Ionic diffusion and the topological origin of fragility in silicate glasses

Mass transport in liquids and glass is intimately connected to the structure and topology of the disordered network. To investigate this problem, we measure the ionic diffusivity and fragility of a series of iron-bearing alkali-alkaline earth silicate glasses, substituting different types of alkali and alkaline earth cations while keeping the same ratio of network modifiers. Diffusion is studied around the glass transition temperature (T_g) under a reducing atmosphere, leading to a reduction of Fe³⁺ to Fe²⁺, and inward diffusion of the modifier cations. In the SiO ₂ -CaO- Fe₂ O₃ - A₂ O (A=Na, K, Rb, or Cs) glass series, we find that the Ca²⁺ ions diffuse faster than alkali ions and that the activation energy of the Ca²⁺ diffusion decreases with alkali size, a trend that is coincident with a decrease in liquid fragility. We have established a simple model for accurately describing the correlation between the fragility index (m) and T_g based on a topological consideration of the glass network. The model builds on a temperature-dependent constraint approach where the Vogel temperature serves as a rigidity percolation threshold. This follows from our derivation of the Vogel-Fulcher-Tammann equation of viscosity from the more accurate Mauro-Yue-Ellison-Gupta-Allan equation. The established model provides an excellent prediction of the relationship between fragility and T_g, except for the MgO-containing glass where Mg²⁺ is known to play a unique topological role in the network. This trend is in coincidence with the considerably faster inward diffusion of Mg²⁺ in comparison to other alkaline earth cations.