Equation of state of theα−PbO2andPa3¯-type phases ofGeO2to 120 GPa

Abstract

The compression behavior of crystalline and amorphous germania holds considerable interest as an analog for silica and for understanding the structural response of $\mathrm{A}{\mathrm{X}}_{2}$ compounds generally. In this paper, the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{O}}_{2}$-type and $Pa\overline{3}$-type polymorphs of $\mathrm{Ge}{\mathrm{O}}_{2}$ were investigated under high pressure using angle-dispersive synchrotron x-ray diffraction in the laser-heated diamond anvil cell. Theoretical calculations based on density functional theory were also performed. The experimental pressure-volume data were fitted to third-order Birch-Murnaghan equations of state. The fit parameters for the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{O}}_{2}$ type are ${V}_{0}=53.8\phantom{\rule{0.16em}{0ex}}(2)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3},{K}_{0T}=293\phantom{\rule{0.16em}{0ex}}(7)\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ with fixed ${K}_{0T}^{\ensuremath{'}}=4$, where $V,{K}_{T}$, and ${K}_{T}^{\ensuremath{'}}$ are the volume, isothermal bulk modulus, and pressure derivative of the bulk modulus and the subscript zero refers to ambient conditions. The corresponding parameters for the $Pa\overline{3}$-type phase are ${V}_{0}=50.3\phantom{\rule{0.16em}{0ex}}(3)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{3},{K}_{0T}=342\phantom{\rule{0.16em}{0ex}}(12)\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ with fixed ${K}_{0T}^{\ensuremath{'}}=4$. The theoretical calculations are in good agreement with the experimental results with slight underestimation and overestimation of ${V}_{0}$ and ${K}_{0T}$, respectively. A theoretical Hugoniot was calculated from our data and compared to shock equation of state data for vitreous and rutile-type $\mathrm{Ge}{\mathrm{O}}_{2}$. The high-pressure phase observed on the Hugoniot is most consistent with either the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Pb}{\mathrm{O}}_{2}$-type or $\mathrm{CaC}{\mathrm{l}}_{2}$-type phase. Finally, we have compared our data on crystalline germania with existing studies on the corresponding phases of $\mathrm{Si}{\mathrm{O}}_{2}$ to better understand the effects of cation substitution on phase transformations and equations of state in group 14 dioxides.