Structure and function of window glass and Pyrex

Window glass is a ternary mixture, while Pyrex (after window glass, the most common form of commercial glass) is a quaternary. Here, we investigate the chemical, physical, and mathematical factors that determine the compositions of these optimized glasses. Previously, we succeeded in deriving exactly the composition of window glass (sodium calcium silicate) without adjustable parameters. Borosilicates are a much more challenging problem, and Pyrex (sodium aluminum borosilicate) requires a different approach. Our analysis shows that mean-field (or global) models (networks without significant clustering) are sufficient for window glass and probably most other commercial silicate glasses. However, it appears that the most important property of pyrex, its ability to resist mechanical shocks, requires a cluster model (large medium range order). We propose such a model, and argue that it also follows from hierarchical principles. Our model is strongly supported by specific experiments, and we suggest further experiments to test the principles underlying commercial glasses.