Defect model for the mixed mobile ion effect revisited: An importance of deformation rates

The progress in understanding the behavior of glassy mixed ionic conductors within the concept of the defect model for the mixed mobile ion effect [V. Belostotsky, J. Non-Cryst. Solids 353 (2007) 1078] is reported. It is shown that in a mixed ionic conductor (e.g., mixed alkali glass) containing two or more types of dissimilar mobile ions of unequal size sufficient local strain arising from the size mismatch of a mobile ion entering a foreign site cannot be, in principle, absorbed by the surrounding network-forming matrix without its damage. Primary site rearrangement occurs immediately, on the time scale close to that of the ion migration process, through the formation of intrinsic defects in the nearest glass network. Neither anelastic relaxation below glass transition temperature, T_g, nor viscoelastic or viscous behavior at or above T_g can be expected being observed in this case because the character of the stress relaxation in a wide temperature range is dictated above all by the deformation rates employed locally to the adjacent network-forming matrix. Since the ion migration occurs on the picosecond time scale, the primary rearrangement of the glass network adjacent to an ionic site occurs at rates orders of magnitude higher than those of the critical minimum values, so the matrix demonstrates brittle-elastic response to the arising strain even at temperatures well above T_g, which explains, among other things, why mixed alkali effect is observable in glass melts.     

Activation volumes and site relaxation in mixed alkali glasses

Evidence is presented for site relaxations occurring in mixed alkali (cation) glasses based on activation volumes, V_A(σ) = −RT[d ln σ/dp]_T, which are determined for sodium aluminoborate glasses of varying Na₂O content, and for mixed alkali glasses where Na⁺ is partially replaced by Li⁺, K⁺ or Cs⁺ ions. In accordance with the ‘updated’ dynamic structure model, activation volumes are identified here with local expansions that accompany the opening up of C′ sites to admit incoming ions. ‘Anomalous’ increases in activation volume in mixed cation glasses correlate with the size of minority (guest) cations. This anomaly is interpreted in terms of a ‘leader follower’ mechanism that involves dynamic coupling between the faster (majority) and slower (minority) cations. Because of mismatch effects in mixed cation glasses this coupling requires the opening up of additional cation sites by the slower follower cations. The resulting disturbances in the glass network are responsible for many characteristic features of the mixed alkali effect, including the appearance of high temperature internal friction peaks and observed minima in glass transition temperatures and melt viscosities.     

Relaxation in mixed alkali fluoride glasses

We have investigated the dynamics of alkali cations as well as fluorine anions in non-oxide fluoride glasses with a total alkali fluoride content varying from 16 to 35 mol% in the frequency range from 10 Hz to 2 MHz and in the temperature range from room temperature to just below the glass transition temperature. We have shown that the dc and ac conductivity, crossover frequency and conductivity relaxation frequency exhibit a minimum in mixed alkali fluoride glasses, where anions also participate in the diffusion processes in addition to cations, unlike mixed alkali oxide glasses and crystals. We have observed lower dimensionality of the conduction pathways in mixed alkali fluoride glasses compared to that in the single alkali glasses. We have shown that the relaxation dynamics in mixed alkali fluoride glasses is independent of temperature.     

Mixed alkali glass spectra and structure

The far infrared and Raman spectra of several series of mixed alkali metaphosphate glasses have been investigated as a function of the mole fraction x of the network-modifying ionic oxides in xM₂O(1?x)M₂′O · P₂O₅. The frequencies of the cation-motion bands in the far infrared spectra, which correspond to cationsite vibrations, do not shift with x, indicating that the vibrationally significant local geometry and forces associated with a particular cation are unaffected by the introduction of the second cation into the glass structure. Each Raman-active band due to vibrations of the metaphosphate network occurs at a different frequency for each pure glass (x = 0 or 1), but for mixed alkali glasses only one band occurs for each type of mode and it varies linearly with x. This indicates that the cations in these mixed alkali glasses are homogeneously distributed, there is no significant molecular-level domain formation and the phosphate chains are associated with an averaged cation environment whose effect on the chain modes varies with x. A simple vibrational model is presented which shows that the cation-dependent shifts are due to small changes in network bond angles and variation of the cationsite forces.     

