A Monte-Carlo Approach for Modeling Glass Transition

Abstract

Glass transition is an important factor in the thermo-forming of glass elements of precision geometries, such as optical glass lenses. Based on the theory of potential energy landscape, the master equations can be established to describe the slowdown of atomic motions in the glass transition range. However, the direct solution of these master equations is almost formidable as the hopping rates between basins vary in many orders of magnitude. To make use of the master equations in the finite element simulation of thermo-forming process, this article develops a Metropolis stochastic process by assuming that the basin-hopping probability at a given time interval depends only on the relative hopping rate between the target state and the present state. It was shown that with an infinitesimal time interval, this stochastic description degenerates to the master equations, and that with coarse time steps, the efficiency can be greatly improved with good accuracy. The advantage of this new method was demonstrated through the glass transition and thermo-forming simulations of selenium by integrating the stochastic process with the finite element method via the constitutive description of the variation of volume and viscosity with temperature and time.