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Effect of network structure on dynamics of lithium ions in molybdenum phosphate mixed former glasses
Solid State Ionics 347 (2020) 115238
Contents lists available at ScienceDirect
Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Effect of network structure on dynamics of lithium ions in molybdenum phosphate mixed former glasses A. Chatterjee, S. Majumdar, A. Ghosh
T
⁎
School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
A R T I C LE I N FO
A B S T R A C T
Keywords: FTIR and Raman spectra Electrical conductivity Mean square displacements
In this work we have studied the effect of network structure on the transport properties of Li2O-P2O5-MoO3 mixed former glasses. We have used Fourier Transform Infrared (FTIR) and Raman spectroscopy to study the network structure. We have measured ac conductivity and dielectric spectra for a wide range of temperature and frequency. We have observed that the conductivity increases and the activation energy decreases with the increase of Li2O content in the composition. The time temperature superposition has been verified using the scaling formalism of the conductivity spectra. We have calculated microscopic lengths of ion dynamics such as the characteristic mean square displacement of mobile ions and the spatial extent of localized motion within the framework of the linear response theory and correlated them with the ion transport properties. Also we have given a qualitative description for the correlation of the ionic transport with the relative strengths of structural units.
1. Introduction The study of conducting glasses is interesting for the understanding of their transport properties. These glasses are also important technologically due to their potential applications in solid state devices such as batteries, capacitors, fuel cells, chemical sensors, etc. [1–6]. The electrical conductivity especially in the phosphate glasses containing transition metal oxides such as tungsten or molybdenum oxide has been studied because of their high electrical conductivity, low melting point, glass transition temperature and strong glass forming nature [7–13]. Also the information obtained from molybdenum phosphate glasses is useful for radioactive waste management [14,15]. It is reported that the structural units of vitreous MoO3-P2O5 are the combination of both PO4 (tetrahedral) and corner sharing MoO6 (octahedral, sometimes both octahedral and tetrahedral) units [7–11,17]. On addition of Li2O as modifier, non-bridging oxygen (NBO) sites like PeO, PO2−, etc. are created, that act as hopping sites along with structural modification [10,11]. So the energy landscape of MoO3-P2O5 is different when compared to binary phosphate glasses [18–20]. Also the study of ionic transport in such multi-component glasses is a challenge due to inherent complex glass structure. In ion conducting glasses, the conductivity arises from the thermally activated mobile ions within variable potential barriers in the energy landscape of the glass structure, where the heights of such potential barriers are dependent on the
⁎
Coulomb interaction that occur between the mobile ions and the glassy network [21–25]. The impedance spectroscopic technique is useful to study ion dynamics and the conduction process [23,26]. It is reported that the ac conductivity of several categories of disordered materials shows universal power law behaviour [27]. At low temperatures and higher frequencies a power-law behaviour of angular frequency (ω) is obeyed, such as ωn, where n is a frequency exponent, generally 0 < n ≤ 1 [27–31]. Many macroscopic and microscopic models have been developed to understand the ionic conduction mechanism in glasses [21–24,32]. But, a concrete relationship between structure and conductivity is still lagging. In the present work, we have studied network structure and dynamics of lithium ions in xLi2O-(1-x)(0.8P2O5–0.2MoO3)glasses, where 0.35 ≤ x ≤ 0.5 for a wide range of temperature and frequency. We have obtained the strength of different vibration modes from FTIR and Raman spectra. We have calculated the mean square displacement of mobile Li+ ions and the spatial extent of localized motion from the conductivity and dielectric spectra respectively. We have presented the effect of network structure on ionic transport. 2. Experimental procedure We prepared glass compositions xLi2O-(1-x)[0.8P2O5–0.2MoO3], where 0.35 ≤ x ≤ 0.5 by quenching melts of the mixture of reagent
Corresponding author. E-mail address: [email protected] (A. Ghosh).
https://doi.org/10.1016/j.ssi.2020.115238 Received 15 November 2019; Received in revised form 9 January 2020; Accepted 20 January 2020 0167-2738/ © 2020 Elsevier B.V. All rights reserved.
Solid State Ionics 347 (2020) 115238
A. Chatterjee, et al.
grade chemicals Li2CO3, NH4H2PO4 and MoO3 (all from SigmaAldrich). The mixtures of these chemicals in appropriate ratio were made in a glove box in argon gas ambient. The preheated mixtures (at 450 °C) were melted in alumina crucibles at temperatures in the range 900–1050 °C. The melts were equilibrated for 2 h for homogeneity and were rapidly quenched between two aluminium plates kept at room temperature. The glass formation was checked using X-ray diffraction patterns and the glass transition temperature was determined from DSC traces. Fourier Transform Infrared (FTIR) spectra of these glass powder, mixed with KBr powder in the ratio 1:100 to form pellets, were recorded at room temperature in the wave-number range 400–4000 cm−1 in a FTIR spectrometer (Perkin Elmer, model Spectrum 100). Raman spectra of the samples were recorded at room temperature in a confocal triple Raman spectrometer (Jovin-Yvon Horiba, model T64000). Measurements of capacitance and conductance of the glass samples were performed in a LCR meter (QuadTech, model 7600 Plus) operating in the frequency range 10 Hz - 2 MHz. Measurements were made in a wide temperature range of 233–473 K. The sample cell was kept inside a cryogenic system with a stability of ± 0.1 K. The dc conductivity of the samples at different temperatures was obtained from the complex impedance plots. 3. Results and discussion The FTIR spectra at room temperature of all the glass samples are shown in Fig. 1. The spectra exhibit superposition of several bands and hence have been de-convoluted to obtain individual band. The deconvoluted spectra of a particular sample are shown in Fig. 2(a). The bands within the region 1350–1270 cm−1 and 1270–1180 cm−1 are assigned to the asymmetric stretching vibration of P]O bond (ν(P=O)asy) and asymmetric stretching vibration of PO2− group (ν(PO2−)asy) respectively. The band centered at around 900 cm−1 is assigned to the response of asymmetric stretching vibration of P-O-P bonding (ν(P-O-P)asy). The position of the bands ν(P=O)asy and ν(PO2−)asy gradually shift to lower wave number side with the increase of Li2O content. The band at around 790 cm−1 is due to stretching vibration of Mo-O-P units, whereas the band at around 630 cm−1 is due of the bending vibration of Mo-O-P units [8,12,16,17]. A less intense
Fig. 2. (a) De-convoluted FTIR spectra for the composition 0.475Li2O0.525[0.8P2O5–0.2MoO3]. (b) Variation of the relative strength of ν(P=O)asy and ν(P-O-P)asy band with Li2O content.
