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A comprehensive treatment of universal dispersive frequency responses in solid electrolytes by immittance spectroscopy: low temperature AgI case

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Abstract

Motivated by the recent work on β″-alumina polycrystalline ceramics, we revisit the frequency dispersion behavior of AgI. Series of admittance and capacitance Bode plots at different temperatures revealed the presence of well-defined parallel capacitance effects and power-law frequency dependencies. Non-trivial bulk dispersion is thus successfully described by the bulk conductance with activation energy of 0.262 eV in parallel connection to several capacitive effects: (i) a mobile-charge contribution, universally observed in many solid electrolytes, approximated by a Cole-Davidson model with Δ𝜖 C ≅ 28, γ C ≅ 0.388, and (τ C)−1 thermally activated by 0.237 eV, (ii) a dipolar and vibratory contribution represented by another Cole-Davidson model of the dielectric strength of Δ𝜖 D ≅ 9.0 with γ D ≅ 0.110, τ D ≅ 0.003 s, corresponding to Nearly-Constant-Loss behavior, and (iii) high frequency limit capacitance corresponding to the dielectric constant 𝜖 S ≅ 6.4. Electrode effects are described by an ideal Warburg response and the coefficient activated by 0.165 eV, which is connected in parallel to the bulk capacitive elements (i) to (iii). The modeling allows a simulation of ac behavior of AgI as a function of temperature as well as frequencies, addressing all of the universally observed dispersive responses.

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References

  1. Barsoukov E, Macdonald JR (2005) Impedance spectroscopy: theory, experiment, and applications. Wiley InterScience

  2. Phillips J (1994) Microscopic theory of the Kohlrausch relaxation constant β k. J Non-Cryst Solids 172:98–103

    Article  Google Scholar 

  3. Macdonald JR (2002) New model for nearly constant dielectric loss in conductive systems: Temperature and concentration dependencies. J Chem Phys 116(8):3401–3409

    Article  CAS  Google Scholar 

  4. Macdonald JR (2005a) Universality, the Barton-Nakajima-Namikawa relation, and scaling for dispersive ionic materials. Phys Rev B 71(18):184,307

    Article  Google Scholar 

  5. Macdonald JR (2005b) Impedance spectroscopy: Models, data fitting, and analysis. Solid State Ionics 176(25):1961–1969

    Article  CAS  Google Scholar 

  6. Macdonald JR (2006) Surprising conductive-and dielectric-system dispersion differences and similarities for two Kohlrausch-related relaxation-time distributions. J Phys: Condens Matter 18:629–644

    CAS  Google Scholar 

  7. Macdonald JR (2012) CNLS immittance, inversion, and simulation fitting program LEVM/LEVNW Manual, 8th edn

  8. Kim JH, Shin EC, Cho DC, Kim S, Lim S, Yang K, Beum J, Kim J, Yamaguchi S, Lee JS (2014) Electrical characterization of polycrystalline sodium β″-alumina: revisited and resolved. Solid State Ionics 264:22–35

    Article  CAS  Google Scholar 

  9. Lee JS, Adams S, Maier J (2000) Defect chemistry and transport characteristics in β-AgI. J Phys Chem Solids 61:1607–1622

    Article  CAS  Google Scholar 

  10. Funke K, Banhatti R, Brückner S, Cramer C, Krieger C, Mandanici A, Martiny C, Ross I (2002) Ionic motion in materials with disordered structures: Conductivity spectra and the concept of mismatch and relaxation. Phys Chem Chem Phys 4(14):3155–3167

    Article  CAS  Google Scholar 

  11. Boukamp BA (1993) Practical application of the Kramers-Kronig transformation on impedance measurements in solid state electrochemistry. Solid State Ionics 62:131–141

    Article  CAS  Google Scholar 

  12. Maier J (1995) Ionic conduction in space charge regions. Prog Solid State Chem 23:171–263

    Article  CAS  Google Scholar 

  13. Fleig J, Maier J (1999) Microcontact impedance measurements of individual highly conductive grain boundaries: General aspects and application to AgCl. Phys Chem Chem Phys 1(14):3315–3320

