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Structure-transport correlation of super-ionic mixed network former glasses
Solid State Ionics 343 (2019) 115126
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Structure-transport correlation of super-ionic mixed network former glasses A. Palui, A. Ghosh
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School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
ARTICLE INFO
ABSTRACT
Keywords: Mixed former glass Characteristic length Structure
We have studied the ion dynamics in several mixed former glasses in wide composition and temperature ranges. The ionic conductivity obtained from complex impedance plot follows the Arrhenius relation. It is observed that the ionic conductivity of these glasses exhibits mixed glass former effect and depends strongly on the dopant salt content as well as on the mixed former ratio. The composition dependence of the activation energy exhibits an opposite trend by that of the conductivity. The characteristic mean square displacement of mobile ions has been determined from the ac conductivity spectra in the framework of linear response theory. It is observed that the ionic conductivity and the mean square displacement of mobile ions are correlated with the population density of structural units of the glass network. The time-temperature superposition principle has been verified using the scaling of the conductivity spectra.
1. Introduction
conductivity (negative glass former effect) has been observed [15,16]. This non-linear variation of the conductivity and other physical properties of these glasses with mixed former ratio is known as mixed glass former effect [17]. Several mixed network former glasses [16–18] have been studied and the electrical conductivity of the glasses is linked with their network structure. The ionic conductivity of borotellurite mixed former glasses has been directly linked with the BO4 tetrahedral units [15]. In these glasses the movement of electron pair of BeO bond temporarily opens up the network structure which assists ion transport [15]. On the other hand, the ionic conductivity of silver selenium-molybdate mixed former glasses has been related to the ratio of population of SeO32− ions to that of the isolated MoO6 units [14]. SeO32− ions consist of nonbridging oxygen which assists in ion migration and this ratio indicates the influence of immobile MoO6 unit on the selenite non-bridging oxygen. Thus, the contributions of both the structural units affect the ionic conductivity at the same time. Further, available free volume in silver selenium-molybdate glasses decreases for higher silver oxide content due to formation of isolated silver selenite unit, which in turn decreases the conductivity [14]. Thus, the above discussion indicates that the network structure units profoundly influence the ion migration. To understand mixed glass former effect, a mixed barrier model has been developed for several mixed former glasses [11]. This model takes into account the reduction of the barrier strength for ion jump with mixing of different network formers and the composition independent coordination environment of the network forming units. Also in this model the barrier energy for ion jump is reduced rapidly for
Superionic mixed former glasses are important from both academic and technological standpoints [1,2]. The study of ion transport properties of glassy conductors and their correlation with the glass network structure is a challenging problem as the microscopic network structure regulates the ion transport mechanism of these glasses [3,4]. For potential application of these ionic glasses in electrochemical devices [5], the enhancement of the ionic conductivity in a methodical way is essential. There are different ways to enhance the ionic conductivity in such ion conducting glasses. One way is to increase the content of network modifier oxides such as Li2O, Ag2O, etc. which de-polymerize the glass network and increase the non-bridging oxygen content, leading to increase in the available hopping sites for mobile ions and hence an enhancement of the conductivity [6]. Addition of alkali or silver halides is another way to achieve superionic conductivity [7,8]. In some particular cases for AgI doped glasses, I− ions lead to construction of O−Ag−I−Ag−O bridges which progressively expands the pathway volume for Ag+ ion conduction, causing enhancement of the ionic conductivity [2,9]. In this case, IeAg distance plays a key role on enhancement of the conductivity. Doping of sulphide salts in a few glasses increases the polarizability and conductivity of these glasses [10]. One of the captivating ways to enhance the conductivity is to incorporate more than one glass former [11]. It is often found that the conductivity of these mixed formers glasses passes through one and sometimes more than one maximum value with the change of mixed former ratio [12–14]. For some mixed former glasses, a minimum in the
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Corresponding author. E-mail address: [email protected] (A. Ghosh).
https://doi.org/10.1016/j.ssi.2019.115126 Received 13 July 2019; Received in revised form 28 September 2019; Accepted 17 October 2019 0167-2738/ © 2019 Elsevier B.V. All rights reserved.
Solid State Ionics 343 (2019) 115126
A. Palui and A. Ghosh
heterogeneous materials than that of the homogeneous materials [11]. The main difficulty to understand the ion dynamics is the lack of knowledge about the complex glass structure. This can be resolved by determining the mean square displacement of the hopping motion of the mobile ions in the framework of linear response theory [19–21]. We know that primarily the hopping motion of the mobile ions between potential minima controls the ion dynamics and the heights of the potential barriers are controlled by the Coulomb interaction between the mobile ions and the network structure. Therefore, we can find out the minimum length, the ion has to travel to overcome these barriers, by determining the characteristic lengths associated with it and can establish a connection with the macroscopic parameters. The present paper reports the perceptive of the different microscopic parameters that can influence the macroscopic ion dynamics in different glass systems. We have shown that the ionic conductivity is directly correlated to the characteristic length scale. We have also shown that the modification of the glass networks plays a leading role on the composition dependence of these microscopic parameters. Fig. 1. Arrhenius temperature dependence of dc conductivity for different compositions of yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) glasses. The solid lines present the least square linear fits to the data.
2. Experimental details Three series of glass compositions has been investigated as stated below. (1) yAg2O-(1 − y)[xSeO2-(1 − x)TeO2], where x = 0–0.6 for y = 0.3 and x = 0–0.5 for y = 0.4; (2) xAgI-(1 − x)[yAg2O-(1 − y)(0.5SeO2–0.5TeO2), where x = 0–0.4 and y = 0.3, 0.4 and (3) xAgI-(1 − x)[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)], where x = 0.1–0.3 and y = 0.3, 0.5 and 0.7. These compositions were prepared by melt quench technique. The details of preparation procedure of these glass samples were given elsewhere [8,22,23]. The proper amounts of reagent grade chemicals were thoroughly mixed and the mixtures were preheated in alumina crucibles at 400 °C for 2 h. The mixtures were then melted at temperatures in the range 550 to 720 °C depending on the composition. The melts were equilibrated for 2 h and finally quenched between two aluminum plates to obtain transparent glass samples. Glass formation was confirmed from X-ray diffraction patterns of the powdered samples taken in an X-ray diffractometer (model Bruker AXS) using Cu Kα radiation. X-ray diffraction patterns of the samples exhibited a wide halo, characteristics of amorphous materials. Density of the glasses was measured at room temperature by Archimedes principle using acetone as the immersion liquid. Fourier transform infrared (FTIR) spectra of the pellets, prepared from the mixtures of glass and KBr powders in the ratio 1:100, were recorded at room temperature in the wave number range 400–4000 cm−1 in a FTIR spectrometer (PerkinElmer, model Spectrum 100). Measurements of the electrical conductivity and the dielectric permittivity of the samples were carried out in the frequency range 10 Hz–2 MHz in a LCR meter (QuadTech, model 7600 Plus) using a parallel electrode configuration in a wide temperature range.
Fig. 2. (a) Dependence of the ionic conductivity and activation energy on glass former ratio for different Ag2O contents at a common temperature for yAg2O(1 − y)(xSeO2-(1 − x)TeO2) glasses. (b) Variation of the ionic conductivity and activation energy at a common temperature with the AgI content for different modifier contents for xAgI-(1 − x)(yAg2O-(1 − y)(0.5SeO2–0.5TeO2)) glasses. The lines are guides for the eyes.
