Towards Glasses with Permanent Stability

Unlike crystals, glasses age or devitrify over time, reflecting their nonequilibrium nature. This lack of stability is a serious issue in many industrial applications. Here, we show by numerical simulations that the devitrification of quasi-hard-sphere glasses is prevented by suppressing volume-fraction inhomogeneities. A monodisperse glass known to devitrify with “avalanchelike” intermittent dynamics is subjected to small iterative adjustments to particle sizes to make the local volume fractions spatially uniform. We find that this entirely prevents structural relaxation and devitrification over aging time scales, even in the presence of crystallites. There is a dramatic homogenization in the number of load-bearing nearest neighbors each particle has, indicating that ultrastable glasses may be formed via “mechanical homogenization.” Our finding provides a physical principle for glass stabilization and opens a novel route to the formation of mechanically stabilized glasses.

Figure 1

Homogenization of local volume fractions. (a) Illustration of the ${\varphi }_i$ flattening algorithm. A Voronoi tessellation is taken of an energy minimized configuration (solid blue). Particles are resized to match the local ${\varphi }_i$ to the $⟨{\varphi }_i⟩$ (dashed red) before being relocated to the center of the Voronoi cell (crosses). The energy is minimized again before the process is repeated until this global operation no longer reduces the standard deviation in the local volume fractions. (b) The probability density function of effective local volume fractions ${\varphi }_i^{\mathrm{eff}}$ with each iteration. (c) The probability density function of particle sizes ${\sigma }_i$ with each iteration.

Figure 2

Spectral density of static structures, from CG to UG. Spectral densities ${\chi }_v$ are given for progressive iterations as the CG state is transformed into a UG state. As the iterations progress, ${\lim }_{q\to 0}{\chi }_v(q)$ systematically decreases, though the scaling does not reach the $q^4$ scaling of a class I hyperuniform state. (inset) Distribution of local number densities $n_i$. The UG state features a significantly wider distribution of $n_i$.

Figure 3

Impact of flattening ${\varphi }_i$ over space on avalanche events and devitrification. (a) Squared displacements over ten $5000{\tau }_B$ runs initiated from the same CG state, the state after one iteration of the ${\varphi }_i$ flattening algorithm, and the final UG state, as indicated. (b) Squared displacements over ten $5000{\tau }_B$ runs initiated from ten independently generated CG states using the same particle sizes as in the UG state (re-CG). Squared displacements for the UG state from (a) are also drawn for comparison. (c) Change in crystalline particles and force network for corresponding CG and UG states. The CG-generated state experiences growth in crystallinity, while the UG state created from it does not change. Changes in force connections between nearest neighbors are also shown. The thin blue lines indicate the original network; red and green lines at $t=5000{\tau }_B$ indicate connections broken and formed.

Figure 4

Impact of ${\varphi }_i^{\mathrm{eff}}$ homogenization on structure, thermodynamics, and mechanics. (a) Average energy per particle $\beta ⟨U⟩$ vs $Q_6$ for 50 independent pairs of CG/UG configurations, and re-CG states generated from the final UG particle size distribution. (b) Compressibility factor $Z=\beta P_V/⟨\sigma {⟩}^3$ vs deviatoric stress invariant $J_2$ over same states as in (a). (c) Average number of force neighbors $⟨n_{\mathrm{FN}}⟩$ for particles with different local volume fractions ${\varphi }_i^{\mathrm{eff}}$ in CG (red), UG (blue), and re-CG (yellow) states. Solid lines are found from energy minimized configurations, dashed lines from thermally fluctuating configurations at the beginning of the Brownian dynamics simulation ($t=5{\tau }_B$). (inset) $⟨\mathrm{\Delta }{n}_{\mathrm{FN}}⟩$ as individual particles with different initial ${\varphi }_i^{\mathrm{eff}}$ in the CG state are transformed to reach a UG state. (d) Hydrostatic contribution to pressure from individual particles $P_{\mathrm{ex},i}$ vs $n_{\mathrm{FN}}$ for CG, UG, and re-CG states. (e) Deviatoric stress invariant contribution from individual particles $⟨J_{2,i}⟩$ for CG, UG, and re-CG states.