Cooling rate and stress relaxation in silica melts and glasses via microsecond molecular dynamics

We have conducted extremely long molecular dynamics simulations of glasses to microsecond times, which close the gap between experimental and atomistic simulation time scales by two to three orders of magnitude. Static, thermal, and structural properties of silica glass are reported for glass cooling rates down to $5\times {10}^9$ K/s and viscoelastic response in silica melts and glasses are studied over nine decades of time. We present results from relaxation of hydrostatic compressive stress in silica and show that time-temperature superposition holds in these systems for temperatures from 3500 to 1000 K.

Figure 1

Plot of the density vs temperature for seven glass quenches completed with linear cooling rates $\gamma$ ranging $7.7\times {10}^{13}$ down to $5\times {10}^9$ K/s. All quenches qualitatively capture silica's anomalous density. Density $\rho \left(T\right)$ is independent of ramp rate down to approximately 4500 K.

Figure 2

Plot of density $\rho$ at 300 K, as a function of the glass quench cooling rate $\gamma$. The blue dashed line is the experimental value. The red dashed line is a linear extrapolation fit to data in the range above $3\times {10}^{12}$ K/s. The statistical error is smaller than the data points.

Figure 3

Plot of the thermal expansion coefficient at constant pressure ${\alpha }_P$, calculated at 300 K, as a function of the glass quench cooling rate $\gamma$. The blue dashed line is the experimental value. The red dashed line is a linear extrapolation fit to data in the range above $3\times {10}^{12}$ K/s. The statistical error is smaller than the data points.

Figure 4

Partial coordination number $z$ as a function of glass cooling rate $\gamma$. (a) Silicon coordination number with oxygen. (b) Oxygen coordination number with silicon. Optimal coordination is $z=4$ for silicon and $z=2$ for oxygen.

Figure 5

Radial distribution function plots for (a) Si-Si, (b) Si-O, and (c) O-O at 300 K after a quench ramp down from 8000 K. Three rates are shown fastest $7.7\times {10}^{13}$ K/s in solid black, medial $3.1\times {10}^{12}$ K/s in dash-dot red, and slowest $5\times {10}^9$ K/s in dash green.

Figure 6

Distribution functions for the Si-O-Si and O-Si-O angles plotted together. Three rates are shown, fastest $7.7\times {10}^{13}$ K/s in solid black, medial $3.1\times {10}^{12}$ K/s in dash-dot red, and slowest $5\times {10}^9$ K/s in dash green. The vertical line is the ideal tetrahedral angle.

Figure 7

(a) The bulk stress relaxation modulus plotted vs log time plotted from picosecond to microsecond times for temperatures from 3500 to 1000 K. (b) The same data, smoothed and shifted horizontally, collapsed to show the master curve for silica.

Figure 8

Partial intermediate scattering function before and after stress relaxation at 2000 K.

Figure 9

The log of the shift factor plotted vs the temperature. The data are fit to both Arrhenius and WLF theories. Error bars are smaller than the data points in the plot.