Modulation and incommensurability in a superionic conductor

The structure factor S(q) is calculated for the Frenkel-Kontorova model at high temperatures. Application to the 1-d ionic conductor K-Hollandite gives an explanation of diffuse X-ray scattering in terms of a modulation phenomenon. The positions of the diffuse sheets are predicted precisely from the stoichiometric composition. It is confirmed thereby that the mobile K⁺ ions behave like a chain with spacing b = 1/n where n is the concentration. The disorder is characterized as short-range crystalline order of wavelength b, competing with and modulated by the framework potential with a different period a.     

Temperature dependences of phonon and mobile-ion spectra in superionic conductor CuBr

The temperature dependence of far-infrared reflectivity spectra in sintered CuBr has been measured from 18 to 570 K. Phonon and mobile-ion parameters are evaluated by the fitting procedure with the factored form of the dispersion relation. A strong fourth order anharmonicity is assigned. Estimated values of optical dielectric constant and optical ionic mobility μ_op decrease with increasing temperature within a limited temperature region. For μ_op value, the effects of mobile ion scattering by optical phonons and of the expansion of interionic distance are discussed with respect to the phonon damping constant and the ionic character of the interionic force.     

Infrared spectroscopy of superionic conductor LiNaSO4: Vibrational modes and thermodynamics

Infrared active phonon spectra of lithium sodium sulphate, LiNaSO₄, were studied at temperatures between 20 K and 780 K. Dielectric constant [ε = ε′ + iε″] and energy loss function [− Im(1/ε)] were obtained from Kramers–Kronig analysis. Our IR data show a more complete set of vibrational modes than previous investigations. The IR data of LiNaSO₄ at 20 K are consistent with the P31c symmetry, indicating that LiNaSO₄ shows no structural phase transitions between 20 K and 300 K, in contrast to LiKSO₄. On heating from 20 K, phonon modes related to Li and Na vibrations show a dramatic line broadening and decrease in intensity. An extra mode is recorded near 380 cm^− 1 at 500 K. The absorption shows a systematic increase in intensity on further heating. These changes are attributed to anharmonic effects and Li diffusion or hopping. Dramatic spectral changes in the internal modes occur near 620 K on heating, suggesting the onset of the rotational disorder of SO₄ tetrahedra, but the Li atom spectrum shows weak response to the rotational disorder.     

Raman measurements of the superionic conductor AgI

Using the Raman technique, we have observed large abrupt reversible changes in the phonon spectrum at the transition temperature, T_c = 147°C, of the superionic conductor AgI. The defect nature of the high temperature phase completely breaks down the selection rules and allows the Raman measurements to give a measure of the frequency dependent conductivity, σ(ω), assuming a frequency independent matrix element. Similarities as well as differences in σ(ω) above and below T_c are shown.     

The phonon spectra of the superionic conductor KBiF4 (a CaF2 Analogue)

Theoretical calculations of the phonon infrared and Raman response in simple superionic conductors such as AgI, CuI, and CaF₂ types are based on two fundamental assumptions. First, most of the response can be understood in terms of a breakdown of the selection rules due to disorder (lack of translational symmetry) and second, harmonic lattice dynamics can be used with a good degree of accuracy. This is tested here experimentally in the superionic conductor K_1?xBi_1+xF_4+2x which has the CaF₂ structure (x=0.0 is analogous to 2CaF₂). By varying x we increase the disorder (via F-ion interstitials and vacancies) and measure broad temperature independent reduced Raman and infrared responses. The broad response is dependent on x in a manner consistent with the first assumption and the lack of temperature dependence is consistent with the second assumption. In order to understand the transverse optic vibrational frequencies (ω_TO) we have found that plots of ω_TO²vs. μ^-1 (reduced mass) are very helpful. The linearity of such plots, for example, for tetrahedrally bonded AgI, CuI, CuBr, CuCl (formal charge Z=1) and the difference of such results for similar materials but with formal charges of 2, 3, and 4 is surprising and not as yet understood. Other conclusions are discussed at the end of the paper.     

The Raman spectra of the superionic conductor CuI in its three phases

We report Raman measurements of the superionic conductor CuI in all three phases. We show that the major features of the spectra, particularly the highest temperature α'-phase, can be accounted for by simple lattice dynamics calculations if the defect nature of the phase is taken into account. Thus, while some of the more specialized ideas that have been proposed to explain these types of spectra are undoubtedly appropriate, the major features actually can be explained rather straightforwardly.     

