Quasiharmonic Lattice Dynamics Calculations of Energy Balances in the   Thermal Expansion of ULE Glass
  Quasiharmonic lattice dynamics calculations are carried out on SiO2-TiO2 glass mixtures (TiO2 less than or equal to 20 weight percent) showing that the addition of TiO2 systematically lowers the thermal expansion of high purity fused silica. Adding ten weight percent titania lowers the thermal expansion coefficient by approximately 0.5 ppm/K in agreement with observations. The driving force for lowering the thermal expansion coefficient in the model system is broken down into mode-by-mode contributions. The driving force is distributed broadly across the frequency spectrum and is not localized into particular frequency ranges that can be associated with the coordination structure of Ti4+ in the simulated glass. 
James R. Rustad
cond-mat.dis-nn