    Article  CAS  Google Scholar 

  14. Lee JS, Adams S, Maier J (2000) Transport and phase transition characteristics in AgI:Al2O3 composite electrolytes. Evidence for a highly conducting 7-layer AgI polytype. J Electrochem Soc 147(6):2407–2418

    Article  CAS  Google Scholar 

  15. Lee JS, Lee JW, Lee JY, Adams S, Guo YG, Maier J (2010) Microscopic evidence of a new 9R-AgI polytype heterostructure. J Nanosci Nanotechnol 10(5):3341–3345

    Article  CAS  Google Scholar 

  16. Lee JS, Adams S, Maier J (2000) A mesoscopic heterostructure as the origin of the extreme ionic conductivity in AgI:Al2O3. Solid State Ionics 136–137:1261–1266

    Article  Google Scholar 

  17. Guo YG, Lee JS, Maier J (2005) AgI nanoplates with mesoscopic superionic conductivity at room temperature. Adv Mater 17(23):2815–2819

    Article  CAS  Google Scholar 

  18. Jonscher AK (1977) The universal dielectric response. Nature 267:673–679

    Article  CAS  Google Scholar 

  19. Jonscher AK (1999) Dielectric relaxation in solids. J Phys D: Appl Phys 32(14):R57

    Article  CAS  Google Scholar 

  20. Cochrane G, Fletcher N (1971) Ionic conductivity and low frequency dispersion in hexagonal silver iodide. J Phys Chem Solids 32(11):2557–2567

    Article  CAS  Google Scholar 

  21. Van Renesse R, Van der Zwaal N (1971) Refractive index and thickness variations of the photographic emulsion. Opt Laser Technol 3(1):41–44

    Article  Google Scholar 

  22. Ngai KL (1999) Properties of the constant loss in ionically conducting glasses, melts, and crystals. J Chem Phys 110(21):10,576–10,584

    Article  CAS  Google Scholar 

  23. Ngai KL, León C (2002) Cage decay, near constant loss, and crossover to cooperative ion motion in ionic conductors: Insight from experimental data. Phys Rev B 66(6):064,308

    Article  Google Scholar 

  24. Roling B, Martiny C, Murugavel S (2001) 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):085,901

    Article  CAS  Google Scholar 

  25. Funke K, Banhatti R, Cramer C (2005) 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):157–165

    Article  CAS  Google Scholar 

  26. Macdonald JR (2001) Nearly constant loss or constant loss in ionically conducting glasses: A physically realizable approach. J Chem Phys 115(13):6192–6199

    Article  CAS  Google Scholar 

  27. Macdonald JR (2002) Discrimination between series and parallel fitting models for nearly constant loss effects in dispersive ionic conductors. J Non-Cryst Solids 307:913–920

    Article  Google Scholar 

  28. Banhatti R, Laughman D, Badr L, Funke K (2011) Nearly constant loss effect in sodium borate and silver meta-phosphate glasses: New insights. Solid State Ionics 192(1):70–75

    Article  CAS  Google Scholar 

  29. Almond D, West A, Grant R (1982) Temperature dependence of the ac conductivity of Na β-alumina. Solid State Commun 44(8):1277–1280

    Article  CAS  Google Scholar 

  30. Sidebottom D, Green P, Brow R (1995) Comparison of KWW and power law analyses of an ion-conducting glass. J Non-Cryst Solids 183(1):151–160

    Article  CAS  Google Scholar 

  31. Nowick A, Vaysleyb A, Kuskovsky I (1998) Universal dielectric response of variously doped CeO2 ionically conducting ceramics. Phys Rev B 58(13):8398

    Article  CAS  Google Scholar 

  32. Sidebottom DL (1999) Universal approach for scaling the ac conductivity in ionic glasses. Phys Rev Lett 82(18):3653

    Article  CAS  Google Scholar 

  33. Macdonald JR, Ahmad MM (2007) Slopes, nearly constant loss, universality, and hopping rates for dispersive ionic conduction. J Phys: Condens Matter 19(4):046,215

