An Empirical Model for the Calorimetrically-Defined Glass Transition Temperature with Applications to Natural Systems

Glassy rocks have long held a special fascination for petrologists and geochemists because they record the composition of the melt phase attending magmatic processes. Naturally-occurring silicate glasses form under a variety of geological conditions and they commonly form the main constituent in silicic volcanic rocks and in rapidly cooled mafic rocks. Glass also occurs in rocks with cooling histories that are substantially slower, such as the interiors of lava flows or mantle xenoliths. The glass transition temperature (Tg) marks the transition from the liquid to the glassy state. From a petrological perspective, the calorimetrically-defined glass transition temperature is an important limiting value for the temperature conditions at which many magmatic processes take place. Glass formation is a boundary between changing environmental states. Above Tg, rates of nucleation, crystallization and vesiculation are sufficiently fast to drive magmatic processes. Conversely, where the liquid line of descent (e.g., T-X_Melt path) intersects the Tg of the melt, glass forms and many magmatic processes effectively cease. The purpose of this paper is to provide a means of exploring the T-X_Melt conditions for glass formation in natural magmatic systems. Specifically, we present an empirical model of predicting the thermodynamic glass transition temperature (Tg) as a function of melt composition. Operationally, the model produces temperature-dependent expressions for the heat contents of a silicate melt and glass of known composition. The point of intersection of the heat content curves for glass and melt defines the calorimetric value of Tg. Our model is constructed from experimental calorimetric heat content and differential scanning calorimetric (DSC) heat capacity measurements on silicate melts and glasses produced over the past 20 years. Calorimetric data in the model include over 500 experiments on 60 melt compositions and 250 observations on 30 glass compositions. Additional constraints on the model derive from independent estimates of the thermodynamic Tg. The model reproduces most of the measured calorimetric-values of Tg to within 30^oC. The model also provides volcanologists with a tool for tracking (T_Magma-Tg) through magmatic processes such as fractional crystallization, vesiculation, partial melting. It can be used to forecast the termination of liquid lines of descent by glass formation and provides geothermometric constraints on magmatic systems by converting glass compositions into minimum pre-eruption temperatures.