Activation energy of ion motion in the nanodimensional lattice of LaF<Subscript>3</Subscript> superionic conductor

Quantum chemistry calculations of the intracrystalline potential relief in the nanolattice of LaF₃ superionic crystal that contains 1200 ions and measures 3.5 × 2.0 × 2.2 nm along the x, y, and z axis, respectively, have been performed. Using the MOPAC 2012 program package, the potential relief profile has been simulated in the central part of the nanolattice for an elementary act of disordering in the lowest melting sublattice of F₁ ions. It has been found that the height E _m of barriers that prevent the motion of F₁ in the dielectric phase of LaF₃ crystal equals 0.37 eV and decreases to 0.15 eV in the superionic state. In addition, activation energy E _a of F₁ sublattice disordering in the dielectric and superionic states is equal to 0.16 and 0.04 eV, respectively. The profiles of the potential relief calculated on the xy and xz faces of the LaF₃ 3D nanolattice for the case when an F₁ ion moves along the x crystal axis in the dielectric state are presented. The corresponding energy barriers are 1.5–2.0 times lower than those at the center of the LaF₃ nanlattice.     

Self-organization of particles in the superionic phase of lanthanum trifluoride

When a laser beam (λ = 396.3 nm) propagates through a nonuniformly heated superionic LaF₃ crystal in the direction of lattice constant c, alternating bright and dark fringes arise on the screen. The fringes run from the warmer face to the colder one. The number and width of the fringes are found to depend on the temperature gradient in the crystal: the smaller (greater) the temperature difference between the faces, the smaller (greater) the number of moving fringes. It is the author’s opinion that this effect is due to the wave transfer of applied heat and reflects the self-organization and collective displacements of the ions of the “quasi-liquid” sublattice in a nonuniform temperature field. A qualitative model of heat wave transfer in the LaF₃ superionic phase is suggested.     

Cooperative interactions in the lattice of LaF3-Type superionic crystals

The mechanism and energy parameters of cooperative interactions between point defects, vacancies, and interstitial ions, in the lattice of LaF3-type superionic trifluorides are studied. The mean energy of interaction between two pairs of the defects is determined (λ = 0.032 eV) in the dipole approximation. It is shown that cooperative interactions in the “quasi-liquid” lattice of LaF₃ decrease the defect formation energy down to values on the order of ≈kT.     

Ferroelectric properties of the LaF<Subscript>3</Subscript> superionic conductor nanocluster

We report on the results of quantum-chemical calculation of the lattice energy in a LaF₃ superionic crystal of size 3.5 × 2.0 × 2.2 nm that contains 1200 ions with different structural configurations of fluorine ions. It has been shown that the most energetically disadvantageous configurations of fluorine ions correspond to arbitrarily (randomly) disordered nanolattices in the case when fluorine ions of all three types (F₁, F₂, and F₃) participate in their melting. It has been found that unidirectionally disordered nanolattices that contain a large number of defect dipoles of the anion vacancy–interstitial fluorine atom type with parallel dipole moments is energetically more advantageous than nanolattices with randomly disordered structure. It has been proposed that the electric field produced by a large number of parallel defect dipoles is formed in disordered LaF₃ nanolattices even at room temperatures. This makes it possible to classify microscopically small LaF₃ crystallites as promising functional materials that can be used, e.g., in modern solid-state technologies.     

Cation disordering in Ag2HgI4 and Cu2HgI4

The cation order-disorder transitions in Ag₂HgI₄ and Cu₂HgI₄ are first order. This is unusual, since in other superionic conductors the cation disordering is gradual with temperature if there is no structural phase transition. These two materials are also unique in that they have two disordering cations rather than one. A study of a two species lattice gas model shows that this extra degree of freedom is responsible for the first order nature of this transition on the fcc lattice.     

Defect interaction and solid electrolyte transition in AgI-based materials

The first-order phase transition that leads to the superionic phase in AgI-based materials is studied by dc-conductivity measurements and a free energy model. By properly adjusting the model parameters, an abrupt change of disordering concentration, Δη?, is predicted at a transition temperature, T_t. The temperature dependence of the dc-conductivity, σ(T), is well fitted to the η?(T) equilibrium configuration obtained from the trial free energy function. The reported comparative study was done using an AgI–KI modified sample. The model also predicts a transition temperature, T_c for a continuous phase transition (Δη? = 0).     