stretching vibration of MoeO bond at around 950 cm−1is also observed [16]. The band within the region 825–700 cm−1 is attributed to the symmetric stretching vibration of P-O-P rings (ν(P-O-P)sym). The band within the region 680–450 cm−1, corresponding to the bending vibration of O-P-O or O=P-O units (δ(PO2)) of (PO2−)n chains, is resolved into two components. In Fig. 2(b) we have shown the variation of the strength of ν(P=O)asy. and ν(P-O-P)asy.with Li2O content, which is found to increase with the increase of Li2O content. The unpolarized Raman spectra for different glass compositions at room temperature are shown in Fig. 3(a). The Raman band centered at around 1310 cm−1 corresponds to the symmetric stretching of (P=O) bond (ν(P=O)sym). The band centered at around 710 cm−1 is due to the symmetric stretching of the (P-O-P) band (ν(P-O-P)sym), while the band around 800 cm−1 is due to the asymmetric stretching of (P-O-P) band (ν(P-O-P)asy) [8,12,17]. The band around 1160 cm−1 is due to the symmetric stretching of (PO2−) group (ν(PO2−)sym). The band in the range 380–200 cm−1 is due to the (P-O-P) bending mode. On increasing the Li2O content, the position of the ν(P=O)sym band shifts to the lower wave number side with decreasing intensity and finally merges with the ν(PO2−)sym group. On the other hand, the position of the band due to the ν(P-O-P)sym moves to higher wave number side on increasing Li2O content. The position of stretching mode of ν(M = O) and its shoulder band as ν(M-O) lies at around 960 cm−1 and 915 cm−1 respectively and these bands are very prominent [8,12,17]. The band at around 390 cm−1 is perhaps due to Mo-O-P stretching mode. This shows that there is an interconnection between PO4 tetrahedra and MoO6 octahedra, connected through Mo-O-P bridges between corners [7–9,12,17]. Also a minor peak is observed at the base of the lower wave number side of ν(MoeO) shoulder, due to the stretching vibration
Fig. 1. FTIR spectra at room temperature for different compositions of xLi2O(1-x)[0.8P2O5–0.2MoO3] glasses. 2
Solid State Ionics 347 (2020) 115238
A. Chatterjee, et al.
Fig. 4. Arrhenius plot for the dc conductivity for different compositions of xLi2O-(1-x)[0.8P2O5–0.2MoO3] glasses. The straight lines are the least square linear fits of the data.
Fig. 3. (a) Raman spectra for different compositions of xLi2O-(1-x) [0.8P2O5–0.2MoO3] glasses. (b) Composition dependence of the shift in peak position of stretching vibration of ν(PO2−)sym, ν(M = O), ν(M-O) and ν(MOP) bands.
of Mo-O-Mo unit from which we can assume that the clustering of MoO6 octahedra is not appreciable due to its negligible intensity [17]. The shift in peak position of stretching mode of ν(PO2−)sym, ν(Mo = O), ν(MoeO) and ν(Mo-O-P) bands with change in composition is shown in Fig. 3(b). It is worthy to mention that the glass transition temperature Tg decreases with the increase of Li2O content in the composition, which correlates well with the corresponding shift of the FTIR and Raman peaks. The reciprocal temperature dependence of the dc ionic conductivity (σdc) obtained from the complex impedance plots for different compositions is displayed in Fig. 4 from where it is observed that the dc conductivity follows the Arrhenius relation:
σdc = σ0 exp[−Eσ /kBT]
Fig. 5. Composition dependence of dc conductivity (σdc) at 303 K and activation energy (Eσ) for xLi2O-(1-x)[0.8P2O5–0.2MoO3] glasses. The broken curve lines are guides for the eyes.
acts as hopping sites, thereby enhancing the conductivity as we see later. The non-bridging oxygen was created by the disruption of the glass network as evidenced by the decrease of Tg due to introduction of Li2O. Fig. 6 shows the real part of the ac conductivity spectra, σ´(ω), at several temperatures for a particular glass composition. The observed nature of σ´(ω) can be described by a power law [29,30]: n
ω σ′(ω) = σdc ⎡1 + ⎛ ⎞ ⎤ ⎢ ω ⎝ c⎠ ⎥ ⎣ ⎦
(1)
⎜
where σo is the pre-exponential factor, Eσ is the activation energy, kB is the Boltzmann constant and T is the temperature. The numerical values of Eσ have been calculated from the least squares straight line fits of the data. Fig. 5 shows the variation of σdc at 303 K and Eσ with Li2O content. We observe that σdc increases, while Eσ decreases with the increase of Li2O content. In case of binary 0.50Li2O-0.50P2O5 glass, σdc at 363 K was 1.04 × 10−6 Ω−1 cm−1 [18], while in case of present 0.50Li2O0.50[0.8P2O5–0.2MoO3] glass σdc at 363 K is 3.46 × 10−6 Ω−1 cm−1. Thus, the conductivity increases on the addition of MoO3. This is due to the increase of total concentration of non-bridging oxygen (NBO) that
⎟
(2)
where σdc is the dc conductivity, ωc is the crossover frequency indicating the onset of the dispersive regime and n (0 < n ≤ 1) is a power law exponent that signifies the dimensionality of conduction pathways [31]. The real part of the ac conductivity of other compositions also showed similar behaviour. The values of n obtained from the best fits of the experimental data to Eq. (2) for the present compositions are in the range 0.6–0.7, which correspond to three dimensional conduction pathways in glasses [31]. In ion conducting glasses, the ac conductivity often follows the time3
Solid State Ionics 347 (2020) 115238
A. Chatterjee, et al.
Fig. 6. Ac conductivity spectra at different temperatures for the glass sample 0.475Li2O-0.525 [0.8P2O5–0.2MoO3]. The solid lines are the power law fits of the data.
