Theories and Models of Ion Diffusion

详细信息    查看全文

• 刊名：Topics in Applied Physics
• 出版年：2017
• 出版时间：2017
• 年：2017
• 卷：132
• 期：1
• 页码：9-60
• 全文大小：1,253 KB
• 参考文献：1.L. Landau, E. Lifschitz, Textbook of Theoretical Physics, Vol. V. Statistical Physics (Akademie-Verlag, Berlin, 1979).
  2.F. Kremer, A. Schönhals (eds.), Broadband Dielectric Spectroscopy (Springer, Berlin, 2012), p. 729
  3.R. de L. Kronig, J. Opt. Soc. Am. 12, 547 (1926)
  4.H. Kramers, Atti Del Congr. Internazionale Dei Fis, 2nd edn. (Bologna Zanichelli, 1927), p. 545
  5.C.F. Bohren, Eur. J. Phys. 31, 573 (2010)CrossRef
  6.J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1999)
  7.H. Nyquist, Phys. Rev. 32, 110 (1928)CrossRef
  8.H.B. Callen, T.A. Welton, Phys. Rev. 83, 34 (1951)CrossRef
  9.G. Williams, J. Fournier, J. Chem. Phys. 104, 5690 (1996)CrossRef
  10.L. Onsager, Phys. Rev. 37, 405 (1931)CrossRef
  11.L. Onsager, Phys. Rev. 38, 2265 (1931)CrossRef
  12.C.J.F. Böttcher, P. Bordewijk, Theory of Electric Polarization, Vol. II: Dielectrics in Time-Dependent Fields (Elsevier, Amsterdam/Oxford/New York, 1978)
  13.P. Debye, Phys. Z. 13, 97 (1912)
  14.P. Debye, Ber. Deut. Phys. Ges. 55, 777 (1913)
  15.G. Adam, J.H. Gibbs, J. Chem. Phys. 43, 139 (1965)CrossRef
  16.K. Schmidt-Rohr, H. Spiess, Phys. Rev. Lett. 66, 3020 (1991)CrossRef
  17.E. Weeks, J. Crocker, A. Levitt, A. Schofield, D. Weitz, Science 287, 627 (2000)CrossRef
  18.K.L. Ngai, Relaxation and Diffusion in Complex Systems (Springer, New York, 2011), p. 835CrossRef
  19.R. Kohlrausch, Ann. Der Phys. Und Chemie 167, 179 (1854)CrossRef
  20.G. Williams, D.C. Watts, Trans. Faraday Soc. 66, 80 (1970)CrossRef
  21.G. Williams, D.C. Watts, S.B. Dev, A.M. North, Trans. Faraday Soc. 67, 1323 (1971)CrossRef
  22.M. Cardona, R.V. Chamberlin, W. Marx, Ann. Phys. 16, 842 (2007)CrossRef
  23.G. Williams, IEEE Trans. Electr. Insul. EI-17, 469 (1982)CrossRef
  24.G. Williams, IEEE Trans. Electr. Insul. EI-20, 843 (1985)CrossRef
  25.K. Tsang, K. Ngai, Phys. Rev. E 56, R17 (1997)CrossRef
  26.K.L. Ngai, J. Habasaki, Y. Hiwatari, C. Leon, J. Phys. Condens. Matter 15, S1607 (2003)CrossRef
  27.S. Havriliak, S. Negami, J. Polym. Sci. Part C Polym. Symp. 14, 99 (1966)CrossRef
  28.A. Jonscher, Dielectric Relaxation in Solids (Chelsea, London, 1983)
  29.K.S. Cole, R.H. Cole, J. Chem. Phys. 9, 341 (1941)CrossRef
  30.D.W. Davidson, R.H. Cole, J. Chem. Phys. 19, 1484 (1951)CrossRef
  31.I.M. Hodge, K.L. Ngai, C.T. Moynihan, J. Non-Cryst. Solids 351, 104 (2005)CrossRef
  32.C. Angell, Annu. Rev. Phys. Chem. 43, 693 (1992)CrossRef
  33.J. Dyre, T. Schrøder, Rev. Mod. Phys. 72, 873 (2000)CrossRef
  34.K.L. Ngai, A.K. Jonscher, C.T. White, Nature 277, 185 (1979)CrossRef
  35.K.L. Ngai, J. Habasaki, C. León, A. Rivera, Z. Phys. Chem. 219, 47 (2005)
  36.C. León, J. Habasaki, K.L. Ngai, Zeitschrift Für Phys. Chemie 223, 1311 (2009)CrossRef
  37.K. Funke, Prog. Solid State Chem. 22, 111 (1993)CrossRef
  38.A.K. Jonscher, Nature 267, 673 (1977)CrossRef
  39.D.P. Almond, A.R. West, R.J. Grant, Solid State Commun. 44, 1277 (1982)CrossRef
  40.C. Cramer, K. Funke, T. Saatkamp, Philos. Mag. Part B 71, 701 (1995)CrossRef
