Unveiling the medium-range order in glass models and its role in glass formation

The correlation between structure and glass formability in glassy systems is a long-standing puzzle. To solve this puzzle, many descriptors based on the short-range order (SRO) have been proposed. Here we show that the SRO, however, offers little help in explaining the glass formability and stability; instead it is the formation of medium-range order that stabilizes the glass against crystallization by suppressing the atomic rearrangement and compositional change. Our results provide a perspective for understanding the correlation between structure and stability in glasses.

Figure 1

(a) The instantaneous potential energy $\left(\mathrm{PE}=E-3k_{\mathrm{B}}\mathrm{T}\right)/\mathrm{atom}$ as a function of temperature for KA (black dots) and MKA (red dots), cooling rate $=1\times {10}^{-5}$, $N=4000$. (b) The instantaneous potential energy per atom as a function of temperature for KA and MKA, cooling rate $=1\times {10}^{-7}$, $N=4000$. (c) The potential energy per atom as a function of time for KA and MKA under annealing. (d) The instantaneous potential energy per atom as a function of temperature for KA and MKA; cooling rate $=1\times {10}^{-7}$, $N=16000$. (e) The total and partial PCFs for KA (black solid line) and MKA (red dots) under different temperatures for the glass samples are obtained using cooling rate $=1\times {10}^{-5}$, $N=4000$. The difference between KA and MKA $g$($r$) were illustrated by the blue solid line. The PCFs were calculated and averaged over 1000 snapshots. (f) The configurations of KA and MKA systems after annealing at $T=0.41$. The A and B particles are represented by red and blue spheres, respectively.

Figure 2

The atomic diffusion constants (D) for KA and MKA systems at different temperatures. The logarithmic scale for the $y$ axis is adopted to demonstrate the dependence of D on temperature more clearly.

Figure 3

The superposed clusters after alignment for (a) KA and (b) MKA system. A and B particles are represented by the red and blue dots. (c) The atomic densities of the first and second atomic shells for the superposed clusters. (d) The atomic structure of MRO in the KA and MKA systems. For clarity, the atoms were colored according to their atomic shell instead of chemical species.

Figure 4

(a), (b) The relative fractions of atoms included in the SRO and MRO network with respect to that of the liquid state; the liquid, undercooling, and glass regions were highlighted using different colors. The data were averaged over five independent runs, with the error bar denoting the standard deviation. (c), (d) Two slabs with thickness of 3σ for the SRO and MRO percolated network from KA and MKA glass. The A and B particles are colored in red and blue, respectively.

Figure 5

(a) The distributions of the potential energies of the central B atoms with (black) and without (red) SRO for KA (left) and MKA (right); (b) the same as (a) for B atoms with and without MRO packing. The data were collected from five independent runs.

Figure 6

Local density distribution of B in KA (black) and MKA (red) glass. The dashed line indicates the average B density in the two systems. The inset shows the cross sections of B-atomic density from KA (upper) and MKA (lower) glass. The scale of the inset is in arbitrary units. A scale bar of 5 was attached for measuring the density fluctuation spatial scale.

Figure 7

Three slabs with thickness of 3σ from the MKA system at different annealing times and the corresponding cross sections of B-atomic density. Only the local crystalline orders are shown; the atoms in bcc, hcp, and fcc packing are colored blue, red, and green, respectively. A scale bar of 5 was attached for measuring the density fluctuation spatial scale.