Journal of the Korean Ceramic Society (한국세라믹학회지)

The Korean Ceramic Society (한국세라믹학회)
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A Superior Description of AC Behavior in Polycrystalline Solid Electrolytes with Current-Constriction Effects

  • Lee, Jong-Sook (School of Materials Science and Engineering, Chonnam National University)
  • Received : 2016.02.12
  • Accepted : 2016.03.03
  • Published : 2016.03.31
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Abstract

The conventional brick-layer model is not satisfactory either in theory or in practice for the description of dispersive responses of polycrystalline solid electrolytes with current-constriction effects at the grain boundaries. Parallel networks of complex dielectric functions have been shown to successfully describe the AC responses of polycrystalline sodium conductors over a wide temperature and frequency range using only around ten model parameters of well-defined physical significance. The approach can be generally applied to many solid electrolyte systems. The present work illustrates the approach by simulation. Problems of bricklayer model analysis are demonstrated by fitting analysis of the simulated data under experimental conditions.

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References

  1. K. Cole and R. Cole, "Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics," J. Chem. Phys., 9 [4] 341-51 (1941). https://doi.org/10.1063/1.1750906
  2. E.-C. Shin, J. Ma, P.-A. Ahn, H.-H. Seo, D. T. Nguyen, and J. S. Lee, "Deconvolution of Four Transmission-Line-Model Impedances in Ni-YSZ/YSZ/LSM Solid Oxide Cells and Mechanistic Insights," Electrochim. Acta, 188 [10] 240-53 (2016). https://doi.org/10.1016/j.electacta.2015.11.118
  3. J.-H. Kim, E.-C. Shin, D.-C. Cho, S. Kim, S. Lim, K. Yang, J. Beum, J. Kim, S. Yamaguchi, and J.-S. Lee, "Electrical Characterization of Polycrystalline Sodium ${\beta}{\prime}{\prime}$-alumina: Revisited and Resolved," Solid State Ionics, 264 22-35 (2014). https://doi.org/10.1016/j.ssi.2014.06.011
  4. S.-H. Moon, D.-C. Cho, D. T. Nguyen, E.-C. Shin, and J.-S. Lee, "A Comprehensive Treatment of Universal Dispersive Frequency Responses in Solid Electrolytes by Immittance Spectroscopy: Low Temperature AgI Case," J. Solid State Electrochem., 19 [8] 2457-64 (2015). https://doi.org/10.1007/s10008-015-2888-6
  5. S.-H. Moon, Y.-H. Kim, D.-C. Cho, E.-C. Shin, D. Lee, W. B. Im, and J.-S. Lee, "Sodium Ion Transport in Polymorphic Scandium NASICON Analog $Na_3Sc_2(PO_4)_3$ with New Dielectric Spectroscopy Approach for Current-Constriction Effects," Solid State Ionics, 289 55-71 (2016). https://doi.org/10.1016/j.ssi.2016.02.017
  6. J. Fleig and J. Maier, "The Impedance of Ceramics with Highly Resistive Grain Boundaries: Validity and Limits of the Brick Layer Model," J. Eur. Ceram. Soc., 19 [6] 693-96 (1999). https://doi.org/10.1016/S0955-2219(98)00298-2
  7. J. Fleig and J. Maier, "Finite-Element Calculations on the Impedance of Electroceramics with Highly Resistive Grain Boundaries: I, Laterally Inhomogeneous Grain Boundaries," J. Am. Ceram. Soc., 82 [12] 3485-93 (1999). https://doi.org/10.1111/j.1151-2916.1999.tb02270.x
  8. B. A. Boukamp, "Practical Application of the Kramers-Kronig Transformation on Impedance Measurements in Solid State Electrochemistry," Solid State Ionics, 62 131-41 (1993). https://doi.org/10.1016/0167-2738(93)90261-Z
  9. B. Boukamp,"A Linear Kronig-Kramers Transform Test for Immittance Data Validation," J. Electrochem. Soc., 142 [6] 1885-94 (1995). https://doi.org/10.1149/1.2044210
  10. D. Davidson and R. Cole, "Dielectric Relaxation in Glycerol, Propylene Glycol, and n-Propanol," J. Chem. Phys., 19 [12] 1484-90 (1951). https://doi.org/10.1063/1.1748105
  11. S. Havriliak and S. Negami, "A Complex Plane Analysis of ${\alpha}$-dispersions in Some Polymer Systems," J. Polym. Sci., Part C: Polym. Symp., 14 [1] 99-117 (1966). https://doi.org/10.1002/polc.5070140111
  12. A. Boersma, J. Van Turnhout, and M. Wubbenhorst, "Dielectric Characterization of a Thermotropic Liquid Crystalline Copolyesteramide: 1. Relaxation Peak Assignment," Macromolecules, 31 [21] 7453-60 (1998). https://doi.org/10.1021/ma9716138
  13. R. Diaz-Calleja, "Comment on the Maximum in the Loss Permittivity for the Havriliak-Negami Equation," Macromolecules, 33 [24] 8924-24 (2000). https://doi.org/10.1021/ma991082i
  14. S. Havriliak and S. Havriliak, "Results from an Unbiased Analysis of Nearly 1000 Sets of Relaxation Data," J. Non-Cryst. Solids, 172 297-310 (1994).
