High-precision equation of state data for ${\mathrm{TiO}}_2$: A structural analog of ${\mathrm{SiO}}_2$

The high-pressure response of titanium dioxide (${\mathrm{TiO}}_2$) is of interest because of its numerous industrial applications and its structural similarities to silica (${\mathrm{SiO}}_2$). We used three platforms—Sandia's Z machine, Omega Laser Facility, and density-functional theory-based quantum molecular dynamics (QMD) simulations—to study the equation of state (EOS) of ${\mathrm{TiO}}_2$ at extreme conditions. We used magnetically accelerated flyer plates at Sandia to measure Hugoniot of ${\mathrm{TiO}}_2$ up to pressures of 855 GPa. We used a laser-driven shock wave at Omega to measure the shock temperature in ${\mathrm{TiO}}_2$. Our Z data show that rutile ${\mathrm{TiO}}_2$ reaches 2.2-fold compression at a pressure of 855 GPa and Omega data show that ${\mathrm{TiO}}_2$ is a reflecting liquid above 230 GPa. The QMD simulations are in excellent agreement with the experimental Hugoniot in both pressure and temperature. A melt curve for ${\mathrm{TiO}}_2$ is also proposed based on the QMD simulations. The combined experimental results show ${\mathrm{TiO}}_2$ is in a liquid at these explored pressure ranges and is not highly incompressible as suggested by a previous study.

Figure 1

Phase diagram of ${\mathrm{TiO}}_2$. Inset: Sixfold coordinated rutile, sevenfold coordinated cotunnite, ninefold coordinated ${\mathrm{Fe}}_2\mathrm{P}$ and predicted tenfold coordinated I4/mmm structure. Blue spheres represent Ti cations and red spheres represent oxygen anions. The data for the solid phases in the phase diagram are obtained from previous studies [2, 3, 4, 5, 6, 7, 8]. The open circles are the QMD melting points obtained from this study. The phase sequence observed in static experiments are rutile $\Rightarrow \alpha \text{−}{\mathrm{PbO}}_2\Rightarrow$ baddeleyite (bad) $\Rightarrow$ orthorhombic I (OI) $\Rightarrow$ cotunnite $\Rightarrow {\text{Fe}}_2\text{P}$.

Figure 2

A typical VISAR trace from a Z experiment showing the aluminum flyer velocity (black) and the shock velocity in the TPX window (blue). The VISAR does not record a velocity signal in the ${\mathrm{TiO}}_2$. Inset: Raw VISAR signal from the ${\mathrm{TiO}}_2$ sample showing the transit-time fiducials and a schematic illustration of the Z-experimental setup.

Figure 3

Top: Representative data from the Omega line-VISAR imaging system. Bottom: Analyzed line-VISAR data showing the ${\mathrm{TiO}}_2$ and quartz shock velocities as a function of time. Inset: Experimental setup for laser experiments.

Figure 4

Typical representative of the SOP data from ${\mathrm{TiO}}_2$ (top half) and quartz (bottom half).

Figure 5

${\mathrm{TiO}}_2$ Hugoniot in the $U_s-U_p$ plane, including data from the current Z experiments, QMD simulations, and the previous Hugoniot data for [100] orientation [13, 14, 15, 16, 17]. The error bars lie within the symbols.

Figure 6

Enlarged ${\mathrm{TiO}}_2$ Hugoniot in the $U_s-U_p$ plane, including data from the current Z experiments, QMD simulations, and the previous Hugoniot data for [100] orientation [13, 14, 15, 16, 17]. The dotted lines are extrapolated linear fits.

Figure 7

${\mathrm{TiO}}_2$ Hugoniot in the $P-\rho$ plane, including data from the current Z experiments, QMD simulations, and the previous Hugoniot data for [100] orientation [13, 14, 15, 16, 17]. The error bars lie within the symbols if not shown in the plot.

Figure 8

$P-U_P$ plot showing the initial Hugoniot states and the corresponding release states calculated from Monte Carlo impedance matching method.

Figure 9

Experimental shock temperature versus shock velocity compared with QMD. The shaded area represents the error on the experimental data. The green line is the average of four different experiments. Note that each color corresponds to a separate experiment. Inset: Reflectivity data as a function of shock velocity.

Figure 10

Phase diagram of ${\mathrm{TiO}}_2$ with experimental $P-T$ points and the QMD calculated melt line. The diamond symbols are experimentally inferred $P-T$ points combining the temperature data from the Omega laser shock data and the pressure data from the Z experiments. The magenta lines for the solid phase are obtained from previous studies [2, 7, 8, 62]. The violet line is the converted Omega data from $U_s-T$ to $P-T$ using the modified $U_s-U_p$ universal liquid fit.