    Google Scholar 

  34. Funke K (1993) Jump relaxation in solid electrolytes. Prog Solid State Chem 22(2):111

    Article  CAS  Google Scholar 

  35. Funke K, Banhatti R (2004) Modelling frequency-dependent conductivities and permittivities in the framework of the MIGRATION concept. Solid State Ionics 169(1):1–8

    Article  CAS  Google Scholar 

  36. Scher H, Lax M (1973) Stochastic transport in a disordered solid. I. Theory. Phys Rev B 7(10):4491

    Article  CAS  Google Scholar 

  37. Macdonald JR (2009) Comparison of some random-barrier, continuous-time random-walk, and other models for the analysis of wide-range frequency response of ion-conducting materials. J Phys Chem B 113(27):9175–9182

    Article  CAS  Google Scholar 

  38. Raistrick I, Ho C, Huggins RA (1976) Ionic conductivity of some lithium silicates and aluminosilicates. J Electrochem Soc 123(10):1469–1476

    Article  CAS  Google Scholar 

  39. Bruce PG, West A (1983) The a-c conductivity of polycrystalline lisicon, Li2+2x Zn1 − x GeO4, and a model for intergranular constriction resistances. J Electrochem Soc 130(3):662–669

    Article  CAS  Google Scholar 

  40. Mariappan CR, Gellert M, Yada C, Rosciano F, Roling B (2012) Grain boundary resistance of fast lithium ion conductors: Comparison between a lithium-ion conductive Li-Al-Ti-P-O-type glass ceramic and a Li1.5Al0.5Ge1.5P3O12 ceramic. Electrochem Comm 14(1):25–28

    Article  CAS  Google Scholar 

  41. Masó N, West AR (2015) Electronic conductivity in yttria-stabilized zirconia under a small dc bias. Chem Mater 27:1552–1558

    Article  Google Scholar 

  42. Havriliak S, Negami S (1966) A complex plane analysis of α-dispersions in some polymer systems. J Polymer Sci C 14(1):99–117

    Article  Google Scholar 

  43. Franceschetti DR, Macdonald JR (1979) Diffusion of neutral and charged species under small-signal ac conditions. J Electroanal Chem Interf Electrochem 101(3):307–316

    Article  CAS  Google Scholar 

  44. Jamnik J, Maier J (1999) Treatment of the impedance of mixed conductors equivalent circuit model and explicit approximate solutions. J Electrochem Soc 146:4183

    Article  CAS  Google Scholar 

  45. Jamnik J, Maier J (2001) Generalised equivalent circuits for mass and charge transport: Chemical capacitance and its implications. Phys Chem Chem Phys 3(9):1668–1678

    Article  CAS  Google Scholar 

  46. Lee JS, Jamnik J, Maier J (2009) Generalized equivalent circuits for mixed conductors: Silver sulfide as a model system. Monatsh Chem 140(9):1113–1119

    Article  CAS  Google Scholar 

  47. Ahn PA, Shin EC, Kim GR, Lee JS (2011) Application of generalized transmission line models to mixed ionic-electronic transport phenomena. J Kor Ceram Soc 48:549–558

    Article  CAS  Google Scholar 

  48. Shin EC, Ahn PA, Seo HH, Jo JM, Kim SD, Woo SK, Yu JH, Mizusaki J, Lee JS (2013) 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

    Article  CAS  Google Scholar 

  49. Lunkenheimer P, Loidl A (2003) Response of disordered matter to electromagnetic fields. Phys Rev Lett 91(20):207,601

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This research was supported by the Fusion Research Program for Green Technologies through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (No. 2011-0019304).

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Authors and Affiliations

  1. School of Materials Science and Engineering, Chonnam National University, Gwangju, South Korea

    Su-Hyun Moon, Dong-Chun Cho, Dang Thanh Nguyen, Eui-Chol Shin & Jong-Sook Lee

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Correspondence to Jong-Sook Lee.

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Moon, SH., Cho, DC., Nguyen, D.T. et al. A comprehensive treatment of universal dispersive frequency responses in solid electrolytes by immittance spectroscopy: low temperature AgI case. J Solid State Electrochem 19, 2457–2464 (2015). https://doi.org/10.1007/s10008-015-2888-6

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