Haven Ratio Research Articles

Ion transport in glass: Influence of glassy structure on spatial extent of nonrandom ion hopping

On short time scales, the diffusion of mobile ions in glasses is nonrandom, i.e., the ions perform correlated forward-backward motions. By using linear response theory, we show in detail how typical distances characterizing the spatial extent of the nonrandom ionic diffusion can be derived from frequency-dependent conductivity data when the Haven ratio is known. We compare the dependence of these typical distances on the alkali content in germanate, borate, and silicate glasses. In all glasses, the typical distances decrease with increasing alkali oxide content. In the germanate and silicate glasses, the decrease is, however, more pronounced than in the borates. This network former effect points to the influence of the network structure on the spatial extent of the nonrandom diffusion.

Diffusion and dielectric studies of the system PPO4000–NH 4CF 3SO 3

A polymer electrolyte system composed of poly(propylene oxide) of molecular weight 4000 (PPO4000) complexed with NH 4CF 3SO 3 (NH 4TF) has been investigated by multinuclear pfg-NMR and AC impedance methods. Samples in the concentration range 0.03–0.69 mol/kg (O:NH 4 ratios of 500:1–22:1) have been investigated over the temperature range 25–75°C. The combination of AC conductance and pfg-NMR diffusion measurements gives clear evidence that extensive ion-aggregation/clustering occurs at low salt concentrations. With increasing salt-content the Haven ratio, defined as Λ calc/ Λ exp, decreases from >100 to ∼2 when going from 0.03 to 0.69 mol/kg. Such gross deviations from the Nernst–Einstein relation (i.e. Λ ∝ D ++ D −) originate in extensively correlated motions of ions. We interpret the results in terms of labile salt-rich sub-domains being further destabilized through an increase in the dielectric constant of the solution with increasing salt content.

Giant Haven Ratio for Proton Transport in Sodium Hydroxide

Solid sodium hydroxide has been prepared and investigated with respect to its transport properties. The proton conductivity depends significantly on the water content. In NaOH with minimum water content (NaOH in phase equilibrium with Na2O) the proton conductivity is much lower than reported in the literature. Defect chemistry and transport characteristics are discussed. For the same dry samples pulsed field gradient NMR revealed a surprisingly high H-diffusion coefficient and thus a Haven ratio of 10–104 in the cubic phase. In fact this value is only the lower limit since the measured conductivity may still be influenced by residual extrinsic effects or due to Na+ contributions. A cooperative mechanism is described which is able to explain this anomaly.

The Haven ratio in glasses

Low values of Haven ratio are shown to arise by the vacancy mechanism if there is a distribution of activation energies for ion migration. Only a fraction of the jump vectors at any given site will be effective leading to low effective coordination numbers. A simplified treatment based on percolation theory is given which suggests that values in the range 0.2–0.5 will occur if the standard deviation is between 0.05 and 0.15 eV. A low positive temperature coefficient is expected in agreement with some experimental results.

Determination of Ionic Diffusion Mechanisms in Solids

ABSTRACTThe experimental and atomistic simulation methodologies by which microscopic diffusion mechanisms can be determined in solids are described. Measurement of the Haven Ratio requires evaluation of the diffusion coefficient and of the ionic conductivity for the species in pure and doped specimens and is, in practice, limited to simpler materials. Atomistic simulations using lattice statics, molecular dynamics and Monte Carlo techniques can yield very detailed information on the pathways followed by migrating ions and are being utilised more extensively for this purpose. Examples of such experimental and simulation studies are discussed.

