Ultrahigh-pressure form of $\mathrm{Si}{\mathrm{O}}_2$ glass with dense pyrite-type crystalline homology

High-pressure synthesis of denser glass has been a longstanding interest in condensed-matter physics and materials science because of its potentially broad industrial application. Nevertheless, understanding its nature under extreme pressures has yet to be clarified due to experimental and theoretical challenges. Here we reveal the formation of $\mathrm{OS}{\mathrm{i}}_4$ tetraclusters associated with that of $\mathrm{Si}{\mathrm{O}}_7$ polyhedra in $\mathrm{Si}{\mathrm{O}}_2$ glass under ultrahigh pressures to 200 gigapascal confirmed both experimentally and theoretically. Persistent homology analyses with molecular dynamics simulations found increased packing fraction of atoms whose topological diagram at ultrahigh pressures is similar to a pyrite-type crystalline phase, although the formation of tetraclusters is prohibited in the crystalline phase. This critical difference would be caused by the potential structural tolerance in the glass for distortion of oxygen clusters. Furthermore, an expanded electronic band gap demonstrates that chemical bonds survive at ultrahigh pressure. This opens up the synthesis of topologically disordered dense oxide glasses.

Figure 1

(a) The increasing sequence of spheres for input data (left). The persistence diagram (right) is obtained as a histogram counting the number of voids on the birth-death plane. (b), (c) The appearance and disappearance of a void for a regular hexagon/triangle. (d) The pairs of birth and death radii for hexagon and triangle in the one-dimensional persistence diagram. (e) The pairs of birth and death radii for tetrahedron and octahedron in the two-dimensional persistence diagram.

Figure 2

High-pressure structural data and pressure evolution of Si-O coordination number of $\mathrm{Si}{\mathrm{O}}_2$ glass. (a) X-ray total structure factors $S$($Q$) of $\mathrm{Si}{\mathrm{O}}_2$ glass up to pressures of 200 GPa. Dotted curves: experimental data; solid curves: MD simulations. (b) Faber-Ziman partial structure factors of $S_{\mathrm{SiSi}}\left(Q\right)$, $S_{\mathrm{SiO}}\left(Q\right)$, and $S_{\mathrm{OO}}\left(Q\right)$ up to 200 GPa. The approximate principal peak positions as labeled by $Q_1$, $Q_2$, and $Q_3$ observed under ambient condition are indicated by the vertical broken lines. (c) Distribution of the Si-O coordination number in $\mathrm{Si}{\mathrm{O}}_2$ glass as a function of pressure up to 200 GPa. The number in the square denotes the average Si-O coordination number at each pressure.

Figure 3

Pressure dependence of the Si-O bond length of silica glass up to pressures of 140 GPa together with the previous results [8, 12, 17, 21]. The shaded areas represent the range of Si-O bond lengths for crystalline silica phases with fourfold- and sixfold-coordinated [38] structures.

Figure 4

Atomic structure and bond angle distribution of $\mathrm{Si}{\mathrm{O}}_2$ glass under high pressure. (a) Snapshot of the local environment around oxygen atoms at 200 GPa, highlighting the oxygen tricluster and tetracluster configurations (O coordinated with three or four silicon). Blue spheres: silicon atoms; yellow spheres: oxygen atoms. (b) Pressure dependence of the O-Si-O (left) and Si-O-Si (right) bond angle distribution up to 200 GPa.

Figure 5

Analysis using Si-centric persistent homology for the topological dimensionality of 1. (a)–(g) Si-centric persistence diagrams $D{\left(\mathrm{Si}\right)}_1$ at 0, 31, 83, and 200 GPa. (h) The probability profiles along with the death line highlighted by colors. Black line: 0 GPa; blue line: 31 GPa; green line: 83 GPa; and brown line: 200 GPa. Light green: stishovite; pink: $\alpha \text{−}\mathrm{Pb}{\mathrm{O}}_2$-type $\mathrm{Si}{\mathrm{O}}_2$; gray: pyrite-type $\mathrm{Si}{\mathrm{O}}_2$.

Figure 6

Analysis using O-centric persistent homology for the topological dimensionality of 2. (a)–(g) O-centric persistence diagrams for $D{\left(\mathrm{O}\right)}_2$ at 0, 31, 83, and 200 GPa. (h) The probability profiles along with the diagonal line highlighted by colors. Black line: 0 GPa; blue line: 31 GPa; green line: 83 GPa; and brown line: 200 GPa. Light green: stishovite; pink: $\alpha \text{−}\mathrm{Pb}{\mathrm{O}}_2$-type $\mathrm{Si}{\mathrm{O}}_2$; gray: pyrite-type $\mathrm{Si}{\mathrm{O}}_2$.

Figure 7

Electronic structure of silica glass under high pressure. The electronic density of states (DOS) of the $\mathrm{Si}{\mathrm{O}}_2$ glass with projections onto O and Si up to 200 GPa.

Figure 8

Local structures of pyrite-type crystalline $\mathrm{Si}{\mathrm{O}}_2$ and $\mathrm{Si}{\mathrm{O}}_2$ glass (at 200 GPa) extracted from persistence diagram. (a) $\mathrm{Si}{\mathrm{O}}_x$ polyhedra extracted from Si-centric persistent homology for the topological dimensionality of 1. (b) $\mathrm{OS}{\mathrm{i}}_y$ clusters extracted from Si-centric persistent homology for the topological dimensionality of 2.