Figure 1

(a) Variation of packing density versus time with different initial densification rates. The fast densification has the initial rate of $q_1=0.0055$ and the slow densification has $q_2=0.0014$. Solid lines represent the results of the current simulations and dash lines represent $\phi \text{−}\tau$ curves using the protocol introduced in Ref. 14. Thin solid lines show the initial slope of the curve in our simulation. (b) Dependence of the final packing density on initial quench, or densification (Ref. 16) rate $\left({\Gamma }^{-1}\right)$ in a one-component system. Our cooling rate $q$ is related to $\Gamma$ by $q=({\sigma }^{2}N\pi ∕2\sqrt{{\sigma }^3∕T_r})\Gamma$. $N$ is the number of spheres in the periodic box, $\sigma$ is their dimensionless diameter, and $T_r$ represents a reduced temperature defined based on dimensionless velocity of spheres. We prefer to use $q$ rather than $\Gamma$ as it is a general definition that can be readily used in binary and polydisperse packing. Each circle represents one MD simulation of the system at a specific quench rate. 500 spheres placed in a cubic box are used. The critical densification rate is $q_c=0.00453$. The sharp division of the crystal and glass phase region can be seen. Results of a continuous size growth algorithm (Ref. 16) is also shown by squares connected by solid line. (c) Quenched samples consisted of different number of spheres (20 000, 3000, and 500). All samples are obtained around their CCR, which is $q_C=0.0039$ with 10% variation. (d) Variation of $PV∕N{k}_{B}T$ with $\phi$ for the cases shown in Fig. 1c. Black, light gray and dark gray colors represent samples with 20 000, 3000, and 500 hard spheres.Reuse & Permissions

Figure 2

(a) The quench rate versus atomic size ratio $(q-\alpha )$ for the binary mixtures with $x_B=0.20$. The vertical bar represents the final packing density ${\phi }_m$. The CCR is shown as a dotted line. (b) The critical quench rates (CCR) versus atomic size ratio $(q-\alpha )$ for the binary mixtures with $x_B=0.10$, 20, and 0.30.Reuse & Permissions

Figure 3

The kinetic diagram for glass formation obtained at three different cooling rates represented by thinner lines. Solid line, dash line, and dotted-dash line stand for the cooling rates of $q_1=1.5\times {10}^{-5}$, $q_2=5.5\times {10}^{-5}$, $q_3=2.8\times {10}^{-4}$, respectively. As a comparison, results from Egami and Waseda (Ref. 7) (thick dash line) and Miracle and Senkov (Ref. 9) (thick dotted-dash line) models are also plotted. The areas representing glassy and crystalline regions are outlined in the figure.Reuse & Permissions

Figure 4

Variation of ${\phi }_{\mathrm{fcc}}^b$ with $\alpha$ for a pure $(x_B=0)$ and binary system $(x_B=0.20)$. Packing densities obtained from simulations are also shown: Filled circles represent the fcc binary solid solution and open circles represent the amorphous phase. Multiple symbols at the same $\alpha$ represent packing densities of the same system under different quench rates.Reuse & Permissions

Figure 5

The atomic structure of a sample with 500 atoms with $\alpha =0.50$, $x=0.25$. The large spheres and small black spheres represent the large atoms and the small atoms, respectively. To show the local clustering of the small atoms, a cross section in the $xy$ plane of the sample is shown. The filled circles represent small solute atoms. The crystalline order of the large atoms in this cross section is clearly seen. The diameters of the circles in the cross section are not in direct proportion to the diameters of the atoms due to the cut.Reuse & Permissions

Figure 6

Atomic structure of a sample with 500 atoms at $\alpha =0.40$ and $x=0.50$. It forms octahedral interstitial solid solution and interstitial compound. Small atoms are shown to occupy octahedral interstitials and a periodic arrangement of small atoms is shown.Reuse & Permissions