Application of Free Volume Theory to Transport Phenomena in Molten Alkali and Alkaline Earth Borate Glasses

Abstract

In previous papers, most of Arrhenius plots for the diffusion coefficients of Cd²⁺, Ni²⁺, Co²⁺ and Cr⁶⁺ ions in molten sodium borate glasses were shown to depart from the linearity. On the diffusion coefficients of Ni²⁺ ions in molten alkaline earth borate glasses (R²⁺=Ca²⁺, Sr²⁺ or Ba²⁺), molten lithium and potassium borate glasses, non-Arrhenius behavior was also demonstrated.
In this paper, applications of “the modified Fulcher equation”, log (D/T^1/2, η/T^1/2, λT^1/2)=A+B/(T-T₀) (where, D: diffusion coefficient, η: viscosity, λ: equivalent conductance, T₀, A, B: constants) derived from the Cohen-Turnbull free volume theory were examined to diffusion behavior. At the same time, the same applications were examined on viscosity and electrical conduction measured by Shartsis et al.
It was ascertained that the proper T₀ values giving the best linear plots of logD/T^1/2 vs. 1/(T-T₀) existed on diffusion of the metal ions in alkali and alkaline earth borate glasses. Moreover, the obtained T₀ values were located below the respective glass transition temperatures T_g, changing almost in parallel with T_g for most of the glass systems. The T_g/T₀ ratios were about 1.2 for almost all glass systems, were not necessarily dependent on the glass compositions. The T₀ values obtained from diffusion of Cd²⁺, Ni²⁺, Co²⁺ and Cr⁶⁺ ions in the molten sodium borate glasses were equal within 40K at the corresponding glass composition.
The T₀ values giving the best linear plots against “the modified Fulcher equation” were found for viscosity and electrical conduction measured by Shartsis et al. The obtained T₀ values were consistent with those of diffusion except a few cases.
As previously discussed by Angell et al., the T_g/T₀ ratio may become a criterion for “ideality” of glass. Departure from ideality in the borate systems was smaller than in the silicate systems because the former had smaller T_g/T₀ values.
Jumping distances of diffusion of Ni²⁺ ions calculated from “the modified Fulcher equation” in the molten alkali and alkaline earth borate glasses were within the range 5-10Å except for BaO-B₂O₃ systems. In the same way, jumping distances of diffusion of Cd²⁺, Ni²⁺, Co²⁺ and Cr⁶⁺ ions in the sodium borate glasses were within the range 5-13Å. In this case, the jumping distances did not apparently correlate on the composition of glass. The diameters of flow units calculated from viscosity in molten alkali borate glasses were about 4Å, suggesting that the flow units were relatively small such as BO₃ and BO₄.