temperature superposition principle, indicating that the conduction mechanism is guided by a common physical mechanism, independent of temperature. To this end different scaling formalisms have been developed [23,24,33]. In our present work, the glass samples appear to obey the scaling formalism given by [33]:
σ′(ω) ω = F⎛ ⎞ σdc ⎝ ωc ⎠ ⎜
Fig. 7. (a) Scaling of the conductivity spectra at different temperatures for the composition 0.475Li2O-0.525 [0.8P2O5–0.2MoO3]. (b) Same for different compositions at 303 K.
⎟
(3)
where σdc is the dc conductivity and ωc is the crossover frequency. It is observed in Fig. 7(a) that the conductivity isotherms at different temperatures for a particular composition perfectly overlap. But, in Fig. 7(b) the isotherms at a particular temperature for different compositions did not overlap perfectly. This is perhaps due to the variation in population density of different structural units with change in composition. In the framework of linear response theory [34], the ac conductivity in thermal equilibrium is related to the mean square displacement (< r2(t) >) of the mobile ions by the following relation [21,23]:
σ ′ (ω) =
Nc q2ω2 6kBTHR
variation of < R2(t) > , calculated from the conductivity spectra using Eq. (6) at different temperatures, for a glass composition, while the same is shown in Fig. 8(b) for different compositions at 303 K. It is observed that at shorter time scale the transport process is characterized by the sub-diffusive motion of the mobile ions, such that < R2(t) > ~ t(1-n), where n is the power law exponent [21]. On the other hand, at longer time scale the transport process is characterized by the diffusive motion of mobile ions, such that < R2(t) > ~ t [21]. Between diffusive and sub-diffusive region, there is a transition region with a characteristic point < R2(tp) > corresponding to a transition time tp. The significance of √ < R2(tp) > is that it is the average distance travelled by the mobile ions to overcome the nearest barrier in the conduction pathways [21,23,24]. We have also calculated another characteristic length, √ < R′2(∞) > , that is the spatial extent of localized motion in the long time limit, in the framework of linear response theory and is given by [21,34,36]:
∞
∫ 〈r2 (t) 〉 sin(ωt)dt 0
(4)
where q is the charge of mobile ions, Nc is charge carrier concentration and HR is the Haven ratio [35,36]. Fourier transformation of Eq. (4) gives < r2(t) > :
〈r 2 (t) 〉 =
12kBTHR Nc q2π
t
∞
0
0
∫ dt′ ∫ σ′ω(ω) sin(ωt′)dω = 〈R2 (t) 〉 HR
12kBTε 0 t →∞ πNc q2
(5)
〈R′ 2 ( ∞ ) 〉 = lim
where
〈R2 (t) 〉 =
12kBT Nc q2π
t
∞
0
0
∫ dt′ ∫ σ′ω(ω) sin(ωt′)dω
6k Tε = B 2 0 Δε Nc q (6)
t
∞
∫ dt′ ∫ [ε′(ω) − ε( ∞ )] cos(ωt)dω 0
0
(7)
where ε0 is the permittivity of the free space and Δε = ε(0)-ε(∞) is the dielectric strength of the material, which was calculated from the frequency dependence of the dielectric permittivity ε´(ω), shown in Fig. 9. The significance of √ < R′2(∞) > lies in fact that it provides the spatial extent of the sub-diffusive motions of the mobile ions that
Here < R2(t) > is the mean square displacement of the centre of charge of the mobile ions, related to < r2(t) > via Haven ratio(HR) [21,37]. For the present glass samples, lack of the exact value of HR leads us to estimate < R2(t) > , instead of < r2(t) > . Fig. 8(a) shows the temporal 4
Solid State Ionics 347 (2020) 115238
A. Chatterjee, et al.
Fig. 9. Dielectric spectra at 303 K for different compositions of xLi2O-(1-x) [0.8P2O5–0.2MoO3] glasses. The dashed lines are guides for the eyes, representing dielectric strength (Δε).
Fig. 8. (a) Temporal variation of < R2(t) > at different temperatures for the composition 0.475Li2O-0.525 [0.8P2O5–0.2MoO3]. (b) Same for different compositions at 303 K. The solid lines are the best fits of the data points in the diffusive and sub-diffusive regions.
perform back and forth hops within the local traps [21,36]. The compositional dependences of √ < R2(tp) > and √ < R′2(∞) > at a particular temperature are shown in Fig. 10(a) and (b) respectively. It is observed that √ < R2(tp) > has a decreasing trend with increase of Li2O content. However, no such particular trend is observed in case of the compositional dependence of √ < R′2(∞) > . Fig. 11 shows the variation of √ < R2(tp) > with the relative strength of ν(P=O)asy/ ν(POP)asy. It is noted that the relative strength decreases with the increase in Li2O content. Though the relative strength of ν(P=O)asy/ ν(POP)asy is the partial concentration of NBOs, yet Fig. 11 gives a qualitative idea of how the variation of √ < R2(tp) > is manifested with change in partial concentration of NBOs, thereby providing an insight regarding the effect of Coulomb interaction on ionic motion in a structurally disordered ionic conductor i. e. the relationship between ionic transport and the glass structure [38]. 4. Conclusions The structure and ion dynamics in Li2O-P2O5-MoO3 glasses have been studied by changing the modifier to former ratio. From FTIR and Raman spectra we have obtained a qualitative idea about the partial concentration of NBOs and shift in different vibrational modes due to structural modifications with the increase of Li2O content. We have observed the increase of the dc conductivity and the decrease of the activation energy with increase in NBO which in turn increases with increase in Li2O content. The ac conductivity isotherms at different
Fig. 10. Compositional dependence of (a) √ √ < R′2(∞) > at 303 K.