3. Results and discussion 3.1. DC conductivity We have obtained ionic conductivity of all the samples from the complex impedance plot. The reciprocal temperature dependence of the ionic conductivity is shown in Fig. 1 for yAg2O-(1 − y)(xSeO2(1 − x)TeO2) glasses. It is noted that the dc conductivity (σ) is thermally activated and follows the Arrhenius relation given by Eq.(1),
T=
0 exp[
E / kB T ]
activation energy (Eσ) has been obtained by least square fitting of the conductivity data. The variation of σ and Eσ with mixed former ratio for yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) glasses is shown in Fig. 2(a) for different modifier contents (Ag2O = 0.3 and Ag2O = 0.4). It is noted that the ionic conductivity shows a maximum for x = 0.4 for each modifier content. It is also noted that the ionic conductivity is higher for
(1)
where σ0 is the pre-exponential factor, Eσ is the activation energy, kB is the Boltzmann constant and T is the absolute temperature. The 2
Solid State Ionics 343 (2019) 115126
A. Palui and A. Ghosh
glasses containing higher modifier content. It is observed that the present yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) mixed network former glasses display higher ionic conductivity than the Ag2O−TeO2 single network former glasses [24]. Thus, the enhanced conductivity is observed by mixing of two different glass network formers and the mixed glass network former effect comes into play. The mixed former effect in the present Ag2O−SeO2−TeO2 mixed former glasses may be compared with that reported in Ag2O-B2O3-TeO2 glasses [15]. It may be noted that the variation of the conductivity for the present mixed former glasses with mixed former ratio is quite different from that of the Ag2O−B2O3−TeO2 mixed former glasses [15]. It has been reported that initially the conductivity of Ag2O − B2O3 − TeO2 glasses decreases slightly with the increase of B2O3 content but shows an increase for higher content of B2O3 [15]. A different phenomenon is observed when the Ag2O−SeO2−TeO2 glasses are doped with AgI salt. Fig. 2(b) shows the variation of σ and Eσ with AgI doping content for xAgI-(1 − x) (yAg2O-(1 − y)(0.5SeO2–0.5TeO2)) glasses for different modifier contents (Ag2O). It is observed that the conductivity is higher for a higher modifier (Ag2O = 0.4) content for undoped glasses. But a discrepancy is observed for higher value of AgI content (x > 0.1), where the conductivity shows a lower value than that of the lower modifier containing glass (Ag2O = 0.3). It has been reported that the increase in the conductivity for AgI-Ag2O-SeO2 glasses [25] is mainly governed by the expansion of the glass network, which leads to an increase in the free volume creating more open network structure for faster ionic conduction [15]. However, the conductivity of the Ag2O-B2O3-P2O5 mixed former glasses is mainly controlled by the de-polymerization of the glass network due to the increase in Ag2O modifier oxide content [26]. The ionic conductivity and activation energy of xAgI-(1 − x) (0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) mixed former glasses are shown in Fig. 3(a) and (b) as a function of glass former ratio and AgI doping content respectively. A minimum in the conductivity is observed for x = 0.2 and 0.3 at y = 0.5 (Fig. 3(b)). In comparison, the conductivity of the undoped 0.3Ag2O-0.7(ySeO2-(1 − y)MoO3) glasses increases with the increase of the SeO2 content up to y = 0.7 and then the conductivity decreases slightly for y = 0.8 [27]. In highly doped xAgI(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses it is clearly seen that the value of the ionic conductivity is less affected by the network structure and is mainly influenced by the AgI content, i.e., the mixed network former effect in these glasses is overridden by the silver ion conductivity of AgI [28]. It is noted in these figures that the composition dependence of the activation energy exhibits a trend which is opposite to that of the conductivity for each case.
Fig. 3. (a) Variation of the ionic conductivity and activation energy with AgI content for different network former ratios at fixed temperature for xAgI(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses. (b) Variation of the ionic conductivity and activation energy with the glass network former ratio for different AgI contents at a fixed temperature for the same glass series. Solid lines are guide to the eye.
( )=
NV q2 2 6k THR
< r 2 (t) > sin( t )dt 0
(2)
where NV is the mobile ion number density, q is the charge of the mobile ions, kB is the Boltzmann constant and T is the absolute temperature and HR is the Haven ratio, which indicates degree of correlation between successive hops [30]. The value of HR depends on the concentration of the mobile ions and varies from 0.2 to 1 in general [30]. The ion transport in glasses with low ionic concentration (30–100 ppm) is uncorrelated (HR ≈ 1), but HR decreases rapidly with increasing ionic concentration and remains nearly constant (HR = 0.2–0.4) for ion rich glasses [30,31]. The average AgeAg interionic distance decreases with increase in ionic concentration, which leads to an increase in the inter-ionic interactions and thus a gradual decrease of HR is observed. The glass compositions in current paper are all ionically rich and as reported for other silver selenite glasses we assume HR ≈ 0.3 [30–32]. The mean square displacement of mobile ions, < r2(t) > can be calculated from the frequency dependent conductivity data using the following transformation [21].
3.2. AC conductivity and mean square displacement The conductivity spectra at different temperatures for atypical glass composition, 0.1AgI-0.9(0.3Ag2O-0.7(0.5SeO2-0.5MoO3)), are shown in Fig. 4(a). All other glass compositions also show similar spectra. In fact, the shape of the ac conductivity spectra for all compositions is remarkably similar to those of different disordered solids [29]. It is observed for all glass compositions that at low temperatures and low frequencies the ac conductivity is almost independent of frequency and corresponds to the dc conductivity, while at higher frequency, the ac conductivity shows a dispersive behavior. It is also observed that the ac conductivity spectra at higher temperatures and low frequencies are influenced by the electrode polarization effect. In order to comprehend the conduction pathways of glass systems we have determined characteristic mean square displacement of mobile ions from the conductivity spectra using linear response theory [19]. In this framework, the frequency dependent conductivity is related to the mean square displacement (< r2(t) >) of the mobile ions at thermal equilibrium by the following relation [21].
< r 2 (t ) > =
12k T NV q2
t
( )
dt 0
0
sin( t ) d
(3)
It is observed that in sub-diffusive regime (i.e. shorter time scale) the value of < r2(t) > is small and the non-random forward-backward motion of ions portrays ionic motion. In this region < r2(t) > increases with increase of time in a sub-linear way given by < r2(t) > ~ t1−n, where n is a power law exponent. On the contrary, in diffusive regime 3
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Fig. 4. (a) Conductivity spectra at different temperatures for 0.1AgI0.9(0.3Ag2O-0.7(0.5SeO2-0.5MoO3)) glasses. (b) Time dependence of < r2(t) > at different temperatures for 0.1AgI-0.9(0.3Ag2O-0.7(0.5SeO20.5MoO3)) glasses. Solid straight lines denote the least square fittings to the diffusive and sub diffusive region. From the crossover of the lines we get the values of tp and < r2(tp) > .
Fig. 5. (a) Variation of the characteristic length < r2(tp) > with mixed former ratio for different values of modifier contents for yAg2O-(1 − y)(xSeO2(1 − x)TeO2) glasses. (b) The variation of < r2(tp) > with AgI for different contents of Ag2O are shown for the glass composition xAgI-(1 − x)(yAg2O(1 − y)(0.5SeO2–0.5TeO2)). Solid lines are guides to the eye.
