TY  - JOUR
A1  - Fricke, Maximilian
A1  - Thomas, Noel W.
T1  - Modelling the structural variation of quartz and germanium dioxide with temperature by means of transformed crystallographic data
Y1  - 2021-05-27
VL  - 77
IS  - 3
SP  - 427
EP  - 440
JF  - Acta Crystallographica Section B
DO  - 10.1107/S2052520621002717
DO  - 10.23689/fidgeo-5174
PB  - International Union of Crystallography
N2  - 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 αPC. In β‐quartz, αPC 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 αPC 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 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 GeO2 supports the view that GeO2 is a good model for quartz at high pressure.
N2  - A pseudocubic parameterization of the O4 tetrahedra of quartz and its structural analogue GeO2 at variable temperatures allows direct calculation of tetrahedral tilt angle, the microscopic order parameter of the α↔β phase transition. The crystal structures at interpolated or extrapolated temperatures can also be predicted.
UR  - http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/9520
ER  -