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.     

Brillouin scattering from thermal fluctuations in superionic conductors

We present a theory of light scattering from long-wavelength thermal fluctuations in superionic conductors using a model of a crystalline cage immersed in a viscous liquid. The local or internal degrees of freedom of the liquid are taken into account by the addition of a frequency dependent contribution to the viscosity. The differences between our theory and that of Huberman and Martin are discussed.     

Brillouin scattering from thermal fluctuations in superionic conductors

We show how the effect of the macroscopic electric field on the coupled cage-liquid system may be included in the theory presented in our recently published article of the same title.     

Liquid-like Raman scattering by superionic materials

The Raman spectrum of a superionic conductor, α-AgI, is compared with the spectra of the melt of AgC$\text{l}$ and AgBr, in order to determine the responsible Raman processes. We conclude that because of the strong anharmonicity and high translational disorder in superionic conductors, spectra analyses based on the concept of harmonic lattice are unsuitable. A dynamical picture of ions similar to that of liquids appears to be more useful than the phonon concepts.     

Correlation between the quasi-elastic light scattering and the ionic-conductivity in superionic conductors

The quasi-elastic light scattering of the superionic conductors, (ZrO₂)_1?x (YO_1.5)_x (x = 0, 0.18, 0.33) has been studied in the region of frequency shift below 2.5 cm^-1. The quasi-elastic scattering far more intense than the Brillouin scattering has been found for a sample with x = 0.18. From the x-dependence of the intensity, it is shown that the ionic diffusion is responsible for the quasi-elastic scattering. The temperature variations of the intensity and the spectral shapes are interpreted in accordance with the macroscopic conductivity data, in terms of a model in which the barrier height distribution is taken into account.     

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.     

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.     

A hard sphere fluid model for superionic conductors

We develop a theory for the mobile constituent of a superionic conductor using the Ornstein-Zernike integral equation for the pair correlation function of an inhomogeneous fluid. We solve this equation in the Percus-Yevick approximation using a simple decoupling procedure and hard core potentials. Comparison is made with molecular dynamics calculations on α-AgI.     

Raman results in the Na β- and β″-gallate superionic conductors

Raman results of two superionic conducting materials, Na β-and β″-gallate, are reported. The spectra divide clearly into a high energy part, above 160 cm^-1, and a low energy part that varies as Na is replaced with K or Rb. The low energy line, associated with the so called attempt frequency, occurs at 57 and 69 cm^-1 for Na β- and β″-gallate respectively. Rather surprisingly, the lines are much narrower than observed in the aluminate analogues. We measure 5.6 and 3.0 cm^-1 respectively. The high energy lines are very similar for the β- and β″-gallate crystals.     

Raman scattering in one-dimensional ionic conductors Rb-priderites

Raman spectra of single crystals of RbAl and RbMg-priderites, which are known to be one-dimensional ionic conductors, have been measured and analyzed. In addition to the spectra due mainly to the vibrations of Ti(Al)-O or Ti(Mg)-O frameworks observed in the frequency region above 100 cm^?1, the Raman bands, which can be assigned to the vibration modes of Rb⁺ ions, have been observed in the frequency region below 100 cm^?1. Raman spectra of the solid solutions (Rb, K)-Al priderites have also been studied.     

Low-frequency Raman scattering in superionic Li2SO4

The low-frequency Raman spectra of fcc Li₂SO₄ are found to contain a broad and a narrow component centered at zero frequency. The narrow component is identified with the relaxation mode due to the time of flight of Li⁺.     

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.     

Unresolved correlation time spectra and interpretation of NMR relaxation time data for superionic conductors

Problems in relating the results of NMR relaxation time measurements to the results of bulk conductivity/diffusion studies for superionics have been discussed in a number of ways, such as their being a result of lack of knowledge of the appropriate motional correlation function. It is argued that, in the case of hydrated proton conductors at least, the problem is more fundamental. When previously unrecognized temperature-dependent correlation time spectra are present, these cannot be resolved in reduction of relaxation time data and information on any single contributory motion is not simply available.     

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.     

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.     

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.     

Comparison of the Raman spectra of superionic conductors AgI and RbAg4I5

The Raman spectra of superionic conductors AgI and RbAg₄I₅ have been measured in both cation disordered and normal phases. Similarities in the observed spectra of these two materials are discussed. The frequency dependent conductivity is obtained from the spectra and compared to infrared results. Several possible interpretations of the observed spectra are considered.