(i.e. in the longer time scale), the motion of ions is set apart by the long range diffusion of mobile ions. In this region < r2(t) > follows a liner relation with time (i.e. < r2(t) > ~ t) and the ionic motion in the glass network can be visualized as the motion through a three dimensional potential landscape, where the barrier heights vary from site to site [21]. The highest barrier in conduction pathways is often referred to as the percolation barrier. In the sub-diffusive regime, the probability of the backward jump of the ion is higher as the ions are unable to overcome the percolation barrier. In this time scale the ionic conduction is characterized by the correlated forward-backward hopping of mobile ions. At diffusive regime, the ions move randomly from a low energy site to the next site as the mobile ions are able to overcome the percolation barrier. The characteristic mean square displacement, < r2(tp) > is defined as the average distance, the mobile ions have to travel to overcome the nearest percolation barrier. We have estimated values of < r2(tp) > at different temperatures for all compositions following the procedure described elsewhere [21]. The values of < r2(t) > at different temperatures for 0.1AgI0.9(0.3Ag2O-0.7(0.5SeO2-0.5MoO3)) have been calculated from the conductivity spectra using Eq. (3) and their temporal dependence is shown in Fig. 4(b). The values of < r2(tp) > have been calculated from the crossover point of dispersive and non-dispersive regions. Fig. 5(a) shows the dependence of < r2(tp) > on the mixed glass former ratio for yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) glasses, while Fig. 5(b) shows the
dependence of < r2(tp) > on AgI doping content for xAgI-(1 − x) (yAg2O-(1 − y)(0.5SeO2–0.5TeO2)) glass systems. It is noted that < r2(tp) > shows an opposite correlation to the dc conductivity for both cases. A similar variation of < r2(tp) > with AgI content and mixed ratio has been observed in Fig. 6(a) and (b) respectively for xAgI(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses. It is noted in Fig. 5(a) that for yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) mixed network former glasses < r2(tp) > shows a minimum for x = 0.4 for both modifier contents (y = 0.3 and 0.4) and shows an inverse correlation to the conductivity observed in Fig. 2(b). As < r2(tp) > decreases, the Ag+ ions have to travel lesser distance to overcome the force causing correlated forward-backward motion and hence the conductivity increases. A similar result has been observed for highly modified xAgI-(1 − x) (0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses mixed former glasses. It has been observed in Fig. 5(b) for AgI-Ag2O-SeO2-TeO2 glasses that < r2(tp) > decreases with increase of doping salt AgI content and shows an inverse correlation with the ionic conductivity. Also < r2(tp) > falls rapidly for lower modifier content than that of the higher value of y which explains the reason for higher conductivity at low modifier content and justifies our result. However, it has been reported that the compositional dependence of < r2(tp) > and σdc shows opposite behaviour for silver and sodium borophosphate [B2O3-P2O5] glasses [26,33]. It is observed for xAgI-(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) 4
Solid State Ionics 343 (2019) 115126
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Fig. 7. (a) FTIR spectra in the wave number range of 400–960 cm−1 for all the glasses of the composition 0.3Ag2O-0.7(ySeO2-(1 − y)TeO2). (b) De-convolution of FTIR spectra in the wave number range of 400–960 cm−1 for the same glass composition. Dotted lines present the resulting spectra of de-convoluted absorption bands.
Fig. 6. (a) Variation of characteristic length < r2(tp) > with AgI content for different mixed network former ratio. (b) Variation of characteristic length < r2(tp) > with network former ratio for different AgI contents for the glass series xAgI-(1 − x)[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)].
lengths, ion dynamics and the modification of the glass networks, we have studied FTIR spectra for different glass compositions. FTIR spectra for 0.3Ag2O-0.7(xSeO2-(1 − x)TeO2) glasses are presented in Fig. 7(a) in the wave number range 400–960 cm−1. Since different bands have overlapped, FTIR spectra of all the samples have been de-convoluted using a Gaussian function for the identification of the individual bands, which appear in these spectra, and their assignments. One such deconvolution is shown in Fig. 7(b). By determining the number of all independent components of the vibrational bands a quantitative analysis is carried out to find the change in the relative content of the different network structural units. The peak frequency, half-width at half-height and area are allowed to float during the iterations, and proportion of a particular vibrational band has been determined from the area of that fitted Gaussian band divided by the total area of all the bands. In fact, this relative area signifies the concentration or strength of the corresponding bond. For yAg2O-(1 − y)[xSeO2-(1 − y)TeO2] glasses the important contribution to the structural modification is found from the bands centered at around ~610–620 cm−1, ~670–680 cm−1, ~750–770 cm−1 and ~870–875 cm−1. The absorption bands located around ~610–620 cm−1 and ~670–680 cm−1 are assigned to the stretching vibration of the Te-O-Te bridges between TeO4 tetragonal bipyramidal units and the band around ~750–770 cm−1 arises from TeeO bending vibration in TeO3 trigonal pyramidal units [36–38]. The band located in the range ~870–880 cm−1 is attributed to the vibration mode of Se-O-Se bond of SeO32− ions [39]. A weak band appearing around ~610–620 cm−1 is
glasses that the value of < r2(tp) > decreases with the increase of AgI content and oppositely correlated to σdc [Fig. 6(a)] similar to our previous results [27]. For present AgI doped silver selenomolybdate [xAgI(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3))] glasses, < r2(tp) > shows a significant change with SeO2 content [Fig. 6(b)]. It may be noted that < r2(tp) > primarily depends on two factors: modification of the glass network structure and Coulomb interaction between the ions. For single former glass systems, the degree of modification of network structure is small and the inter-ionic Coulomb interaction mainly controls the compositional variation of < r2(tp) > , while the structural modification is the main reason for the compositional variation of < r2(tp) > for the mixed former glasses. Therefore, this dissimilar behaviour reported for different compositions indicates a strong correlation between the ion dynamics and the characteristic length scale. Alternatively, the expansion of glass network due to the addition of AgI has been proposed for fast ion conduction [34,35]. EXAFS studies of these glasses [2] have indicated that the IeAg distance increases with increase of AgI content, leading to a decrease of the activation energy and signifying a correlation between the expansion of the glass network and the activation energy. Therefore, mixed network former effect in these glasses is overridden by the silver ion conductivity of AgI. 3.3. FTIR and Influence of structural parameters over transport property For further investigation of the correlation among these microscopic 5
Solid State Ionics 343 (2019) 115126
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Fig. 9. (a) Variation of relative proportion for the vibration band (Ag2SeO3) centered at 820 cm−1 with mixed network former ratio for different modifier ratio of the glass series yAg2O-(1 − y)(xSeO2-(1 − x)TeO2). (b) Variation of the relative proportion of the vibration band (SeO32−) centered at 875 cm−1 with the AgI content for different modifier contents for the glass series xAgI-(1 − x) (yAg2O-(1 − y)(0.5SeO2–0.5TeO2)). Solids lines are guides to the eye.
Fig. 8. (a) Variation of the relative population for the vibration band (TeO3) centered at 760 cm−1 with mixed former ratio for different Ag2O contents. (b) Variation of relative population for the vibration band (SeO32−) centered at 875 cm−1 with mixed former ratio for different Ag2O contents for yAg2O(1 − y)(xSeO2-(1 − x)TeO2) glasses. Solids lines are guides to the eye.