5
<
R2(tp)
>
and (b)
Solid State Ionics 347 (2020) 115238
A. Chatterjee, et al.
Acknowledgements AG acknowledges DST-SERB, Govt. of India for J. C. Bose Fellowship grant (SB/S2/JCB-33/2014). The financial support from DST-SERB, Govt. of India, through research grant (EMR/2015/000149) is also thankfully acknowledged. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] M. Duclot, J.-L. Souquet, J. Power Sources 97–98 (2001) 610. [2] C.R. Mariappan, B. Roling, Solid State Ionics 179 (2008) 671. [3] T. Okura, K. Kawada, N. Yoshida, H. Monma, K. Yamashita, Solid State Ionics 225 (2012) 367. [4] J. Hong, D. Zhao, J. Gao, M. He, H. Li, G. He, J. Non-Cryst. Solids 356 (2010) 1400. [5] F. de Mestral, R.A.L. Drew, J. Eur. Ceram. Soc. 5 (1989) 47. [6] I. Ahmed, M. Lewis, I. Olsen, J.C. Knowles, Biomaterials 25 (2004) 491. [7] U. Selvaraj, K.J. Rao, J. Non-Cryst. Solids 72 (1985) 315. [8] S.H. Santagneli, C.C. de Araujo, W. Strojek, H. Eckert, G. Poirier, S.J.L. Ribeiro, Y. Messaddeq, J. Phys. Chem. B 111 (2007) 10109. [9] S. Sen, A. Ghosh, J. Phys. Condens. Matter 11 (1999) 1529. [10] B.V.R. Chowdari, K.L. Tan, W.T. Chia, R. Gopalakrishnan, J. Non-Cryst. Solids 128 (1991) 18. [11] B.V.R. Chowdari, K.L. Tan, W.T. Chia, Solid State Ionics 53–56 (1992) 1172. [12] J. Nikoli, L. Pavic, A. Santic, P. Mosner, L. Koudelka, D. Pajic, A.M. Milankovi, J. Am. Ceram. Soc. 101 (2017) 1221. [13] P. Kalenda, L. Koudelka, P. Mosner, L. Benes, Z. Cernosek, J. Therm. Anal. Calorim. 131 (2018) 2303. [14] O. Pinet, J.L. Dussossoy, C. David, C. Fillet, J. Nuclear Materials 377 (2008) 307. [15] P. Sengupta, J. Hazard. Mater. 235–236 (2012) 17. [16] Muthupari, K.J. Rao, J. Phvs. Chem. Solids 57 (1996) 553. [17] M. Jamnicky, P. Znasik, D. Tunega, M.D. Ingram, J. Non-Cryst. Solids 185 (1995) 151. [18] A. Chatterjee, A. Ghosh, Solid State Ionics 314 (2018) 1. [19] R.K. Brow, J. Non-Cryst. Solids 263-264 (2000) 1. [20] U. Hoppe, J. Non-Cryst. Solids 195 (1996) 138. [21] B. Roling, C. Martiny, S. Bruckner, Phys. Rev. B 63 (2001) 214203. [22] G.N. Greaves, S. Sen, Adv. Phys. 56 (2007) 1. [23] J.C. Dyre, P. Maass, B. Roling, D.L. Sidebottom, Rep. Prog. Phys. 72 (2009) 046501. [24] D.L. Sidebottom, Rev. Mod. Phys. 81 (2009) 999. [25] D.I. Novita, P. Boolchand, M. Malki, M. Micoulaut, Phys. Rev. Lett. 98 (2007) 46501. [26] I.D. Raistrick, Ann. Rev. Mater. Sci. 16 (1986) 343. [27] J.C. Dyre, T.B. Schroder, Rev. Mod. Phys. 72 (2000) 873. [28] A.K. Jonscher, Nature 267 (1977) 673. [29] D.P. Almond, A.R. West, Nature 306 (1983) 456. [30] D.P. Almond, A.R. West, Solid State Ionics 9-10 (1983) 277. [31] D.L. Sidebottom, Phys. Rev. Lett. 83 (1999) 983. [32] O.L. Anderson, D.A. Stuart, J. Am. Ceram. Soc. 37 (1954) 573. [33] A. Ghosh, A. Pan, Phys. Rev. Lett. 84 (2000) 2188. [34] R. Kubo, J. Phys. Soc. Jpn. 12 (1957) 570. [35] J.O. Issard, J. Non-Cryst. Solids 246 (1999) 16. [36] B. Roling, C. Martiny, K. Funke, J. Non-Cryst. Solids 249 (1999) 201. [37] B. Roling, J. Non-Cryst. Solids 244 (1999) 34. [38] P. Maass, J. Petersen, A. Bunde, W. Dieterich, H.E. Roman, Phys. Rev. Lett. 66 (1991) 52.
Fig. 11. Variation of √ < R2(tp) > at 303Kwith the relative strength of ν(P=O)asy/ν(POP)asy for different compositions.
temperatures are perfectly scaled to a single master curve for a particular composition. But the ac conductivity isotherms for different compositions at a particular temperature did not superpose perfectly. We have found that the characteristic length √ < R2(tp) > decreases with the increase of Li2O content, revealing that Li+ ions have to cover shorter distance in order to overcome the backward correlating forces. This suggests a relationship between the characteristic mean square displacement of the center of charge of mobile ions and the modification of the glassy network. On addition of Li2O in the glassy matrix, the concentration of non-bridging oxygen increases due to the de-polymerization of the molybdo-phosphate network. The non-bridging oxygen behaves as hopping sites, the increase of which enhances the conductivity. However, in case of the compositional dependence of spatial extent of localized motion, √ < R′2(∞) > , we have not observed any systematic trend. Therefore we are unable predict about the average cage width of the potential landscape, where the ions perform hopping motion. CRediT authorship contribution statement A. Chatterjee: Methodology, Formal analysis, Investigation. S. Majumdar: Validation, Resources. A. Ghosh: Conceptualization, Supervision, Writing - review & editing.
