Spectral proxies for bonding transitions in ${\mathrm{SiO}}_2$ and ${\mathrm{MgSiO}}_3$ polymorphs at high pressure up to 270 GPa by O $K$-edge x-ray Raman scattering

Advances in synchrotron x-ray Raman scattering (XRS) techniques enable probing of pressure-induced element-specific bonding transitions in diverse oxides beyond megabar pressures. Evolution of the electronic structures under extreme pressure involves an emergence of additional oxygen $1s$ electron excitation pattern and shifts in the electronic states toward high-energy ranges in an XRS spectrum. Structural origins of such changes and proper spectral proxy for the corresponding evolution in electronic density of states remain to be established. Here, we calculated the O $K$-edge features in the XRS spectrum for diverse crystalline ${\mathrm{SiO}}_2$ polymorphs, from α-quartz (1 atm) to a pyrite-type structure (at ∼271 GPa), beyond the current experimental pressure limit (∼160 GPa). The ab initio results unravel the electronic origins of the evolution in the XRS patterns, such as the emergence of the bimodal feature with decreasing oxygen-oxygen distance $\left(d_{\mathrm{O}\text{−}\mathrm{O}}\right) <\sim 2.5 \AA$ and a subsequent merging of the doublet patterns with a further decrease in $d_{\mathrm{O}\text{−}\mathrm{O}}$ down to $\sim 2.3–2.4 \AA$. Ab initio simulations of the XRS spectrum of pyrite-type ${\mathrm{SiO}}_2$ phase at $\sim 271 \mathrm{GPa}$ revealed the significant electron dispersion in $2p^{*}$ states and the pronounced electron density between edge-sharing oxygen atoms with $d_{\mathrm{O}\text{−}\mathrm{O}}$ of ∼2.1 Å, in contrast to an earlier prediction with a negligible electron density between those oxygen atoms. The pressure-induced increase in electron interactions leads to a systematic change in the edge energy at half of the spectrum area $\left(E_M\right)$ and the edge energy at the center of mass of the spectrum $\left(E_C\right)$ of XRS patterns beyond multimegabar pressures. Particularly, the $E_M$ and $E_C$ increase linearly with decreasing oxygen proximity $\left(d_{\mathrm{O}\text{−}\mathrm{O}}\right)$ and bulk density up to 270 GPa. The $E_M$ and $E_C$ for ${\mathrm{MgSiO}}_3$ phases show larger changes with varying $d_{\mathrm{O}\text{−}\mathrm{O}}$ than those in ${\mathrm{SiO}}_2$ phases, demonstrating the effect of the electronic hybridization between Mg and O on the evolution of the XRS patterns. The strong linear correlation among $E_M$, $E_C$, and $d_{\mathrm{O}\text{−}\mathrm{O}}$ (and density) up to ∼270 GPa confirms that the $E_M$ and $E_C$ can be effective spectral proxies to quantify the densification of crystalline and noncrystalline oxides. The results with the statistical evaluations of the electronic density of states provide improved prospects for the prediction of the evolution in core-level excitation features of diverse complex, multicomponent oxides under multimegabar pressure conditions toward the deep lower mantle of Earth and other super-Earth bodies.

Figure 1

Crystal structures of (a) α-quartz, (b) β-quartz, (c) α-cristobalite, (d) coesite (O1–O5), (e) hp-cristobalite, (f) penta-${\mathrm{SiO}}_2$ (O1 and O2), (g) stishovite, (h) $\mathrm{Ca}{\mathrm{Cl}}_2$-type, (i) $\alpha \text{−}{\mathrm{PbO}}_2$-type, and (j) pyrite-type structures. Details of crystal structure information are summarized in Table 1.

Figure 2

(a) The average Si-O bond lengths ($d_{\mathrm{Si}\text{−}\mathrm{O}}$) of the crystalline ${\mathrm{SiO}}_2$ polymorphs with increasing pressures. (b) The average interatomic distances between nearest-neighboring O atoms ($d_{\mathrm{O}\text{−}\mathrm{O}}$) with increasing pressures. (c) Relationship between the densities of ${\mathrm{SiO}}_2$ polymorphs (ρ) and $d_{\mathrm{Si}\text{−}\mathrm{O}}$. (d) Relationship between ρ and $d_{\mathrm{O}\text{−}\mathrm{O}}$. The black line shows the linear trend line for the density of ${\mathrm{SiO}}_2$ polymorphs with varying $d_{\mathrm{O}\text{−}\mathrm{O}}$.

Figure 3

The partial radial distributions of the Si-O and OO-O pairs in the ${\mathrm{SiO}}_2$ polymorphs (α-quartz, β-quartz, α-cristobalite, coesite, hp-cristobalite, penta-${\mathrm{SiO}}_2$, stishovite, $\mathrm{Ca}{\mathrm{Cl}}_2$-type, $\alpha \text{−}{\mathrm{PbO}}_2$-type, and pyrite-type structures). The $d_{\mathrm{O}\text{−}\mathrm{O}}$ thresholds for characteristic x-ray Raman scattering (XRS) patterns are presented: (1) the α-quartzlike XRS patterns within ∼2.7 to ∼2.5 Å, (2) the stishovitelike XRS patterns within ∼2.5 to ∼2.4 Å (i.e., the doublet of O $p\text{−}p$ hybridization), and (3) the single broad features within ∼2.4 to ∼2.1 Å (i.e., the O $p\text{−}p$ doublet is apparently merged).

