Effect of glass composition on activation energy of viscosity in glass-melting-temperature range

Abstract

Viscosity, a key property for glass processing, is a function of glass composition and temperature. Nuclear waste glasses must be formulated to obtain a desired viscosity at the melter processing temperature for each waste composition to be vitrified. Over the past decades, a large viscosity database has been accumulated at various laboratories in the US. The database, compiled at the Pacific Northwest National Laboratory, comprises over 1300 compositions with 83 components and 6800 viscosity data. We used this database to develop a mathematical model for the viscosity-composition relationship for viscosities lower than 1000 Pa·s that are important for the melting process. In this high-temperature range, the viscosity-temperature relationship has the form of an Arrhenius function, i.e., ln(η) = A + B/T, where η is the viscosity, T is the absolute temperature, A is a constant coefficient, and B is the activation energy. We obtained B for each data point and then fitted a first-or second-order model to B as a function of glass composition while A was kept constant for all glasses. Altogether, we have developed 12 versions of viscosity-composition relationships with a variety of first-and second-order coefficients. Two models, one first order and one second order, are presented in this paper. I. VISCOSITY-COMPOSITION RELATIONSHIPSViscosity-temperature relationships are important for both glass melting and glass forming. Over the wide interval of temperatures-from the glass transition temperature to the temperature at which glass is being refined-viscosity spans 12 orders of magnitude. Many approximation functions have been suggested in the literature to model the viscosity-temperature relationship. The most popular among them are the Vogel-Fulcher-Tammann equation and the Adam-Gibbs equation, 1 the latter of which is more versatile and allows better fitting of high-temperature data. 2,3As has been demonstrated with various viscosity databases, both for commercial 4,5 and waste glasses, 5,6 high-temperature viscosity is best fitted by an Arrhenius function,where η is the viscosity, T is the temperature, A is a constant coefficient, and B is the activation energy. In Equation (1), both A and B are independent of temperature. Thus, for low viscosities, η < 10 3 Pa·s, the activation energy depends on composition only. Because the melting temperatures of glass are usually below 10 Pa·s, Equation (1) fully suffices for formulating glasses to meet melt-processing constrains with respect to glass formulation as well as mathematical modeling of glass-melting furnaces.

Effects of heating rate, quartz particle size, viscosity, and form of glass additives on high‐level waste melter feed volume expansion

“…For the viscosity‐glass composition relationship, we used the formulawhere η is viscosity, A is a constant coefficient, B i is the i th component's partial specific activation energy, x i is the i th component's mass fraction, T is the absolute temperature, and N is the number of components. The values of coefficients used were A =−11.19 (to obtain η in Pa·s), and B i =3.00 × 10 4 K for SiO 2 , 0.32 × 10 4 K for B 2 O 3 , −0.04 × 10 4 K for Na 2 O, and −3.91 × 10 4 K for Li 2 O …”

Viscosity of glass‐forming melt at the bottom of high‐level waste melter‐feed cold caps: Effects of temperature and incorporation of solid components

“…From several Arrhenius models, we opted for Model B in Ref. [38], which is based on a data set containing over 1300 compositions of HLW glasses with nearly 6000 viscosity data and a composition range wider than that of more recent models based on glasses designed for Hanford melters.…”

“…For the glass‐forming melt viscosity, we used the Arrhenius relationship.where A is a constant coefficient and B is a composition‐dependent activation energy ( x is the composition vector), which we estimated using Model B from Ref. [38]. As described in Refs.…”

“…In this work, we estimated the glass‐forming melt viscosity within both the TBL and the primary foam layer using viscosity models presented in Ref. [37‐40] and compared the results to actual feed and glass viscosities measured by rotating‐spindle viscometer. The feed expansion test (FET) and evolved gas analysis (EGA) allowed us to determine the T FO and T B values.…”

Evaluation of glass viscosity of dental bioceramics by the SciGlass information system

“…There are several models available to predict the viscosity of glasses, like the viscosity-temperature relation described by the Vogel-Fulcher-Tammann (VFT) equation and the AdamGibbs equation [22,23]. Since viscosity depends strongly on the glass chemical composition, there are also various viscosity-composition relations, such as structural/chemical models [24].…”