Equation of state of theα−PbO2andPa3¯-type phases of

Rajkrishna Dutta

¹

,

Claire E. White

²

,

Eran Greenberg

³

et al.

Abstract

The compression behavior of crystalline and amorphous germania holds considerable interest as an analog for silica and for understanding the structural response of AX 2 compounds generally. In this work, the α-PbO 2 -type and 3-type polymorphs of GeO 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 3 rd order Birch-Murnaghan equations of state. The fit parameters for the α-PbO 2 -type are: V 0 = 53.8 (2) Å 3 , K 0T = 293 (7) GPa with fixed 4; where V, K T , and are the volume, isothermal bulk modulus, and pressure derivative of the bulk modulus and the subscript 0 refers to ambient conditions. The corresponding parameters for the 3-type phase is: V 0 = 50.3 (3) Å 3 , K 0T = 342 (12) GPa with fixed 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 GeO 2 . The high-pressure phase observed on the Hugoniot is most consistent with either the α-PbO 2 -type or CaCl 2 -type phase. Finally, we have compared our data on crystalline germania with existing studies on the corresponding phases of SiO 2 to better understand the effects of cation substitution on phase transformations and equations of state in Group 14 dioxides.

Ge coordination inNaAlGe3O8glass upon compression to 131 GPa

“…This simple comparison of the pressure dependence of the Ge-O distance evidences that there is a strong difference in the compressional behavior of the Ge coordination polyhedron between NaAlGe 3 O 8 and GeO 2 glass. The weaker shortening of the Ge-O bond distance beyond 110 GPa in NaAlGe 3 O 8 might indicate the onset of polyhedral distortions similar to those observed for GeO 2 in the α-PbO 2 structure [43].…”

Density of amorphous GeO2 to 133 GPa with possible pyritelike structure and stiffness at high pressure

“…2). At such pressure the material has a high bulk modulus of about 300 GPa, derived from our third-order BM fit (V 0 = 15.39(1.5) cm −3 /mol, K 0 = 304 (8) GPa and K 0 = 4, Table S2; see Supplemental Material [44]), almost similar to the one of the crystalline GeO 2 in the pyrite structure, with K 0 = 347 (12) GPa (K 0 = 4) [1] and also equivalent to the one of the α-PbO 2 structure with K 0 = 292 (10) GPa (K 0 = 4). At higher pressure, the propagated values for the bulk modulus will also be comparable between the crystalline and amorphous phases, because of the similarity in the parameters for the EOS (same K values).…”

“…Our density data as a function of pressure (Table S1; see Supplemental Material [44]) are reported in Fig. 2 and compared with previous measurements carried out using the x-ray absorption method [11], tomography imaging [46], or AIMD calculation [41], as well as with the density of the crystalline high-pressure GeO 2 polymorphs [1]. The compressibility of GeO 2 can be analyzed using a finite strain plot in the Vinet form [47], or f -F plot, to reveal the different pressure domains of dominant coordination species for which individual equations of state can be derived, as it was shown for the compressed amorphous SiO 2 [20].…”

“…SiO 2 is the most abundant component in naturally occurring silicate melts on Earth and other telluric planetary bodies. GeO 2 is a structural analog to SiO 2 , being a network former in the amorphous state at ambient pressures and exhibiting a similar succession of crystalline high-pressure structures and transitions, with minor differences only at low pressure [1][2][3][4][5][6]. At ambient conditions, the structure of both oxides consists of an infinitely extended network of SiO 4 4− and GeO 4 4− tetrahedra, respectively.…”

Local structural investigation of non-crystalline materials at high pressure: the case of GeO2 glass

“…GeO 2 glass is of particular interest because the local structure of Ge atoms at high pressure can be determined by x-ray absorption fine structure (XAFS) technique in diamond anvil cell (DAC). The pressure-induced local structural changes of GeO 2 glass have been extensively studied using x-ray-absorption spectroscopy [7][8][9][10], x-ray diffraction (XRD) [11][12][13][14][15][16], neutron diffraction (ND) [17][18][19][20][21], inelastic x-ray scattering [22,23], x-ray Raman scattering at the oxygen K-edge [24,25], x-ray emission spectroscopy [26], and a number of theoretical studies such as classical [27][28][29] and first-principles molecular dynamics simulations [30][31][32]. Important structural and spectroscopic details on the local short-range order (SRO) and the intermediate-range order (IRO) of GeO 2 glass under compression have been successfully revealed [3,6,18,33].…”