  15. J. R. Macdonald, "New Model for Nearly Constant Dielectric Loss in Conductive Systems: Temperature and Concentration Dependencies," J. Chem. Phys., 116 [8] 3401-9 (2002). https://doi.org/10.1063/1.1434953
  16. J. R. Macdonald, "Universality, the Barton-Nakajima-Namikawa Relation, and Scaling for Dispersive Ionic Materials," Phys. Rev. B, 71 [18] 184307 (2005). https://doi.org/10.1103/PhysRevB.71.184307
  17. E. Barsoukov and J. R. Macdonald, Impedance Spectroscopy: Theory, Experiment, and Application; Wiley Inter-Science, Hoboken, New Jersey, 2005.
  18. J. R. Macdonald, "Impedance Spectroscopy: Models, Data Fitting, and Analysis," Solid State Ionics, 176 [25] 1961-69 Hokken, New Jerser (2005). https://doi.org/10.1016/j.ssi.2004.05.035
  19. J. R. Macdonald, Impedance spectroscopy: Theory, Experiment, and Applications; Chapter 4, pp. 264-82, Wiley Inter-Science, Hoboken, New Jersey, 2005.
  20. J. R. Macdonald, "Surprising Conductive-and Dielectric-System Dispersion Differences and Similarities for Two Kohlrausch-related Relaxation-Time Distributions," J. Phys.: Condens. Matter, 18 [2] 629-44 (2006). https://doi.org/10.1088/0953-8984/18/2/019
