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

Extended X-ray absorption fine structure (EXAFS) spectra near the Si and Ge K-edge for SiO and GeO 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 -tridymite, -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 -quartz [1.618 (5) Å]. The temperature variation of the local structural parameters for quartz-type GeO (q-GeO) and rutile-type GeO (r-GeO) have been determined in the temperature range 7-1000 K. The harmonic effective interatomic potential was evaluated from the contribution to the thermal vibration, where is the deviation of the bond distance from the location of the potential minimum. The potential coefficient for the Ge-O bond of the tetrahedron in q-GeO is 24.6 eV Å^-2. The potential coefficients for the four coplanar Ge-O bonds and the two axial bonds of the octahedron in r-GeO are 12.9 and 14.9 eV Å^-2, respectively. The potential coefficient for the second-nearest Ge-Ge distance in q-GeO is 9.57 eV Å^-2. The potential coefficients for the second- and third-nearest Ge-Ge distances in r-GeO 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-GeO and r-GeO were estimated along [100] by calculating the dynamical matrix using the potential coefficients 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 meV and a highest energy of 149 meV, whereas the rutile-type structure has a continuous distribution and a highest energy of 126 meV.