Hydrodynamics of superionic conductors

Using the Mori method we present a rigorous hydrodynamic theory for the collective excitations in superionic conductors at low frequencies and long wavelengths. By means of static and dynamic linear response theory all microscopic quantities of the theory are expressed as derivatives of the free energy or as transport coefficients. Explicit expressions for the dispersion and the damping of the modes and for the density correlation function are worked out for high-symmetry directions and numerically evaluated for-AgI. In particular we show that the two non-propagating modes can give rise to a small central component (width~k ², constant intensity) and a broad central component (constant width fork0, intensity ~k ²) in scattering spectra. Extrapolating our theory to larger wave vectors we offer a new explanation for the broad central component found recently in neutron scattering spectra of-AgI.     

Sedimentation in superionic conductors

The homogeneous distribution of mobile atoms in a simple of a nonstoichiometric superionic conductor with mixed (ionic and electronic) conductivity is changed when the sample is placed in a centrifugal field. The steepness of the resulting equilibrium gradient and the rate at which the equilibrium is attained depend upon the reduced mass of atoms and their ambipolar diffusivity.     

Dynamical structure of superionic conductors

Ionic motion is analysed of a model system for α-AgI which has ionic potentials consisting of only a Coulombic and a soft-core repulsive terms. A tetrahedron (abbreviated as TH) in the anion bcc sublattice is investigated from a dynamical point of view. The residence time of a cation in a TH is rigorously evaluated. Dynamical correlation between anions and cations is examined by the observation of dynamical behaviors of anions forming a TH and a cation. A mechanism of cation diffusion will be suggested.     

Collective motion in superionic conductors

A theory of collective motion in superionic conductors is described by the use of a model of a crystalline cage immersed in a viscous liquid. The viscoelastic force and the interionic Coulomb force are considered as the cage—liquid interaction. The density-correlation functions and the frequency-dependent conductivity are calculated. The calculated conductivities for α-AgI are in good agreement with experiments. It is concluded that the structure in a.c. conductivity experimentally observed for α-AgI at frequencies below 10 cm^-1 can be ascribed to acoustic phonons.     

Particle correlation in superionic conductors

A molecular-dynamics method is applied to study the particle correlation in superionic conductor α-AgI. It is found that there is a close connection between the particle correlation λ_i,j (i,j=I or Ag) and the radial distribution function. The values of λ_II and λ_IAg at the nearest neighbor site are below 0.3. The values of λ_AgAg at the nearest neighbor site and λ_II at the next nearest neighbor site are about 1/2 ≈ 1/3 of it of λ_II (and λ_IAg) at the nearest neighbor site.     

Thermal conductivity in superionic conductors

The contribution of mobile ions to the thermal conductivity in superionic conductors is investigated by making use of the lattice gas model with a hopping term. The thermal conductivity is obtained as a function of an ion concentration and a repulsive interaction energy between the nearest neighbors. It is shown that the contribution of mobile ions to the thermal conductivity is of an Arrhenius type in the usual temperature region in which measurements are conducted.     

Neutron scattering in superionic conductors

The coherent dynamical structure factor S(q,ω) of one-dimensional superionic conductors is studied in a model of Brownian particles with harmonic interactions moving in a periodic potential. We present results for the q-dependence of the halfwidth of the quasielastic peak, which reflects the commensurability ratios of the periodic potential and the molten sublattice. Furthermore the influence of the periodic potential on the collective excitations of the mobile ions is discussed.     

Theoretical models for superionic conductors

The present theoretical understanding of various properties of superionic conductors is reviewed. Emphasis is put on their treatment as classical many-particle systems and on the analysis of their dynamic behaviour. Different kinds of approaches pertaining to the low frequency dynamics are considered in detail. They include stochastic models, like hopping or Fokker-Planck models as well as a hydrodynamic theory. The high frequency (phonon-) dynamics and the information obtained from computer simulations is also analysed. As far as possible, the relevance of the different approaches with respect to experiments on specific materials is discussed. Possible directions for future investigations are outlined.     

