Pressure-induced structural modulations in coesite

Silica phases, $\mathrm{Si}{\mathrm{O}}_2$, have attracted significant attention as important phases in the fields of condensed-matter physics, materials science, and (in view of their abundance in the Earth's crust) geoscience. Here, we experimentally and theoretically demonstrate that coesite undergoes structural modulations under high pressure. Coesite transforms to a distorted modulated structure, coesite-II, at 22–25 GPa with modulation wave vector $q=0.5b^{*}$. Coesite-II displays further commensurate modulation along the $y$ axis at 36–40 GPa and the long-range ordered crystalline structure collapses beyond $\sim 40\mathrm{GPa}$ and starts amorphizing. First-principles calculations illuminate the nature of the modulated phase transitions of coesite and elucidate the modulated structures of coesite caused by modulations along the $y$-axis direction. The structural modulations are demonstrated to result from phonon instability, preceding pressured-induced amorphization. The recovered sample after decompression develops a rim of crystalline coesite structure, but its interior remains low crystalline or partially amorphous. Our results not only clarify that the pressure-induced reversible phase transitions and amorphization in coesite originate from structural modulations along the $y$-axis direction, but also shed light on the densification mechanism of silica under high pressure.

Figure 1

Indexed x-ray diffraction patterns of coesite at 20.3 and 25.2 GPa. (a) Coesite $\left(C2/c\right)$ at 20.3 GPa and (b) coesite-II ($P{2}_1/c$) at 25.2 GPa. (c), (d) Zoomed-in pictures corresponding to the dashed boxes in (a) and (b), respectively. The reciprocal lattice reconstruction is marked in (c) and (d) by grids.

Figure 2

X-ray diffraction patterns of coesite at (a) 25.2, (b) 33.0, and (c) 36.8 GPa.

Figure 3

X-ray diffraction patterns of coesite at high pressures. (a) X-ray diffraction pattern at 50.3 GPa. (b) Zoomed-in pictures corresponding to the dashed box in (a) and track phase transformations of coesite from 20.3 to 50.3 GPa. The diffraction peak marked in the orange box starts from (0 4 0) of coesite and then (0 8 0) of coesite-II.

Figure 4

Raman spectra of (a) coesite and (b) mode frequencies during compression and decompression. The asterisks on the quenched ambient spectrum in (a) indicate two diffuse Raman bands at $\sim 520$ and $\sim 620\mathrm{c}{\mathrm{m}}^{-1}$. The solid stars in (b) represent Raman peak positions of the quenched ambient spectrum. The dashed lines in (b) indicate the phase boundaries of polymorphs for coesite.

Figure 5

Raman spectra collected at different positions within the recovered sample after decompression from 42.8 GPa to ambient conditions. The asterisks indicate two diffuse Raman bands at $\sim 520$ and $\sim 620\mathrm{c}{\mathrm{m}}^{-1}$.

Figure 6

Phonon dispersion curves of coesite $\left(C2/c\right)$ at (a) 0 and (b) 25 GPa.

Figure 7

The energy of coesite with the increased atomic displacement. Atomic displacement is defined as the proportion of atomic amplitude. Blue and cyan arrows represent the directions of displacement for Si and O atoms, respectively, along the unstable vibrational eigenvectors.

Figure 8

The relative enthalpies of coesite $\left(C2/c\right)$ and coesite-II ($P{2}_1/c$) structures at high pressures.

Figure 9

Phonon-dispersion curves of coesite-II ($P{2}_1/c$) at (a) 20 GPa and (b) 40 GPa.