Universal curve of ionic conductivities in binary alkali tellurite glasses

Abstract

The main objective of this work is to present an analysis and brief discussion of experimental ionic conductivity s data in the binary alkali tellurite system, including on 47 glasses that extend the ionic conductivity range by more than 14 orders of magnitude in a wide compositional range. A 'universal' behavior is obtained, using log sigma or log sigmaT vs. E A/kB T, where E A is the activation enthalpy for conduction, kB is the Boltzmann constant and T is the absolute temperature. This finding further indicates the importance of a scaling factor F recently proposed, that is correlated to the free volume of glass composition. For a given value of E A/kB T, the difference between large and small values of sigma is only one order of magnitude in 87% of these glass systems. The influence of alkali content and temperature was minor on the pre-exponential terms, considering both expressions log10sigma and log10sigmaT. Indeed, the pre-exponential term sigma0 varies around an average value of 50 omega-1cm-1 considering different compositions in this system. The fact that s lies on these single 'universal' curves for so many ion-conducting binary tellurite glasses means that sigma is governed mainly by E A. The composition dependence of the activation enthalpy is explained in the context of the Anderson-Stuart theory.

Glass; Electrical properties; Ionic conduction

a38v363a

REGULAR ARTICLES

Universal curve of ionic conductivities in binary alkali tellurite glasses

Marcio Luis Ferreira Nascimento^I; Shigueo Watanabe^II

^IDepartment of Materials Engineering, Federal University of São Carlos, Rod. Washington Luiz, km 235, São Carlos 13565-905, Brazil

^IIIonic Crystals, Thin Films and Dating Laboratory, Institute of Physics, University of São Paulo, Rua do Matão 187, São Paulo 05508-900, Brazil

ABSTRACT

The main objective of this work is to present an analysis and brief discussion of experimental ionic conductivity s data in the binary alkali tellurite system, including on 47 glasses that extend the ionic conductivity range by more than 14 orders of magnitude in a wide compositional range. A 'universal' behavior is obtained, using log s or log sT vs. E_A/k_BT, where E_A is the activation enthalpy for conduction, k_B is the Boltzmann constant and T is the absolute temperature. This finding further indicates the importance of a scaling factor F recently proposed, that is correlated to the free volume of glass composition. For a given value of E_A/k_BT, the difference between large and small values of s is only one order of magnitude in 87% of these glass systems. The influence of alkali content and temperature was minor on the pre-exponential terms, considering both expressions log₁₀s and log₁₀sT. Indeed, the pre-exponential term s₀ varies around an average value of 50 W^-1cm^-1 considering different compositions in this system. The fact that s lies on these single 'universal' curves for so many ion-conducting binary tellurite glasses means that s is governed mainly by E_A. The composition dependence of the activation enthalpy is explained in the context of the Anderson-Stuart theory.

Keywords: Glass; Electrical properties; Ionic conduction

I. INTRODUCTION

The room temperature ionic conductivity in solid materials is technologically interesting for various solid state electrochemical devices such as batteries, sensors and 'smart windows'. It is well know that the ionic conductivity increases rapidly when a network glass former (for instance TeO₂) is modified by the addition of a metal alkali. So far only a limited number of publications have been concerned with the study of the ionic conduction in tellurite glasses. The importance of studying such phenomenon in this system is due to many industrial and technological applications, as excellent optical properties (good transmission in the visible and infrared regions). Also, tellurite glasses have been widely studied due to their chemical stability, high homogeneity, high electrical conductivity and resistance to devitrification.

Since the initial studies of the fast ionic conductivity in glasses, there has been a large interest in explaining the diffusion mechanism. Despite considerable experimental and theoretical attempts, there is currently no consensus regarding the involved diffusion mechanism [1]. Several models have been proposed, and they vary from thermodynamics models based on liquid electrolytes, such as the weak electrolyte model [2], to models based on solid state concepts such as the jump diffusion model [3], the strong electrolyte model [4], and the dynamic structure model [5].

Ionic conductivity s in glass is a thermally activated process of mobile ions surmounting a potential barrier E_A, according to the equation

where s₀ is a pre-exponential factor, k_B is the Boltzmann constant and T is the temperature. Arrhenius plots according to Eq. (1) are presented in Fig. 1 for 47 alkali tellurite glasses and demonstrate the noticeable scattering values of E_A against composition. As will be detailed below, Eq. (1) may be more useful when one considers s = s( E_A ,T ), leading, in fact, to a more general rule.

Extensive studies have recently been made for obtaining a 'universal' equation from the glass structure standpoint. For example, Nascimento et al. [6] presented 23 and 30 binary rubidium and cesium silicate glasses, respectively, that follow a 'universal' conductivity rule. Swenson and Börjesson [7] proposed a common cubic scaling relation between s and the expansion volumes of the networking forming units in salt-doped and -undoped glasses. This fact suggested that the glass network expansion, which is related to the available free volume, is a key parameter determining the increase of the high ionic conductivity in some types of fast ion conducting glasses.

