Glass formation and crystallization of a simple monatomic liquid

A simple monatomic system in two dimensions with a double-well interaction potential is investigated in a wide range of temperatures by molecular-dynamics simulation. The system is melted and equilibrated well above the melting temperature, and then it is quenched to a temperature 88% below the melting temperature at several cooling rates to produce an amorphous state. Various thermodynamic quantities are measured as functions of temperature while the system is heated at a constant rate. The glass transition is observed with a sudden increase in the energy and the glass transition temperature is shown to be an increasing function of the cooling rate in the preparation process of the amorphous state. In a relatively high-temperature region, the system gradually transforms into crystals, and the time-temperature-transformation curve shows a typical nose shape. It is found that the transformation time to a crystalline state is the shortest at a temperature $14–15\%$ below the melting temperature and that at sufficiently low temperatures the system does not transform into a crystalline state within an observation time in our simulation. This indicates that a long-lived glassy state is realized.

Figure 1

(Color online) The LJG potential for the parameters $r_G=1.47r_0$, $ϵ=1.5{ϵ}_0$, and ${\sigma }^2=0.02r_0^2$.

Figure 2

(Color online) Tiling structures in real space and diffraction images of a glass and crystal after a long run. Upper panels are the structure of crystal at $T^{\ast }=0.35$ and lower ones are that of glass at $T^{\ast }=0.10$. Left panels show the tiling structures in real space. These are constructed by basic tiles. Right panels show the diffraction images.

Figure 3

(Color online) The radial distribution function of a glassy state at $T^{\ast }=0.1$ and local structures.

Figure 4

(Color online) The temperature dependence of the total energy in a heating process from a glassy state. If the system can be described only by the term of lattice vibration, plots are supposed to lie on the line in above figure.

Figure 5

(Color online) The cooling rate dependence of $T_g^{\ast }$.

Figure 6

(Color online) (a) Three characteristic tiling structures. (b) The time dependence of the number of characteristic tiling structures. The curve (all) represents the number of atoms surrounded by any of the pentagon, triangle, or square tiles. The curves PPPT, PPP, and PPTS correspond to the structures shown in (a).

Figure 7

(Color online) The time-temperature-transformation diagram for monatomic LJ and LJG liquids.

Figure 8

(Color online) Time dependence of potential energy at several temperatures. (a) shows the region close to $T_m^{\ast }$, $0.33\le T^{\ast }\le 0.338$. (b) shows the region at low temperatures, $0.20\le T^{\ast }\le 0.23$.

Figure 9

(Color online) The process of nucleation and growth at a temperature close to $T_m^{\ast }$. (a) The nucleation occurs in the center. (b) The nucleation grows rapidly. (c) A part of crystalline phase is destroyed and rearrangement occurs. (d) Eventually, the system becomes an almost perfect crystal.

Figure 10

(Color online) The system-size dependence of the time-temperature-transformation diagram for monatomic LJG liquids. The numbers of particles in each system are 1024 and 4096. The temperature range in $N=4096$ system is from 0.24 to 0.341.

Figure 11

(Color online) The boundary condition dependence of the time-temperature-transformation diagram for monatomic LJG liquids.