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

The pseudocubic (PC) parameterization of O 4 tetrahedra [Reifenberg & Thomas (2018). Acta Cryst. B 74 , 165–181] is applied to quartz (SiO 2 ) and its structural analogue germanium dioxide (GeO 2 ). In α-quartz and GeO 2 , the pseudocubes are defined by three length parameters, a PC , b PC and c PC , 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), B 72 , 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 , x Si , x O , y O and z O at interpolated or extrapolated temperatures is demonstrated for α-quartz. A reverse transformation to crystallographic parameters a , c , x O is likewise carried out for β-quartz. This capability corresponds to a method of structure prediction. Support for the applicability of the approach to GeO 2 is provided by analysing the structural refinements of Haines et al. [ J. Solid State Chem. (2002), 166 , 434–441]. An analysis of trends in tetrahedral distortion and tilt angle in α-quartz and GeO 2 supports the view that GeO 2 is a good model for quartz at high pressure.