The Role of Effective Rate Constants in Interfacial Kinetics

ABSTRACTA brief excerpt of a more comprehensive quantitative theoretical analysis on the role of effective rate constants in interfacial processes is given (in particular [1], see also [2,3]). Chemical incorporation, tracer incorporation and steady state electrical experiments are considered. It is shown that besides experimental differences there are mechanistic and conceptual differences between the three effective rate constants (kδ, k*, Qq). The treatment based on irreversible thermodynamics and chemical kinetics shows similarities and differences with respect to the analogous situation in the bulk. As special cases adsorption and transfer limited kinetics are considered. Having related the k-values to the exchange rates of the rate determining step and to the chemical capacitance outside the boundary zone, the characteristic dependencies on controlling parameters and also the correlation with diffusion coefficients can be derived. This is done for electron-rich materials such as SOFC cathodes. A further point which is briefly mentioned in this context is the fact that flux constriction effects may lead to apparent surface rate constants. The role of space charges is briefly discussed for the case of grain boundary kinetics [4]. In electron-poor materials such as SrTiO3(Fe2O3) or Zr02(Y203) additional mechanistic differences should occur, since in the tracer case mechanisms are possible at the surfaces which do not have to involve electrons directly. Here also discrepancies with respect to electrical experiments are predicted (leading to a surface analogue of a Haven ratio). Some experimental results obtained with SrTiO3 are discussed in this context.

The kinetics of oxygen transport in 9.5 mol % single crystal yttria stabilised zirconia

Isotope Exchange/Depth Profiling (IEDP) using secondary ion mass spectrometry (SIMS) has been used to determine the oxygen tracer diffusion and surface exchange coefficients of (100) oriented 9.5 mol % yttria stabilised zirconia single crystals. The activation enthalpy for oxygen tracer diffusion was found to be 0.9 eV in the temperature range 450–650 °C, and 0.8 eV in the temperature range 650–1100 °C. The activation enthalpy for the surface exchange reaction showed a marked transition from . The ionic conductivity of the samples was measured by ac impedance spectroscopy which gave an activation enthalpy of 1.1 eV. The Arrhenius plots of the ac impedance data showed some curvature due to vacancy trapping by (Y′ ZrV o ..) . defect associates at lower temperatures, and it was found that the binding enthalpy of these associates (0.26 eV) contributed significantly to the overall activation enthalpy. An intercomparison between the oxygen diffusivities obtained from the two techniques shows a high degree of correlation across the temperature range examined, however, we identify two temperature regimes where the correlation differs slightly. At higher temperatures ( T > 650 °c) the diffusivities are related by a Haven ratio of 0.48, whereas at lower temperatures ( T < 650 °c) the Haven ratio was found to be 0.33. To investigate this change in the Haven ratio, protonic transport was examined using ac impedance measurements in dry and wet atmospheres.

Percolation transition in Ag-doped germanium chalcogenide-based glasses: conductivity and silver diffusion results

Conductivity and silver diffusion measured using a 110mAg tracer have been investigated in AgGeS and AgGeSbSe glasses with silver concentration ranging from 0.008 to 25 at.% Ag. It has been found that the room-temperature conductivity in both systems increases by 9.0–9.5 orders of magnitude with increasing silver content, and its activation energy decreases from ∼ 1 to 0.4 eV. Accordingly, the silver tracer diffusion coefficient at 298 K increases by 5.0–5.5 orders of magnitude with similar decrease of the diffusion activation energy. A comparison of the conductivity and silver diffusion results clearly shows that the ionic transport is predominant in the two systems, even at lowest Ag concentrations. The Haven ratio, H R , decreases with increasing silver content: extremely diluted glasses (0.008–0.1 at.% Ag) exhibit H R ≈ 1; Ag-rich vitreous alloys are characterized by H R = 0.2–0.4. The composition dependencies of the ionic conductivity, σ i , and silver tracer diffusion coefficient, D Ag, exhibit two drastically different transport regimes at low (≤ 2–5 at.%) and high (> 10 at.%) silver concentrations. A power-law composition dependence of σ i and D Ag over 2.5 orders of magnitude in the Ag concentration and 3.5–5.0 orders of magnitude in the ionic conductivity (2–3 orders of magnitude in the diffusion coefficient) is observed at low silver concentrations. This transport regime is attributed to percolation in the critical region just above the percolation threshold. Recent theoretical considerations (the dynamic structure model and statistical (occupation) effects on percolative ionic conduction) are also in good agreement with experimental findings. After essential structural transformations of the glass network on the short- and intermediate-range scales at higher silver content (> 10 at.%), the ionic transport is not caused any more by percolation, i.e., it becomes network-dependent with a strongly correlated motion of the Ag + ions.

