Abstract
A Hamiltonian is constructed for superionic conductors taking into account the mutual interactions and transports of the mobile ions, and their interactions with the phonons of the cage. Under special conditions we recover the phenomenological results of Rice et al. and Huberman in regard to phase transitions. Two transition points are shown to be possible in the presence of the mutual interactions of cations (as observed in RbAg4I5 and CuBr). Structural phase transitions involving the cage when exist are found to occur at the same temperature at which the conductivity becomes critical, in agreement with experiments. Dynamical aspects of our Hamiltonian are also discussed. The collective modes of the phonon-cation system are calculated and used to explain the abrupt disappearance of certain modes above the critical temperature as observed in the Raman spectra of RbAg4I5, KAg4I5 and AgI. Our theory does contain the possibility that there is no soft mode with nonzero frequency, in accordance with the existing experimental situation. Our Hamiltonian is compared to others. The similarities between superionic conductors and other systems (Hubbard model, ferroelectrics, Jahn-Teller systems, molecular crystals) are emphasized.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Mahan, G.D., Roth, L.R. (eds.): Superionic Conductors. New York: Plenum Press 1976; Funke, K.: Prog. Solid State Chem.11, 345 (1976); van Gool, W.: Fast Ion Transport in Solids. Amsterdam: North-Holland 1973
Proceedings of International Conference on Lattice Dynamics, Paris 1977, Sept. 5–9
Burns, G., Dacol, F.H., Shafer, M.W.: Solid State Commun.19, 287 (1976)
Burns, G., Dacol, F.H., Shafer, M.W.: Solid State Commun.19, 291 (1976); Phys. Rev. B16, 1416 (1977)
Rice, M.J., Strässler, S., Toombs, G.A.: Phys. Rev. Lett.32, 596 (1974) Huberman, B.A.: Phys. Rev. Lett.32, 1000 (1974)
Rice, M.J., Roth, W.L.: J. Solid State Chem.4, 294 (1972) Huberman, B.A., Sen, P.N.: Phys. Rev. Lett.33, 1379 (1974) Sato, H., Kikuchi, R.: J. Chem. Phys.55, 677 (1971)
Brüesch, P., Strässler, S., Zeller, H.R.: Phys. Stat. Solidi (a)31, 217 (1975) Brüesch, P., Pietronero, L., Strässler, S., Zeller, H.R.: Phys. Rev. B15, 4631 (1977) Fulde, P., Pietronero, L., Schneider, W.R., Strässler, S.: Phys. Rev. Lett.35, 1776 (1975) Dieterich, W., Peschel, I., Schneider, W.R.: Z. Physik B27, 177 (1977)
Schommers, W.: Phys. Rev. Lett.38, 1536 (1977)
Zeyher, R.: Theory of Correlation Functions in Superionic Conductors, in Ref. 2
Hinkelmann, H., Huberman, B.A.: Solid State Commun.19, 365 (1976) Hinkelmann, H.: Solid State Commun.21, 975 (1977)
Pardee, W.J., Mahan, G.D.: J. Solid State Chem.15, 310 (1975)
Mahan, G.D.: Phys. Rev. B14, 780 (1976)
Salamon, M.B.: Phys. Rev. B15, 2236 (1977)
Girvin, S.M., Mahan, G.D.: Solid State Commun.23, 629 (1977)
Lam, L.: to be published
Pines, D.: Elementary Excitations in Solids. Reading, Mass.: Benjamin 1964
Michel, K.H., Naudts, J.: Phys. Rev. Lett.39, 212 (1977); J. Chem. Phys.67, 547 (1977)
Kobayashi, K.K.: J. Phys. Soc. Japan24, 497 (1968)
Hubbard, J.: Proc. Roy. Soc. (London) A276, 238 (1964)
Lam, L., Bunde, A.: Microscopic Theory of Superionic Conductors, in Ref. 2
Mukamel, D., Blume, M.: Phys. Rev. A10, 610 (1974)
Lajzerowicz, J., Sivardiere, J.: Phys. Rev. A11, 2079 (1975)
Chestnut, D.B.: J. Chem. Phys.40, 405 (1964)
Zhu Yong, Zhang Dao-fan, Cheng Xi-min: Acta Physica Sinica26, 115 (1977)
Remoissenet, M., Garandet, J., Arend, H.: Mat. Res. Bull.10, 181 (1975)
Shapiro, S.M., Semmingsen, D., Salamon, M.: Neutron Scattering Study of the Solid Electrolyte: RbAg4I5, in Ref. 2
Blinc, R., Zeks, B.: Ad. in Phys.21, 693 (1972)
Gehring, G.A., Gehring, K.A.: Rep. Prog. Phys.38, 1 (1975)
Rice, M.J.: Phys. Rev. Lett.37, 36 (1976)
Browall, K.W., Kasper, J.S., Wiedemeier, H.: J. Solid State Chem.10, 20 (1974);15, 54 (1975)
Blinc, R., Pintar, M., Zupancic, I.: J. Phys. Chem. Solids28, 405 (1967) Blinc, R., Cevc, P., Shara, M.: Phys. Rev.159, 411 (1967)
Strom, U., Taylor, P.C., Bishop, S.G., Reineke, T.L., Ngai, K.L.: Phys. Rev. B13, 3329 (1976) McWhan, D.B., Allen, S.J., Remeika, J.P., Dernier, P.D.: Phys. Rev. Lett.35, 953 (1975)
Schneider, W.R., Strässler, S.: Z. Physik B27, 357 (1977)
Huberman, B.A., Martin, R.M.: Phys. Rev. B13, 1498 (1976)
Huberman, B.A., Martin, R.M.: Phys. Rev. Lett.39, 478 (1977)
Sears, V.F.: Proc. Phys. Soc. (London)84, 951 (1964) Elliott, R.J., Parkinson, J.B.: Proc. Phys. Soc. (London)92, 1024 (1967)
Moore, M.A., Williams, H.C.W.L.: J. Phys. C5, 3222 (1972)
Lam, L., Bunde, A.: J. Phys. C10, 693 (1977) Bunde, A., Lam, L.: Phys. Lett.58A, 234 (1976)
Pytte, E.: Phys. Rev. B8, 3954 (1973)
Yamada, Y., Takatera, Huber, D.: J. Phys. Soc. Japan36, 641 (1974)
Thomas, H., Müller, K.A.: Phys. Rev. Lett.28, 820 (1972)
Eckold, G., Funke, K., Kalus, J., Lechner, R.E.: J. Phys. Chem. Solids37, 1097 (1976)
Michel, K.H., Naudts, J.: Dynamics of Translations and Rotations in Molecular Crystals, preprint 1977
Bunde, A., Lam, L.: Statistical Mechanics of Superionic Conductors, in Proceeding of 13th Conference on Statistical Physics, Haifa, August 24–30, 1977
Bunde, A.: Z. Physik B22, 381 (1975)
Blinc, R., Zeks, B.: Adv. in Phys.91, 693 (1972)
Brinkmann, D., Freudenreich, W.: Solid State Commun. to be publ.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lam, L., Bunde, A. Phase transitions and dynamics of superionic conductors. Z Physik B 30, 65–78 (1978). https://doi.org/10.1007/BF01323670
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01323670