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β-quartz
A detailed examination of the experimental and model ARDFs has revealed that the interatomic distances for all atoms belonging to one helical chain in the glass are identical to those in the β-quartz crystal over the entire ordering range.
      
A similar effect is predicted for a positronium in crystalline quartz at temperatures above the transition from α-to β-quartz (846 K).
      
X-ray diffraction examination indicates that β-quartz is crystallized from the amorphous matrix around 850°C firstly and then MgO-Al2O3 spinel and α-cordierite appears.
      
The glass-ceramics contain a few crystal phases in which the main crystal phase is β-quartz solid solution and the second crystal phase is β-spodumene solid solution.
      
When the heat treatment temperature is not higher than 650°C, the transparent glass-ceramics containing β-quartz solid solution can be prepared.
      
β-quartz solid solution changes into β-spodumene solid solution at about 750°C.
      
A statistical treatment is presented for the stability loss in monodisperse fractions of β-quartz from soils in the completely dry state.
      
In addition to kaolin and alunite, the following minerals are present: white mica, smectite, barite, pyrophyllite, tridymite, cristobalite, α- and β-quartz, chamosite, gibbsite, and aluminum-phosphate-sulphate minerals (APS).
      
Finally, the Raman spectrum of Mg2Al4Si5O18 with a stuffed β-quartz structure has been obtained.
      
An interpretation of the structures of α- and β-quartz based on coulomb repulsion forces
      
For oxygen in quartz, 3 models are obtained with the symmetry of α-quartz and one with the symmetry of β-quartz.
      
For Si, only one model is obtained which has more similarity with α- than with β-quartz.
      
We have also used our ab initio force field to calculate the vibrational spectrum for β-quartz.
      
This exchange becomes observable up to 150° C below the transition, and persists above the transition, resulting in β-quartz being a time and space average of α1 and α2.
      
Lattice dynamical calculations of anisotropic temperature factors of atoms in quartz, and the structure of β-quartz
      
Temperature factors for oxygen and silicon atoms in β-quartz were calculated on a Born-von Karman lattice dynamical model of an ordered structure.
      
The negative expansion known in β-quartz were interpreted in terms of asymmetrical forces exerting on oxygen atoms in Si-O-Si bending modes.
      
Computer modelling and theoretical analysis are used to explain the nearly zero and slightly negative coefficients of thermal expansion in β-quartz well above the α-β phase transition temperature.
      
Yet, the fast oscillations of oxygen atoms are around (time-dependent) positions that do not correspond to the ideal oxygen positions in β-quartz.
      
A further contribution to the thermal diffusivity behavior is related to the higher symmetry of β-quartz, resulting in a reduced phonon-phonon-scattering probability.
      
 

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