Ionic diffusion and local hopping in copper chalcohalide glasses measured using 64Cu tracer and 129I-Mössbauer spectroscopy

For the first time, 64Cu tracer measurements of ionic diffusion were performed for several copper-rich glass compositions in the CuIAs 2Se 3, CuISbI 3As 2Se 3, CuIPbI 2As 2Se 3, CuIPbI 2SbI 3As 2Se 3 and Cu 2SeAs 2Se 3 systems. In accordance with previous a.c. impedance results and Wagner d.c. polarization measurements, it was found that pure Cu + ion-conducting glasses (50CuI17PbI 233As 2Se 3 and 50CuI20PbI 210SbI 320As 2Se 3) exhibit the highest copper tracer diffusion coefficients, D Cu , and the lowest diffusion activation energies. The values of D Cu at room temperature are higher by 4.5–5.5 orders of magnitude than those in an As 2Se 3 glass. The Haven ratio, H R , is found to be 0.52–0.61 (ternary glass) and 0.93–1.00 (quaternary glass). Short-range diffusional displacements of the iodide ions induced by the hopping Cu + ions are also detected in the CuIPbI 2SbI 3As 2Se 3 glassy system using 129I-Mössbauer spectroscopy in the temperature range of 4.2 to 305 K. The activation energy of local hopping, E h ≈ 0.31 eV, is very similar to that of bulk ionic conductivity (0.37 eV) and copper diffusion (≈ 0.33 eV). In contrast to CuI-based vitreous alloys, 50Cu 2Se50As 2Se 3 glass exhibits D Cu that are two to five orders of magnitude lower, and the copper ion transport number, t Cu + , is between 10 −3 and 10 −4 in the temperature range 140–170 °C.

Relaxation Processes and the Mixed Alkali Effect in Alkali Metasilicate Glasses

ABSTRACTA molecular dynamics simulation (MD) of lithium metasilicate (Li2SiO3) and related mixed alkali system (LiKSiO3) has been performed. Changes in the mean squared displacement and the corresponding clear two-step (β and α1) relaxations in a density correlation function have been observed at 700 K (self-part) for each ion in Li2SiO3 following an exponential decay by vibrational motion in a simulation up to 300 ps (run I). The mean squared displacement of the atoms shows the change in the slope at ca. 300 ps when the simulation is extended up to 1 ns (run II). Here we call the slowest relaxation (ca. 300 ps∼) the α2 region.Oscillation, which is clearer for O and Si than for Li, is found in the second (β-relaxation) region of the function, which is attributed to the so called “boson peak”. Both the β-relaxation and the boson peak are found to be due to the correlated motion.The slower relaxation (α1-relaxation) can be fitted to a stretched exponential form and the origin of this type of decay is confirmed to be waiting time distribution of jump motions. The back-correlated jumps also decrease the decay rate.Components A and B in α1 and α2 regions for Li ion are analyzed, where the Li ion of component A is located within the first neighboring sites and that of component B moves longer than the nearest neighbor distances by cooperative jump motion. The component B shows accelerated dynamics larger than t-linear ones (∼ t1.77) in the region 50–300 ps, and the dynamics can be characterized as Lévy flight.We have found that the contribution of the cooperative jumps decreases in the mixed alkali glass. This explains the maximum of the Haven ratio accompanied with the mixed alkali effect.

Reconciling ionic-transport properties with atomic structure in oxide glasses.