Electrical conductivity and permittivity of the one-dimensional superionic conductor LiCuVO<Subscript>4</Subscript>

The electrical conductivity σ^a and permittivities ?^a, ?^b, and ?^c of a LiCuVO₄ single crystal have been measured along the a, b, and c crystallographic axes, respectively, in the temperature range 300–390 K at a frequency of 10³ Hz. The temperature dependences σ(T) and ?(T) were found to be typical for superionics.     

Intracellular potential relief and size effects in the lattice of a LaF3 superionic conductor

The potential relief in the lattice of a LaF₃ crystal is calculated by quantum-mechanical methods for clusters containing from 24 to 1200 ions. For the dielectric phase, formation energy E _a for defects of the vacancy-interstitial fluorine ion type and potential barrier E _d preventing the motion of fluorine ions are found to grow from minimal values E _a = 0.12 eV and E _d = 0.22 eV for a cluster of 24 ions to maximal values E _a = 0.16 eV and E _d = 0.26 eV for clusters of 576 and 1200 ions. The values of E _a and E _d obtained in quasi-mechanical calculations are in good agreement with those obtained from Raman and quasi-elastic light scattering data.     

129I-Mössbauer study of diffusion effects in the superionic conductor Ag3SI

The superionic conductor Ag₃SI was studied by¹²⁹I-Mössbauer spectroscopy in the rhombohedral γ-phase and in the cubic β-phase at temperatures between 4.2 K and 180 K. In the low-temperature γ-phase, one observes well below the γ-β phase transition at 157 K a motional-narrowing-like decrease of the electric-quadrupole interaction, roughly linear with temperature, which points to a diffusional motion of the Ag⁺ ions already in the γ-phase. Diffusional effects are also reflected by anomalous decrease of thef-factor in the same temperature region, which originates from a restricted short-range diffusional displacement of the iodide ions induced by the hopping Ag⁺ ions.     

Far-infrared absorption of the superionic conductor Li3N. temperature and isotope effects

The far-infrared absorption spectrum (20–250cm^–1) of the superionic conductor Li₃N —with⁶Li- and⁷Li-isotopes in the starting material—has been measured for different polarizations and temperatures (4–150 K). TheE c spectrum yields two lines near 80 and 140 cm^–1, which are not observed forE c. From the isotopic frequency ratio ( ₆/ ₇1.07) and from the comparison to lattice dynamics it is concluded that these lines are due to resonant modes, weakly coupled to the lattice. Measurements of the isotope effects on the dielectric properties (10 Hz to 1 MHz) establish that the local diffusive type motion in shallow potentials and the low lying resonant modes originate from the same defect system (including Li-ions in non-regular positions).     

Molecular dynamics simulation of the superionic conductor BaF2

Molecular dynamics simulations of the BaF₂ fluoride crystal were carried out over a wide range of temperatures in order to study structural and transport characteristics in the low-temperature, the high-temperature superionic, and the molten state. The experimental temperature dependence of the lattice constant was taken into account. A sharp change in total energy of the system in the vicinity of T=1200 K indicates a phase transition to the high-temperature state with a transition energy U=(18.8±0.2) kJ/mol which is close to the value of the latent heat Q=18.36 kJ/mol obtained experimentally at 1275 K. Calculation of the radial distribution functions g(r) shows that in the high-temperature superionic state the F^– sublattice is already disordered while the Ba²⁺ sublattice stays regularly ordered, which keeps the crystal in the solid state. In the low-temperature state both sublattices are regularly ordered, and in the molten state both sublattices are disordered. The calculated diffusion constants of F^– in the superionic state is about 10^–9m²/s which is a typical value for superionic conductors. The temperature dependence of the diffusion constant obeys the Arrhenius equation. Higher statistical moments of the trajectories are used to characterise the type of ion movement.     

Sodium nuclear magnetic resonance and dynamic second order quadrupole effects in the superionic conductor nazirpsio

The sodium nuclear magnetic resonance interaction in nazirpsio, Na_1+xZr₂P_3-xSi_xO₁₂ (x = 1.9) is dominated by dynamic second order quadrupole interactions. This has been determined by observing the temperature and frequency dependence of the dipolar-quadrupolar linewidth of the $\text{m=+}\text{1}\text{2}\text{?m=-}\text{1}\text{2}$ transition. This behaviour has been anticipated by Werbelow. The motional narrowing of the quadrupole interaction appears to be thermally activated process and agrees with a model of three dimensional diffusion of the sodium ions. The measured activation energies are consistent with those derived from conductivity measurements.     

