Atomistic modeling of multiple amorphous-amorphous transitions in SiO${}_2$ and GeO${}_2$ glasses at megabar pressures

We present molecular dynamics simulations of SiO${}_2$ and GeO${}_2$ glasses up to megabar pressures, 120 and 160 GPa, respectively, and show direct parallels between polyamorphism of glasses and polymorphism of their crystalline counterparts under compression. The glasses undergo a set of several smooth transformations in much the same manner as the corresponding crystals at nearly the same pressures, where coordination numbers of Si and Ge atoms considerably exceed 6, reaching 6.4 and 7.6, respectively, at maximum simulation pressures. The transformations in glasses, unlike those in crystals, occur with rather small hysteresis. High coordination states are not retained in a metastable form at room pressure.

Figure 1

Polyhedron representation of the simulated SiO${}_2$ glass network fragments (a) at zero pressure (tetrahedrons SiO${}_4$ are visible), (b) at $P$ $=$ 20 GPa (SiO${}_4$, SiO${}_5$, and SiO${}_6$ units), and (c) at 110 GPa (highly distorted SiO${}_5$, SiO${}_6$, and SiO${}_7$ units).

Figure 2

Polyhedron representation of the simulated GeO${}_2$ glass network fragments (a) at zero pressure (tetrahedrons GeO${}_4$ are visible), (b) at $P$ $=$ 40 GPa (GeO${}_4$, GeO${}_5$, and GeO${}_6$ units), and (c) at 160 GPa (highly distorted GeO${}_5$, GeO${}_6$, GeO${}_7$ and GeO${}_8$ units).

Figure 3

Pressure dependence of the average coordination number for Si ($Z_{\mathrm{Si}}$ versus $P^{1/2}$) in compression-decompression cycle for the simulated SiO${}_2$ glass (at the bottom) and the transition pressure interval diagrams for the simulated amorphous and real crystalline SiO${}_2$ (at the top). For the amorphous state the pressure diagram illustrates intervals of intensive increase of $Z_{\mathrm{Si}}$ in the simulation, whereas for crystalline phases the diagram shows pressure intervals of the key phase transitions. The inset at the bottom presents the relative volume versus $P^{1/2}$ dependence. Point A corresponds to the glass state obtained after isobaric (80 GPa) heating up to 1000 K. Point B corresponds to the final state of the glass obtained during additional decompression cycle at low temperature (10 K).

Figure 4

Pressure dependence of the average coordination number for Ge ($Z_{\mathrm{Ge}}$ versus $P^{1/2}$) in compression-decompression cycle for the simulated GeO${}_2$ glass (at the bottom) and the transition pressure interval diagrams for the simulated amorphous and real crystalline GeO${}_2$ (at the top). For amorphous state the pressure diagram illustrates intervals of intensive increase of $Z_{\mathrm{Ge}}$ in the simulation, whereas for crystalline phases the diagram shows pressure intervals of the key phase transitions. The $\alpha$-quartz type GeO${}_2$ phase is metastable at normal conditions, and the shown transition to the rutile type phase (at 300 K) is nonequilibrium. The inset at the bottom presents the relative volume versus $P^{1/2}$ dependence. The levels a, b, and c ($Z_{\mathrm{Ge}}$ ≈ 5.5, 5.9, and 6.5, respectively) correspond to relatively stable (with respect to pressure change) states of GeO${}_2$ glass.