According to Adams and Swenson [8], the ion conduction should be determined by the ionic motion within an infinite pathway cluster. For various silver ion conducting glasses [9-10], it was found that the cubic root of the volume fraction F of infinite pathways for a fixed valence mismatch threshold is closely related to both the absolute conductivity and the activation enthalpy of the conduction process,

where s₀' is the pre-exponential factor (in K/W·cm). The cubic root of F may be thought of as proportional to the mean free path of the mobile ion [7].

II. RESULTS AND DISCUSSION

According to Bahgt and Abou-Zeid [11], the TeO₂ glass has a unique structure as a consequence of the structural unit and its connecting style differs from conventional glass formers as B₂O₃, SiO₂, GeO₂ and P₂O₅. TeO₂ glass is composed mostly of TeO₄ trigonal bipyramids. Generally, it was shown that the primary structural unit of tellurite glasses having high TeO₂ content is TeO₆ polyhedron. Together with distorted TeO₄ trigonal bipyramids and fractions of TeO₃ trigonal pyramids the proportions of the structural units increase with increasing monovalent cation content [11]. So, when the alkali oxides are introduced in the tellurite network there exist different structural units at different alkali oxide contents [12].

In recent papers the present authors have shown the existence of a 'universal' behavior in binary silicate [13], borate [14], and germanate [15] glasses, considering both Eqs. (1) and (2). This paper aims to present new results considering binary alkali tellurite glasses.

Figure 2 shows modified Arrhenius plots of s for 47 binary alkali tellurite glasses, of the form xA₂O ·(1-x)TeO₂ (A = Li, Na, K, Cs x in wt. %, indicated [16]), ranging from 3.6×10 ^{- 4}W ^{- 1}cm ^{- 1} to less than 6×10 ^{- 18}W ^{- 1}cm ^{- 1} between 20ºC to 400ºC. The range of activation enthalpy E_A lies between 0.6 and 1.2 eV in all of the studied glasses. These data were compared with 'universal' equation for s₀ = 50 W^{- 1}cm ^{- 1} in Eq. (1). Following previous work by Nascimento et al., the "universal" equation appears in Fig. 2 as a dashed line. Only a few glasses do not obey the 'universal' curve, as 3.86, 4.4, 4.47, 5.21 and 27.24 Li₂O plus 4.14 Na₂O composition (in wt%). It is important to note that similar compositions, as 3.94 and 5.29 Li₂O are between the dotted lines, and this different behavior should be investigated.

The replacement of a mobile ion with one of another type affects the ionic conductivity in various ways, such as causing modifications in the glass structure. Therefore, the results shown in Fig. 2 are remarkable in the sense that so many different binary alkali tellurite glasses present linear plots of log s vs. E_A/k_BT very close to each other and to the "universal curve". There is then a strong correlation between s and E_A values in a wide range of temperatures. It is interesting to note that the increase in ionic conductivity with alkali content is almost entirely due to the fact that the activation enthalpy E_A required for a cation jump decreases, as presented in ref. [4].

In addition, one can conclude that the pre-exponential factor s₀ varies only weakly with glass composition. The frequency of s₀ distribution is shown in Fig. 3. It is possible to note that the medium value is near 50 W ^{- 1}cm ^{- 1}, the intercepting value at y-axis of Fig. 2. Thus, the s₀-value in Eq. (1) is practically unaffected by alkali content. Other results, considering binary alkali silicate [13], borate [14], and germanate [15] glasses, also display this behavior.

It is important to note that the s-values for several binary alkali tellurite glasses lie close to a "universal" curve. Although the s-values for each glass at very low and very high temperatures differ by more than 14 orders of magnitude, for a given value of E_A/k_BT, the difference between large to small values of s is only one order of magnitude in 87% of the glass systems considered in Fig. 2. Therefore, if one measures s at a fixed temperature, it is possible to estimate E_A from Eq. (1) considering s₀ = 50/W·cm, and obtain a rough sketch of s at different temperatures. This means that, if E_A is obtained by some experimental or theoretical technique, the ionic conductivity can be readily calculated.

Another "universal" curve, following Eq. (2), was obtained, and is presented in Fig. 4. The pre-exponential value was = 50 000 K/W·cm, considering the same conductivity data of Figs. 1-2. The conclusions for this case are similar.