A mechanism for ferrimagnetism and incommensurability in one-dimensional systems

In this paper I discuss a mechanism for ferrimagnetism in 1+1 dimensions. The mechanism is related to a special class of interactions described by operators with non-zero Lorentz spin. Such operators are present in such problems as the problem of tunneling between Luttinger liquids and the problem of frustrated spin ladder. Exact solutions are presented for a representative class of models possessing a continuous isotopic symmetry. It is shown that the interactions (i) dynamically generate static oscillations with the wave vector dependent on the coupling constant, (ii) give rise to spontaneous breaking of this symmetry at T=0 accompanied by generation of the magnetic moment and appearance of gapless modes with a non-relativistic (ferromagnetic) dispersion E∼k², (iii) generate massive (roton) modes.     

Interlayer vacancy effects on the phonon modes in AB stacked bilayer graphene nanoribbon

We explore the effects of interlayer vacancy defects on the vibrational properties of Bernal (AB) stacking bilayer armchair graphene nanoribbons (BiAGNRs) using the forced vibrational method. It is observed that the Raman active longitudinal optical (LO) phonon of BiAGNR is shifted downward with the decrease of the ribbon width and an increase of the vacancy concentrations. We find that vacancies induce some new peaks in the low frequency regime of the phonon density of states. Our calculated typical mode patterns elucidate that the localized transverse optical phonon at the K-point is shifted towards the defect sites from the edges with increased vacancy concentrations. In addition, the impact of defect induced phonon modes on the specific heat capacity and thermal conductivity of BiAGNRs are discussed. These results present a new way of understanding the heat dissipation phenomena of graphene-based high-performance nanodevices and to clarify the Raman and the experiments related to the phonon properties.     

The properties of one-dimensional quasiperiodic lattice's phonon spectrum

A numerical method with renormalization group transformation is used to study the scaling properties of phonon spectrum and its relevant state of one-dimensional quasiperiodic lattice which is constructed by reduced map. We find that the phonon spectrum at finite gaps' edges in the binary chain Fibonacci model is a Cantor-like set spectrum. The spectrum is singularly continuous and the state is a critical state.     

The influence of structural disorder on the phonon modes in zinc oxide

Undoped zinc oxide thin films and nanostructured layers were grown by pulsed laser deposition on different substrates. They were characterized by scanning electron microscopy and Raman backscattering spectroscopy. Larger substrate mismatch leads to higher structural disorder in the thin films. Simultaneously, the intensity of the phonon mode at 580 cm⁻¹ increases. However, for the nanostructured layers it remains constant. These observations are discussed in terms of the disorder activation of forbidden Raman modes.     

The absence of a measurable hall effect in the superionic conductor RbAg4I5

Thin film samples of RbAg₄I₅ have been prepared by evaporation and several of their electrical properties have been determined. The behavior of the conductivity of these films is identical to that found in bulk RbAg₄I₅. An attempt to reproduce the Hall effect results of Kaneda and Mizuki was unsuccessful, and we conclude that the Hall mobility of silver ions in this material is less than 2 × 10^-3cm²/V·sec.     

Microwave conductivity evidence for order-disorder transition in the superionic conductor β-eucryptite

The impedance of LiAlSiO₄ (β-eucryptite) at 9 GHz shows a marked decrease in activation energy as the temperature is raised above 450°C, where X-ray data indicate an order-disorder transition.     

Ab initio nonequilibrium molecular dynamics in the solid superionic conductor LiBH4

The color-diffusion algorithm is applied to ab initio molecular dynamics simulation of hexagonal LiBH(4) to determine the lithium diffusion coefficient and diffusion mechanisms. Even in the best solid lithium ion conductors, the time scale of ion diffusion is too long to be readily accessible by ab initio molecular dynamics at a reasonable computational cost. In our nonequilibrium method, rare events are accelerated by the application of an artificial external field acting on the mobile species; the system response to this perturbation is accurately described in the framework of linear response theory and is directly related to the diffusion coefficient, thus resulting in a controllable approximation. The calculated lithium ionic conductivity of LiBH(4) closely matches published measurements, and the diffusion mechanism can be elucidated directly from the generated trajectory.