Simulation of Ion Diffusion During Float Glass Processing

Abstract

Float glass is widely used in architecture and in the automotive industry. During the float process tin diffuses into and reacts with the glass melt. The presence of tin in the glass surface region causes mismatch in thermoelastic properties between the bulk and the surface. This, in turn, can lead to wrinkling of the surface after the glass is subject to a toughening heat treatment. This project involves trying to understand the diffusion and reaction mechanisms that contribute to this phenomenon. A set of partial differential equations describing the important reaction-diffusion mechanisms has been proposed. This mathematical model is based on 3 redox reactions in the glass melt. 6 diffusing and reacting species have been considered, which comprise 3 redox couples, namely stannous and stannic tin, ferrous and ferric iron, and hydrogen atoms and ions. Using guessed parameters, the computer simulation shows the most striking feature of the tin depth profile - the tin hump, which is observed experimentally by Secondary Ion Mass Spectrometry (SIMS) and Electron Probe Micro-Analysis (EPMA). It can be observed from the simulations that stannous tin diffusing into the glass is oxidised to stannic tin by ferric iron. The tin hump is due to the immobile stannic tin. The shape and location of the hump can be influenced by the float bath atmosphere and the oxidising species in the glass. These features are in agreement with experimental findings. The simulation also reveals that the tin hump forming process is a dynamic process. The Sn(IV) forms and converts back to Sn(II) simultaneously as the hump moves in the glass melt. However, an inverse method has not been found to recover the parameters of the mathematical model from SIMS data. This is due to SIMS's data being only qualitative, as well as the complexity of the model.