 Δφ(0) = 0.5 V pO 2 dependency additional n-type conduction in the grain boundaries under reducing conditions grain boundary conductivity increases with increasing bias Increased concentration of Y in the grain boudnaries compared to grain interior C. Kjølseth, H. Fjeld, P.I. Dahl, C. Estournès, R. Haugsrud, T. Norby, Submitted (2008)

35. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 35/36 UNIVERSITY OF OSLO Some examples Proton conductors: Sr-doped LaNbO 4 High grain boundary resistance Schottky barrier height 0.7 V at 400 °C R bulk R gb R electrode Q bulk Q gb Q electrode H. Fjeld, unpublished data

36. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 36/36 UNIVERSITY OF OSLO Short summary Blocking impurities in the grain boundary increases the resistance Grain boundary resistance exits in pure materials Depletion of charge carriers in space charge layers adjacent to a charged core can account for this intrinsic grain boundary resistance A grain boundary core – space charge model has been developed Experiments investigating the grain boundary response to dc bias, increased concentration of electrons and electrical properties under uniaxial load can give indications on the existence of space charge layers Quantitative analysis have proven the existence in several materials Thank you for listening

37. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 37/36 UNIVERSITY OF OSLO

38. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 38/36 UNIVERSITY OF OSLO

39. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 39/36 UNIVERSITY OF OSLO

40. Christian Kjølseth, University of Oslo, Norway ― NorFERM, Gol, Norway, 04 October 2008 40/36 UNIVERSITY OF OSLO Decreasing the resistance Immobile negative effective defects → localized electrons Space- charge layer Grain interior TiO 2 Grain interior Space- charge layer – – Ti 2 O 3 ++++++ ++++++++++ –