Symmetry Transitions Beyond the Nanoscale in Pressurized Silica Glass

Abstract

Silica is the paradigmatic network glass-former and understanding its response to pressure is essential for comprehending the mechanical properties of silica-based materials and the behavior of silicate melts in the Earth's interior. While pressure-induced changes in the short-range structure - particularly the breakdown of tetrahedral symmetry - have been well documented, structural transformations on larger length scales, important for many material properties, remain poorly understood. Here, we numerically investigate the three-dimensional structure of silica glass as a function of compression up to $P \approx 100$~GPa. Using a novel many-body correlation function, we reveal a complex medium-range order: While for $P \lesssim 10$~GPa, one finds tetrahedral, octahedral, and cubic symmetries, the structure at higher $P$s exhibits alternating cubic and octahedral particle arrangements. The $P$-dependence of the corresponding structural correlation length displays two distinct maxima, which permits to rationalize the anomalous compressibility of silica. The identified complex structural organization on intermediate range scales is the result of a pressure-and scale-dependent interplay between directional bonding, packing efficiency, and network stiffness. Since these competing effects are common in network glass-formers, the identified three-dimensional medium-range order, and hence the physical properties of the glass, are expected to be universal features of such materials under extreme conditions.

Figures (17)

• Figure 1: Equation of state and pair distribution function. (A) Pressure dependence of volume, normalized by its value at $P=0$ (left ordinate). Experimental data are from Refs. sugiura1981dynamicsato_high-pressure_2010. Right ordinate: The compressibility $\kappa$ shows two maxima before it decays monotonically at high $P$. (B) The SiSi pair distribution function $g_{\rm SiSi}(r)$ for different pressures. The inset is a two-dimensional schematic diagram of the network structure of silica glass, featuring rings of different size. Typical distances corresponding to the various peak positions are indicated by the arrows. (C) Relative change of the peak positions of $g_{\rm SiSi}(r)$. $r_1$ to $r_6$ for $P=0$ are respectively 3.17, 5.07, 7.49, 9.65, 11.95, and 14.13 Å. The solid line is the compressive strain $\epsilon = (L(P)-L(0))/L(0)$ which corresponds to an affine deformation. Figure \ref{['SI_Fig1']} shows zooms of panels (A) and (C) on the pressure range 0-20 GPa.
• Figure 2: Three-dimensional structure as a function of distance and pressure. The density distribution of the Si atoms in a local reference frame formed by a Si and two neighboring O atoms (cartoon in the lower right corner). Only the area belonging to the top 25% in density is shown and colored based on the normalized density which goes from 0.5 (dark blue) to 1 (dark red).
• Figure 3: Symmetry of the structure as a function of pressure and length scale. The shape of the symbols reflects the symmetry of the 3D Si-distribution at a given distance $r$. The points connected by the dashed lines correspond to the peak positions (marked by $r_n$) of $g_{\rm SiSi}(r)$, while the points between the lines correspond to the minima.
• Figure 4: Quantitative characterization of the three dimensional structure. (A) The reduced Shannon entropy $H_M-H(r,P)$ measures the numbers of motifs in the structure on the length scale $r$. The vertical dashed lines indicate the positions of the maxima in $g_{\rm SiSi}(r)$ at $P=0$ GPa. The bold dashed lines highlight the change of local slope due to the presence of steps in the correlation function. (B) The correlation functions $r'S_\rho(3,r')$ (filled symbols) and $r'S_\rho(4,r')$ (open symbols), respectively. The curves $r'S_\rho(4,r')$ are divided by ten to avoid overlap with $r'S_\rho(3,r')$.
• Figure 5: Non-monotonic pressure-dependence of the medium-range order. (A) Structural correlation length $\xi$ as estimated from the decay of $S_\rho$ and $g(r)$. (B) Fraction of the Si species with a given coordination number. The bluish and the reddish background highlight the two maxima in $\xi$ at small and intermediate pressures, respectively. (C) Snapshots of the system at different pressures. The scale bar is 1 nm. The three relevant polyhedral units are shown in different colors. (D) Partial structure factor for Si atoms having 4, 5, and 6 nearest neighbor oxygen atoms (left to right).