Phases and phase transitions of the superionic conductor Ag2HgI4 in the temperature range between 4.2 K and 370 K detected by diffuse reflectance spectrometry

Diffuse reflectance spectra of the superionic conductor Ag₂HgI₄ powder were recorded between 4.2 K and 370 K and transformed into the Kubelka-Munk function. Six parameters of the spectral band of this function, related to the absorption band of the particular phase, were considered. The graph representing the logarithm of the integrated Kubelka-Munk spectral band versus inverse temperature was most informative. The Arrhenius behaviour of this function, in a temperature interval, was related to the existence of a phase with constant lattice structure. The non-Arrhenius behaviour was tentatively attributed to a temperature sensitive phase. Thus fifteen different crystalline phases were found, only four of them having been, up to now, unquestionably admitted. In particular, evidence was given for the existence of two superionically conducting phases and two room temperature phases. All the graphs representing the chosen parameters versus inverse temperature pointed to the existence of two separate sequences of phases: one generated by cooling gradually the β-phase, stable at room temperature, to low temperatures (β sequence), the other by heating the β-phase above the σ → β (T)₊ transition point and cooling gradually the formed α'′-phase (α′ sequence). The concept of photon absorption thermal activation energy was introduced. Its largest value was of the order of magnitude of the electrical conductivity thermal activation energy of Ag₂HgI₄. Estimates of energy band gaps and their evolution with temperature were made. It is suggested that the polymorphism of the substance is the main reason for the hysteresis loop in the superionic conductivity transition region. The low temperature phases manifested luminescence caused by exciton decay.     

Oxygen diffusion in uranium dioxide in the temperature range of phase transitions

The structure of and oxygen diffusion in UO₂ are studied by the molecular dynamics method in the range of transition to the superionic state (melting of the oxygen sublattice) and near the melting point of UO₂. The temperature dependence of the diffusion coefficient of a doubly charged oxygen ion in UO₂ is constructed. In the crystalline state at temperatures between 1800 and 2600 K, this dependence is described by an exponential dependence with a diffusion activation energy of 2.6±0.2 eV. In the superionic state (2600–3100 K), the activation energy of diffusion of an oxygen anion decreases to 1.88±0.13 eV. In melt (3100–3600 K), the exponential dependence of the diffusion coefficient of O^2- persists but the activation energy of diffusion decreases still further, to 0.8±0.2 eV. Our experimental results agree (within the limits of experimental error) with data on oxygen diffusion in the crystalline phase obtained by other researchers.     

A model for the heat of transport in ionic conductors

The ion flow caused by a temperature gradient originates the ionic thermopower which is quantified by the heat of transport. Experimentally, it is known that in superionic conductors, the heat of transport Q is nearly equal to the activation energy for ion transport E_a. In the present paper, a model for the heat of transport in ionic conductors has been proposed based on a lattice dynamical theory of diffusion. We have shown that the relationship between Q and E_a is determined by the participation degree of different phonon modes, in particular the short wavelength phonons to the atomic jump processes. The implication of this finding to the transport properties of superionic conductors has been discussed, and it is suggested that the degree of the collective motion in ionic conductors increases with the increase in Q/E_a. The model predicts that good ionic conductors will show large value of Q/E_a. The importance of the acoustic phonons in the ion transport processes has been also pointed out.     

129I-Mössbaurer study of superionic glasses AgI−Sb2S3: Local structure and diffusion effects

The local environment and the short-range diffusional displacements of the iodide ions induced by the hoppingAg ⁺ ions have been studied inAgI?Sb ₂ S ₃ superionic glasses using¹²⁹ I-Mössbauer spectroscopy in the temperature range 4.2 K to 240 K. It was found that the nearest neighbours of the iodide ions are only silver ions; the local environment of iodide is therefore close to that in the crystalline superionic conductorAg ₃ SI. Diffusion effects are observed above 140 K by characteristic changes in isomer shift, electric-quadrupole interaction and recoil-free fraction. The derived activation energy for theAg ⁺ ion local hopping is 2 times larger than that of crystallineAg ₃ SI.     

Absorption spectrum and excitons in thin films of the solid electrolyte RbCu4Cl3I2

We have investigated the absorption spectrum of thin films of the superionic conductor RbCu₄Cl₃I₂ synthesized on NaCl crystalline substrates. It is shown that the electron and exciton excitations in the energy interval 3–6 eV are associated with optical transitions in the CuHal sublattice, and the edge of the fundamental band is controlled by optical transitions in the Cu(II)Hal sublattice. It is found that the large band gap of this compound (E _g =3.86 eV) in comparison with those of CuCl and CuI is a result of the small number of Cu ions in the second coordination sphere. The temperature dependence of the spectral position and half-width of the low-temperature exciton band reveals features associated with the phase transitions γ→β (T _c1=170 K) and β→α (T _c2=220 K) and with disordering of the cation sublattice attendant to the transition to the superionic state. Fiz. Tverd. Tela (St. Petersburg) 40, 1022–1026 (June 1998)     

The ionic Seebeck effect and heat of cation transfer in Cu2−δSe superionic conductors

The ionic Seebeck coefficients of Cu_2?δSe superionic conductors are measured in the temperature range 340–380°C. The data obtained are used to determine the heat of transfer Q _i of copper ions as a function of the degree of nonstoichiometry and the temperature. The heat of transfer of copper cations increases from 0.19 to 0.22 eV as the degree of nonstoichiometry δ increases from 0.015 to 0.050. It is noted that the heat of transfer Q _i tends to increase with an increase in the temperature. Assumptions regarding the specific features of the cation diffusion in the Cu_2?δSe superionic conductors are made from the observed closeness of the heat of transfer and the activation energy for ionic conduction.     

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.     

