Modeling Glass Formation: A Markov Chain Approach to Understanding the Critical Cooling Rate in Lennard-Jones Mixtures

Amorphous solids form when a liquid is cooled faster than the critical cooling rate R_c. The value of R_c determines the glass forming ability and varies by more than ten orders for different alloys. We investigate the competition between glass formation and crystallization using molecular dynamics simulations of equimolar binary Lennard-Jones (LJ) mixtures as a function of the cohesive energies and heats of mixing of the mixtures. We develop a Markov Chain model to characterize the cooling process based on calculations of the probability of finding an atom with a particular local bond orientational order parameter and local packing fraction over time. The Markov Chain model reproduces the dynamics during cooling and can recapitulate the critical cooling rate for each alloy. We also apply the Markov chain model to purely repulsive Lennard-Jones atoms and cyclic shear of frictionless repulsive spheres to understand the differences in glass formation between Lennard-Jones mixtures during cooling and purely repulsive systems undergoing athermal driving.