Structure and compressibility of the high-pressure molecular phase II of carbon dioxide

Abstract

The structure and equation of state of the crystalline molecular phase II of carbon dioxide have been investigated at room temperature from 15.5 to 57.5 GPa using synchrotron x-ray diffraction methods. The CO${}_{2}$ samples were embedded in neon pressure medium in order to provide quasihydrostatic conditions. The x-ray diffraction patterns of phase II are best described by a tetragonal structure, with space group $P{4}_{2}/mnm$ and 2 molecules per unit cell, in accordance with a previous study [Yoo et al., Phys. Rev. B 65, 104103 (2002)]. There is however a large (15%) difference in the intramolecular C=O bond length between the present study, 1.14(3) \AA{}, and the latter work (1.329--1.366 \AA{}). The present value is similar to that of the free molecule and is in very good agreement with predictions based on density functional theory. The compressibility of CO${}_{2}$-II determined here also disagrees with the previous study: our value for the zero-pressure bulk modulus, ${B}_{0}=8.5(3)$ GPa [with ${B}_{0}^{\ensuremath{'}}={(\ensuremath{\partial}B/\ensuremath{\partial}P)}_{0}=6.29$], is 15.5 times smaller. These findings oppose the view that CO${}_{2}$-II is an intermediate state between the low-pressure molecular phases and the high-pressure nonmolecular forms, consistent with our previous results for phase IV [Datchi et al., Phys. Rev. Lett. 103, 185701 (2009)]. The x-ray diffraction patterns of CO${}_{2}$-II above 15 GPa indicate the presence of a large orthorhombic microstrain. Carrying out density functional theory calculations of the elastic tensor and stress-strain relation, we interpret this as due to the softness of the crystal against deviatoric stress in the [110] and symmetry-related directions. Unlike the other dioxides of the group-14 elements, there is however no mechanical or dynamical instability of the $P{4}_{2}/mnm$ structure in CO${}_{2}$ up to 57.5 GPa at 295 K, and therefore no symmetry lowering to $Pnnm$.