  21. J. R. Macdonald, CNLS Immittance, Inversion, and Simulation Fitting Program LEVM/LEVNW Manual; 8.13 edition, 2015.
  22. A. K. Jonscher, "The Universal Dielectric Response," Nature, 267 673-79 (1977). https://doi.org/10.1038/267673a0
  23. K. Funke, "Jump Relaxation in Solid Electrolytes," Prog. Solid State Chem., 22 [2] 111 (1993). https://doi.org/10.1016/0079-6786(93)90002-9
  24. A. K. Jonscher, "Dielectric Relaxation in Solids," J. Phys. Appl. Phys., 32 [14] R57 (1999). https://doi.org/10.1088/0022-3727/32/14/201
  25. D. Almond, A. West, and R. Grant, "Temperature Dependence of the Ac Conductivity of Na ${\beta}$ Aumina," Solid State Comm., 44 [8] 1277-80 (1982). https://doi.org/10.1016/0038-1098(82)91103-6
  26. D. Sidebottom, P. Green, and R. Brow, "Comparison of KWW and Power Law Analyses of an Ion-Conducting Glass," J. Non-Cryst. Solids, 183 [1] 151-60 (1995). https://doi.org/10.1016/0022-3093(94)00587-7
  27. A. Nowick, A. Vaysleyb, and I. Kuskovsky, "Universal Dielectric Response of Variously Doped $CeO_2$ Ionically Conducting Ceramics," Phys. Rev. B, 58 [13] 8398 (1998). https://doi.org/10.1103/PhysRevB.58.8398
  28. D. L. Sidebottom, "Universal Approach for Scaling the Ac Conductivity in Ionic Glasses," Phys. Rev. Lett., 82 [18] 3653 (1999). https://doi.org/10.1103/PhysRevLett.82.3653
  29. K. L. Ngai, "Properties of the Constant Loss in Ionically Conducting Glasses, Melts, and Crystals," J. Chem. Phys., 110 [21] 10576-84 (1999). https://doi.org/10.1063/1.478989
  30. K. L. Ngai and C. Leon, "Cage Decay, Near Constant Loss, and Crossover to Cooperative Ion Motion in Ionic Conductors: Insight from Experimental Data," Phys. Rev. B, 66 [6] 064308 (2002). https://doi.org/10.1103/PhysRevB.66.064308
  31. B. Roling, C. Martiny, and S. Murugavel, "Ionic Conduction in Glass: New Information on the Interrelation between the 'Jonscher Behavior' and the 'Nearly Constant-Loss Behavior' from Broadband Conductivity Spectra," Phys. Rev. Lett., 87 [8] 085901 (2001). https://doi.org/10.1103/PhysRevLett.87.085901
  32. K. Funke, R. Banhatti, and C. Cramer, "Correlated Ionic Hopping Processes in Crystalline and Glassy Electrolytes Resulting in MIGRATION-type and Nearly-Constant-Loss-Type Conductivities," Phys. Chem. Chem. Phys., 7 [1] 157-65 (2005). https://doi.org/10.1039/b414160c
  33. J. R. Macdonald, "Nearly Constant Loss or Constant Loss in Ionically Conducting Glasses: A Physically Realizable Approach," J. Chem. Phys., 115 [13] 6192-99 (2001). https://doi.org/10.1063/1.1398299
  34. J. R. Macdonald, "Discrimination between Series and Parallel Fitting Models for Nearly Constant Loss Effects in Dispersive Ionic Conductors," J. Non-Cryst. Solids, 307 913-20 (2002).
  35. R. Banhatti, D. Laughman, L. Badr, and K. Funke, "Nearly Constant Loss Effect in Sodium Borate and Silver Meta- Phosphate Glasses: New Insights," Solid State Ionics, 192 [1] 70-5 (2011). https://doi.org/10.1016/j.ssi.2010.04.032
  36. P. Lunkenheimer and A. Loidl, "Response of Disordered Matter to Electromagnetic Fields," Phys. Rev. Lett., 91 [20] 207601 (2003). https://doi.org/10.1103/PhysRevLett.91.207601
  37. J.-S. Lee, J. Jamnik, and J. Maier, "Generalized Equivalent Circuits for Mixed Conductors: Silver Sulfide as a Model System," Monatash. Chem. Chem. Mon., 140 [9] 1113-19 (2009). https://doi.org/10.1007/s00706-009-0130-x
  38. E.-C. Shin, P.-A. Ahn, H.-H. Seo, J.-M. Jo, S.-D. Kim, S.-K. Woo, J. H. Yu, J. Mizusaki, and J.-S. Lee, "Polarization Mechanism of High Temperature Electrolysis in a Ni-YSZ/ YSZ/LSM Solid Oxide Cell by Parametric Impedance Analysis," Solid State Ionics, 232 80-96 (2013). https://doi.org/10.1016/j.ssi.2012.10.028
