Modelling the structural variation of quartz and germanium dioxide with temperature by means of transformed crystallographic data

The pseudocubic (PC) parameterization of O4 tetrahedra [Reifenberg& Thomas (2018). Acta Cryst. B74, 165 – 181] is applied to quartz (SiO2) and its structural analogue germanium dioxide (GeO2). In α -quartz and GeO2, the pseudocubes are defined by three length parameters, aPC, bPC and cPC, together with an angle parameter α PC. In β -quartz, α PC has a fixed value of 90 ° . For quartz, the temperature evolution of parameters for the pseudocubes and the silicon ion network is established by reference to the structural refinements of Antao [Acta Cryst. (2016), B72, 249 – 262]. In α -quartz, the curve-fitting employed to express the non-linear temperature dependence of pseudocubic length and Si parameters exploits the model of a first-order Landau phase transition utilized by Grimm& Dorner [J. Phys. Chem. Solids (1975), 36, 407 – 413]. Since values of tetrahedral tilt angles about 〈 100 〉 axes also result from the pseudocubic transformation, a curve for the observed non-monotonic variation of α PC with temperature can also be fitted. Reverse transformation of curve-derived values of [Si+PC] parameters to crystallographic parameters a, c, xSi, xO, yO and zO at interpolated or extrapolated temperatures is demonstrated for α -quartz. A reverse transformation to crystallographic parameters a, c, xO is likewise carried out for β -quartz. This capability corresponds to a method of structure prediction. Support for the applicability of the approach to GeO2 is provided...

Source: Acta Crystallographica Section B - May 20, 2021 Category: Chemistry Authors: Fricke, M. Thomas, N.W. Tags: quartz pseudocubic INA tilt angle structure prediction GeO2 research papers Source Type: research