  41.K. Funke, Solid State Ionics 169, 1 (2004)CrossRef
  42.D. Sidebottom, B. Roling, K. Funke, Phys. Rev. B 63, 024301 (2000)CrossRef
  43.J.C. Dyre, P. Maass, B. Roling, D.L. Sidebottom, Rep. Prog. Phys. 72, 046501 (2009)CrossRef
  44.D. Sidebottom, Phys. Rev. Lett. 82, 3653 (1999)CrossRef
  45.C. León, M. Lucia, J. Santamaria, Phys. Rev. B 55, 882 (1997)CrossRef
  46.C.T. Moynihan, J. Non-Cryst. Solids 172–174, 1395 (1994)CrossRef
  47.C. Moynihan, Solid State Ionics 105, 175 (1998)CrossRef
  48.K.L. Ngai, C.T. Moynihan, MRS Bull. 23, 51 (1998)CrossRef
  49.P.B. Macedo, C.T. Moynihan, R. Bose, Phys. Chem. Glas. 13, 171 (1972)
  50.T.J. Higgins, L.P. Boesch, V. Volterra, C.T. Moynihan, P.B. Macedo, J. Am. Ceram. Soc. 56, 334 (1973)CrossRef
  51.F.S. Howell, R.A. Bose, P.B. Macedo, C.T. Moynihan, J. Phys. Chem. 78, 639 (1974)CrossRef
  52.C.T. Moynihan, L.P. Boesch, N.L. Laberge, Phys. Chem. Glas. 14, 122 (1973)
  53.J.R. Macdonald, J. Chem. Phys. 102, 6241 (1995)CrossRef
  54.B.A. Boukamp, Solid State Ionics 20, 31 (1986)
  55.B. Boukamp, J.R. Macdonald, Solid State Ionics 74, 85 (1994)CrossRef
  56.C. León, M.L. Lucía, J. Santamaría, Philos. Mag. Part B 75, 629 (1997)CrossRef
  57.F. Alvarez, A. Alegra, J. Colmenero, Phys. Rev. B 44, 7306 (1991)CrossRef
  58.K.L. Ngai, J. Chem. Phys. 98, 6424 (1993)CrossRef
  59.P. Kofstad, T. Norby, Defects and Transport in Crystalline Solids (University of Oslo, Oslo, 2007)
  60.M.S. Islam, C.A.J. Fisher, Chem. Soc. Rev. 43, 185 (2014)CrossRef
  61.G. Ceder, MRS Bull. 35, 693 (2011)CrossRef
  62.L. Malavasi, C.A.J. Fisher, M.S. Islam, Chem. Soc. Rev. 39, 4370 (2010)CrossRef
  63.Y. Wang, W.D. Richards, S.P. Ong, L.J. Miara, J.C. Kim, Y. Mo, G. Ceder, Nat. Mater. 14, 1026 (2015)CrossRef
  64.Z. Wojnarowska, M. Paluch, J. Phys. Condens. Matter 27, 073202 (2015)CrossRef
  65.T. Norby, Mater. Res. Soc. Bull. 34, 923 (2009)
  66.C. Zener, Proc. R. Soc. A Math. Phys. Eng. Sci. 137, 696 (1932)CrossRef
  67.K. Ngai, Solid State Ionics 105, 231 (1998)CrossRef
  68.L. Van Hove, Phys. Rev. 95, 249 (1954)CrossRef
  69.A. Rahman, K.S. Singwi, A. Sjölander, Phys. Rev. 126, 986 (1962)CrossRef
  70.R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)CrossRef
  71.T. Odagaki, M. Lax, Phys. Rev. B 24, 5284 (1981)CrossRef
  72.D. Ben-Avraham, S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, 2000), p. 316CrossRef
  73.S. Elliott, Solid State Ionics 27, 131 (1988)CrossRef
  74.T. Odagaki, M. Lax, Phys. Rev. Lett. 45, 847 (1980)CrossRef
  75.T. Odagaki, Phys. Rev. B 38, 9044 (1988)CrossRef
  76.T. Nakayama, Rep. Prog. Phys. 65, 1195 (2002)CrossRef
  77.T. Ishii, J. Phys. Soc. Jpn. 61, 924 (1992)CrossRef
  78.T. Ishii, Solid State Ionics 40–41, 244 (1990)CrossRef
  79.A. Bunde, H. Roman, S. Russ, A. Aharony, A. Harris, Phys. Rev. Lett. 69, 3189 (1992)CrossRef
  80.E. Bacry, J. Delour, J.F. Muzy, Phys. Rev. E. Stat. Nonlin. Soft Matter Phys. 64, 026103 (2001)
  81.M. Shlesinger, B. West, J. Klafter, Phys. Rev. Lett. 58, 1100 (1987)CrossRef
  82.T. Geisel, J. Nierwetberg, A. Zacherl, Phys. Rev. Lett. 54, 616 (1985)CrossRef
  83.J. Habasaki, K.L. Ngai, J. Chem. Phys. 129, 194501 (2008)CrossRef
  84.J. Habasaki, I. Okada, Y. Hiwatari, Phys. Rev. B 55, 6309 (1997)CrossRef
