Equation of state of the α − Pb O 2 and P a 3 ¯ -type phases of Ge O 2 to 120 GPa

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.