Abstract
Cristobalite, a high temperature phase of silica, SiO2, undergoes a (metastable) first-order phase transition from a cubic, \(Fd\bar 3m\), to a tetragonal, P43212 (or P41212), structure at around 220° C. The cubic C9-type structure for β-cristobalite (Wyckoff 1925) is improbable because of two stereochemically unfavorable features: a 180° Si-O-Si angle and an Si-O bond length of 1.54 Å, whereas the corresponding values in tetragonal α-cristobalite are ∼146° and 1.609 Å respectively. The structure of the β-phase is still controversial. To resolve this problem, a symmetry analysis of the \(Fd\bar 3m \to P4_3 2_1 2\) (or P41212) transition in cristobalite has been carried out based on the Landau formalism and projection operator methods. The starting point is the ideal cubic (\(Fd\bar 3m\)) C9-type structure with the unit cell dimension a (7.432 Å) slightly larger than the known a dimension (7.195 Å at 205° C) of β-cristobalite, such that the Si-O-Si angle is still 180°, but the Si-O bond length is 1.609 Å. The six-component order parameter driving the phase transition transforms according to the X4 representation. The transition mechanism essentially involves a simultaneous translation and rotation of the silicate tetrahedra coupled along 〈110〉. A Landau free-energy expression is given as well as a listing of the three types of domains expected in α-cristobalite from the β→α transition. These domains are: (i) transformation twins from a loss of 3-fold axes, (ii) enantiomorphous twins from a loss of the inversion center, and (iii) antiphase domains from a loss of translation vectors 1/2 〈110〉 (F→P). These domains are macroscopic and static in α-cristobalite, and microscopic and dynamic in β-cristobalite. The order parameter η, couples with the strain components as ɛη2, which initiates the structural fluctuations, thereby causing the domain configurations to dynamically interchange in the β-phase. Hence, the α-β cristobalite transition is a fluctuation-induced first-order transition and the β-phase is a dynamic average of α-type domains.
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Hatch, D.M., Ghose, S. The α-β phase transition in cristobalite, SiO2 . Phys Chem Minerals 17, 554–562 (1991). https://doi.org/10.1007/BF00202234
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DOI: https://doi.org/10.1007/BF00202234