6
Contents lists available at ScienceDirect
Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Effect of network structure on dynamics of lithium ions in molybdenum phosphate mixed former glasses A. Chatterjee, S. Majumdar, A. Ghosh
T
⁎
School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
A R T I C LE I N FO
A B S T R A C T
Keywords: FTIR and Raman spectra Electrical conductivity Mean square displacements
In this work we have studied the effect of network structure on the transport properties of Li2O-P2O5-MoO3 mixed former glasses. We have used Fourier Transform Infrared (FTIR) and Raman spectroscopy to study the network structure. We have measured ac conductivity and dielectric spectra for a wide range of temperature and frequency. We have observed that the conductivity increases and the activation energy decreases with the increase of Li2O content in the composition. The time temperature superposition has been verified using the scaling formalism of the conductivity spectra. We have calculated microscopic lengths of ion dynamics such as the characteristic mean square displacement of mobile ions and the spatial extent of localized motion within the framework of the linear response theory and correlated them with the ion transport properties. Also we have given a qualitative description for the correlation of the ionic transport with the relative strengths of structural units.
1. Introduction The study of conducting glasses is interesting for the understanding of their transport properties. These glasses are also important technologically due to their potential applications in solid state devices such as batteries, capacitors, fuel cells, chemical sensors, etc. [1–6]. The electrical conductivity especially in the phosphate glasses containing transition metal oxides such as tungsten or molybdenum oxide has been studied because of their high electrical conductivity, low melting point, glass transition temperature and strong glass forming nature [7–13]. Also the information obtained from molybdenum phosphate glasses is useful for radioactive waste management [14,15]. It is reported that the structural units of vitreous MoO3-P2O5 are the combination of both PO4 (tetrahedral) and corner sharing MoO6 (octahedral, sometimes both octahedral and tetrahedral) units [7–11,17]. On addition of Li2O as modifier, non-bridging oxygen (NBO) sites like PeO, PO2−, etc. are created, that act as hopping sites along with structural modification [10,11]. So the energy landscape of MoO3-P2O5 is different when compared to binary phosphate glasses [18–20]. Also the study of ionic transport in such multi-component glasses is a challenge due to inherent complex glass structure. In ion conducting glasses, the conductivity arises from the thermally activated mobile ions within variable potential barriers in the energy landscape of the glass structure, where the heights of such potential barriers are dependent on the
⁎
Coulomb interaction that occur between the mobile ions and the glassy network [21–25]. The impedance spectroscopic technique is useful to study ion dynamics and the conduction process [23,26]. It is reported that the ac conductivity of several categories of disordered materials shows universal power law behaviour [27]. At low temperatures and higher frequencies a power-law behaviour of angular frequency (ω) is obeyed, such as ωn, where n is a frequency exponent, generally 0 < n ≤ 1 [27–31]. Many macroscopic and microscopic models have been developed to understand the ionic conduction mechanism in glasses [21–24,32]. But, a concrete relationship between structure and conductivity is still lagging. In the present work, we have studied network structure and dynamics of lithium ions in xLi2O-(1-x)(0.8P2O5–0.2MoO3)glasses, where 0.35 ≤ x ≤ 0.5 for a wide range of temperature and frequency. We have obtained the strength of different vibration modes from FTIR and Raman spectra. We have calculated the mean square displacement of mobile Li+ ions and the spatial extent of localized motion from the conductivity and dielectric spectra respectively. We have presented the effect of network structure on ionic transport. 2. Experimental procedure We prepared glass compositions xLi2O-(1-x)[0.8P2O5–0.2MoO3], where 0.35 ≤ x ≤ 0.5 by quenching melts of the mixture of reagent
Corresponding author. E-mail address: [email protected] (A. Ghosh).
https://doi.org/10.1016/j.ssi.2020.115238 Received 15 November 2019; Received in revised form 9 January 2020; Accepted 20 January 2020 0167-2738/ © 2020 Elsevier B.V. All rights reserved.
Solid State Ionics 347 (2020) 115238
A. Chatterjee, et al.
grade chemicals Li2CO3, NH4H2PO4 and MoO3 (all from SigmaAldrich). The mixtures of these chemicals in appropriate ratio were made in a glove box in argon gas ambient. The preheated mixtures (at 450 °C) were melted in alumina crucibles at temperatures in the range 900–1050 °C. The melts were equilibrated for 2 h for homogeneity and were rapidly quenched between two aluminium plates kept at room temperature. The glass formation was checked using X-ray diffraction patterns and the glass transition temperature was determined from DSC traces. Fourier Transform Infrared (FTIR) spectra of these glass powder, mixed with KBr powder in the ratio 1:100 to form pellets, were recorded at room temperature in the wave-number range 400–4000 cm−1 in a FTIR spectrometer (Perkin Elmer, model Spectrum 100). Raman spectra of the samples were recorded at room temperature in a confocal triple Raman spectrometer (Jovin-Yvon Horiba, model T64000). Measurements of capacitance and conductance of the glass samples were performed in a LCR meter (QuadTech, model 7600 Plus) operating in the frequency range 10 Hz - 2 MHz. Measurements were made in a wide temperature range of 233–473 K. The sample cell was kept inside a cryogenic system with a stability of ± 0.1 K. The dc conductivity of the samples at different temperatures was obtained from the complex impedance plots. 3. Results and discussion The FTIR spectra at room temperature of all the glass samples are shown in Fig. 1. The spectra exhibit superposition of several bands and hence have been de-convoluted to obtain individual band. The deconvoluted spectra of a particular sample are shown in Fig. 2(a). The bands within the region 1350–1270 cm−1 and 1270–1180 cm−1 are assigned to the asymmetric stretching vibration of P]O bond (ν(P=O)asy) and asymmetric stretching vibration of PO2− group (ν(PO2−)asy) respectively. The band centered at around 900 cm−1 is assigned to the response of asymmetric stretching vibration of P-O-P bonding (ν(P-O-P)asy). The position of the bands ν(P=O)asy and ν(PO2−)asy gradually shift to lower wave number side with the increase of Li2O content. The band at around 790 cm−1 is due to stretching vibration of Mo-O-P units, whereas the band at around 630 cm−1 is due of the bending vibration of Mo-O-P units [8,12,16,17]. A less intense
Fig. 2. (a) De-convoluted FTIR spectra for the composition 0.475Li2O0.525[0.8P2O5–0.2MoO3]. (b) Variation of the relative strength of ν(P=O)asy and ν(P-O-P)asy band with Li2O content.
