Crystal Nucleation in a Supercooled Liquid with Glassy Dynamics

In simulations of supercooled, high-density liquid silica we study a range of temperature $T$ in which we find both crystal nucleation as well as the characteristic dynamics of a glass forming liquid, including a breakdown of the Stokes-Einstein relation. We find that the liquid cannot be observed below a homogeneous nucleation limit (HNL) at which the liquid crystallizes faster than it can equilibrate. We show that the HNL would occur at lower $T$, and perhaps not at all, if the Stokes-Einstein relation were obeyed, and hence that glassy dynamics plays a central role in setting a crystallization limit on the liquid state in this case. We also explore the relation of the HNL to the Kauzmann temperature, and test for spinodal-like effects near the HNL.

Figure 1

(a) Behavior of ${\tau }_{\alpha }$, ${\tau }_n$, and ${\tau }_{\alpha }^{\mathrm{SE}}$ as a function of $T$. The model functions ${\tau }_{\alpha }^{\mathrm{VFT}}$ (solid line), ${\tau }_{\alpha }^{\mathrm{VFT}}/R$ (dashed line), and $\mathcal{E}{\tau }_{\alpha }^{\mathrm{VFT}}$ (dot-dashed line) are also shown. (b) $T$ dependence of ${\tau }_n/{\tau }_{\alpha }$ and ${\tau }_n/{\tau }_{\alpha }^{\mathrm{SE}}$. The model functions $\mathcal{E}$ (solid line) and $\mathcal{E}R$ (dashed line) are also shown.

Figure 2

(a) VFT and (b) AG plots of $D/T$ (circles) and $1/{\tau }_{\alpha }$ (squares). Filled symbols are data generated for $T\ge 3200\mathrm{K}$ from single simulation runs. Open symbols are data found using the 20 longest runs from the ensemble of 200 conducted at each $T<3200\mathrm{K}$. Fits of a straight line to each data set are also shown. In (a) $T_0=2254\mathrm{K}$. In (b) the data for $S_c$ from Fig. 3a are used to evaluate $1/T{S}_c$.

Figure 3

(a) $S_c$ as a function of $T$ (thick solid line). The dashed line is an extrapolation based on the finding in Fig. 2 that both the VFT and AG relations are satisfied. That is, we solve $A\exp [B/(T-T_0)]=C\exp [E/(T{S}_c)]$ for $S_c$, where the fitting parameters $A$, $B$, $T_0$, $C$, and $E$ are taken from the fits to $D/T$ in Fig. 2. This curve models the case where $S_c$ approaches an ideal glass transition at $T_K=T_0$. (b) $T$ dependence of the SE ratio $D{\tau }_{\alpha }/T$, normalized by $c_0$, the value of $D{\tau }_{\alpha }/T$ at 5000 K. The solid line is the model function $R$.

Figure 4

$\Delta G(n)/RT$ as function of $n$ for $T=2900$, 3000, 3100, 3200, and 3300 K (data sets from bottom to top). Solid curves are fits to the CNT prediction $\Delta G(n)/RT=-an+b{n}^{2/3}$, where $a$ and $b$ are fitting parameters. Inset: $\Delta G^{*}/RT$ and $n^{*}$ as a function of $T$.