Structural evidence for the microsegregation of alkalis in oxide glasses is reviewed and the implications for ionic transport, viz., nearest-neighbor hopping, cooperative and correlation effects, are considered. Distinctions are drawn between the hopping of alkalis in silicate glasses, where changes in the configurations of neighboring bridging and nonbridging oxygens are expected, and alkali hopping in fully compensated aluminosilicate glasses where nonbridging oxygens are absent and conformational changes in the network are minimized. A simple expression is introduced for the microscopic energy barrier facing a migrating alkali ${\mathit{E}}_{\mathit{a}}$, and this is corrected to account for the cooperative effects of the other ions involved by dividing by the Kohlrausch exponent \ensuremath{\beta}, which defines the conductivity relaxation function exp[-(t/${\mathrm{\ensuremath{\tau}}}^{\mathrm{*}}$)\ensuremath{\beta}]. Structural parameters determined by x-ray and NMR spectroscopy enable us to calculate ${\mathit{E}}_{\mathit{a}}$. Conductivity relaxation experiments give a measure of \ensuremath{\beta}. The macroscopic diffusion enthalpy that is measured, W, is given by the ratio ${\mathit{E}}_{\mathit{a}}$/\ensuremath{\beta}. Thus we are able to show how the local structure of an alkali in a silicate glass can be used to predict the measured diffusion enthalpy. The smaller values of W reported for aluminosilicate glasses are rationalized structurally in terms of the removal of nonbridging oxygens from the modified network. In considering silicate glasses containing small concentrations x of alkali, as this necessarily leads to reductions in alkali microsegregation, decreased cooperative effects and increased hopping distances are expected.Taken together with the attendant fall in the high-frequency dielectric constant and the rise in \ensuremath{\beta}, this combination of changes naturally explains the increased enthalpies observed in low alkali glasses and the rise in alkali diffusion frequency factors. Increased hopping distances are also invoked to explain the crossover dependences of the diffusion coefficients and enthalpies of the separate alkalis in mixed alkali glasses. In particular, the increase in W for a given alkali, as its proportion \ensuremath{\gamma} drops for a fixed alkali concentration x, is attributed to an increase in the hopping distance and can again be predicted from the local structure, providing allowance is made for an associated reduction in cooperative effects. From the separate local structures of the two alkalis, the observed fall in the diffusion coefficients of the two alkalis and the minima in the isothermal dc electrical conductivity resulting from the increase in the respective diffusion enthalpies are well reproduced. In addition, the maxima in the measured dc electrical conductivity enthalpy W in the Kohlrausch exponent \ensuremath{\beta} and also in the Haven ratio f, all characteristic of alkali mixing, are closely predicted. Finally the increase in magnitude of the mixed alkali effect reported in aluminosilicate glasses is explained in terms of increased cooperativity associated with the reduced energy barriers ${\mathit{E}}_{\mathit{a}}$ for the two alkalis resulting from there being fewer nonbridging oxygens present in the glass structure.

About the influence of charge delocalization at the sites on the Na+ motion in oxide glasses

The HAVEN ratio of three Na2O-rich, stoichiometric composed oxide glasses with very distinct network structures has been estimated. The Na+ motion is discussed as a hopping process with a dominant COULOMB interaction between the Na+ ions and the negative charges, fixed on the charged oxo-coordination polyhedrons of the glass networks. For the first time, the investigation demonstrates the immediate influence of the oxo-coordination and charge delocalization at the sites on the correlation of Na+ motion, caused by (short range order) jumps between equivalent positions around the negative charge of a site.

Importance of structure in electrical conductivity relaxation

The electrical conductivity relaxation behavior of ionic conductors has been examined in terms of Kohlrausch exponent, β. Usually β decreases with increasing mobile ion concentration. The literature suggests that it should directly correlate with the magnitude of dc resistivity, the decoupling index, the activation energy of conductivity and nominal cation-cation distance, but each correlation is shown to have limited validity. An anomalous variation of β has been found in a high purity quartz crystal. It is explained by a structure-based model which illustrates the importance of ion distribution, the interaction between mobile cation and its charge compensating center, and the relation between β and Haven ratio.

Transport and ac response in a model of glassy electrolytes

By Monte Carlo simulation we investigate a model where ions are diffusing in the presence of randomly placed, immobile counterions. All Coulombic effects are taken into account. Calculations of dc- and ac-transport properties in a range of temperatures and ion concentrations show that our counterion model can qualitatively explain several experimental features common to glassy ionic conductors, including the characteristic concentration-dependence of the dc-activation energy, the Haven ratio and also the frequency-dispersion in the ac conductivity. We also present some preliminary simulation results for the nuclear-spin lattice relaxation rate T -1 1.

