Phase Diagram of Kob-Andersen-Type Binary Lennard-Jones Mixtures

The binary Kob-Andersen (KA) Lennard-Jones mixture is the standard model for computational studies of viscous liquids and the glass transition. For very long simulations, the viscous KA system crystallizes, however, by phase separating into a pure $A$ particle phase forming a fcc crystal. We present the thermodynamic phase diagram for KA-type mixtures consisting of up to 50% small ($B$) particles showing, in particular, that the melting temperature of the standard KA system at liquid density 1.2 is 1.028(3) in $A$ particle Lennard-Jones units. At large $B$ particle concentrations, the system crystallizes into the CsCl crystal structure. The eutectic corresponding to the fcc and CsCl structures is cutoff in a narrow interval of $B$ particle concentrations around 26% at which the bipyramidal orthorhombic ${\mathrm{PuBr}}_3$ structure is the thermodynamically stable phase. The melting temperature’s variation with $B$ particle concentration at two constant pressures, as well as at the constant density 1.2, is estimated from simulations at pressure 10.19 using isomorph theory. Our data demonstrate approximate identity between the melting temperature and the onset temperature below which viscous dynamics appears. Finally, the nature of the solid-liquid interface is briefly discussed.

Figure 1

Determining the standard KA system’s melting temperature and pressure when the liquid at coexistence has density 1.2. (a) The pressure of the KA liquid at density 1.2 as a function of temperature. (b) The fraction of $B$ particles in the liquid phase of an equilibrated two-phase simulation at this pressure. The melting temperature of the density 1.2 KA liquid is seen to be given by $T_m=1.028(3)$ at pressure $p=10.19(3)$.

Figure 2

(Upper) Snapshot of a two-phase simulation in a periodic box at the coexistence temperature 1.028 and pressure $p=10.19$ ($A$ particle LJ units). $A$ particles are gray and $B$ particles are red. The density of the liquid phase is 1.2. (Lower) Overall density (black dotted line) and $B$ particle density (red line) along the $z$ direction. The fraction of $B$ particles in the liquid phase is $0.24/1.20=20\%$.

Figure 3

Phase diagram of KA-type mixtures at pressure $p=10.19$, where ${\chi }_B$ is the fraction of $B$ particles in the equilibrium liquid phase. The solid blue line shows the melting temperature of the pure $A$ particle fcc crystal, the solid red line shows the melting temperature of the CsCl structure, and the short solid purple line shows the melting temperature of the ${\mathrm{PuBr}}_3$ structure. Orange symbols give the melting temperature of other, less stable structures at selected compositions (see text). The two dashed black lines are isodiffusional lines. The green crosses show the temperature $T_{\min }$ of minimum crystallization time for a given ${\chi }_B$; the colored regions are where rapid crystallization occurs, defined by $t^{*}<2\times {10}^5$ for 8000 particles. (Upper) Minimum crystallization time. Extrapolations based on third-order polynomials (red dashed lines) suggest that the best glass former is at a higher $B$ particle composition than the eutectic.

Figure 4

Isomorph-theory estimated melting temperature as a function of $B$ particle concentration at fixed liquid-phase density $\rho =1.2$ (triangles), as well as at pressures $p=0$ and $p=30$ (squares and diamonds). The circles connected by colored full lines are the results from Fig. 3, giving the reference states from which the open symbols are predicted. Red crosses are the actual melting temperatures. (Inset) Melting temperature $T_m$ versus the onset temperatures $T_0$ (not to be confused with the above isomorph reference temperature), identified by Coslovich and Pastore at which the $A$ and $B$ particle dynamics (black and red) change from Arrhenius to non-Arrhenius temperature dependence [45]. The four points shown represent different densities (pressures) of the standard $80/20$ KA model.

Figure 5

The crystal order parameter $Q$ [36] plotted as a function of time averaged over $10^3$ LJ time units. The blue crosses are from a fcc-liquid coexistence simulation at $T=1.028$, and the red crosses are from a CsCl-liquid coexistence simulation at $T=1$. These results indicate that the fcc interface is rough, whereas the CsCl interface is smooth and flat. The latter property impedes growth of the CsCl crystal. Particles with $Q_6>0.25$ are highlighted in the inserted coexistence pictures, where $Q_6$ is the rotational order parameter [38].