Aging and crystallization in a lattice glass model

We have studied the three-dimensional lattice glass of Pica Ciamarra et al. [Phys. Rev. E 67, 057105 (2003)], which has been shown to reproduce several features of the structural glass phenomenology, such as the cage effect, exponential increase of relaxation times, and aging. We show, using short-time dynamics, that the metastability limit is above the estimated Kauzmann temperature. We also find that in the region where the metastable liquid exists the aging exponent is lower than 0.5, indicating that equilibrium is reached relatively quickly. We conclude that the usefulness of this model to study the deeply supercooled regime is rather limited.

Figure 1

Comparison of real (wall) simulation times of standard Monte Carlo and kinetic Monte Carlo. Kinetic MC times highly depend on the density, which is directly related to the available moves. Inset: Inverse density vs $T/\mu$ of a perfect crystal heated at a rate $\dot{T}/T={10}^{-8}$ in grand canonical MC and KMC runs, showing both algorithms give the same results.

Figure 2

${\rho }^{-1}$ as a function of $T$ for different cooling rates. For $\dot{T}/T=-{10}^{-5}$ (red plus) the system goes quickly out of equilibrium, while $\dot{T}/T=-{10}^{-6}$ (green cross), $\dot{T}/T=-{10}^{-7}$ (blue star) and $\dot{T}/T=-{10}^{-8}$ (purple square) allow the supercooled metaequilibrium liquid to be found at progressively lower temperatures. Heating from the perfect crystal can be used to estimate $T_m$, as in the cyan solid squares ($\dot{T}/T={10}^{-8}$) and yellow circles ($\dot{T}/T={10}^{-9}$) curves.

Figure 3

Angell plot showing non-Arrhenius behavior. Full curve is a Vogel-Fulchner-Tamman fit with $T_0=0.048\mu$.

Figure 4

Density vs time for (from bottom to top) $T/\mu =1/5$, $1/6$, $1/7$, $1/8$, $1/9$, $1/10$, and $1/12$.

Figure 5

Crystal mass fraction for (from bottom to top) $T/\mu =1/5$, $1/6$, $1/7$, $1/8$, $1/9$, $1/10$, and $1/12$.

Figure 6

Evolution of the crystal mass fraction starting from the disordered initial condition ($T_i=4T_c$) with final temperatures $T_f=0.08\mu$ (circle), $0.09\mu$ (square), $0.104\mu$ (triangle), and $0.112\mu$ (diamond), and using a system of side $L=21$. Continuous lines are the same temperatures for a bigger system of side $L=30$.

Figure 7

Evolution of the normalized fluctuations for different temperatures (as indicated) for a system of side $L=30$. For $T=T_{\text{sp}}=0.104\mu$ we obtain a power-law behavior; the dashed black line is a fit of a power law with exponent $\varphi =0.203$. The inset shows results for $T=T_{\text{sp}}$ and two system sides $L=21$ (black squares) and $L=30$ (green circles).

Figure 8

Overlap vs time at $T=\mu /9$ for $t_w={10}^6$ (red plus), $t_w={10}^7$ (green cross) $t_w=2\times {10}^8$ (blue stars) and $t_w=2\times {10}^9$ (purple squares).

Figure 9

Characteristic time of the relaxation ($t_c$) vs $t_w$ for $T=\mu /9$. The full line is a fit to a four parameter sigmoid $S\left(t\right)=A+\frac{B}{1+e^{-(t/D-C)}}$. Inset: effective exponent ${\nu }_{\text{eff}}=\partial ln{t}_c/\partial ln{t}_w$.