Elasticity of a Pseudoproper Ferroelastic Transition from Stishovite to Post-Stishovite at High Pressure

Elastic moduli ($C_{ij}$) of single-crystal stishovite and post-stishovite are determined using Brillouin light scattering, impulsive stimulated light scattering, and x-ray diffraction up to 70 GPa. The $C_{12}$ of stishovite converges with the $C_{11}$ at $\sim 55\mathrm{GPa}$, where the transverse wave $V_{S1}$ propagating along [110] also vanishes. Landau modeling of the $C_{ij}$, $B_{1g}$ optic mode, and lattice parameters reveals a pseudoproper type ferroelastic post-stishovite transition. The transition would cause peculiar anomalies in $V_S$ and Poisson’s ratio in silica-bearing subducting slabs in the mid-lower mantle.

Figure 1

Representative BLS and ISLS spectra of single-crystal stishovite and post-stishovite at high pressure. Pressures and crystallographic orientations of each platelet are labeled in BLS panels. Open circles in (a), (d), and (g) are collected raw BLS data while red lines are best fits to derive $V_{S1}$ and $V_{S2}$ of the crystal. ISLS spectra in (b), (e), and (h) display signals of the sample, interface, and diamond extracted from the raw data. (c), (f), and (i) are modeled power spectra for the derived $V_P$ of the sample. Insets show representative optical images of the sample chambers.

Figure 2

Elastic moduli of single-crystal stishovite and post-stishovite at high pressure. Solid circles are derived $C_{ij}$ values in this study and solid black lines represent best fits using Landau theory modeling [20, 40]. Error bars are smaller than symbols when not shown. The gray vertical band represents the ferroelastic transition region at $\sim 55\mathrm{GPa}$. Literature data are also plotted for comparison [14, 19, 23, 24, 41, 42].

Figure 3

Lattice distortions and acoustic wave velocity dispersions across the post-stishovite transition at high pressure. (a) and (b) The lattice shear distortion across the ferroelastic transition. Blue and red spheres denote Si and O atoms, respectively. The tetragonal (a) and orthorhombic (b) unit cells under strains are schematically shown in red areas with dashed lines. The strains, labeled as ${ϵ}_2$ and ${ϵ}_3$ depict that the off-diagonal moduli $C_{12}$ and $C_{13}$ become anomalous (see Fig. 2). (c) and (d) Velocity dispersions of $V_P$ (black lines), $V_{S2}$ (blue lines), and $V_{S1}$ (red lines) across the transition. The $V_{S1}$ disappears at the transition that propagates along [110] [dashed gray lines with arrows in (a) and (b)] and has polarization along [$1\overline{1}0$] (thin black lines with arrows).

Figure 4

Optical, elastic, and mechanical behaviors across the post-stishovite transition. (a) Pressure dependence of squared Raman shifts (${\omega }^2$) of $B_{1g}$ and $A_g$ mode, where the transition pressure ($P_C^{*}$) and critical pressure ($P_C$) are labeled. (b) $V_{S1[110]}$ vanishes and aggregate $V_S$ softens at the transition. (c) Born stability criteria $B_1^{St}$ (in GPa), $B_1^{Pst}$ (in $5\times {10}^2{\mathrm{GPa}}^2$), and $B_2^{Pst}$ (in ${10}^6{\mathrm{GPa}}^3$) vanish at the transition whereas $B_2^{St}$ (in ${10}^3{\mathrm{GPa}}^2$) does not. (d) Squared symmetry-breaking spontaneous strain ${(e_1-e_2)}^2$ emerges in the post-stishovite phase. Experimental data from this study are plotted as solid circles. Black solid lines are results from the Landau model. Early studies are also shown for comparison [14, 17, 18, 19, 23, 24, 41, 42]. The gray vertical band shows the transition pressure.