Lattice Dynamics Calculation of the Thermal Expansion of Pure and   Ti-Bearing Fused Silica in the Quasi-Harmonic Approximation
  The thermal expansion of pure and Ti-bearing fused silica was estimated using free energy minimization lattice dynamics calculations in the quasiharmonic approximation. While the calculations give the expected drop in the coefficient of thermal expansion in going from quartz to fused silica, the overall shape of the coefficient of thermal expansion versus temperature curve for the high-purity and titanium-bearing fused silica is not reproduced by the quasiharmonic approximation. This result is robust and insensitive to system size and annealing density of the glass. 
James R. Rustad
cond-mat.mtrl-sci