Photoluminescence study of disordering in the cation sublattice of Cu2ZnSnS4

In this study we investigated the influence of the degree of disordering in the cation sublattice on low temperature photoluminescence (PL) properties of Cu₂ZnSnS₄ (CZTS) polycrystals. The degree of disordering was changed by using different cooling rates after post-annealing at elevated temperatures. The results suggest that in the case of higher degree of cation sublattice disorder radiative recombination involving defect clusters dominates at T = 10 K. These defect clusters induce local band gap energy decrease in CZTS. The concentration of defect clusters can be reduced by giving more time for establishing ordering in the crystal lattice. As a result, radiative recombination mechanism changes and band-to-impurity recombination involving deep acceptor defect with ionization energy of about 200 meV starts to dominate in the low temperature PL spectra of CZTS polycrystals.     

Molecular dynamics simulation of the surface properties of nanocrystalline uranium dioxide

The molecular dynamics method is used to simulate the nanosized UO₂ crystals. The phase-transition temperatures are calculated for the nanosized crystals of the uranium dioxide. It is demonstrated that the melting point and the temperature of the transition to the superionic state (melting of the anion sublattice) of the crystals decrease with decreasing sizes. In particular, melting point (T _m ～ 2300 K) for the cubic nanocrystal with a size of 3.3 nm is lower than the melting point of the single crystal by almost 1000 K. The calculated surface energies are in agreement with the experimental results. The dependence of the surface energy on the size of the UO₂ nanocrystals is obtained. The effect of the nanocrystal temperature on the surface energy is studied. The temperature dependence of the thickness of the melt layer is obtained in the framework of the model of the heterogeneous melting. The parameters and dependences can be used for the further analysis of the microstructure properties of nuclear fuel in working systems.     

Fano interference between the E2 (17 cm−1) optical mode and one-phonon continuum scattering from β-AgI

Resonant interference between the E₂ (17 cm^?1) optical mode and the continuum of one-phonon partial density of states has been observed in β-AgI, and has been shown to follow Fano formalism. The temperature dependence of the coupling parameter q shows a substantial variation as T approaches T_c. A qualitative explanation of such behaviour is made in terms of phonon assisted activation of Frenkel defects, which increases more rapidly as the superionic transition temperature is approached.     

Impurity effect on low-temperature polarisation of the charge-density-waves in o-TaS3

The temperature dependence of the low-temperature dielectric response is studied in o-TaS₃ samples doped by Nb, Se, and Ni and for nominally pure ones. It is found that the low-temperature dielectric constant depends anomalously on doping and is higher for doped crystals, whereas the temperature dependence of the characteristic time of all samples follows the activation law with nearly the same activation energy ∼400 K (T > 20 K). The observed behaviour is inconsistent with all available explanations of the low-temperature dielectric anomaly.     

Investigation of ionic conduction in the mixed AgI-PbI2 system

Study of ionic conductivity in AgI-PbI₂ system has a function of composition and temperature shows that PbI₂ has a definite role in the process of superionic phase transition. It has been found that at 80 mole % of AgI, superionic phase transition temperature passes through a minimum value of as low as 105°C. The maximum conductivity (at room temperature) is also obtained in this region. The results are discussed qualitatively in terms of a lattice loosening model.     

Ionic conductivity in the single crystals of non-stoichiometric fluorite phases M1−xRxF2+x (M=Ca,Sr, Ba; R=Y,La-Lu)

The ionic conductivity has been measured of single crystals of rare earth fluoride solid solutions in Ca, Sr and Ba fluorides described by the formula M_1?xR_xF_2+x (M=Ca, Sr, Ba; R=Y, La-Lu). The measurements have been done using dc and ac within the temperature range 300–850 K. With the increase of RF₃ concentration up to x=0.05–0.15 (in different systems) conductivity steeply increases. With the further concentration growth the conductivity increases only slightly, reaching saturation value for the solid solution Ba_1?xR_xF_2+x. The dependence of solid solution conductivity on the chemical composition has been studied for isoconcentrates M_0.9R_0.1F_2.1. It has been established that in CaF_2- based series the crystals with R=Gd, Tb possess maximum conductivity and minimum activation energy. For SrF₂ and BaF₂-based series the highest conductivity was observed for crystals containing LaF₃. It has been established that for all the crystals, independent of the chemical composition and defect concentration, the conductivity logarithm at definite temperature linearly depends on the activation energy. Within the investigated class of substances the optimum composition for solid electrolytes is Sr_0.69La_0.31F_2.31.     

Study of the superionic system AgI-PbI2-Ag2O-B2O3

The superionic system AgI-PbI₂-Ag₂O-B₂O₃ with two compositions has been prepared. The pelletised samples were investigated with regard to conductivity, modulus and dielectric analysis at various temperatures and frequencies. The activation energy determined for the samples was found to be varying between 0.09 to 0.10 eV. The effect of polarization at the electrode has been analyzed from conductivity spectra. From the impedance and modulus analysis it has been found that the system is non-ideal and there exists a distribution of relaxation times which is independent of temperature.