stretching vibration of MoeO bond at around 950 cm−1is also observed [16]. The band within the region 825–700 cm−1 is attributed to the symmetric stretching vibration of P-O-P rings (ν(P-O-P)sym). The band within the region 680–450 cm−1, corresponding to the bending vibration of O-P-O or O=P-O units (δ(PO2)) of (PO2−)n chains, is resolved into two components. In Fig. 2(b) we have shown the variation of the strength of ν(P=O)asy. and ν(P-O-P)asy.with Li2O content, which is found to increase with the increase of Li2O content. The unpolarized Raman spectra for different glass compositions at room temperature are shown in Fig. 3(a). The Raman band centered at around 1310 cm−1 corresponds to the symmetric stretching of (P=O) bond (ν(P=O)sym). The band centered at around 710 cm−1 is due to the symmetric stretching of the (P-O-P) band (ν(P-O-P)sym), while the band around 800 cm−1 is due to the asymmetric stretching of (P-O-P) band (ν(P-O-P)asy) [8,12,17]. The band around 1160 cm−1 is due to the symmetric stretching of (PO2−) group (ν(PO2−)sym). The band in the range 380–200 cm−1 is due to the (P-O-P) bending mode. On increasing the Li2O content, the position of the ν(P=O)sym band shifts to the lower wave number side with decreasing intensity and finally merges with the ν(PO2−)sym group. On the other hand, the position of the band due to the ν(P-O-P)sym moves to higher wave number side on increasing Li2O content. The position of stretching mode of ν(M = O) and its shoulder band as ν(M-O) lies at around 960 cm−1 and 915 cm−1 respectively and these bands are very prominent [8,12,17]. The band at around 390 cm−1 is perhaps due to Mo-O-P stretching mode. This shows that there is an interconnection between PO4 tetrahedra and MoO6 octahedra, connected through Mo-O-P bridges between corners [7–9,12,17]. Also a minor peak is observed at the base of the lower wave number side of ν(MoeO) shoulder, due to the stretching vibration
Fig. 1. FTIR spectra at room temperature for different compositions of xLi2O(1-x)[0.8P2O5–0.2MoO3] glasses. 2
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Fig. 4. Arrhenius plot for the dc conductivity for different compositions of xLi2O-(1-x)[0.8P2O5–0.2MoO3] glasses. The straight lines are the least square linear fits of the data.
Fig. 3. (a) Raman spectra for different compositions of xLi2O-(1-x) [0.8P2O5–0.2MoO3] glasses. (b) Composition dependence of the shift in peak position of stretching vibration of ν(PO2−)sym, ν(M = O), ν(M-O) and ν(MOP) bands.
of Mo-O-Mo unit from which we can assume that the clustering of MoO6 octahedra is not appreciable due to its negligible intensity [17]. The shift in peak position of stretching mode of ν(PO2−)sym, ν(Mo = O), ν(MoeO) and ν(Mo-O-P) bands with change in composition is shown in Fig. 3(b). It is worthy to mention that the glass transition temperature Tg decreases with the increase of Li2O content in the composition, which correlates well with the corresponding shift of the FTIR and Raman peaks. The reciprocal temperature dependence of the dc ionic conductivity (σdc) obtained from the complex impedance plots for different compositions is displayed in Fig. 4 from where it is observed that the dc conductivity follows the Arrhenius relation:
σdc = σ0 exp[−Eσ /kBT]
Fig. 5. Composition dependence of dc conductivity (σdc) at 303 K and activation energy (Eσ) for xLi2O-(1-x)[0.8P2O5–0.2MoO3] glasses. The broken curve lines are guides for the eyes.
acts as hopping sites, thereby enhancing the conductivity as we see later. The non-bridging oxygen was created by the disruption of the glass network as evidenced by the decrease of Tg due to introduction of Li2O. Fig. 6 shows the real part of the ac conductivity spectra, σ´(ω), at several temperatures for a particular glass composition. The observed nature of σ´(ω) can be described by a power law [29,30]: n
ω σ′(ω) = σdc ⎡1 + ⎛ ⎞ ⎤ ⎢ ω ⎝ c⎠ ⎥ ⎣ ⎦
(1)
⎜
where σo is the pre-exponential factor, Eσ is the activation energy, kB is the Boltzmann constant and T is the temperature. The numerical values of Eσ have been calculated from the least squares straight line fits of the data. Fig. 5 shows the variation of σdc at 303 K and Eσ with Li2O content. We observe that σdc increases, while Eσ decreases with the increase of Li2O content. In case of binary 0.50Li2O-0.50P2O5 glass, σdc at 363 K was 1.04 × 10−6 Ω−1 cm−1 [18], while in case of present 0.50Li2O0.50[0.8P2O5–0.2MoO3] glass σdc at 363 K is 3.46 × 10−6 Ω−1 cm−1. Thus, the conductivity increases on the addition of MoO3. This is due to the increase of total concentration of non-bridging oxygen (NBO) that
⎟
(2)
where σdc is the dc conductivity, ωc is the crossover frequency indicating the onset of the dispersive regime and n (0 < n ≤ 1) is a power law exponent that signifies the dimensionality of conduction pathways [31]. The real part of the ac conductivity of other compositions also showed similar behaviour. The values of n obtained from the best fits of the experimental data to Eq. (2) for the present compositions are in the range 0.6–0.7, which correspond to three dimensional conduction pathways in glasses [31]. In ion conducting glasses, the ac conductivity often follows the time3
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Fig. 6. Ac conductivity spectra at different temperatures for the glass sample 0.475Li2O-0.525 [0.8P2O5–0.2MoO3]. The solid lines are the power law fits of the data.
