Local structure and mean-square relative displacement in SiO2 and GeO2 polymorphs

Abstract

Extended X-ray absorption fine structure (EXAFS) spectra near the Si and Ge K-edge for SiO2 and GeO2 polymorphs were measured in transmission mode with synchrotron radiation at the Photon Factory, Tsukuba. The local structures and mean-square relative displacements were determined in α-tridymite, α-quartz and stishovite. In stishovite, Si is octahedrally coordinated and the four coplanar Si-O bonds [1.755 (8) Å] are shorter than the other two axial bonds [1.813 (15) Å]. The high-temperature phase tridymite [1.597 (3) Å] has a smaller local bond distance than α-quartz [1.618 (5) Å]. The temperature variation of the local structural parameters for quartz-type GeO2 (q-GeO2) and rutile-type GeO2 (r-GeO2) have been determined in the temperature range 7-1000 K. The harmonic effective interatomic potential V(u) = αu2/2 was evaluated from the contribution to the thermal vibration, where u is the deviation of the bond distance from the location of the potential minimum. The potential coefficient α for the Ge-O bond of the tetrahedron in q-GeO2 is 24.6 eV Å-2. The potential coefficients α for the four coplanar Ge-O bonds and the two axial bonds of the octahedron in r-GeO2 are 12.9 and 14.9 eV Å-2, respectively. The potential coefficient α for the second-nearest Ge-Ge distance in q-GeO2 is 9.57 eV Å-2. The potential coefficients α for the second-and third-nearest Ge-Ge distances in r-GeO2 are 11.6 and 7.18 eV Å-2, respectively. The effective interatomic potential is largely influenced by the local structure, particularly by the coordination numbers. The phonon dispersion relations for q-GeO2 and r-GeO2 were estimated along [100] by calculating the dynamical matrix using the potential coefficients α for the Ge-O and Ge-Ge motions. The quartz-type structure has a more complex structure with a wide gap between 103 and 141 me V and a highest energy of 149 me V, whereas the rutile-type structure has a continuous distribution and a highest energy of 126 me V.