depolymerises the three-dimensional trigonal bipyramid structure of TeO4 units which increases the proportion of SeO32− and TeO3 isolated groups [39]. For higher mixed former ratio, the SeO32− ions have an affinity to bond with Ag+ ions and form isolated Ag2SeO3 crystalline structure, which in turn reduces the availability of the effective nonbridging hopping sites [22,23,27]. It has been observed in various SeO2-B2O3 [39] and SeO2-MoO3 [27] glasses that a part of SeO2 contributes to the formation of Ag2SeO3 immobile structure, when adequate Ag+ ions are present in the glass structure. Formation of a composite Cu2SeO3 structure has been also observed in some selenite glasses containing Cu2+ ions [44]. The feeble band observed at around 820 cm−1 corresponds to the Ag2SeO3 unit [45], which grows at a higher value of SeO2 content. Fig. 9(a) shows the growth of the Ag2SeO3 structure with composition in the glass matrix. A sharp increase is observed for glasses containing higher SeO2 content (x = 0.5 and 0.6, for y = 0.3), so the collective effect of decrease in the relative proportion of SeO32− ions and the decrease in free volume due to the increase in isolated Ag2SeO3 crystalline structures, decrease the conductivity. Also a similar result has been observed for xAgI-(1 − x)[yAg2O-(1 − y) (0.5SeO2-0.5TeO2) glasses [23]. A reduction in relative proportion of selenite non-bridging oxygen is observed in Fig. 9(b) due to formation of immobile Ag2SeO3 structure, which explains the decrease of conductivity of the Ag+ ion rich glasses, as shown in Fig. 2(b). For xAgI-
attributed to the vibration of SeeO bond present in SeO3 unit [40]. The band around ~920–930 cm−1 does not show any significant change, which may appear from the formation of some complex selenium-tellurium composite. It is observed in Fig. 8(a) that the relative population of TeeO bending vibration in TeO3 trigonal pyramidal units increases with the increase of glass network former ratio (x ≤ 0.4) but decreases at higher SeO2 content. In Fig. 8(b) relative proportion of SeO32− unit also shows a similar trend and confirms a direct correlation with < r2(tp) > . These results can be explained as follows: the number of TeO4 groups is reduced with the increase of SeO2 content, because some of the tetragonal TeO4 bipyramidal units are converted into trigonal TeO3 pyramidal units with insert of selenium oxide in the glass network [36]. For example, in Li2O−TeO2 glasses TeO4 trigonal bipyramids transform to TeO3 trigonal pyramids with the increase of Li2O content [41]. Similarly, in Li2O−B2O3 glasses a conversion of BO4 to BO3 unit of glass network has been observed with the increase of Li2O [42]. Also in TeO2−P2O5 glasses P−O−Te linkages are formed, which serve as a mechanism for more effective anionic charge diffusion in the network, resulting in shallower Coulomb traps and thus improved ionic conductivity [43]. The increase of TeO3 and BO3 units in the glass network indicates that the concentration of non-bridging oxygen increases, helping in faster migration of mobile ions. In the present cases SeO2 6
Solid State Ionics 343 (2019) 115126
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∼910 cm−1. The band at ∼500 cm−1 is attributed to the vibration of SeeO bond present in the SeO3 unit [39]. This band is very weak and shifts to lower wave number with increase of AgI. Bands centred at ∼600–610 cm−1 and ∼880 cm−1 are attributed to the vibration of MoO-Mo bridging bond of the isolated MoO6 units [46–48]. These bands remain almost unaltered with the change in composition. The acquired bands at ∼690 cm−1, ∼780 cm−1 and ∼840 cm−1 are consigned to the vibration of SeO32− selenite ion [39,45,46],. The band at ∼690 cm−1 remains unaltered with composition. The band at ∼910 cm−1 is related to the Mo2O8 molybdate octahedral units. It is observed that the oscillator strength of the SeO32− vibration band increases with the increase of the AgI content as well as with the increase of the SeO2 content [Figs. 10 (a) and (b)]. This result is opposite to that of < r2(tp) > for different network former ratio. With the increase of the mixed former ratio, more SeO32− ions happen to be available in the glass network. The non-bridging oxygen of SeO32− creates more available hopping sites for Ag+ ions, resulting in a decrease in the characteristic displacement < r2(tp) > [Fig. 11]. These results indicate that the ion dynamics and the microscopic length scales are directly connected to the network structural units of the glasses. 3.4. Validity of time-temperature superposition principle To get further insight into ion-dynamics we have checked whether the conductivity spectra follow the time temperature superposition principle using scaling of the conductivity spectra. Scaling is a significant feature in any data assessment program. The ability to scale different data sets so as to collapse all to one common master curve indicates the process can be separated into a common physical mechanism modified only by thermodynamic scales [49]. It is generally possible to scale ac conductivity data for different temperatures and different compositions into one single master curve. The subsistence of such a master curve is referred to as the “time-temperature superposition principle” (TTSP). In that case the conductivity spectra of a particular composition should overlap perfectly onto the master curve with proper scaling. The usefulness of the idea of scaling often can be observed in the coexistence of gas-liquid in many molecular fluids [50,51]. Various models have been proposed by different workers [52–54] for scaling of conductivity spectra. However, we have used here the model proposed by Sidebottom [54] due to the following reason. The network structure of the present glass series is modified due to the change in glass former ratio as well as doping content, resulting in a change in potential landscape in which the mobile ions are moving. As the glass network structure changes, the hopping distance for the mobile ions also changes. This change in hopping length was accounted by scaling formalism proposed by Sidebottom given by [54].
Fig. 10. (a) Variation of relative proportion for the vibration band (SeO32−) centred at 840 cm−1 with glass former ratio for fixed AgI contents. (b) The variation of the same with AgI content for different glass former ratios.
( )
=F
0
(4)
where ε0 is vacuum permittivity, Δε is dielectric loss strength given by Δε = ε(0) − ε∞, where ε∞ is the high frequency dielectric constant and ε(0)) is the low frequency static value. The values of ε(0) and ε∞ have been estimated by fitting the dielectric spectra in the high frequency region with the help of Cole-Cole equation [55]. The values of Δε have been calculated following the procedure reported elsewhere [8,15]. Frequency dependence of dielectric constant ε′ of a particular composition of selenium-molybdate glass has been shown in Fig. 12 at several temperatures. The scaling of the conductivity spectra at different temperatures has been performed for all compositions following Eq. (4). The scaling results for the xAgI-(1 − x)[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)] glass series are shown in Fig. 13(a) for a glass composition at different temperatures. The scaling results for different AgI contents and glass former ratio of the same glass series at a fixed temperature are shown in Fig. 13(b) and inset of Fig. 13(b) respectively. It is noted that the scaling of the conductivity spectra at different temperatures for different
Fig. 11. Variation of < r2(tp) > on relative proportion of SeO32− units for different glass former ratio for the composition 0.1AgI-0.9[0.3Ag2O-0.7(ySeO2(1 − y)MoO3)]. The solid line is a guide to the eye.
(1 − x)[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)] system the major contributing bands found centred at: ∼500 cm−1, ∼600–610 cm−1, ∼690 cm−1, ∼780–790 cm−1, ∼840–845 cm−1, ∼880 cm−1 and 7
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glasses containing different AgI contents and mixed former ratio is perfect. Similar scaling results have been also obtained for yAg2O(1 − y)[xSeO2-(1 − x)TeO2] and xAgI-(1 − x)[yAg2O-(1 − y)(0.5SeO20.5TeO2) glass series. The near perfect superposition of different conductivity spectra onto a single master curve signifies that the ion conduction process follows a common mechanism, which is independent of temperature, doping salt content and glass former ratio. 4. Concluding remarks Ion dynamics in several mixed glass former systems has been studied by changing modifier content, mixed glass former ratio and doping salt content. The ionic conductivity exhibits strong composition dependence on the glass former ratio. The mean square displacement < r2(tp) > shows strong dependence on composition. < r2(tp) > shows an opposite correlation to relative population of TeO3 and SeO32− units for yAg2O-(1 − y)(xSeO2-(1 − y)TeO2) glasses. SeO2 depolymerises the three-dimensional structure of TeO4 unit which results in an increase of SeO32− and TeO3 units proportionately. With the increase of the nonbridging oxygen the available hopping sites for the Ag+ ions increase in the glass network, decreasing the characteristic distance the ion has to travel to overcome the neighbouring high energy percolation barrier. At higher SeO2 content, the relative population of SeO32− ions decreases due to the formation of immobile Ag2SeO3 crystalline structure, which reduces the availability of free volume for ion migration as well as the ion concentration, and subsequently a decrease in the conductivity is observed at higher SeO2 content for these glasses. For xAgI-(1 − x) (0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses also the characteristic displacement < r2(tp) > of the ion dynamics shows an inverse correlation to the ionic conductivity. The scaling of the conductivity spectra indicates that the ion conduction mechanism is independent of temperature as well as composition i. e. doping salt content and mixed glass former ratio.
Fig. 12. Frequency dependence of dielectric constant ε′ for 0.1AgI0.9[0.3Ag2O-0.7(0.5SeO2–0.5MoO3)] glass at several temperatures.
Declaration of competing interest There is no conflict of interest. Acknowledgement A. Ghosh thanks the Department of Science and Technology, Government of India, for the award of J. C. Bose Fellowship (grant No. SB/S2/JCB-33/2014). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
Fig. 13. (a) Scaled master curves of the ac conductivity spectra according to the Sidebottom scaling model for the 0.1AgI-0.9[0.3Ag2O-0.7(0.5SeO2-0.5MoO3)] glass composition for several temperatures. (b) Scaling of the conductivity spectra for different AgI contents for xAgI-(1 − x)[0.3Ag2O-0.7(0.5SeO20.5MoO3)]. The inset shows the scaled curves for different glass former ratio for 0.1AgI-0.9[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)] glasses.