Figure 4

(a) Site-resolved O partial densities of states (PDOSs) and (b) O $K$-edge x-ray Raman scattering (XRS) features of coesite (O1–O5). (c) Site-resolved O PDOSs and (d) O $K$-edge XRS features of penta-${\mathrm{SiO}}_2$ structure (O1 and O2). Numbers in the left side of (a) and (c) are the maximum intensity used for the normalization of PDOS.

Figure 5

(a) Calculated $l$-resolved partial density of states (PDOS) in the unoccupied states of O atoms for ${\mathrm{SiO}}_2$ polymorphs. The core-hole effects have been considered. Red, blue, and green solid lines refer to the unoccupied O $s$, $p$, and $d$ states, respectively. Numbers in the left side of (a) are the maximum intensity used for the normalization of PDOS. (b) Calculated O $K$-edge x-ray Raman scattering (XRS) features for ${\mathrm{SiO}}_2$ polymorphs.

Figure 6

Total electron densities of the stishovite (at ∼29.1 GPa) and pyrite-type structure (at ∼271 GPa), (a) in the (110) plane of stishovite, (b) in the (110) plane of pyrite-type structure, (c) in the (100) plane of pyrite-type structure, and (d) in the plane perpendicular to ${\mathrm{C}}_4$ symmetry axis of ${\mathrm{SiO}}_6$ octahedron (including four planar oxygen atoms). Atoms labeled in black and red are those lying or not lying in the given plane, respectively. Solid and dashed lines refer to the Si-O bonds lying or not lying in the given plane, respectively. While the electron densities for stishovite and the pyrite-type structure vary from ∼0.05 to $\sim 7.5\mathrm{e}{\AA }^{-3}$ and from ∼0.1 to $\sim 7.7\mathrm{e}{\AA }^{-3}$, respectively; the projected electron densities are presented from 0.1 to $1.5\mathrm{e}{\AA }^{-3}$ to enhance the visibility of the low electron density distribution between oxygen atoms (see Sec. 6 of the SM for the details of calculation [50]; see also Refs. [75, 76] therein).

Figure 7

Relationships among the absorption threshold ($E_A$), the median of spectrum ($E_M$), the edge energies at the center of gravity ($E_C$), and the average interatomic distances between nearest-neighboring O atoms ($d_{\mathrm{O}\text{−}\mathrm{O}}$) of the crystalline ${\mathrm{SiO}}_2$ polymorphs as labeled: (a) $E_A$ vs $d_{\mathrm{O}\text{−}\mathrm{O}}$, (b) $E_M$ vs $d_{\mathrm{O}\text{−}\mathrm{O}}$, and (c) $E_C$ vs $d_{\mathrm{O}\text{−}\mathrm{O}}$. (d) Correlations among each spectral proxy ($E_A$, $E_M$, and $E_C$) and $d_{\mathrm{O}\text{−}\mathrm{O}}$ to compare the trend for each dataset. The black, blue, and red lines refer to the trends for $E_C$ (circles), $E_M$ (triangles), and $E_A$ (squares), respectively.

Figure 8

Relationships among the median of spectrum ($E_M$), the edge energies at the center of gravity ($E_C$), and the average interatomic distances between nearest-neighboring O atoms ($d_{\mathrm{O}\text{−}\mathrm{O}}$) for crystalline ${\mathrm{SiO}}_2$ and ${\mathrm{MgSiO}}_3$ high-pressure polymorphs as labeled: (a) $E_M$ vs $d_{\mathrm{O}\text{−}\mathrm{O}}$ and (b) $E_C$ vs $d_{\mathrm{O}\text{−}\mathrm{O}}$. Relationships among $E_M$, $E_C$, and the densities (ρ) for ${\mathrm{SiO}}_2$ and ${\mathrm{MgSiO}}_3$ crystals (empty) and glasses (filled) under high pressures as labeled: (c) $E_M$ vs ρ and (d) $E_C$ vs ρ. The black and blue lines refer to the trends for ${\mathrm{SiO}}_2$ and ${\mathrm{MgSiO}}_3$, respectively. Data of crystalline ${\mathrm{MgSiO}}_3$ polymorphs (from ab initio calculations) [27] and ${\mathrm{SiO}}_2$ and ${\mathrm{MgSiO}}_3$ glasses [from in situ high-pressure x-ray Raman scattering (XRS) experiments] [29, 30] were retrieved from our earlier studies.

Figure 9

Calculated O $K$-edge x-ray Raman scattering (XRS) spectra for $\alpha \text{−}{\mathrm{PbO}}_2$-type ${\mathrm{SiO}}_2$ at 120 GPa (blue) and ${\mathrm{MgSiO}}_3$ bridgmanite at ∼120 GPa (black). Experimental O $K$-edge XRS spectra of ${\mathrm{SiO}}_2$ (blue) and ${\mathrm{MgSiO}}_3$ (black) glasses under similar pressure conditions are shown for comparison. The XRS spectra for ${\mathrm{MgSiO}}_3$ bridgmanite at ∼120 GPa (from ab initio calculations) [27] and ${\mathrm{SiO}}_2$ and ${\mathrm{MgSiO}}_3$ glasses (from in situ high-pressure XRS experiments) [29, 30] were retrieved from our earlier studies.