For small tension the response of a solid to an applied stress is given by Hooke’s law. Outside this linear regime the relation between stress and strain is no longer universal and at present there is no satisfactory insight on how to connect for disordered materials the stress-strain relation to the microscopic properties of the system. Here we use atomistic computer simulations to establish this connection for the case of silicate glasses containing alkali modifiers. By probing how in the highly non-linear regime the stress-strain curve depends on composition, we are able to identify the microscopic mechanisms that are responsible for the complex dependence of stress on strain in these systems, notably the presence of an unexpected quasi-plateau in the tangent modulus. We trace back this dependence to the mobility of the modifiers which, without leaving their cage or modifying the topology of the network, are able to relieve the local stresses. Since the identified mechanism is general, the results obtained in this study will also be helpful for understanding the mechanical response of other disordered materials.

Amorphous–amorphous transformations under pressure are generally explained by changes in the local structure from low- to higher-fold coordinated polyhedra1–4. However, as the notion of scale invariance at the critical thresholds has not been addressed, it is still unclear whether these transformations behave similarly to true phase transitions in related crystals and liquids. Here we report ab initio-based calculations of compressed silica (SiO2) glasses, showing that the structural changes from low- to high-density amorphous structures occur through a sequence of percolation transitions. When the pressure is increased to 82 GPa, a series of long-range (‘infinite’) percolating clusters composed of corner- or edge-shared tetrahedra, pentahedra and eventually octahedra emerge at critical pressures and replace the previous ‘phase’ of lower-fold coordinated polyhedra and lower connectivity. This mechanism provides a natural explanation for the well-known mechanical anomaly around 3 GPa, as well as the structural irreversibility beyond 10 GPa, among other features. Some of the amorphous structures that have been discovered mimic those of coesite IV and V crystals reported recently5,6, highlighting the major role of SiO5 pentahedron-based polyamorphs in the densification process of vitreous silica. Our results demonstrate that percolation theory provides a robust framework to understand the nature and pathway of amorphous–amorphous transformations and open a new avenue to predict unravelled amorphous solid states and related liquid phases7,8.

New interaction potentials were developed for molecular dynamics simulations to study the role of Mg and Ca in modifying the structure and properties of alkaline earth silicates and borates. Competition between the depolymerization of the silica network and the formation of new bonds between oxygen atoms and modifiers leads to the enhancement of the elastic moduli with increasing modifier content in alkaline earth silicate glasses. Compared with calcium silicate, the higher elastic moduli of magnesium silicate result from a higher connectivity of the overall glass network due to the incorporation of fourfold coordinated magnesium and a more rigid connection between oxygen atoms and modifiers. In contrast to the silicates, the effect of modifier on the elastic moduli of alkaline earth borates is dominated by the formation of fourfold coordinated boron (N4). Calcium borate with higher N4 shows a more rigid network structure and higher elastic moduli.

We use ab initio molecular dynamics simulations to investigate the properties of the dry surface of pure silicaand sodium silicate glasses. The surface layers are defined based on the atomic distributions along the direction(z direction) perpendicular to the surfaces. We show that these surfaces have a higher concentration of danglingbonds as well as two-membered (2M) rings than the bulk samples. Increasing the concentration of Na 2 O reducesthe proportion of structural defects. From the vibrational density of states, one concludes that 2M rings have aunique vibrational signature at a frequency ≈850 cm −1 , compatible with experimental findings. We also findthat, due to the presence of surfaces, the atomic vibration in the z direction is softer than for the two otherdirections. The electronic density of states shows clearly the differences between the surface and interior and wecan attribute these to specific structural units. Finally, the analysis of the electron localization function allows toget insight on the influence of local structure and the presence of Na on the nature of chemical bonding in theglasses.