Size of CaF₂ Crystals Precipitated from Glasses in the Na₂O/K₂O/CaO/CaF₂/Al₂O₃/SiO₂ System and Percolation Theory

Glasses with the compositions (in wt %) x Na 2 O·7.69K 2 O·10.58CaO·12.5CaF 2 ·5.77Al 2 O 3 ·(63.45 − x )SiO 2 (with x = 7.65−12.65) were thermally treated at 550 and 570 °C for 1−160 h. This resulted in the precipitation of crystalline CaF 2 . The crystallite sizes of this phase depended on neither the time nor the temperature of thermal treatment. During the crystallization process, the viscosity of the residual glass melt increased, and supposedly a viscous layer is formed around the growing crystals, which hinders further crystal growth. However, the chemical composition strongly affected the mean crystallite size that was calculated from XRD line broadening. With increasing Na 2 O concentration, the crystals get larger and their number decreases. This was explained by percolation theory. Here, a statistical distribution of network modifiers within the glass network is assumed. Above an average number of covalent bonds per network forming unit of 2.4, the network is rigid; however, within the rigid network, tiny floppy regions occur. The maximum size of a floppy region can be calculated from the respective glass composition and increases with increasing Na 2 O concentration. This runs parallel to the mean size of the crystallites.