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Structure-transport correlation of super-ionic mixed network former glasses A. Palui, A. Ghosh
⁎
T
School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
ARTICLE INFO
ABSTRACT
Keywords: Mixed former glass Characteristic length Structure
We have studied the ion dynamics in several mixed former glasses in wide composition and temperature ranges. The ionic conductivity obtained from complex impedance plot follows the Arrhenius relation. It is observed that the ionic conductivity of these glasses exhibits mixed glass former effect and depends strongly on the dopant salt content as well as on the mixed former ratio. The composition dependence of the activation energy exhibits an opposite trend by that of the conductivity. The characteristic mean square displacement of mobile ions has been determined from the ac conductivity spectra in the framework of linear response theory. It is observed that the ionic conductivity and the mean square displacement of mobile ions are correlated with the population density of structural units of the glass network. The time-temperature superposition principle has been verified using the scaling of the conductivity spectra.
1. Introduction
conductivity (negative glass former effect) has been observed [15,16]. This non-linear variation of the conductivity and other physical properties of these glasses with mixed former ratio is known as mixed glass former effect [17]. Several mixed network former glasses [16–18] have been studied and the electrical conductivity of the glasses is linked with their network structure. The ionic conductivity of borotellurite mixed former glasses has been directly linked with the BO4 tetrahedral units [15]. In these glasses the movement of electron pair of BeO bond temporarily opens up the network structure which assists ion transport [15]. On the other hand, the ionic conductivity of silver selenium-molybdate mixed former glasses has been related to the ratio of population of SeO32− ions to that of the isolated MoO6 units [14]. SeO32− ions consist of nonbridging oxygen which assists in ion migration and this ratio indicates the influence of immobile MoO6 unit on the selenite non-bridging oxygen. Thus, the contributions of both the structural units affect the ionic conductivity at the same time. Further, available free volume in silver selenium-molybdate glasses decreases for higher silver oxide content due to formation of isolated silver selenite unit, which in turn decreases the conductivity [14]. Thus, the above discussion indicates that the network structure units profoundly influence the ion migration. To understand mixed glass former effect, a mixed barrier model has been developed for several mixed former glasses [11]. This model takes into account the reduction of the barrier strength for ion jump with mixing of different network formers and the composition independent coordination environment of the network forming units. Also in this model the barrier energy for ion jump is reduced rapidly for
Superionic mixed former glasses are important from both academic and technological standpoints [1,2]. The study of ion transport properties of glassy conductors and their correlation with the glass network structure is a challenging problem as the microscopic network structure regulates the ion transport mechanism of these glasses [3,4]. For potential application of these ionic glasses in electrochemical devices [5], the enhancement of the ionic conductivity in a methodical way is essential. There are different ways to enhance the ionic conductivity in such ion conducting glasses. One way is to increase the content of network modifier oxides such as Li2O, Ag2O, etc. which de-polymerize the glass network and increase the non-bridging oxygen content, leading to increase in the available hopping sites for mobile ions and hence an enhancement of the conductivity [6]. Addition of alkali or silver halides is another way to achieve superionic conductivity [7,8]. In some particular cases for AgI doped glasses, I− ions lead to construction of O−Ag−I−Ag−O bridges which progressively expands the pathway volume for Ag+ ion conduction, causing enhancement of the ionic conductivity [2,9]. In this case, IeAg distance plays a key role on enhancement of the conductivity. Doping of sulphide salts in a few glasses increases the polarizability and conductivity of these glasses [10]. One of the captivating ways to enhance the conductivity is to incorporate more than one glass former [11]. It is often found that the conductivity of these mixed formers glasses passes through one and sometimes more than one maximum value with the change of mixed former ratio [12–14]. For some mixed former glasses, a minimum in the
⁎
Corresponding author. E-mail address: [email protected] (A. Ghosh).
https://doi.org/10.1016/j.ssi.2019.115126 Received 13 July 2019; Received in revised form 28 September 2019; Accepted 17 October 2019 0167-2738/ © 2019 Elsevier B.V. All rights reserved.
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heterogeneous materials than that of the homogeneous materials [11]. The main difficulty to understand the ion dynamics is the lack of knowledge about the complex glass structure. This can be resolved by determining the mean square displacement of the hopping motion of the mobile ions in the framework of linear response theory [19–21]. We know that primarily the hopping motion of the mobile ions between potential minima controls the ion dynamics and the heights of the potential barriers are controlled by the Coulomb interaction between the mobile ions and the network structure. Therefore, we can find out the minimum length, the ion has to travel to overcome these barriers, by determining the characteristic lengths associated with it and can establish a connection with the macroscopic parameters. The present paper reports the perceptive of the different microscopic parameters that can influence the macroscopic ion dynamics in different glass systems. We have shown that the ionic conductivity is directly correlated to the characteristic length scale. We have also shown that the modification of the glass networks plays a leading role on the composition dependence of these microscopic parameters. Fig. 1. Arrhenius temperature dependence of dc conductivity for different compositions of yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) glasses. The solid lines present the least square linear fits to the data.
2. Experimental details Three series of glass compositions has been investigated as stated below. (1) yAg2O-(1 − y)[xSeO2-(1 − x)TeO2], where x = 0–0.6 for y = 0.3 and x = 0–0.5 for y = 0.4; (2) xAgI-(1 − x)[yAg2O-(1 − y)(0.5SeO2–0.5TeO2), where x = 0–0.4 and y = 0.3, 0.4 and (3) xAgI-(1 − x)[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)], where x = 0.1–0.3 and y = 0.3, 0.5 and 0.7. These compositions were prepared by melt quench technique. The details of preparation procedure of these glass samples were given elsewhere [8,22,23]. The proper amounts of reagent grade chemicals were thoroughly mixed and the mixtures were preheated in alumina crucibles at 400 °C for 2 h. The mixtures were then melted at temperatures in the range 550 to 720 °C depending on the composition. The melts were equilibrated for 2 h and finally quenched between two aluminum plates to obtain transparent glass samples. Glass formation was confirmed from X-ray diffraction patterns of the powdered samples taken in an X-ray diffractometer (model Bruker AXS) using Cu Kα radiation. X-ray diffraction patterns of the samples exhibited a wide halo, characteristics of amorphous materials. Density of the glasses was measured at room temperature by Archimedes principle using acetone as the immersion liquid. Fourier transform infrared (FTIR) spectra of the pellets, prepared from the mixtures of glass and KBr powders in the ratio 1:100, were recorded at room temperature in the wave number range 400–4000 cm−1 in a FTIR spectrometer (PerkinElmer, model Spectrum 100). Measurements of the electrical conductivity and the dielectric permittivity of the samples were carried out in the frequency range 10 Hz–2 MHz in a LCR meter (QuadTech, model 7600 Plus) using a parallel electrode configuration in a wide temperature range.
Fig. 2. (a) Dependence of the ionic conductivity and activation energy on glass former ratio for different Ag2O contents at a common temperature for yAg2O(1 − y)(xSeO2-(1 − x)TeO2) glasses. (b) Variation of the ionic conductivity and activation energy at a common temperature with the AgI content for different modifier contents for xAgI-(1 − x)(yAg2O-(1 − y)(0.5SeO2–0.5TeO2)) glasses. The lines are guides for the eyes.
