Rapid communication
Potential energy landscape of Li+ ions in lithium silicate glasses: Implications on ionic transport

https://doi.org/10.1016/j.jnoncrysol.2005.08.025Get rights and content

Abstract

The potential energy landscapes of Li+ ions in Li2O–SiO2 glasses containing 3.3–15 mol% Li2O have been studied using molecular dynamics simulation. It is shown for the first time that the densities of states for Li+ ions follow a nearly universal logarithmic distribution irrespective of the Li concentration. Such a functional form of the ionic density of states is shown to provide an explanation for the experimentally observed logarithmic dependence of the activation energy of dc conductivity on the modifier ion concentration in a wide variety of glasses.

Introduction

Ionic conduction in glasses and other structurally disordered materials have been studied in great detail for the last several decades. However, no single unanimously accepted theoretical model exists to date that can explain some of the most intriguing yet universal phenomena associated with ionic conduction in glasses. The universally observed logarithmic decrease of the activation energy of dc conductivity Edc with increasing mobile ion concentration in glasses is an example of such a phenomenon [1], [2], [3]. Another important example is the mixed-alkali effect where for the same total alkali content the ionic conductivity of a glass containing two dissimilar alkali ions is always significantly lower than that of the single-alkali end members and goes through a deep minimum when the two alkalis are present in roughly equal mole fraction [4].

Recently Maass, Dyre and coworkers have proposed microscopic models for ionic transport in glasses that address both the mixed-alkali effect and the concentration dependence of Edc[1], [2], [5], [6]. These models are based on the reasonable assumption that at low enough temperatures (e.g. below glass transition temperature, Tg) the motional time scale of the mobile network-modifying cations is orders of magnitude faster than that of the glassy network defined by the network-forming ions such as Si, B and O. Therefore, the mobile modifier ions move around in a nearly static energy landscape with well-defined site energies governed principally by their interaction with the relatively immobile network-formers and to a lesser extent by the Coulombic interaction between the modifier ions themselves. Different types of modifier ions are characterized by different site energy landscapes owing to their different interactions with the network. Each of the network-modifier sites can accommodate only one modifying ion and these sites are filled from bottom up in energy such that there is a well defined energy level EF designated as the ‘Fermi energy’ that corresponds to the site with the highest energy that is occupied with a modifier ion. This potential energy landscape may change locally due to the modulation of the Coulombic interaction between the modifier ions during their hopping from one site to another. However, such dynamical changes become appreciable only at high modifier ion concentration [6]. The potential energy landscape is also characterized by a critical energy Ec which is the energy corresponding to the site percolation threshold. Therefore Ec represents the minimum energy needed by a mobile ion in order to overcome all energy barriers on the percolation backbone that connects the two ends of the sample. The activation energy for dc conductivity Edc in that case is given simply by the difference between the Fermi energy EF and the critical energy Ec i.e. Edc = Ec  EF[5].

Qualitatively EF is expected to decrease with decreasing modifier ion concentration. On the other hand Ec is expected to be significantly less sensitive to the modifier ion concentration compared to EF especially at low modifier oxide concentrations. As a result Edc = Ec  EF increases with decreasing modifier concentration, in agreement with experimental observation [1], [2], [3]. Similarly, in a mixed-alkali glass, the EF for one alkali ion decreases due to an effective lowering in its concentration on replacement with a second type of alkali ion. Moreover, the Coulombic interaction between the alkali ions in the mixed-alkali glass is stronger due to its higher total alkali ion concentration compared to a diluted single-alkali glass. The stronger Coulomb interaction results in higher values of the critical energy Ec in the mixed-alkali glass compared to its single-alkali counterpart [5]. Therefore, a combination of low EF and high Ec gives rise to a sharp rise in Edc in the mixed-alkali glass, again in complete agreement with experimental observation.

However, any quantitative predictions on the basis of these theoretical models becomes impossible without making a priori assumption about the functional form of the site energy distribution or the ionic density of states and consequently about the compositional dependence of Ec and EF. Molecular dynamics (MD) provides a unique way to directly obtain the energy landscape and the related site energy distribution for the network-modifier ions on the basis of the known inter-atomic interaction potential between these ions and the immobile network-formers such as Si and O in a silicate glass. In this letter we report the key findings of a classical MD study of the energy landscape for the mobile Li ions in Li-silicate glasses with relatively low Li2O concentration varying between 3.3 and 15.0 mol%.

Section snippets

Computational details

The classical MD simulations are performed on a system of 900 atoms. Four glass compositions with 3.3, 6.6, 10.0 and 15.0 mol% Li2O are studied. These Li2O concentration levels correspond to 20, 40, 60 and 90 Li atoms, respectively, in the simulation cell. A micro-canonical (NVE) ensemble is used. The atoms are treated as non-polarizable point charges with formal charges of +1e, +4e and −2e for Li, Si and O, respectively. The long-range electrostatic interactions between the atoms are evaluated

Results and discussion

The densities of states for the Li ions in all glasses show a logarithmic increase in energy with the number of sites and follow a trend that is nearly independent of glass composition at least for the first 150 sites in the simulation cell in the order of increasing site energy (Fig. 1). It is interesting to note the lack of any significant compositional dependence in this low energy part of the densities of states in spite of the expected increase in the average Li–Li Coulombic repulsion in

Summary

The site energy distributions for Li+ ions in Li2O–SiO2 glasses containing 3.3–15 mol% Li2O have been calculated from their potential energy landscapes obtained from molecular dynamics simulation. The densities of the lowest energy states for the Li+ ions shows a logarithmic variation which imparts a logarithmic dependence of the activation energy of dc conductivity on Li+ concentration. The calculated Edc values are found to be in good agreement with the experimental results.

References (16)

  • A. Bunde et al.

    J. Non-Cryst. Solids

    (1994)
  • A. Pradel et al.

    J. Non-Cryst. Solids

    (1994)
  • D.E. Day

    J. Non-Cryst. Solids

    (1976)
  • P. Maass

    J. Non-Cryst. Solids

    (1999)
  • J.C. Dyre

    J. Non-Cryst. Solids

    (2003)
  • S. Sen et al.

    J. Non-Cryst. Solids

    (2001)
  • X. Yuan et al.

    J. Non-Cryst. Solids

    (2001)
    X. Yuan et al.

    J. Non-Cryst. Solids

    (2003)
  • J. Horbach et al.

    Phys. Rev. Lett.

    (2002)
There are more references available in the full text version of this article.

Cited by (5)

  • La<inf>2</inf>O<inf>3</inf>-added lithium-ion conducting silicate oxynitride glasses

    2018, Solid State Ionics
    Citation Excerpt :

    These structural modifications affect the electrical and mechanical behavior of alkali silicate glasses. The presence of conduction pathways has been proposed to understand the dynamics of mobile ions in alkali silicate and other ionic conducting glasses [19–20]. Relevant literature shows that addition of nitrogen to silicate glass improves their thermal stability and chemical stability [21–22].

View full text