Monte Carlo investigations of Coulombic correlations in lattice gas models

Monte Carlo simulations were performed on lattice gas systems with Coulombic interactions. Emphasis was placed on two lattice gases. The first consists of both mobile anions and cations while the second is composed of mobile anions and a random distribution of fixed cations. Comparisons are made to a strictly repulsive lattice gas. The addition of attractive forces is shown to significantly retard particle motion relative to the repulsive system. In the mobile-anion, mobile-cation system, at temperatures high enough to suppress ion clustering, the effect of backward correlations on the particle diffusivity is found to be similar to that for the strictly repulsive system. In the mobile-anion, fixed-cation system, however, backward correlations are much stronger due to the presence of immobile Coulomb traps. Both systems deviate from Nernst–Einstein behavior. The mobile-anion, mobile-cation system exhibits diminished conductivity (Haven ratio ≳1) due to the migration of neutral ion pairs, whereas the mobile-anion, fixed-cation system exhibits slightly enhanced conductivity (Haven ratio &amp;lt;1) due to the mutual repulsions between mobile charge carriers. The results of these simulations are discussed in terms of multiple timescale behavior, specifically including Funke’s jump relaxation model, and observations on relaxation times are reported.

Fast-ion conduction in fluorite CaF2 studied by equilibrium and nonequilibrium molecular dynamics.

We present the results of a direct determination of the superionic conductivity of ${\mathrm{CaF}}_{2}$, by using equilibrium and nonequilibrium molecular dynamics at constant temperature. The conductivity values obtained by both techniques are comparable to and in good agreement with the experimental data. Our results suggest that the failure of similar previous attempts should be attributed to an inefficient sampling of the phase space in computing the expectation value of the conductivity. Moreover, the nonequilibrium calculations show that the response of the studied system is linear over a surprisingly wide interval of external forces up to a value ${10}^{7}$ eV/cm. By computing independently the anionic conductivity and diffusivity, we found a Haven ratio H\ensuremath{\approxeq}0.35, a value consistent with previous work, which established that superionic diffusion and conductivity in fluorites result from numerous correlated hopping processes involving many anions.

Interpretation of ionic transport properties of some silver chalcogenides

An analysis of the composition dependence of ionic transport properties is reported which concentrates on the α- and β- silver chalcogenides. The numerous assumptions inherent in the evaluation of the ionic caterpillar-type motion in structurally disordered Ag 2+δTe are stated and it is shown that the Haven ratio measured need not necessarily originate from ionic motion by the caterpillar mechanism. General relations for coulometric titration curves are derived which allow for the contributions of the electrons and ions to the electromotive force. For compounds of structural cation disorder a procedure for calculating the composition dependence of the chemical potential of the cations, μ i , is proposed. It results from an estimation of the configurational free energy. In the case of silver telluride at 250dgC it yields dμ i /dδ = 1.08 kT, thus confirming the negligibility of the ionic contribution to the emf. Relations describing the composition dependence of the chemical diffusion coefficient are given and supplemented with vivid interpretation. The maximum of the chemical diffusion coefficient of structurally disordered silver telluride near the stoichiometric composition and the absence of such a maximum for Frenkel-disordered silver selenide are shown to conform with theory. The theoretical description of diffusion in compounds of several mobile components is reconsidered.

Caterpillar motion in α-Ag 2Te

The diffusion process of silver ions in α-Ag 2Te is investigated. It is assumed that Ag ions occupy the tetrahedral sites and octahedral sites with different probability. To give an explanation of the Haven's ratio obtained by a molecular dynamics calculation, a theory of caterpillar mechanism is used. It is shown that the ratio of the frequency of a single jump to that of cooperative jumps increases with increasing temperature.

Caterpillar motion of silver ions in α-Ag 2Te

The diffusion process of silver ions in α-Ag 2Te is investigated. It is assumed that silver ions occupy the tetrahedral sites and octahedral sites with different probability. To interprete the value of the Haven ratio by molecular dynamics calculations, a “caterpillar mechanism” theory is used. It is shown that the ratio of the jump frequency of a single jump to that of a cooperative jump increases with the temperature.

Diffusion of silver and ionic conductivity in the solid electrolytes Ag 8HgS 2I 6 and Ag 6I 4WO 4

Ionic conductivity and silver diffusion in the Ag 8HgS 2I 6 and Ag 6I 4WO 4 superionic conductors have been studied. The obtained diffusion coefficients of the silver ions are in equations: Ag 8HgS 2I 6 (100–260°C) D ∗=2.3×10 −4 exp(−0.128 eV/kT) , Ag 6I 4WO 4 (100–200°C) D ∗ = 6.0×10 −4 exp (−0.183 eV/kT) . The calculated values of Haven ratio confirm the existence of essential differences in transfer properties for the solid electrolytes with α-AgI-type structure.