temperature superposition principle, indicating that the conduction mechanism is guided by a common physical mechanism, independent of temperature. To this end different scaling formalisms have been developed [23,24,33]. In our present work, the glass samples appear to obey the scaling formalism given by [33]:
σ′(ω) ω = F⎛ ⎞ σdc ⎝ ωc ⎠ ⎜
Fig. 7. (a) Scaling of the conductivity spectra at different temperatures for the composition 0.475Li2O-0.525 [0.8P2O5–0.2MoO3]. (b) Same for different compositions at 303 K.
⎟
(3)
where σdc is the dc conductivity and ωc is the crossover frequency. It is observed in Fig. 7(a) that the conductivity isotherms at different temperatures for a particular composition perfectly overlap. But, in Fig. 7(b) the isotherms at a particular temperature for different compositions did not overlap perfectly. This is perhaps due to the variation in population density of different structural units with change in composition. In the framework of linear response theory [34], the ac conductivity in thermal equilibrium is related to the mean square displacement (< r2(t) >) of the mobile ions by the following relation [21,23]:
σ ′ (ω) =
Nc q2ω2 6kBTHR
variation of < R2(t) > , calculated from the conductivity spectra using Eq. (6) at different temperatures, for a glass composition, while the same is shown in Fig. 8(b) for different compositions at 303 K. It is observed that at shorter time scale the transport process is characterized by the sub-diffusive motion of the mobile ions, such that < R2(t) > ~ t(1-n), where n is the power law exponent [21]. On the other hand, at longer time scale the transport process is characterized by the diffusive motion of mobile ions, such that < R2(t) > ~ t [21]. Between diffusive and sub-diffusive region, there is a transition region with a characteristic point < R2(tp) > corresponding to a transition time tp. The significance of √ < R2(tp) > is that it is the average distance travelled by the mobile ions to overcome the nearest barrier in the conduction pathways [21,23,24]. We have also calculated another characteristic length, √ < R′2(∞) > , that is the spatial extent of localized motion in the long time limit, in the framework of linear response theory and is given by [21,34,36]:
∞
∫ 〈r2 (t) 〉 sin(ωt)dt 0
(4)
where q is the charge of mobile ions, Nc is charge carrier concentration and HR is the Haven ratio [35,36]. Fourier transformation of Eq. (4) gives < r2(t) > :
〈r 2 (t) 〉 =
12kBTHR Nc q2π
t
∞
0
0
∫ dt′ ∫ σ′ω(ω) sin(ωt′)dω = 〈R2 (t) 〉 HR
12kBTε 0 t →∞ πNc q2
(5)
〈R′ 2 ( ∞ ) 〉 = lim
where
〈R2 (t) 〉 =
12kBT Nc q2π
t
∞
0
0
∫ dt′ ∫ σ′ω(ω) sin(ωt′)dω
6k Tε = B 2 0 Δε Nc q (6)
t
∞
∫ dt′ ∫ [ε′(ω) − ε( ∞ )] cos(ωt)dω 0
0
(7)
where ε0 is the permittivity of the free space and Δε = ε(0)-ε(∞) is the dielectric strength of the material, which was calculated from the frequency dependence of the dielectric permittivity ε´(ω), shown in Fig. 9. The significance of √ < R′2(∞) > lies in fact that it provides the spatial extent of the sub-diffusive motions of the mobile ions that
Here < R2(t) > is the mean square displacement of the centre of charge of the mobile ions, related to < r2(t) > via Haven ratio(HR) [21,37]. For the present glass samples, lack of the exact value of HR leads us to estimate < R2(t) > , instead of < r2(t) > . Fig. 8(a) shows the temporal 4
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Fig. 9. Dielectric spectra at 303 K for different compositions of xLi2O-(1-x) [0.8P2O5–0.2MoO3] glasses. The dashed lines are guides for the eyes, representing dielectric strength (Δε).
Fig. 8. (a) Temporal variation of < R2(t) > at different temperatures for the composition 0.475Li2O-0.525 [0.8P2O5–0.2MoO3]. (b) Same for different compositions at 303 K. The solid lines are the best fits of the data points in the diffusive and sub-diffusive regions.
perform back and forth hops within the local traps [21,36]. The compositional dependences of √ < R2(tp) > and √ < R′2(∞) > at a particular temperature are shown in Fig. 10(a) and (b) respectively. It is observed that √ < R2(tp) > has a decreasing trend with increase of Li2O content. However, no such particular trend is observed in case of the compositional dependence of √ < R′2(∞) > . Fig. 11 shows the variation of √ < R2(tp) > with the relative strength of ν(P=O)asy/ ν(POP)asy. It is noted that the relative strength decreases with the increase in Li2O content. Though the relative strength of ν(P=O)asy/ ν(POP)asy is the partial concentration of NBOs, yet Fig. 11 gives a qualitative idea of how the variation of √ < R2(tp) > is manifested with change in partial concentration of NBOs, thereby providing an insight regarding the effect of Coulomb interaction on ionic motion in a structurally disordered ionic conductor i. e. the relationship between ionic transport and the glass structure [38]. 4. Conclusions The structure and ion dynamics in Li2O-P2O5-MoO3 glasses have been studied by changing the modifier to former ratio. From FTIR and Raman spectra we have obtained a qualitative idea about the partial concentration of NBOs and shift in different vibrational modes due to structural modifications with the increase of Li2O content. We have observed the increase of the dc conductivity and the decrease of the activation energy with increase in NBO which in turn increases with increase in Li2O content. The ac conductivity isotherms at different
Fig. 10. Compositional dependence of (a) √ √ < R′2(∞) > at 303 K.
