International Symposium CRYSTALLIZATION IN GLASSES AND LIQUIDS Liechtemstein, 2000 The Role of Network Rigidity on Crystallization Behaviour of Glasses

It is well known that oxide glasses build up continuous networks. Therefore the rigidity of the latter plays a key role in understanding glass properties. The network switches from floppy to rigid if the number of covalent bridges between the network formers exceeds a certain threshold value. One and the same structure could behave as rigid network in respect to some properties and could be floppy networks in respect to some other properties. Kinetics of phase transition (and most the nucleation processes) is very sensitive to the rigidity of the network. Some tiny floppy regions still exist inside the rigid network close above the threshold concentration. They can serve as active centers for the beginning of nucleation process. Much later, nucleation can appear in the rigid part of the network. Therefore, we predict a certain interval of concentration of rigid bounds in which a bimodal size distribution function of the formed phase will be observed. This prediction is confirmed by experimental data we find in literature. INTRODUCTION One of approaches to treat glass formation is based on strength considerations. The stronger the bonds in the melt are, the more sluggish the rearrangement process will be. Oxide glasses are well described by the continuous-random-network model of Zachariasen [1]. The aim of the present article is to link this idea to the rigidity percolation theory. The latter shows [2-6] that networks change from floppy to rigid at a critical point where the number of constraints exceeds the number of degrees of freedom. CONSTRAINTS COUNTING MODEL Two sources of constraints are involved. The first one is generated by the fixed length of the bridges connecting nodes of the network (bridge stretching constraints BC). There is one BC constraint associated with each bridge. Therefore, the average number nl of BC per node is