Modeling the properties of silicates

• Main Author: Bartelmehs, Kurt Lane
• Other Authors: Geological Sciences
• Format: Others
• Language: en
• Published: Virginia Tech 2014
• Subjects: LD5655.V856 1993.B377; Silicates > Mathematical models
• Online Access: http://hdl.handle.net/10919/37706; http://scholar.lib.vt.edu/theses/available/etd-05042006-164529/

Assuming a simple force field involving only short range Non-Coulombic molecular energy terms along with P1 symmetry, a variation of the SQLOO model (Boisen and Gibbs, 1993) successfully generates the structure types of both α and β1 quartz along with at least five alternative structure types of silica not yet observed to our knowledge. These structure types are identified by the existence of symmetry elements represented in the optimized atomic coordinates and cell parameters that define a minimizer in the model. A family of minimizers is discovered through the combined use of Monte Carlo simulated annealing followed by quasi-Newton minimization techniques. The results are in contrast with the assertion made by Tse et al. (1992) that new structure types of SiO₂ can only be arrived at by Molecular Dynamic methods. By varying the parameters used in the minimization process, different families of structure types are discovered. Several structure types were found to have high symmetries. These results are in contrast with the findings by Kramer et aL (1991) that the stability of high symmetry structures of silica are stabilized in part by ionicity. The results reported here are for calculations involving Z = 3 and 6 formula units. This strategy may be useful in the prediction of possible high silica zeolite structure types. An examination of the atomic displacement parameters (ADPs) obtained for TO₄ tetrahedra (T = Si, Al) suggest rigid TO bonds are more common in non-framework than in framework silicates. Correlated motion is found among the ADPs that is consistent with TLS rigid body motion. For these data, the translational motion is represented by the ADPs of the central T atom while both the librational and translational motion is contained in those of the surrounding O atoms. The libration angle for rigid tetrahedra is linearly dependent on the difference between the isotropic equivalent displacement parameter of the T and O atoms, B(T) and B(O), respectively. The value of B(O) is on average twice that of B(T) with a maximum value of ~ 2.0Ų. Variations in the SiO bond lengths of rigid tetrahedra in the silica polymorphs is related only to f_s(O). Rigid TO and OO bonds are a necessary but not sufficient condition for rigid body motion. Nonrigid tetrahedra may represent crystals containing disorder or problems with the refinement. The computer program EXCALIBR (Bloss and Riess, 1973; Bloss, 1981, p. 202) has been rewritten and markedly improved. Like EXCALIBR, EXCALIBR II solves optical extinction data, as determined with a spindle stage, and determines the optic axial angle 2V and the orientation of the crystal’s optical indicatrix. EXCALIBR II uses a modification to Joel’s equation as a means of obtaining the optic axes of a crystal. Furthermore, EXCALIBR II successfully solves extinction data where one optic axis of a biaxial crystal is 90° to the spindle axis, an orientation that had thwarted its predecessor. EXCALIBR II also accurately determines the optical indicatrix orientation for uniaxial crystals. After solving extinction data for several different wavelengths and/or temperatures, EXCALIBR II calculates the angular change of each optic direction with wavelength and/or temperature along with the error on the angle. Using a simple t-test, it then computes a p-value to aid in the decision as to whether the optical direction truly exhibits dispersion. This is a more valid and sensitive procedure than the χ² test used by EXCALIBR, particularly because the covariance in each optic vector’s coefficients are taken into consideration and the results are invariant to the vector’s orientation. === Ph. D.