Formation of a glassy solid by computer simulation

The Hamiltonian dynamics of a Lennard-Jones system is examined to study the formation process of a glassy solid, by using the mapping-onto-minima method. Four types of dynamics are found, which depend on temperature regimes classified by three characteristic temperatures $T_1$, $T_2$, and $T_3$. (1) The high-temperature regime $T_1$≤T: The state point describing the system of motion wanders over various local minima. (2) The intermediate-temperature regime $T_2$≤T<$T_1$: The state point wanders over an energetically widely spread local minimum for a specific time interval after the system cooling stops but gradually tends to stay in the single local minimum or a few local minima. (3) The low–intermediate-temperature regime $T_3$≤T<$T_2$: The state point assumes the several local minima intermittently and finally relaxes into a single local minimum or a few local minima with almost equal potential energies. The crystallization occurs stepwise by wandering over several local minima. (4) The low-temperature regime T<$T_3$: The state point stays in the single local minimum or a few local minima with almost equal potential energy for the entire time interval. From the observation that the number of the local minima over which the state point wanders decreases drastically for T<$T_2$, it is concluded that $T_2$ corresponds to the glass transition temperature, and a glassy solid is formed for T<$T_2$. The distances between the local minima over which the state point wanders are also studied for each temperature regime. It is found that the small (or large) distances between the local minima generally correspond to the small (or large) differences of the potential energies at the local minima. The stepwise-occurring crystallization is discussed by examining the diffusion length of each particle, and it is found that the crystallization appears as a result of a cascade diffusion of particles, triggered by a few particles.