Topologically disordered systems at the glass transition

Abstract

The thermodynamic approach to the viscosity and fragility of amorphous oxides was used to determine the topological characteristics of the disordered network forming systems. Instead of the disordered system of atoms we considered the congruent disordered system of interconnecting bonds. The Gibbs free energy of network breaking defects (configurons) was found based on available viscosity data. Amorphous silica and germania were used as reference disordered systems for which we found an excellent agreement of calculated and measured glass transition temperatures. We revealed that the Hausdorff dimension of the system of bonds changes from Euclidian three-dimensional below to fractal 2.55±0.05-dimensional geometry above the glass transition temperature.

Durable Glass for Thousands of Years

“…Marians and Hobbs [93] developed a nomenclature scheme to describe the local topology surrounding the SiO 4 anion groups in glass and their most immediate neighbors, "local clusters or quasicrystals." This enables higher order polymerization modeling of these local clusters into various types of rings, sub-networks, and networks that define the percolation channels [65]. The polymerization scheme is similar in many aspects to the classification of silicate minerals into cyclosilicates (linkage of SiO 4 tetrahedra into rings), sorosilicates (linkage of two SiO 4 tetrahedra sharing an oxygen), ionsilicates (linkage of SiO 4 tetrahedra into linear chains by the sharing of oxygen), etc.…”

“…The effect of insufficient Al 2 O 3 was first reported by French researchers [63] who determined that many glass durability models were non-linear, e.g., glasses had release rates far in excess of those predicted by most models, in regions corresponding to low Al 2 O 3 and in excess of 15 wt% B 2 O 3 and independently by Jantzen, et.al [40,41,64] Homogeneous glass formulations, or formulations with only 1-2 wt% crystals, are targeted for HLW in the US. Crystals such as iron spinels have little impact on glass durability as they are themselves very durable and cause minimal grain boundary dissolution since the spinels and the glass are both isotropic [61,65]. However, for other phases such as nepheline, acmite, and lithium silicates which are less durable than iron spinels and not isotropic, the impact on glass durability from the crystal and the grain boundary can be pronounced.…”

Igneous Rock Associations 12. A Geologist’s Look at Archaeological Ceramics and Glass

“…The glass transition is characterized by a dramatic change in viscosity, and by changes in heat capacity and thermal expansivity (Ojovan and Lee 2006). Glass in the transition has a rubbery character; below the transition, it is hard and solid, above the transition, it is relatively fluid.…”

Glassy Wasteforms for Nuclear Waste Immobilization

“…Melting of a material can be considered as a percolation via broken bonds, [23] e.g., melting of an amorphous oxide material occurs when the configurons form a percolation cluster. [24,25] T g depends on quasiequilibrium thermodynamic parameters of the bonds, e.g., on the enthalpy (H d ) and entropy (S d ) of configurons, which can be found from available experimental data on viscosity [24][25][26] …”

“…For strong melts such as SiO 2 , the percolation threshold in the previous equation h c = 0 c , where 0 c is the universal Scher-Zallen critical density in the 3-D space 0 c = 0.15 ± 0.01. [24,25] However, for fragile materials, the percolation thresholds are material dependent, and h c < < 1. [26] The connectivity of a bond lattice is characterized by its geometry and Hausdorff dimension.…”