Homogeneous crystallization in four-dimensional Lennard-Jones liquids

We observe homogeneous crystallization in simulated high-dimensional $(d>3)$ liquids that follow physically realistic dynamics and have system sizes that are large enough to eliminate the possibility that crystallization was induced by the periodic boundary conditions. Supercooled four-dimensional (4D) Lennard-Jones (LJ) liquids maintained at zero pressure and constant temperatures $0.59<T<0.63$ crystallized within $\sim 2\times {10}^4\tau$, where $\tau$ is the LJ time unit. Weeks-Chandler-Andersen (WCA) liquids that were maintained at the same densities and temperatures at which their LJ counterparts nucleated did not crystallize even after $2.5\times {10}^5\tau$, showing that the presence of long-ranged attractive interactions dramatically speeds up 4D crystallization, much as it does in 3D. On the other hand, the overlap of the liquid and crystalline phases' local-bond-order distributions is smaller for LJ systems than for WCA systems, which is the opposite of the 3D trend. This implies that the widely accepted hypothesis that increasing geometrical frustration rapidly suppresses crystallization as the spatial dimension $d$ increases is only generally valid in the absence of attractive interparticle forces.

Figure 1

Average packing fraction $\varphi \equiv \rho V_{\mathrm{is}}$, average pair energy $E_{\mathrm{pair}}$, and average two-particle bond-order correlators $\langle q_6(i,j)\rangle$ and $\langle q_4(i,j)\rangle$ in supercooled 4D Lennard-Jones liquids maintained at zero pressure and the temperatures indicated in the legend of panel (a).

Figure 2

Fluctuations in the per-particle bond-order correlator ${\tilde{q}}_6\left(i\right)$ and the local packing fraction ${\varphi }_{\mathrm{loc}}\left(i\right)$ in supercooled 4D Lennard-Jones liquids maintained at zero pressure and the temperatures indicated in the legend of panel (a).

Figure 3

Evolution of local structural order in Lennard-Jones systems at $T=0.625$ and $P=0$. Panels (a)–(c) respectively show the pair correlation functions $g\left(r\right)$, the probability distributions $P\left[q_6(i,j)\right]$, and the probability distributions $P\left[{\varphi }_{\mathrm{loc}}\left(i\right)\right]$ at selected times.

Figure 4

Evolution of local structural order in Lennard-Jones systems at $T=0.600$ and $P=0$. Panels (a) and (b) respectively show the probability distributions $P\left[q_6(i,j)\right]$ and the probability distributions $P\left[{\varphi }_{\mathrm{loc}}\left(i\right)\right]$ at selected times.

Figure 5

Pressure $p$, average two-particle bond-order correlator $\langle q_6(i,j)\rangle$, and average fractional density fluctuations $\mathrm{\Delta }{\varphi }_{\mathrm{loc}}/\langle {\varphi }_{\mathrm{loc}}\rangle$ in supercooled 4D WCA liquids maintained at constant densities and temperatures (Table 1).

Figure 6

Time-averaged results for $P\left[q_6(i,j)\right]$ [panel (a)] and $g\left(r\right)$ [panel (b)] in LJ and WCA liquids at the same $\rho =1.202$ and LJ and WCA single $D_4$ crystals at the same $\rho =1.372$.