Fragility in mixed alkali tellurites

Linear viscoelastic stress relaxation and calorimetric measurements were performed on a series of mixed alkali tellurite glasses of composition 0.3([xNa₂O+(1−x)Li₂O])+0.7TeO₂ at temperatures near and above the glass transition temperature, T_g. The stress relaxation data were well described by the stretched exponential function, G(t)=G₀exp[−(t/τ)^β], where τ is the relaxation time, β is the distribution of relaxation times and G₀ is the high frequency modulus. The fragility, determined from the temperature dependence of τ, exhibited a minimum in the middle of the mixed alkali composition. A possible connection between the kinetic and the thermodynamic dimensions of this system was established, wherein the heat capacity change at the T_g, ΔC_p(T_g), and the fragility are correlated.     

The AC conductivity of superionic conducting glasses (AgI)x−(Ag4P2O7)1−x (x = 0.8, 0.75, 0.7): Experiment and analysis based on the generalized Langevin equation

The frequency-dependent complex impedance of superionic conducting glasses (AgI)_x − (Ag₄P₂O₇)_1−x (x = 0.3, 0.25, 0.20) was measured from 5 Hz to 500 kHz below room temperature. The frequency dependence of the conductivity and the electric modulus observed here cannot be expressed by a single relaxation equation, but it is well described by an equivalent circuit involving a contribution due to Jonscher's universal law σ [ω] ∼ ωⁿ (0 < n < 1). A linear relation between the DC conductivity and the relaxation time was observed irrespective of the sample compositions. These results are explained on the basis of the generalized Langevin equation associated with a non-exponential memory function. The physical basis of this approach is discussed in terms of the distribution of transition times arising from non-periodic potentials formed by immobile anions and many-body interactions among mobile cations at very high concentration in the superionic conducting glass.     

Local structure and medium range ordering of tetrahedrally coordinated Fe3+ ions in alkali–alkaline earth–silica glasses

Tetrahedral iron (III) environments in alkali–alkaline earth–silica glasses have been studied as functions of alkali and alkaline earth cation type and Fe₂O₃ content using photoluminescence and optical absorption spectroscopies. The luminescence band centered at 13 000–15,500 cm⁻¹ is attributed to the ⁴T₁(G) → ⁶A₁(S) transition of tetrahedral Fe³⁺ ions. This band has Gaussian linewidths of 1500–3000 cm⁻¹ but linewidths exhibit no clear compositional dependency. Ligand field strength, 10Dq, and the Racah parameters B and C are consistent with tetrahedral Fe³⁺ and here for the first time their linear variation with the alkali/alkaline earth ratio of ionic radii, cation field strengths or individual oxide basicities is demonstrated. This is attributed to the effects of near-neighbor cations on length and covalency of Fe³⁺–O bonds and on host glass structure. Alkali cations stabilize Fe³⁺ ions in tetrahedral coordination; stabilization increases linearly with increasing alkali ionic radius and therefore with decreasing alkali field strength. The role of alkaline earth cations in Fe³⁺ stabilization in these glasses is not clear, although their effect is the inverse of that of the alkalis. The structural behavior of Fe³⁺ is defined as selective, reflecting its strong local ordering effects.     

The influence of dissolved heavy water on the internal friction of lithium metaphosphate glasses containing 1% potassium metaphosphate

A batch of very dry lithium metaphosphate glass, containing 1% potassium metaphosphate, was prepared and dissolved completely in nearly pure heavy water. From this solution, a series of glasses with varying deuterium oxide content was prepared. The internal friction and dielectric loss data were taken. The amount of dissolved deuterium oxide was determined from the weight-loss of specimens during heating in vacuum, and checked by means of tritium labeling. It is found that dissolved deuterium oxide influences the internal friction and dielectric losses, in the same was as additions of dissimilar alkali ions do (mixed alkali effect) so that one can say that deuterium behaves similarly to alkali ions.A comparison of the present data with the results of a recent study on the influence of protons on the mechanical and electric properties in an identical host glass illustrates clearly that the mixed alkali effect is not governed by mass differences of the cations.     