  39. E.-C. Shin, Y.-H. Kim, S.-J. Kim, C.-N. Park, J. Kim, and J.-S. Lee, "Pneumatochemical Immittance Spectroscopy for Hydrogen Storage Kinetics," J. Phys. Chem. C, 117 [39] 19786-808 (2013). https://doi.org/10.1021/jp4023647
  40. S. Kim, J. Fleig, and J. Maier, "Space Charge Conduction: Simple Analytical Solutions for Ionic and Mixed Conductors and Application to Nanocrystalline Ceria," Phys. Chem. Chem. Phys., 5 [11] 2268-73 (2003). https://doi.org/10.1039/B300170A
  41. J.-S. Lee, S. Adams, and J. Maier, "Defect Chemistry and Transport Characteristics in ${\beta}$ -AgI," J. Phys. Chem. Solids, 61 1607-22 (2000). https://doi.org/10.1016/S0022-3697(00)00020-2
  42. X. Guo and R. Waser, "Electrical Properties of the Grain Boundaries of Oxygen Ion Conductors: Acceptor-Doped Zirconia and Ceria," Prog. Mater. Sci., 51 [2] 151-210 (2006). https://doi.org/10.1016/j.pmatsci.2005.07.001
  43. C. Kjolseth, H. Fjeld, O. Prytz, P. Dahl, C. Estournes, R. Haugsrud, and T. Norby, "Space-Charge Theory Applied to the Grain Boundary Impedance of Proton Conducting $BaZr_{0.9}Y_{0.1}O_{3-{\delta}}$," Solid State Ionics, 181 [5-7] 268-75 (2010). https://doi.org/10.1016/j.ssi.2010.01.014
  44. C.-T. Chen, C. E. Danel, and S. Kim, "On the Origin of the Blocking Effect of Grain-Boundaries on Proton Transport in Yttrium-doped Barium Zirconates," J. Mater. Chem., 21 [14] 5435-42 (2011). https://doi.org/10.1039/c0jm03353g
  45. M. Shirpour, R. Merkle, C. Lin, and J. Maier, "Nonlinear Electrical Grain Boundary Properties in Proton Conducting Y-$BaZrO_3$ Supporting the Space Charge Depletion Model," Phys. Chem. Chem. Phys., 14 [2] 730-40 (2012). https://doi.org/10.1039/C1CP22487E
  46. C. R. Mariappan, M. Gellert, C. Yada, F. Rosciano, and B. Roling, "Grain Boundary Resistance of Fast Lithium Ion Conductors: Comparison between a Lithium-Ion Conductive Li-Al-Ti-P-O-type Glass Ceramic and a $Li_{1.5}Al_{0.5}Ge_{1.5}P_3O_{12}$ Ceramic," Electrochem. Comm., 14 [1] 25-8 (2012). https://doi.org/10.1016/j.elecom.2011.10.022
  47. I. Raistrick, C. Ho, and R. A. Huggins, "Ionic Conductivity of Some Lithium Silicates and Aluminosilicates," J. Electrochem. Soc., 123 [10] 1469-76 (1976). https://doi.org/10.1149/1.2132621
  48. P. G. Bruce and A. R. West, "The A-C Conductivity of Polycrystalline LISICON, $Li_{2+2x}Zn_{1-x}GeO_4$, and a Model for Intergranular Constriction Resistances," J. Electrochem. Soc., 130 [3] 662-69 (1983). https://doi.org/10.1149/1.2119778
  49. J.-S. Lee, E.-C. Shin, D.-K. Shin, Y. Kim, P.-A. Ahn, H.-H. Seo, J.-M. Jo, J.-H. Kim, G.-R. Kim, Y.-H. Kim, J.-Y. Park, C.-H. Kim, J.-O. Hong, and K.-H. Hur, "Impedance Spectroscopy Models for X5R Multilayer Ceramic Capacitors," J. Korean Ceram. Soc., 49 [5] 475-83 (2012). https://doi.org/10.4191/kcers.2012.49.5.475
  50. H.-I. Yoo, T.-S. Oh, H.-S. Kwon, D.-K. Shin, and J.-S. Lee, "Electrical Conductivity-Defect Structure Correlation of Variable-Valence and Fixed-Valence Acceptor-Doped $BaTiO_3$ in Quenched State," Phys. Chem. Chem. Phys., 11 [17] 3115-26 (2009). https://doi.org/10.1039/b822381p
  51. J. R. Macdonald, "Comparison of the Universal Dynamic Response Power-Law Fitting Model for Conducting Systems with Superior Alternative Models," Solid State Ionics, 133 [1] 79-97 (2000). https://doi.org/10.1016/S0167-2738(00)00737-2

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