3. Results and discussion 3.1. DC conductivity We have obtained ionic conductivity of all the samples from the complex impedance plot. The reciprocal temperature dependence of the ionic conductivity is shown in Fig. 1 for yAg2O-(1 − y)(xSeO2(1 − x)TeO2) glasses. It is noted that the dc conductivity (σ) is thermally activated and follows the Arrhenius relation given by Eq.(1),
T=
0 exp[
E / kB T ]
activation energy (Eσ) has been obtained by least square fitting of the conductivity data. The variation of σ and Eσ with mixed former ratio for yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) glasses is shown in Fig. 2(a) for different modifier contents (Ag2O = 0.3 and Ag2O = 0.4). It is noted that the ionic conductivity shows a maximum for x = 0.4 for each modifier content. It is also noted that the ionic conductivity is higher for
(1)
where σ0 is the pre-exponential factor, Eσ is the activation energy, kB is the Boltzmann constant and T is the absolute temperature. The 2
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glasses containing higher modifier content. It is observed that the present yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) mixed network former glasses display higher ionic conductivity than the Ag2O−TeO2 single network former glasses [24]. Thus, the enhanced conductivity is observed by mixing of two different glass network formers and the mixed glass network former effect comes into play. The mixed former effect in the present Ag2O−SeO2−TeO2 mixed former glasses may be compared with that reported in Ag2O-B2O3-TeO2 glasses [15]. It may be noted that the variation of the conductivity for the present mixed former glasses with mixed former ratio is quite different from that of the Ag2O−B2O3−TeO2 mixed former glasses [15]. It has been reported that initially the conductivity of Ag2O − B2O3 − TeO2 glasses decreases slightly with the increase of B2O3 content but shows an increase for higher content of B2O3 [15]. A different phenomenon is observed when the Ag2O−SeO2−TeO2 glasses are doped with AgI salt. Fig. 2(b) shows the variation of σ and Eσ with AgI doping content for xAgI-(1 − x) (yAg2O-(1 − y)(0.5SeO2–0.5TeO2)) glasses for different modifier contents (Ag2O). It is observed that the conductivity is higher for a higher modifier (Ag2O = 0.4) content for undoped glasses. But a discrepancy is observed for higher value of AgI content (x > 0.1), where the conductivity shows a lower value than that of the lower modifier containing glass (Ag2O = 0.3). It has been reported that the increase in the conductivity for AgI-Ag2O-SeO2 glasses [25] is mainly governed by the expansion of the glass network, which leads to an increase in the free volume creating more open network structure for faster ionic conduction [15]. However, the conductivity of the Ag2O-B2O3-P2O5 mixed former glasses is mainly controlled by the de-polymerization of the glass network due to the increase in Ag2O modifier oxide content [26]. The ionic conductivity and activation energy of xAgI-(1 − x) (0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) mixed former glasses are shown in Fig. 3(a) and (b) as a function of glass former ratio and AgI doping content respectively. A minimum in the conductivity is observed for x = 0.2 and 0.3 at y = 0.5 (Fig. 3(b)). In comparison, the conductivity of the undoped 0.3Ag2O-0.7(ySeO2-(1 − y)MoO3) glasses increases with the increase of the SeO2 content up to y = 0.7 and then the conductivity decreases slightly for y = 0.8 [27]. In highly doped xAgI(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses it is clearly seen that the value of the ionic conductivity is less affected by the network structure and is mainly influenced by the AgI content, i.e., the mixed network former effect in these glasses is overridden by the silver ion conductivity of AgI [28]. It is noted in these figures that the composition dependence of the activation energy exhibits a trend which is opposite to that of the conductivity for each case.
Fig. 3. (a) Variation of the ionic conductivity and activation energy with AgI content for different network former ratios at fixed temperature for xAgI(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses. (b) Variation of the ionic conductivity and activation energy with the glass network former ratio for different AgI contents at a fixed temperature for the same glass series. Solid lines are guide to the eye.
( )=
NV q2 2 6k THR
< r 2 (t) > sin( t )dt 0
(2)
where NV is the mobile ion number density, q is the charge of the mobile ions, kB is the Boltzmann constant and T is the absolute temperature and HR is the Haven ratio, which indicates degree of correlation between successive hops [30]. The value of HR depends on the concentration of the mobile ions and varies from 0.2 to 1 in general [30]. The ion transport in glasses with low ionic concentration (30–100 ppm) is uncorrelated (HR ≈ 1), but HR decreases rapidly with increasing ionic concentration and remains nearly constant (HR = 0.2–0.4) for ion rich glasses [30,31]. The average AgeAg interionic distance decreases with increase in ionic concentration, which leads to an increase in the inter-ionic interactions and thus a gradual decrease of HR is observed. The glass compositions in current paper are all ionically rich and as reported for other silver selenite glasses we assume HR ≈ 0.3 [30–32]. The mean square displacement of mobile ions, < r2(t) > can be calculated from the frequency dependent conductivity data using the following transformation [21].
3.2. AC conductivity and mean square displacement The conductivity spectra at different temperatures for atypical glass composition, 0.1AgI-0.9(0.3Ag2O-0.7(0.5SeO2-0.5MoO3)), are shown in Fig. 4(a). All other glass compositions also show similar spectra. In fact, the shape of the ac conductivity spectra for all compositions is remarkably similar to those of different disordered solids [29]. It is observed for all glass compositions that at low temperatures and low frequencies the ac conductivity is almost independent of frequency and corresponds to the dc conductivity, while at higher frequency, the ac conductivity shows a dispersive behavior. It is also observed that the ac conductivity spectra at higher temperatures and low frequencies are influenced by the electrode polarization effect. In order to comprehend the conduction pathways of glass systems we have determined characteristic mean square displacement of mobile ions from the conductivity spectra using linear response theory [19]. In this framework, the frequency dependent conductivity is related to the mean square displacement (< r2(t) >) of the mobile ions at thermal equilibrium by the following relation [21].
< r 2 (t ) > =
12k T NV q2
t
( )
dt 0
0
sin( t ) d
(3)
It is observed that in sub-diffusive regime (i.e. shorter time scale) the value of < r2(t) > is small and the non-random forward-backward motion of ions portrays ionic motion. In this region < r2(t) > increases with increase of time in a sub-linear way given by < r2(t) > ~ t1−n, where n is a power law exponent. On the contrary, in diffusive regime 3
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Fig. 4. (a) Conductivity spectra at different temperatures for 0.1AgI0.9(0.3Ag2O-0.7(0.5SeO2-0.5MoO3)) glasses. (b) Time dependence of < r2(t) > at different temperatures for 0.1AgI-0.9(0.3Ag2O-0.7(0.5SeO20.5MoO3)) glasses. Solid straight lines denote the least square fittings to the diffusive and sub diffusive region. From the crossover of the lines we get the values of tp and < r2(tp) > .
Fig. 5. (a) Variation of the characteristic length < r2(tp) > with mixed former ratio for different values of modifier contents for yAg2O-(1 − y)(xSeO2(1 − x)TeO2) glasses. (b) The variation of < r2(tp) > with AgI for different contents of Ag2O are shown for the glass composition xAgI-(1 − x)(yAg2O(1 − y)(0.5SeO2–0.5TeO2)). Solid lines are guides to the eye.