Bond character and properties of the mixed alkali system Na2OK2OAl2O3SiO2

The mixed alkali glass system Na₂OK₂OAl₂O₃SiO₂ was investigated. Density, transformation temperature, refractive index, and chemical durability were studied. Optical absorption and ESR spectra of the CuO-doped glasses were determined.Calculations of the polarizability of O^2?, bonding parameters of the Cu²⁺ complex, and the packing density are presented. It was found that for the mixed alkali glasses, the oxygen- alkali bond has a more ionic character than expected from additivity. This fact enables the non-linear changes of the refractive index, of the shift of the Cu²⁺ absorption band, and of the covalency to be interpreted as the Na mole fraction is varied. It is also possible to explain qualitatively the density, T_g and chemical durability non-linear variations with change of the Na content by the ionicity deviations of the bond character and the postulated pairs of Na⁺ and K⁺ ions in the mixed alkali glasses.     

Mössbauer spectroscopic study of potassium borate glasses at low temperatures

Mössbauer studies of potassium borate glasses containing a small amount of iron were performed at dry ice and liquid nitrogen temperatures in order to investigate the physical properties of non-bridging oxygens in the glasses. The Mössbauer spectra at the temperature of dry ice were almost the same as those at room temperature. On the other hand, the spectra at the temperature of liquid nitrogen consisted of quadrupole doublet and hyperfine structure due to Fe³⁺ ions with tetrahedral symmetry. Magnetic suceptibility measurements revealed that the hyperfine structure was observed because of a paramagnetic relaxation effect. Isomer shift values for both the quadrupole doublet and the hyperfine structure were constant in the alkali region below 20 mol.%, and continuously decreased when the alkali content of the glasses was in the region ? 20 mol.%. The absorption areas for the hyperfine structure were also constant in the alkali region below 20 mol.%, and linearly decreased with alkali content in the region ? 20 mol.%. The internal magnetic field for the hyperfine structure also showed the same tendency as the absorption area. These results were attributed to the formation of non-bridging oxygen at the site adjacent to the iron, and the decrease of the absorption area for the hyperfine structure seemed to be directly related to the fraction of non-bridging oxygen in the oxygens constituting FeO₄ tetrahedra.     

Non-random cation distribution in sodium-strontium-phosphate glasses

Vitreous compositions in the (0.55−x)Na₂O:xSrO:0.45P₂O₅ (0?x?0.55) system were characterized by differential scanning calorimetry and ³¹P solid state NMR. High strontium containing glasses were found to be partly crystallized. In the pure glass samples a general increase in T_g and a decrease in isotropic chemical shift with increasing x were observed. Two distinct linear ranges were observed in plots of these parameters against composition, with a transition point at x≈0.20. This composition corresponds to the point at which all Na⁺ ions associated with charge balance of the terminal Q¹ phosphate tetrahedra are substituted for Sr²⁺. In the mixed cation glasses, this suggests a non-random distribution of cations, with preferential location of Sr²⁺ ions near the chain ends. Crystalline models have been used to discuss trends in the variation of chemical shift anisotropy and propose possible coordination environments for the metal cations in the glasses.     

Synthesis and characterization of potassium, rubidium, and cesium thiogermanate glasses

Glass-forming regions were investigated for the binary xM₂S + (1 − x)GeS₂ (M=K, Rb, Cs) systems. Glasses were prepared from 0?x?0.20 mole fraction alkali sulfide using a novel preparation route involving the decomposition of the alkali hydrosulfides in situ. At higher alkali concentrations near x=0.33, the glass-forming regions are limited by the readily formed adamantane-like M₄Ge₄S₁₀ crystals. Structural characterization of the glasses and polycrystals for x?0.33 were performed using Raman scattering and IR absorption. Terminal Ge-S⁻ vibrational modes, observed between 473 and 479 cm⁻¹, increased in intensity and decreased in frequency with increasing alkali modifier content. Glass transition temperatures decreased with increasing alkali modifier, ranging from 250 to 215 °C. Corresponding crystallization onset temperatures were between 340 and 385 °C. DC conductivity values of the glasses ranged from 10⁻¹⁰ to 10⁻⁷ (Ω cm)⁻¹ with activation energies between 0.54 and 0.93 eV for the temperature range of ∼100-250 °C. Higher ionic conductivities were observed with increasing alkali concentration and decreasing alkali radii. Additionally, an increase in the activation energy was observed above the glass transition temperature.     