  85.A. Blumen, J. Klafter, B.S. White, G. Zumofen, Phys. Rev. Lett. 53, 1301 (1984)CrossRef
  86.J. Habasaki, I. Okada, Y. Hiwatari, J. Phys. Soc. Jpn. 67, 2012 (1998)CrossRef
  87.K. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (Routledge Classics, New York, 1963) 
  88.J.C. Kimball, L.W. Adams, Phys. Rev. B 18, 5851 (1978)CrossRef
  89.J.C. Dyre, T.B. Schroeder, Phys. Status Solidi 230, 5 (2002)CrossRef
  90.P.N. Butcher, J. Phys. C Solid State Phys. 7, 879 (1974)CrossRef
  91.D.L. Stein, C.M. Newman, Phys. Rev. E 51, 5228 (1995)CrossRef
  92.J.W. Haus, K.W. Kehr, Phys. Rep. 150, 263 (1987)CrossRef
  93.J.C. Dyre, J. Appl. Phys. 64, 2456 (1988)CrossRef
  94.T.B. Schrøder, J.C. Dyre, Phys. Chem. Chem. Phys. 4, 3173 (2002)CrossRef
  95.V. Ambegaokar, B.I. Halperin, J.S. Langer, Phys. Rev. B 4, 2612 (1971)CrossRef
  96.T. Schrøder, J. Dyre, Phys. Rev. Lett. 84, 310 (2000)CrossRef
  97.S.D. Baranovskii, H. Cordes, J. Chem. Phys. 111, 7546 (1999)CrossRef
  98.W. Dieterich, P. Maass, Chem. Phys. 284, 439 (2002)CrossRef
  99.B. Roling, C. Martiny, K. Funke, J. Non-Cryst. Solids 249, 201 (1999)CrossRef
  100.J.O. Isard, J. Non-Cryst. Solids 246, 16 (1999)CrossRef
  101.K. Funke, R.D. Banhatti, S. Brückner, C. Cramer, C. Krieger, A. Mandanici, C. Martiny, I. Ross, Phys. Chem. Chem. Phys. 4, 3155 (2002)CrossRef
  102.K. Funke, R.D. Banhatti, J. Non-Cryst. Solids 353, 3845 (2007)CrossRef
  103.K. Funke, R.D. Banhatti, D.M. Laughman, L.G. Badr, M. Mutke, A. Santic, W. Wrobel, E.M. Fellberg, C. Biermann, Zeitschrift Für Phys. Chemie 224, 1891 (2010)CrossRef
  104.K. Funke, R.D. Banhatti, Solid State Ionics 177, 1551 (2006)CrossRef
  105.P. Singh, R.D. Banhatti, K. Funke, Phys. Chem. Glas. 46, 241 (2005)
  106.K.L. Ngai, Comment Solid State Phys. 9, 141 (1980)
  107.K.L. Ngai, C.T. White, Phys. Rev. B 20, 2475 (1979)CrossRef
  108.K.L. Ngai, Comment Solid State Phys. 9, 127 (1980)
  109.M. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, Berlin, 1990)CrossRef
  110.M.V. Berry, Proc. R. Soc. A Math. Phys. Eng. Sci. 413, 183 (1987)
  111.M. Berry, Phys. Scr. 40, 335 (1989)CrossRef
  112.O. Bohigas, Chaos Phys. Quantique Chaos Quantum Phys. 87 (1989)
  113.O. Bohigas, M.J. Giannoni, C. Schmit, Phys. Rev. Lett. 52, 1 (1984)CrossRef
  114.E.P. Wigner, Proceedings of Fourth Canadian Mathematical Congress (University Toronto Press, Toronto, 1957), p. 174
  115.M.L. Mehta, Random Matrices, 2nd edn. (Academic, New York, 1991)
  116.F.J. Dyson, J. Math. Phys. 3, 140 (1962)CrossRef
  117.L. Gor’kov, G. Eliashberg, JETP 21, 940 (1965)
  118.K.L. Ngai, S. Capaccioli, J. Phys. Condens. Matter 19, 205114 (2007)CrossRef
  119.D. Bedrov, G.D. Smith, Macromolecules 39, 8526 (2006)CrossRef
  120.I.A. Campbell, C. Giovannella (eds.), Relaxation in Complex Systems and Related Topics (Springer, Boston, 1990)
  121.G. Kolata, Science 223, 917 (1984)CrossRef
  122.E. Weeks, D. Weitz, Phys. Rev. Lett. 89, 095704 (2002)CrossRef
  123.J. Habasaki, K.L. Ngai, J. Non-Cryst. Solids 352, 5170 (2006)CrossRef
  124.T. Pakula, J. Mol. Liq. 86, 109 (2000)CrossRef
  125.P. Polanowski, T. Pakula, J. Chem. Phys. 117, 4022 (2002)CrossRef
  