The composition dependence of the activation enthalpy in a wide composition range can be understood in the framework of the Anderson-Stuart model [4]. The expansion of the glass skeleton and the introduction of the alkali ions in voids in the structure forming narrow pathways lead to two effects that lower the activation enthalpy and thus promote the ionic conductivity. In this model the total activation enthalpy E_A for ionic conduction is the sum of two parts, the binding energy, E_b (the average energy that a cation requires to leave its site), and the strain energy, E_s (the average kinetic energy that a cation needs to structurally distort the environment and to create a "doorway" through which it can diffuse to a new site). The A-S theory leads to the equation

where z and z₀ are the valence of the mobile ion and of the fixed counterion (in this case the alkali and oxygen, respectively), r and r_O are the corresponding Pauling ionic radii for the alkali ion and O^{2 -} , e is the electronic charge, and r_D is the effective radius of the (un-opened) doorway. The parameters of interest in the A-S model are the elastic modulus (G), the 'Madelung' constant (b » 0.3), which depends on how far apart the ions are, and the relative dielectric permitivitty (e), which indicates the degree of charge neutralization between the ion and its nearest neighbours [4].

The cation-induced expansion of the network skeleton leads to a lowering of the strain energy part E_s of the activation energy and the formation of pathways, in which the cations may coordinate with oxygens of the network, leading to a lowering of E_b.

The ionic conductivity in the lithium tellurite glasses with varying Li₂O content have been recently investigated by Pan and Ghosh [12]. Thus, in this system the strain energy part is expected to play a dominant role in the total activation enthalpy E_A, as expected if one considerers that structural changes could modify ionic conductivity, as expressed in Eq. 2 (due to the scaling factor F). In other words, the cubic root of (V_m - V)/V is proportional to F and should increase slightly, following similar procedures by Swenson and Börjesson [7]. Following this approach, the necessary condition for ion transport may rather be the presence of microscopic pathways available for alkali ions. A given material may be called 'conductive' if it is equipped with ample ionic pathways, irrespective of the amount of the free volume. Better approximations for free volume could be provided using positron annihilation spectroscopy, as recently published [17].

III. CONCLUSIONS

In summary, there are strong connections between the microscopic structure and the ionic conductivity. At first sight, E_A and k_BT are independent, and E_A varies strongly with composition (the effect of glass composition is clearly demonstrated in Fig. 1). But almost all of these compositions fall into identifiable patterns where conductivity is related to structure, as expressed by modified Arrhenius plots.

These relations have an important feature. Regardless of the type of ionic conductor, or the oxide glassformer, if one plots log s or log sT against E_A/k_BT, all systems will follow the same rule, with a few exceptions. In other words, as it has been recently proposed, both E_A and k_BT are related to the cubic root of the scaling factor F. Furthermore, the frequency distribution of the pre-exponential term s₀ (or ) varies weakly with glass composition (and also temperature), and could be considered as an other evidence of the 'universal' finding.

Acknowledgments

The Brazilian agencies FAPESP and CNPq are acknowleged for financial support.

Received on 13 April, 2006. Revised version received on 12 June, 2006

References

• [1] C. A. Angell, Ann. Rev. Phys. Chem. 43, 693 (1992).
• [2] D. Ravaine and J. L. Souquet, Phys. Chem. Glasses 18, 27 (1977).
• [3] K. Funke, Prog. Solid State Chem. 22, 11 (1993).
• [4] O. L. Anderson and D. A. Stuart, J. Am. Ceram. Soc. 37, 573 (1954).
• [5] A. Bunde, M. D. Ingram, and P. Maass, J. Non-Cryst. Solids 172/174, 1222 (1994).
• [6] M. L. F. Nascimento, E. do Nascimento, and S. Watanabe, Braz. J. Phys. 35, 626 (2005).
• [7] J. Swenson and L. Börjesson, Phys. Rev. Lett. 77, 3569 (1996).
• [8] S. Adams and J. Swenson, Phys. Chem. Chem. Phys. 4, 3179 (2002).
• [9] J. Swenson and S. Adams, Phys. Rev. B 64, 024204 (2001).
• [10] S. Adams and J. Swenson, Solid State Ion. 154/155, 151 (2002).
• [11] A. A. Bahgat and Y. M. Abou-Zeid, Phys. Chem. Glasses 42, 361 (2001).
• [12] A Pan and A. Ghosh, Phys. Rev. B 60, 3224 (1999).
• [13] M. L. F. Nascimento and S. Watanabe, J. Mater. Sci. 40, 5079 (2005).
• [14] M. L. F. Nascimento and S. Watanabe, J. Mater. Sci. 40, 4423 (2005).
• [15] M. L. F. Nascimento, E. do Nascimento, and S. Watanabe, Mat. Chem. Phys. 96, 55 (2006).
• [16] Sciglass^® database. http://www.esm-software.com/sciglass
• [17] M. D. Ingram, S. J. Pas, C. Cramer, Y. Gao, and A. J. Hill, Phys. Chem. Chem. Phys. 7, 1620 (2005).

Publication Dates

• Publication in this collection
  16 Oct 2006
• Date of issue
  Sept 2006

History

• Reviewed
  12 June 2006
• Received
  13 Apr 2006