Peculiar temperature-dependent fluorescence of EuCl3 in LiCl molten salt as a result of phase changes

Fluorescence spectra were obtained in situ as a function of temperature (ranging from room temperature to 956 K) from a melt of EuCl₃ and LiCl. Three different characteristic Eu²⁺ fluorescence bands, associated with phase changes, were observed. The critical fluorescence dependence on temperature appearing in the blue fluorescence were resulted from the radiative relaxation from 4f⁶5d¹ excited state to 4f⁷ (⁸S_7/2) ground state of Eu²⁺, which was reduced from Eu³⁺ of EuCl₃ at high temperature. The fluorescence studies could provide information regarding the phase changes estimated as the stable dihalide, aggregation, and precipitation states of Eu²⁺ in alkali halide not only crystallic but also fluidic melting matrix.     

Relaxation effects in glassy selenium

Thermal relaxation phenomena were measured in samples of both melt-quenched and evaporated selenium. On the basis of earlier studies, the two methods of preparation produced samples with polymeric chain concentrations of 30–50% and 0% respectively; the rest of the material was in the form of eight member rings. The relaxation peak occurred between 320 and 330 K, and had an activation energy of ≈22.5 kcal/mole for the melt-quenched sample. A decrease of 1 K in the glass relaxation temperature and 0.5 kcal (a at)^?1 in the activation energy was observed in samples which had been initially evaporated. No change was observed as a result of melting and quenching these evaporated samples.It is postulated that there was no change when the evaporated sample was melt-quenched be because rings and chains can interconvert and equilibrate relatively readily at temperatures as low as T_g (50° C), and consequently the samples all had the same structure after once being heated above T_g. The differences observed are probably due to accidental impurities in the evaporated samples which help catalyze the interconversion of rings and chains. Further, since the equilibrium concentration of polymeric chains is temperature dependent, it is postulated that the large relaxation effects seen at T < T_g are due to the equilibration of these chains with the rings. The observed activation energy for the relaxation supports this view. It is about the same energy as has been previously measured for Se₈ ring breaking in liquid selenium. Two consequences of this postulate are that the selenium analog to the sulfur polymerization transition must occur well below room temperature if it exists, and therefore, that the equilibrium ring-chain ratio can be smoothly extrapolated down to room temperature from the published high-temperature data.     

Modulus and internal friction in phosphate-silicate bioactive glass

The real and imaginary parts of the dynamic shear modulus, G′ and G″, respectively, of a “bioactive glass” Na₂O, CaO, SiO₂, P₂O₅ have been measured from 10^?4 Hz to 1 Hz at temperatures from 160 K to 610 K. The mechanical loss tangent of the glass (T_g = 816 K) at 1 Hz shows two relaxation regions: one centred at 312 K and the second at 585 K. The low-temperature peak appears in the same region as the peak attributed to Na ion motion in silicate glasses. The modulus of the glass is 32 GPa at 295 K. The spectrum of the high temperature peak has a broad distribution of relaxation times with a half width of five decades of frequency, and Arrhenius “activation energy” of 164 kJ mol.^?1, and the amplitude of this relaxation decreases on cooling. The similarity of these features with those observed in rigid molecular and other types of glasses suggests that the relaxations observed in the bioglass may be more appropriately considered as an intrinsic property of the non-periodic arrangement of atoms or ions in a solid than as being due to the diffusion of specific types of ions in it. It is pointed out that isothermal and isochronal measurements of internal friction in glasses do not give the same relaxation rate at the same temperature, due mainly to a rapid decrease in the amplitude of relaxation with temperature. The shear, Young's and bulk moduli of the glass are, 31.9, 76.6 and 43.0 GPa, respectively, and the Poisson's ratio is 0.20.A sample of the same bioglass containing 0.05% more water showed a shoulder in its tan φ at ～ 400 K and a peak at ～ 560 K, with little change in its modulus or T_g. Thus the presence of water above a certain amount had less significant effect on the internal friction of the bioactive glass.     