• 作者单位：Junko Habasaki (7)
  Carlos León (8)
  K. L. Ngai (9)
  
  7. Tokyo Institute of Technology, Yokohama, Kanagawa, Japan
  8. Facultad de Fisica, Universidad Complutense Madrid, Madrid, Spain
  9. IPCF, CNR, Pisa, Italy
  
• 丛书名：Dynamics of Glassy, Crystalline and Liquid Ionic Conductors
• ISBN：978-3-319-42391-3
• 刊物类别：Physics and Astronom
• 刊物主题：Physics
  Magnetism and Magnetic Materials
  Optical and Electronic Materials
  Laser Technology and Physics and Photonics
  Quantum Computing, Information and Physics
  Applied Optics, Optoelectronics and Optical Devices
  Solid State Physics and Spectroscopy
  Condensed Matter
  
• 出版者：Springer Berlin / Heidelberg
• 卷排序：132

文摘

This chapter describes some models that are often used in trying to understand experimental data and fundamental questions in ion diffusion in ionically conducting materials. The basics of linear response theory are introduced first, with the definition of the linear response function, the Kramers-Kronig relations, and the Fluctuation-Dissipation theorem. A second section is devoted to present the Debye model and several other phenomenological descriptions of dielectric relaxation in materials whose electrical response is dominated by bound charges. This helps to understand the conductivity relaxation that occurs in materials with mobile charges like ionic conductors, and to introduce the so called conductivity formalism and electric modulus formalism for the analysis of experimental data of ion diffusion dynamics. A simple model of ion hopping is introduced that accounts for the thermally activated behavior often found in ionic conductivity data. The relationship between non-Debye relaxation and non-Gaussianity of the dynamics in the real space is also discussed in this chapter. Finally, three different models for ion diffusion are described in some detail. These are the Random Barrier Model, the MIGRATION concept, and the Coupling Model.