Geometry of Slow Structural Fluctuations in a Supercooled Binary Alloy

The liquid structure of a glass-forming binary alloy is studied using molecular dynamics simulations. The analysis employs the geometrical approach of Frank and Kasper to establish that the supercooled liquid contains extended clusters characterized by the same short range order as the crystal. The steep increase in the heat capacity on cooling is directly coupled to the growing fluctuations of the Frank-Kasper clusters. The relaxation of particles in the clusters dominates the slow tail of the self-intermediate scattering function.

Figure 1

Illustration of the unit cell (blue box) of the ${\mathrm{MgZn}}_2$ structure and the three coordination polyhedra found in the crystal. The $A$ (small) particles are green and the $B$ (large) particles are gray (size reduced for visibility). Six $A$ particles of a Frank-Kasper bond are shown connected by red links.

Figure 2

The temperature dependence of the average number of $B$ particles of FK clusters (black X’s), the average number of $B$ particles of the largest FK cluster (red crosses), the average number of $A$ particles participating in FK bonds (blue triangles) and the average number of $B$ particles with 4 FK bonds (green circles) in inherent structures.

Figure 3

A picture of the FK clusters in a supercooled liquid at $T=0.599$. (The inherent structure used corresponds to time $0.5\times {10}^6$ in Fig. 4.) All the FK bonds in a common cluster are depicted as cylinders with the same color. $A$ and $B$ particles are depicted (size reduced for visibility) as green and gray spheres, respectively.

Figure 4

The inherent structure energy per particle $U_{\mathrm{is}}/N$, the number of $B$ particles in the largest FK cluster and the number of $B$ particles with 4 FK bonds (collected using the inherent structures) as a function of time during a simulation run. In each case the points correspond to the actual values and, the solid lines are local averages to indicate the trend.

Figure 5

The heat capacity $C_V$ (black circles) versus temperature along with the contribution from fluctuations in the inherent structure $C_{\mathrm{is}}$ (red triangles) and the difference $C_V\mathrm{\text{−}}{C}_{\mathrm{is}}$ (green X’s). A theoretical prediction due to Rosenfeld and Tarazona [17] (dashed line) breaks down at low temperatures.

Figure 6

Log-log plots of the self-intermediate scattering function $F_s(q=6.47,t)$ from the $A$ particles (black crosses), the contribution $F_{\mathrm{FK}}(t)/F_{\mathrm{FK}}(0)$ due to the $A$ particles initially in an FK cluster (red triangles) and $F_{n-\mathrm{FK}}(t)/F_{n-\mathrm{FK}}(0)$, the contribution due to those $A$ particles not in FK clusters at $t=0$ (green circles) for $T$ 0.599. Dashed lines represent stretched exponential fits to the data.