(i.e. in the longer time scale), the motion of ions is set apart by the long range diffusion of mobile ions. In this region < r2(t) > follows a liner relation with time (i.e. < r2(t) > ~ t) and the ionic motion in the glass network can be visualized as the motion through a three dimensional potential landscape, where the barrier heights vary from site to site [21]. The highest barrier in conduction pathways is often referred to as the percolation barrier. In the sub-diffusive regime, the probability of the backward jump of the ion is higher as the ions are unable to overcome the percolation barrier. In this time scale the ionic conduction is characterized by the correlated forward-backward hopping of mobile ions. At diffusive regime, the ions move randomly from a low energy site to the next site as the mobile ions are able to overcome the percolation barrier. The characteristic mean square displacement, < r2(tp) > is defined as the average distance, the mobile ions have to travel to overcome the nearest percolation barrier. We have estimated values of < r2(tp) > at different temperatures for all compositions following the procedure described elsewhere [21]. The values of < r2(t) > at different temperatures for 0.1AgI0.9(0.3Ag2O-0.7(0.5SeO2-0.5MoO3)) have been calculated from the conductivity spectra using Eq. (3) and their temporal dependence is shown in Fig. 4(b). The values of < r2(tp) > have been calculated from the crossover point of dispersive and non-dispersive regions. Fig. 5(a) shows the dependence of < r2(tp) > on the mixed glass former ratio for yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) glasses, while Fig. 5(b) shows the
dependence of < r2(tp) > on AgI doping content for xAgI-(1 − x) (yAg2O-(1 − y)(0.5SeO2–0.5TeO2)) glass systems. It is noted that < r2(tp) > shows an opposite correlation to the dc conductivity for both cases. A similar variation of < r2(tp) > with AgI content and mixed ratio has been observed in Fig. 6(a) and (b) respectively for xAgI(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses. It is noted in Fig. 5(a) that for yAg2O-(1 − y)(xSeO2-(1 − x)TeO2) mixed network former glasses < r2(tp) > shows a minimum for x = 0.4 for both modifier contents (y = 0.3 and 0.4) and shows an inverse correlation to the conductivity observed in Fig. 2(b). As < r2(tp) > decreases, the Ag+ ions have to travel lesser distance to overcome the force causing correlated forward-backward motion and hence the conductivity increases. A similar result has been observed for highly modified xAgI-(1 − x) (0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses mixed former glasses. It has been observed in Fig. 5(b) for AgI-Ag2O-SeO2-TeO2 glasses that < r2(tp) > decreases with increase of doping salt AgI content and shows an inverse correlation with the ionic conductivity. Also < r2(tp) > falls rapidly for lower modifier content than that of the higher value of y which explains the reason for higher conductivity at low modifier content and justifies our result. However, it has been reported that the compositional dependence of < r2(tp) > and σdc shows opposite behaviour for silver and sodium borophosphate [B2O3-P2O5] glasses [26,33]. It is observed for xAgI-(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) 4
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Fig. 7. (a) FTIR spectra in the wave number range of 400–960 cm−1 for all the glasses of the composition 0.3Ag2O-0.7(ySeO2-(1 − y)TeO2). (b) De-convolution of FTIR spectra in the wave number range of 400–960 cm−1 for the same glass composition. Dotted lines present the resulting spectra of de-convoluted absorption bands.
Fig. 6. (a) Variation of characteristic length < r2(tp) > with AgI content for different mixed network former ratio. (b) Variation of characteristic length < r2(tp) > with network former ratio for different AgI contents for the glass series xAgI-(1 − x)[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)].
lengths, ion dynamics and the modification of the glass networks, we have studied FTIR spectra for different glass compositions. FTIR spectra for 0.3Ag2O-0.7(xSeO2-(1 − x)TeO2) glasses are presented in Fig. 7(a) in the wave number range 400–960 cm−1. Since different bands have overlapped, FTIR spectra of all the samples have been de-convoluted using a Gaussian function for the identification of the individual bands, which appear in these spectra, and their assignments. One such deconvolution is shown in Fig. 7(b). By determining the number of all independent components of the vibrational bands a quantitative analysis is carried out to find the change in the relative content of the different network structural units. The peak frequency, half-width at half-height and area are allowed to float during the iterations, and proportion of a particular vibrational band has been determined from the area of that fitted Gaussian band divided by the total area of all the bands. In fact, this relative area signifies the concentration or strength of the corresponding bond. For yAg2O-(1 − y)[xSeO2-(1 − y)TeO2] glasses the important contribution to the structural modification is found from the bands centered at around ~610–620 cm−1, ~670–680 cm−1, ~750–770 cm−1 and ~870–875 cm−1. The absorption bands located around ~610–620 cm−1 and ~670–680 cm−1 are assigned to the stretching vibration of the Te-O-Te bridges between TeO4 tetragonal bipyramidal units and the band around ~750–770 cm−1 arises from TeeO bending vibration in TeO3 trigonal pyramidal units [36–38]. The band located in the range ~870–880 cm−1 is attributed to the vibration mode of Se-O-Se bond of SeO32− ions [39]. A weak band appearing around ~610–620 cm−1 is
glasses that the value of < r2(tp) > decreases with the increase of AgI content and oppositely correlated to σdc [Fig. 6(a)] similar to our previous results [27]. For present AgI doped silver selenomolybdate [xAgI(1 − x)(0.3Ag2O-0.7(ySeO2-(1 − y)MoO3))] glasses, < r2(tp) > shows a significant change with SeO2 content [Fig. 6(b)]. It may be noted that < r2(tp) > primarily depends on two factors: modification of the glass network structure and Coulomb interaction between the ions. For single former glass systems, the degree of modification of network structure is small and the inter-ionic Coulomb interaction mainly controls the compositional variation of < r2(tp) > , while the structural modification is the main reason for the compositional variation of < r2(tp) > for the mixed former glasses. Therefore, this dissimilar behaviour reported for different compositions indicates a strong correlation between the ion dynamics and the characteristic length scale. Alternatively, the expansion of glass network due to the addition of AgI has been proposed for fast ion conduction [34,35]. EXAFS studies of these glasses [2] have indicated that the IeAg distance increases with increase of AgI content, leading to a decrease of the activation energy and signifying a correlation between the expansion of the glass network and the activation energy. Therefore, mixed network former effect in these glasses is overridden by the silver ion conductivity of AgI. 3.3. FTIR and Influence of structural parameters over transport property For further investigation of the correlation among these microscopic 5
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Fig. 9. (a) Variation of relative proportion for the vibration band (Ag2SeO3) centered at 820 cm−1 with mixed network former ratio for different modifier ratio of the glass series yAg2O-(1 − y)(xSeO2-(1 − x)TeO2). (b) Variation of the relative proportion of the vibration band (SeO32−) centered at 875 cm−1 with the AgI content for different modifier contents for the glass series xAgI-(1 − x) (yAg2O-(1 − y)(0.5SeO2–0.5TeO2)). Solids lines are guides to the eye.
Fig. 8. (a) Variation of the relative population for the vibration band (TeO3) centered at 760 cm−1 with mixed former ratio for different Ag2O contents. (b) Variation of relative population for the vibration band (SeO32−) centered at 875 cm−1 with mixed former ratio for different Ag2O contents for yAg2O(1 − y)(xSeO2-(1 − x)TeO2) glasses. Solids lines are guides to the eye.
