Test of Anderson-Stuart model and the "universal" conductivity in rubidium and cesium silicate glasses

Abstract

An analysis and brief discussion of experimental ionic conductivity σ and activation energy E A in the binary rubidium and cesium silicate systems is presented, exemplified on 23 and 30 glasses respectively, in a wide composition range (5-45 Rb 2 O and Cs 2 O mole%). The Anderson and Stuart model has been considered to describe the variation of activation energy E A with alkali concentration in both alkali-silica systems. In this analysis were considered experimental parameters, like shear modulus G and relative dielectric permittivity ε. An "universal" finding is obtained using log σ × E A /k B T in 51 of 53 glasses considering both alkali systems, where E A is the activation energy for conduction, k B is the Boltzmann constant and T is the absolute temperature. This strong correlation by more than 13 (Rb-based glasses) and 15 (Cs-based glasses) orders of magnitude means that σ is governed mainly by E A . An explanation for this behavior links ionic conductivity and microscopic structure.

Correlation between conductivity and free volume in rubidium and cesium silicate glasses

“…where σ 0 ' is the pre-exponential factor (in K/Ω·cm), that seems to be near constant and equal to 50 Ω −1 cm −1 , as recently showed [6] for the systems in this work. The cubic root of F may be understood as proportional to a mean free path length for the mobile ion [10], and could be related to the free volume as explained below.…”

“…The shear modulus G from Nemilov [24] and Shelby and Day [46] showed a decrease with increasing rubidium content. Data from Nemilov [24], Takahashi and Osaka [28] and Terai [29,30] presented the same decreasing behavior with increasing cesium content, according to previous work [6]. In fact, following this recent paper, it was verified that G presented a linear fit of form G = G 0 − dG dn n, where n is the alkali oxide mol percentage (mol%) and G 0 is a constant.…”

“…As will be detailed below, Eq. (1) may be more usefull when one considers σ = σ (E A , T ), leading, in fact, to a more general rule, as presented recently [6]. of rubidium and cesium systems, respectively.…”

“…In view of the most cited models, the Anderson-Stuart (A-S) [4] is considered to be the most directly related to physically meaning parameters, such as ionic radii, relative dielectric permittivity and the elastic modulus, as described below. For the rubidium and cesium silicate systems only recently has been published an analysis of conductivity considering wide composition range [6].…”

“…In this work was considered the modified expression using λ as a fitting parameter to all data, following McElfresh & Howitt's proposal [7], different that was presented previously [6], where the original A-S theory was applied. The shear modulus G from Nemilov [24] and Shelby and Day [46] showed a decrease with increasing rubidium content.…”