Lattice dynamics of simple superionic conductors

Using harmonic lattice dynamics we are able to calculate 1st order Raman results in the superionic conducting phases of AgI and CuI. We find that much of the calculated response is allowed because of the structural disorder that occurs in these materials. The evidence for the 1st order nature of the experimental results is given and the calculation is compared to experiment. It is also pointed out that Raman experiments (and calculations) can be performed on oriented single crystals of these disordered cubic materials yielding response that transforms as the A, E, and T irreducible representations of the cubic point groups.     

On the thermopower of superionic conductors

We investigate the thermoelectric power of a superionic conductor within the Brownian particle model. The dependence on temperature and friction is calculated numerically for the one-dimensional case. The results are compared to those of other models and approaches.     

Millimeterwave spectra of some superionic conductors

Using a quasi-optical continuously tunable spectrometer in the frequency range of 40–90 GHz (=7.5-3.3 mm) the absorption spectra of the superionic conductors Na-alumina, Ag-alumina,-AgI and CuTeBr have been measured at various temperatures. In the measured spectral range all the materials showed a monotonic increase in the absorption as a function of frequency. These results are discussed in the light of existing theoretical models.Alfred P. Sloan Foundation Fellow     

Long-wavelength density fluctuations in superionic conductors

In order to study the long-wavelength collective motions in superionic conductors we propose a continuum model in which the relative motion of the two ionic components is governed by a viscoelastic force and the interionic Coulomb forces. We predict that under the influence of the Coulomb forces the diffusion mode is converted into a relaxation mode which has a finite frequency fork0.     

Ternary superionic conductors: Structural aspects

Summary A survey of the present state of research (both experimental and theoretical) on the structural aspects of ternary superionic conductors is presented. The discussion concentrates on the β- and β″ and the AgI-based conductors. Paper presented at the ?V International Conference on Ternary and Multinary Compounds?, held in Cagliari, September 14–16, 1982.     

Ionic plasma oscillations in superionic conductors

Some superionic conductors behave as if their charge was carried by nearly free charged particles. If this is the case, these free particles should undergo plasma oscillations. The plasma oscillations may already have been observed in superionic AgI and CuI. Similar oscillations might also be observable in ionic liquids such as melted AgI.     

Nanotechnology studies of layered fluoride superionic conductors

A computer simulation by a molecular dynamics method at constant volume has been performed on a model material that is composed of accumulating two different fluoride conductors: ⋯BaF₂–CaF₂–BaF₂–CaF₂⋯. The average value of CaF₂ and BaF₂ for the lattice constant of the new layered material is prepared to hold its mechanical strength. The CaF₂ region is compressed and the BaF₂ region is stretched along the c axis (z axis) in the thermal equilibrium state. It is obtained that the diffusion coefficient and ionic conductivity of F− ions in the layered fluoride conductors increases with decreasing periods, more specifically with the number of interfaces. The layer depth dependence on transport coefficients approximately coincides with the experiment.     

Phase transitions and dynamics of superionic conductors

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.     

The role of disorder in superionic conductors

This paper illustrates from a phenomenological point of view why the study of superionic conductors is essentially a study of disorders. Crystals that are good ionic conductors lack a long-range order in their mobile-ion sublattice. Moreover, low-temperature anomalies typical of amorphous materials appear to be rather common in superionic crystals. In several solid electrolytes the coupling between “disorder modes” typical of glasses and translational degrees of freedom of the ions can be shown to enhance ionic diffusion. The observed, or expected, properties of these superionic conductors are briefly discussed. The hypothesis that disorder may often play a dynamic role in ion transport in solids suggests ways to synthesize materials of technological interest.     

Specific heat and thermal conductivity of superionic conductors in the superionic phase

The temperature dependences of the specific heat and the thermal conductivity of crystalline superionic conductors LnF₃ (Ln = La, Ce, Pr), Li₂B₄O₇ and α-LiIO₃ in the superionic phase have been investigated experimentally. The specific heat C _p and the thermal conductivity K are observed to increase monotonically over a wide range of temperatures above the Debye temperature Θ_D. This increase is attributed to the relaxational interaction of high-frequency phonons with two-level systems. Fiz. Tverd. Tela (St. Petersburg) 39, 1548–1553 (September 1997)