depolymerises the three-dimensional trigonal bipyramid structure of TeO4 units which increases the proportion of SeO32− and TeO3 isolated groups [39]. For higher mixed former ratio, the SeO32− ions have an affinity to bond with Ag+ ions and form isolated Ag2SeO3 crystalline structure, which in turn reduces the availability of the effective nonbridging hopping sites [22,23,27]. It has been observed in various SeO2-B2O3 [39] and SeO2-MoO3 [27] glasses that a part of SeO2 contributes to the formation of Ag2SeO3 immobile structure, when adequate Ag+ ions are present in the glass structure. Formation of a composite Cu2SeO3 structure has been also observed in some selenite glasses containing Cu2+ ions [44]. The feeble band observed at around 820 cm−1 corresponds to the Ag2SeO3 unit [45], which grows at a higher value of SeO2 content. Fig. 9(a) shows the growth of the Ag2SeO3 structure with composition in the glass matrix. A sharp increase is observed for glasses containing higher SeO2 content (x = 0.5 and 0.6, for y = 0.3), so the collective effect of decrease in the relative proportion of SeO32− ions and the decrease in free volume due to the increase in isolated Ag2SeO3 crystalline structures, decrease the conductivity. Also a similar result has been observed for xAgI-(1 − x)[yAg2O-(1 − y) (0.5SeO2-0.5TeO2) glasses [23]. A reduction in relative proportion of selenite non-bridging oxygen is observed in Fig. 9(b) due to formation of immobile Ag2SeO3 structure, which explains the decrease of conductivity of the Ag+ ion rich glasses, as shown in Fig. 2(b). For xAgI-
attributed to the vibration of SeeO bond present in SeO3 unit [40]. The band around ~920–930 cm−1 does not show any significant change, which may appear from the formation of some complex selenium-tellurium composite. It is observed in Fig. 8(a) that the relative population of TeeO bending vibration in TeO3 trigonal pyramidal units increases with the increase of glass network former ratio (x ≤ 0.4) but decreases at higher SeO2 content. In Fig. 8(b) relative proportion of SeO32− unit also shows a similar trend and confirms a direct correlation with < r2(tp) > . These results can be explained as follows: the number of TeO4 groups is reduced with the increase of SeO2 content, because some of the tetragonal TeO4 bipyramidal units are converted into trigonal TeO3 pyramidal units with insert of selenium oxide in the glass network [36]. For example, in Li2O−TeO2 glasses TeO4 trigonal bipyramids transform to TeO3 trigonal pyramids with the increase of Li2O content [41]. Similarly, in Li2O−B2O3 glasses a conversion of BO4 to BO3 unit of glass network has been observed with the increase of Li2O [42]. Also in TeO2−P2O5 glasses P−O−Te linkages are formed, which serve as a mechanism for more effective anionic charge diffusion in the network, resulting in shallower Coulomb traps and thus improved ionic conductivity [43]. The increase of TeO3 and BO3 units in the glass network indicates that the concentration of non-bridging oxygen increases, helping in faster migration of mobile ions. In the present cases SeO2 6
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∼910 cm−1. The band at ∼500 cm−1 is attributed to the vibration of SeeO bond present in the SeO3 unit [39]. This band is very weak and shifts to lower wave number with increase of AgI. Bands centred at ∼600–610 cm−1 and ∼880 cm−1 are attributed to the vibration of MoO-Mo bridging bond of the isolated MoO6 units [46–48]. These bands remain almost unaltered with the change in composition. The acquired bands at ∼690 cm−1, ∼780 cm−1 and ∼840 cm−1 are consigned to the vibration of SeO32− selenite ion [39,45,46],. The band at ∼690 cm−1 remains unaltered with composition. The band at ∼910 cm−1 is related to the Mo2O8 molybdate octahedral units. It is observed that the oscillator strength of the SeO32− vibration band increases with the increase of the AgI content as well as with the increase of the SeO2 content [Figs. 10 (a) and (b)]. This result is opposite to that of < r2(tp) > for different network former ratio. With the increase of the mixed former ratio, more SeO32− ions happen to be available in the glass network. The non-bridging oxygen of SeO32− creates more available hopping sites for Ag+ ions, resulting in a decrease in the characteristic displacement < r2(tp) > [Fig. 11]. These results indicate that the ion dynamics and the microscopic length scales are directly connected to the network structural units of the glasses. 3.4. Validity of time-temperature superposition principle To get further insight into ion-dynamics we have checked whether the conductivity spectra follow the time temperature superposition principle using scaling of the conductivity spectra. Scaling is a significant feature in any data assessment program. The ability to scale different data sets so as to collapse all to one common master curve indicates the process can be separated into a common physical mechanism modified only by thermodynamic scales [49]. It is generally possible to scale ac conductivity data for different temperatures and different compositions into one single master curve. The subsistence of such a master curve is referred to as the “time-temperature superposition principle” (TTSP). In that case the conductivity spectra of a particular composition should overlap perfectly onto the master curve with proper scaling. The usefulness of the idea of scaling often can be observed in the coexistence of gas-liquid in many molecular fluids [50,51]. Various models have been proposed by different workers [52–54] for scaling of conductivity spectra. However, we have used here the model proposed by Sidebottom [54] due to the following reason. The network structure of the present glass series is modified due to the change in glass former ratio as well as doping content, resulting in a change in potential landscape in which the mobile ions are moving. As the glass network structure changes, the hopping distance for the mobile ions also changes. This change in hopping length was accounted by scaling formalism proposed by Sidebottom given by [54].
Fig. 10. (a) Variation of relative proportion for the vibration band (SeO32−) centred at 840 cm−1 with glass former ratio for fixed AgI contents. (b) The variation of the same with AgI content for different glass former ratios.
( )
=F
0
(4)
where ε0 is vacuum permittivity, Δε is dielectric loss strength given by Δε = ε(0) − ε∞, where ε∞ is the high frequency dielectric constant and ε(0)) is the low frequency static value. The values of ε(0) and ε∞ have been estimated by fitting the dielectric spectra in the high frequency region with the help of Cole-Cole equation [55]. The values of Δε have been calculated following the procedure reported elsewhere [8,15]. Frequency dependence of dielectric constant ε′ of a particular composition of selenium-molybdate glass has been shown in Fig. 12 at several temperatures. The scaling of the conductivity spectra at different temperatures has been performed for all compositions following Eq. (4). The scaling results for the xAgI-(1 − x)[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)] glass series are shown in Fig. 13(a) for a glass composition at different temperatures. The scaling results for different AgI contents and glass former ratio of the same glass series at a fixed temperature are shown in Fig. 13(b) and inset of Fig. 13(b) respectively. It is noted that the scaling of the conductivity spectra at different temperatures for different
Fig. 11. Variation of < r2(tp) > on relative proportion of SeO32− units for different glass former ratio for the composition 0.1AgI-0.9[0.3Ag2O-0.7(ySeO2(1 − y)MoO3)]. The solid line is a guide to the eye.
(1 − x)[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)] system the major contributing bands found centred at: ∼500 cm−1, ∼600–610 cm−1, ∼690 cm−1, ∼780–790 cm−1, ∼840–845 cm−1, ∼880 cm−1 and 7
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glasses containing different AgI contents and mixed former ratio is perfect. Similar scaling results have been also obtained for yAg2O(1 − y)[xSeO2-(1 − x)TeO2] and xAgI-(1 − x)[yAg2O-(1 − y)(0.5SeO20.5TeO2) glass series. The near perfect superposition of different conductivity spectra onto a single master curve signifies that the ion conduction process follows a common mechanism, which is independent of temperature, doping salt content and glass former ratio. 4. Concluding remarks Ion dynamics in several mixed glass former systems has been studied by changing modifier content, mixed glass former ratio and doping salt content. The ionic conductivity exhibits strong composition dependence on the glass former ratio. The mean square displacement < r2(tp) > shows strong dependence on composition. < r2(tp) > shows an opposite correlation to relative population of TeO3 and SeO32− units for yAg2O-(1 − y)(xSeO2-(1 − y)TeO2) glasses. SeO2 depolymerises the three-dimensional structure of TeO4 unit which results in an increase of SeO32− and TeO3 units proportionately. With the increase of the nonbridging oxygen the available hopping sites for the Ag+ ions increase in the glass network, decreasing the characteristic distance the ion has to travel to overcome the neighbouring high energy percolation barrier. At higher SeO2 content, the relative population of SeO32− ions decreases due to the formation of immobile Ag2SeO3 crystalline structure, which reduces the availability of free volume for ion migration as well as the ion concentration, and subsequently a decrease in the conductivity is observed at higher SeO2 content for these glasses. For xAgI-(1 − x) (0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)) glasses also the characteristic displacement < r2(tp) > of the ion dynamics shows an inverse correlation to the ionic conductivity. The scaling of the conductivity spectra indicates that the ion conduction mechanism is independent of temperature as well as composition i. e. doping salt content and mixed glass former ratio.
Fig. 12. Frequency dependence of dielectric constant ε′ for 0.1AgI0.9[0.3Ag2O-0.7(0.5SeO2–0.5MoO3)] glass at several temperatures.
Declaration of competing interest There is no conflict of interest. Acknowledgement A. Ghosh thanks the Department of Science and Technology, Government of India, for the award of J. C. Bose Fellowship (grant No. SB/S2/JCB-33/2014). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
Fig. 13. (a) Scaled master curves of the ac conductivity spectra according to the Sidebottom scaling model for the 0.1AgI-0.9[0.3Ag2O-0.7(0.5SeO2-0.5MoO3)] glass composition for several temperatures. (b) Scaling of the conductivity spectra for different AgI contents for xAgI-(1 − x)[0.3Ag2O-0.7(0.5SeO20.5MoO3)]. The inset shows the scaled curves for different glass former ratio for 0.1AgI-0.9[0.3Ag2O-0.7(ySeO2-(1 − y)MoO3)] glasses.
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