Atomic scale foundation of temperature-dependent bonding constraints in network glasses and liquids

The behaviour of bonding constraints with temperature is analyzed from an atomic scale approach (Molecular Dynamics, MD) combined with partial bond angle distributions (PBAD). The latter allows to have access to the second moments (standard deviations) of the distributions. Large (small) standard deviations correspond to large (small) angular excursions around a mean value, and are identified as broken (intact) bond-bending constraints. A similar procedure is used for bond-stretching constraints. Systems examined include glassy and liquid disilicate 2SiO2–Na2O (NS2). In the glass, MD constraint counting closely matches Maxwell enumeration of constraints using the octet binding (8-N) rule. Results show that the standard deviations of the partial bond angle distributions increase with temperature and suggest a softening of bond-bending constraints. A bimodal bonding oxygen distribution is obtained for T> Tg, and the fraction of thermally activated broken bond-bending constraints computed as a function of temperature. Overall, these results provide a microscopic rationale for extending constraint counting from chalcogenides to complex oxides, and also a numerical basis for recent functional forms of temperature-dependent constraints proposed from energy landscape approaches.