Increased Si NMR sensitivity in glasses with a Carr-Purcell-Meiboom-Gill echotrain

The use of a Carr-Purcell-Meiboom-Gill (CPMG) echotrain to increase the ²⁹Si NMR sensitivity in glasses was investigated. The echo intensity decay follows a stretched exponential behavior M(t) = M₀ exp[−(t/t2)^β] with values for the exponent β in the range of 0.41-0.65. The signal to noise in the spectra can be increased by a factor of up to 4 by taking the weighted sum of the spectra obtained from the individual echoes. However, differential T2 relaxation for the different Qⁿ species is observed, with a shorter relaxation time for Q⁴ than Q³. Thus, summing of the echoes leads to distorted spectral intensities and quantitative information can no longer be obtained from the spectra. To circumvent the problem with differential T2 relaxation, an alternative approach is developed in which the spectral intensity for each chemical shift value is determined from the stretched exponential fit to its echo decay. With this approach, the sensitivity can be increased by a factor of up to 2.4, while quantitative information can still be obtained from the spectra. The increased sensitivity permitted the detection of five-coordinated silicon in a potassium silicate glass with natural ²⁹Si abundance at ambient pressure.     

Distribution of electrical relaxation times,determined from current decay curves on alkali-còntaining silicate glasses,and an attempt at its explanation

A theory is formulated which offeres the possibility of explaining the occurrence of the very broad distribution of relaxation times with a single activation energy for all relaxation times. It is derived from the potential model of Fröhlich, but with the acceptance of the existence of different long paths through the glass structure for the alkali ions. The theory relates the relaxation spectrum to a distribution of path-lengths of the alkali ions.Electrical decay curves on three silicate glasses, one with Na₂O, one with Na₂O + K₂O, and the third with K₂O only as an alkali, were determined having a time range of almost seven decades (beginning at less than 10^?5 sec). The relaxation spectra could be calculated over 15 decades by superposition of measurements obtained at various temperatures. The disturbing influence of electrode polarization could be minimized by the application of Na-amalgam electrodes. Special distribution functions for the relaxation times fit the measured data according to the theory presented here.     

Dielectric studies of segmental dynamics in poly(dimethylsiloxane)/titania nanocomposites

Differential scanning calorimetry, thermally stimulated depolarization currents and dielectric relaxation spectroscopy techniques, covering together a broad frequency range of 10⁻⁴ to 10⁶ Hz, were employed to investigate the effects of in situ synthesized titania nanoparticles on thermal transitions, segmental dynamics and interfacial interactions in poly(dimethylsiloxane)/titania nanocomposites. Titania particles (TiO₂, 20-40 nm in diameter) were prepared and well dispersed into the polymer network through sol-gel technique, aiming at stable and mechanically reinforced systems. The interactions between polymer and fillers were found to be strong, supressing crystallinity and affecting the temperature development of the glass transition. The segmental relaxation associated with the glass transition consists of three contributions, arising, in the order of decreasing mobility, from the bulk (unaffected) amorphous polymer fraction (α relaxation), from polymer chains restricted between condensed crystal regions (α_c relaxation), and from the semi-bound polymer in an interfacial layer with strongly reduced mobility due to interactions with hydroxyls on the nanoparticle surface (α? relaxation). The thickness of the interfacial layer was estimated to be in the range of 3-5 nm. Measurements using different thermal protocols proved very effective in analyzing the origin of each relaxation and the respective effects of filler addition.     

Multichannel conduction in alkali silicate glasses

The qualitative change of the electrical conduction of alkali silicate glasses with alkali mixing is discussed in connection with dielectric and mechanical relaxation. The observed conduction is understood as the additive effect of two kinds of independent diffusion processes — I and II. In single alkali glass, diffusion process-I is always observed as the dominant conduction process. However, when one alkali is progressively substituted by another, the dominant conduction process is altered from diffusion process-I to II. In the mixed alkali glass containing equal amounts of two alkali ions, diffusion process-I disappears, so that only diffusion process-II is observed. Consequently, it becomes evident that the mixed alkali effect is not only the successive change of conductivity, but the alternation of the dominant conduction process.