Physics of Superionic Conductors

Superionic conductors are solids whose ionic conductivities approach, and in some cases exceed, those of molten salts and electrolyte solutions. This implies an un­ usual state of matter in which some atoms have nearly liquidlike mobility while others retain their regular crystalline arrangement. This liquid-solid duality has much appeal to condensed matter physicists, and the coincident development of powerful new methods for studying disordered solids and interest in superionic conductors for technical applications has resulted in a new surge of activity in this venerable field. It is the purpose of this book to summarize the current re­ search in the physics of superionic conduction. with special emphasis on those aspects which set these materials apart from other solids. The volume is aimed to­ wards the materials community and will, we expect, stimulate further research on these potentially useful substances. The usual characterization of the superionic phase lists high ionic conductivity; low activation energy; and the open structure of the crystal, with its interconne­ ted network of vacant sites available to one ionic species. To these, as we demon­ strate in this volume, should be added important dynami~ and collective effect~: the absence of well-defined optical lattice modes, the presence of a pervasive, low-energy excitation, an infrared peak in the frequency-dependent conductivity, unusual NMR prefactors, phase transitions, and a strong tendency for the mobile ion to be found between allowed sites.

1. Introduction.- References.- 2. Structure and Its Influence on Superionic Conduction: EXAFS Studies.- 2.1 Technique of EXAFS.- 2.1.1 Theory.- 2.1.2 Experiment.- 2.1.3 Data Reduction and Analysis.- 2.1.4 Contrast with Diffraction Studies.- 2.2 Structural Considerations for Superionic Conduction.- 2.2.1 General Considerations.- 2.2.2 Pair Potentials.- 2.2.3 Anharmonic Model.- 2.2.4 Excluded Volume Model and Cation-Anion Correlations.- 2.3 EXAFS Investigations of bcc Superionic Conductors: AgI.- 2.3.1 Early Structural Studies.- 2.3.2 EXAFS Study.- 2.3.3 Other Recent Structural Studies.- 2.3.4 Structural Model for Superionic Conduction in bcc Conductors.- 2.4 EXAFS Investigations of fcc Superionic Conductors: Cuprous Halides.- 2.4.1 CuI Structural Studies.- 2.4.2 EXAFS and Structural Models for CuI.- 2.4.3 CuBr.- 2.4.4 CuCl.- 2.4.5 Discussion.- 2.5 Summary.- References.- 3. Neutron Scattering Studies of Superionic Conductors.- 3.1 Neutron Scattering.- 3.1.1 Scattering function.- 3.1.2 Elastic Scattering.- 3.1.3 Inelastic Scattering.- 3.2 Structural Studies.- 3.2.1 AgI.- 3.2.2 Fluorites.- 3.2.3 ?-Alumina.- 3.3 Inelastic Studies.- 3.3.1 AgI.- 3.3.2 RbAg4I5.- 3.3.3 Fluorites.- 3.3.4 ?-Alumina.- 3.4 Conclusions.- References.- 4. Statics and Dynamics of Lattice Gas Models.- 4.1 General Theory of the Lattice Gas Model for Superionic Conductors.- 4.1.1 Definition of the Lattice Gas Model.- 4.1.2 Liouvillian Approach to Lattice Gas Dynamics.- 4.1.3 Master-Equation Approximation.- 4.1.4 High-Frequency Limit.- 4.1.5 Extension to All Frequencies.- 4.2 Extended Dynamical Theory.- 4.2.1 ?trap and Its Relation to a Soliton Model.- 4.2.2 Low-Frequency Conductivity.- 4.3 Applications to Silver Iodide and Hollandite.- 4.3.1 Silver Iodide: Structural Properties, Lattice Gas Representation.- 4.3.2 The Disorder Entropy of AgI.- 4.3.3 Dynami c Properties of ?-AgI.- 4.3.4 Collective Excitations in One-Dimensional Systems: Hollandite.- 4.4 Conclusions.- Appendix A.- Appendix B.- Appendix C.- References.- 5. Light Scattering in Superionic Conductors.- 5.1 Raman Scatteri ng.- 5.1.1 Silver Iodide.- 5.1.2 M+Ag4I5 (M+ = Rb+, K+, NH+4).- 5.1.3 Copper Halides.- 5.1.4 ?-Aluminas.- 5.1.5 Anion Conducting Fluorites.- 5.2 Low-Frequency Raman and Brillouin Scattering.- 5.2.1 Theoretical Considerations.- 5.2.2 Silver Halides.- 5.2.3 Other Superionic Conductors.- 5.3 Infrared Absorption and Frequency Dependent Conductivity.- 5.4 Conclusion.- References.- 6. Magnetic Resonance in Superionic Conductors.- 6.1 Theory of NMR Relaxation of and by Rapidly Diffusing Ions.- 6.1.1 General Correlation Functions and Interactions.- 6.1.2 Calculation of T1 and T2 from Correlation Functions.- 6.1.3 T1/T2 Ratio.- 6.1.4 Simple Random-Walk Values.- 6.1.5 Diffusion in Lower Dimensions.- 6.1.6 Effects of Correlated Hopping.- 6.2 Comparison with Experiment.- 6.2.1 Thermal Activation.- 6.2.2 Frequency Dependence.- 6.2.3 Prefactors.- 6.2.4 Coupling to Paramagnetic Impurities.- 6.3 Electron Paramagnetic Resonance.- 6.4 Structure Determination.- 6.5 Summary and Conclusions.- References.- 7. Phase Transitions in Ionic Conductors.- 7.1 Modern Theory of Phase Transitions.- 7.1.1 Landau Criteria.- 7.1.2 Renormalization Group.- 7.2 Models for Critical Behavior in Superionic Conductors.- 7.2.1 Quasi-Chemical Models.- 7.2.2 Lattice Gas Models.- 7.2.3 The Order Parameter for RbAg4I5.- 7.3 Critical Behavior of Physical Properties.- 7.3.1 Specific Heat.- 7.3.2 Ionic Conductivity.- 7.3.3 Acoustic Properties.- 7.3.4 Other Properties.- 7.4 Conclusions.- References.- 8. Continuous Stochastic Models.- 8.1 Models for Superionic Conductors.- 8.1.1 The Hamiltonian.- 8.1.2 Comparison of the Models from Microscopic Considerations.- 8.1.3 Correlation Functions.- 8.2 Continuous Models.- 8.2.1 Langevin Equation.- 8.2.2 Fokker-Planck Equation and Liouvillian.- 8.2.3 Continued-Fraction Expansion.- 8.2.4 Static Mobility, Diffusion Constant, dc Conductivity.- 8.2.5 Dynamic Mobility, ac Conductivity.- 8.2.6 Approximate Solutions and Similar Models.- 8.2.7 Dynamic Structure Factor for Jump Diffusion.- 8.2.8 Dynamic Structure Factor for Large Friction.- 8.2.9 Dynamic Structure Factor for General Friction.- 8.2.10 Light Scattering: Continuous and Continuum Models.- 8.2.11 Microscopic Foundation.- 8.3 Computer Simulations.- 8.4 Correlations Among the Mobile Ions.- References.- Additional References with Titles.