5
<
R2(tp)
>
and (b)
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Acknowledgements AG acknowledges DST-SERB, Govt. of India for J. C. Bose Fellowship grant (SB/S2/JCB-33/2014). The financial support from DST-SERB, Govt. of India, through research grant (EMR/2015/000149) is also thankfully acknowledged. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] M. Duclot, J.-L. Souquet, J. Power Sources 97–98 (2001) 610. [2] C.R. Mariappan, B. Roling, Solid State Ionics 179 (2008) 671. [3] T. Okura, K. Kawada, N. Yoshida, H. Monma, K. Yamashita, Solid State Ionics 225 (2012) 367. [4] J. Hong, D. Zhao, J. Gao, M. He, H. Li, G. He, J. Non-Cryst. Solids 356 (2010) 1400. [5] F. de Mestral, R.A.L. Drew, J. Eur. Ceram. Soc. 5 (1989) 47. [6] I. Ahmed, M. Lewis, I. Olsen, J.C. Knowles, Biomaterials 25 (2004) 491. [7] U. Selvaraj, K.J. Rao, J. Non-Cryst. Solids 72 (1985) 315. [8] S.H. Santagneli, C.C. de Araujo, W. Strojek, H. Eckert, G. Poirier, S.J.L. Ribeiro, Y. Messaddeq, J. Phys. Chem. B 111 (2007) 10109. [9] S. Sen, A. Ghosh, J. Phys. Condens. Matter 11 (1999) 1529. [10] B.V.R. Chowdari, K.L. Tan, W.T. Chia, R. Gopalakrishnan, J. Non-Cryst. Solids 128 (1991) 18. [11] B.V.R. Chowdari, K.L. Tan, W.T. Chia, Solid State Ionics 53–56 (1992) 1172. [12] J. Nikoli, L. Pavic, A. Santic, P. Mosner, L. Koudelka, D. Pajic, A.M. Milankovi, J. Am. Ceram. Soc. 101 (2017) 1221. [13] P. Kalenda, L. Koudelka, P. Mosner, L. Benes, Z. Cernosek, J. Therm. Anal. Calorim. 131 (2018) 2303. [14] O. Pinet, J.L. Dussossoy, C. David, C. Fillet, J. Nuclear Materials 377 (2008) 307. [15] P. Sengupta, J. Hazard. Mater. 235–236 (2012) 17. [16] Muthupari, K.J. Rao, J. Phvs. Chem. Solids 57 (1996) 553. [17] M. Jamnicky, P. Znasik, D. Tunega, M.D. Ingram, J. Non-Cryst. Solids 185 (1995) 151. [18] A. Chatterjee, A. Ghosh, Solid State Ionics 314 (2018) 1. [19] R.K. Brow, J. Non-Cryst. Solids 263-264 (2000) 1. [20] U. Hoppe, J. Non-Cryst. Solids 195 (1996) 138. [21] B. Roling, C. Martiny, S. Bruckner, Phys. Rev. B 63 (2001) 214203. [22] G.N. Greaves, S. Sen, Adv. Phys. 56 (2007) 1. [23] J.C. Dyre, P. Maass, B. Roling, D.L. Sidebottom, Rep. Prog. Phys. 72 (2009) 046501. [24] D.L. Sidebottom, Rev. Mod. Phys. 81 (2009) 999. [25] D.I. Novita, P. Boolchand, M. Malki, M. Micoulaut, Phys. Rev. Lett. 98 (2007) 46501. [26] I.D. Raistrick, Ann. Rev. Mater. Sci. 16 (1986) 343. [27] J.C. Dyre, T.B. Schroder, Rev. Mod. Phys. 72 (2000) 873. [28] A.K. Jonscher, Nature 267 (1977) 673. [29] D.P. Almond, A.R. West, Nature 306 (1983) 456. [30] D.P. Almond, A.R. West, Solid State Ionics 9-10 (1983) 277. [31] D.L. Sidebottom, Phys. Rev. Lett. 83 (1999) 983. [32] O.L. Anderson, D.A. Stuart, J. Am. Ceram. Soc. 37 (1954) 573. [33] A. Ghosh, A. Pan, Phys. Rev. Lett. 84 (2000) 2188. [34] R. Kubo, J. Phys. Soc. Jpn. 12 (1957) 570. [35] J.O. Issard, J. Non-Cryst. Solids 246 (1999) 16. [36] B. Roling, C. Martiny, K. Funke, J. Non-Cryst. Solids 249 (1999) 201. [37] B. Roling, J. Non-Cryst. Solids 244 (1999) 34. [38] P. Maass, J. Petersen, A. Bunde, W. Dieterich, H.E. Roman, Phys. Rev. Lett. 66 (1991) 52.
Fig. 11. Variation of √ < R2(tp) > at 303Kwith the relative strength of ν(P=O)asy/ν(POP)asy for different compositions.
temperatures are perfectly scaled to a single master curve for a particular composition. But the ac conductivity isotherms for different compositions at a particular temperature did not superpose perfectly. We have found that the characteristic length √ < R2(tp) > decreases with the increase of Li2O content, revealing that Li+ ions have to cover shorter distance in order to overcome the backward correlating forces. This suggests a relationship between the characteristic mean square displacement of the center of charge of mobile ions and the modification of the glassy network. On addition of Li2O in the glassy matrix, the concentration of non-bridging oxygen increases due to the de-polymerization of the molybdo-phosphate network. The non-bridging oxygen behaves as hopping sites, the increase of which enhances the conductivity. However, in case of the compositional dependence of spatial extent of localized motion, √ < R′2(∞) > , we have not observed any systematic trend. Therefore we are unable predict about the average cage width of the potential landscape, where the ions perform hopping motion. CRediT authorship contribution statement A. Chatterjee: Methodology, Formal analysis, Investigation. S. Majumdar: Validation, Resources. A. Ghosh: Conceptualization, Supervision, Writing - review & editing.
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