Test of the Anderson–Stuart model and correlation between free volume and the ‘universal’ conductivity in potassium silicate glasses

Abstract

Following recent finding it is shown that using conductivity and molar volume in binary potassium silicate glasses (considering the same batches) there is a common cubic scaling relation between them due to increase in alkali content. Emphasis is placed on the application of Anderson-Stuart model to describe the variation of activation enthalpy for conduction E A with potassium concentration. In this analysis were considered experimental parameters, like shear modulus G and relative dielectric permittivity ε, in wide composition range (between 1.7 and 40 K 2 O mol%). The effects of G, ε and free volume are taken into account. The drastic drop in conductivity up to 17 orders of magnitude for so many ion-conducting binary alkali silicate glasses is then mainly caused by the structure and the ion content. In particular, it is suggested that the glass network expansion, which is related to the available free volume, is a parameter that could explain the increase in ionic conductivity for this binary system.

Laboratory measurements of electrical conductivities of hydrous and dry Mount Vesuvius melts under pressure

“…As the activation energy Ea in our melts decreases with increasing sodium content and is probably function of the ionic characteristics of the charge carrier (ionic radius, valency, jump distance), we have used the Anderson‐Stuart model to compute Ea values for natural melts [ Anderson and Stuart , 1954; Nascimento and Watanabe , 2007, and references therein]. This model, initially based on ionic crystal and elasticity theories, predicts the activation energy of ionic conduction in silicate glasses.…”

“…This model, initially based on ionic crystal and elasticity theories, predicts the activation energy of ionic conduction in silicate glasses. The activation energy, Ea, is expressed as the sum of two energies: the electrostatic binding energy, Eb, and the strain energy, Es, which are expressed as where β is the Madelung constant (taken equal to 0.23 [ Nascimento and Watanabe , 2007]), z i is the valence of the mobile ion, and z is that of the fixed counterion (O 2− ), e is the electronic charge (C), γ is the covalency parameter (taken equivalent to the permittivity (F/m) [ Anderson and Stuart , 1954]), r i is the ionic radius of i (m), r O is the ionic radius of the oxygen ion (m), G is the shear modulus (Pa), λ is the jumping distance (m) and r D is the effective radius of the “doorway” through which the sodium passes (taken equal to 9.3 × 10 −11 m [ Nascimento and Watanabe , 2007]). In our case, i corresponds to the sodium, the main charge carrier.…”

“…In our case, i corresponds to the sodium, the main charge carrier. Nascimento and Watanabe [2007] have proposed an empirical linear relation between γ , G , and composition for binary SiO 2 ‐K 2 O glasses. We have assumed that for our three studied compositions, γ and G vary linearly with the sodium content.…”

“…The effect of the addition of water was considered to be essentially mechanical, inducing a local dilatation effect of the structure, allowing Na + ions to move more freely. Consequently, a modification of the Es term was introduced, since Es describes the mechanical forces applied on the charge carrier [ Nascimento and Watanabe , 2007]. The strain energy Es of hydrous melts can be written as where wt % H 2 O is the water content of the melt (wt %).…”

Determination of Mobility and Charge Carriers Concentration from Ionic Conductivity in Sodium Germanate Glasses above and below Tg

“…1.7850 ± 0.0024 0.1817 ± 0.0006 1.0742 ± 0.0055 0.10 10 5.66±0.69 1.9023 ± 0.0015 0.1828 ± 0.0012 1.134 ± 0.081 0.15 10 5.08±0. 23 1.6597 ± 0.0011 0.1791 ± 0.0041 1.009 ± 0.027 0.20 10 5.044±0.046 1.4778 ± 0.0024 0.1771 ± 0.0008 0.9160 ± 0.0055 0.25 10 5.63±0. 27 1.3796 ± 0.0038 0.1767 ± 0.0031 0.866 ± 0.030 0.296 10 5.05±0.…”