Topological model of alkali germanate glasses and exploration of the germanate anomaly

Germanate glasses are of particular interest for their excellent optical properties as well as their abnormal structural changes that appear with the addition of modifiers, giving rise to the so-called germanate anomaly. This anomaly refers to the nonmonotonic compositional scaling of properties exhibited by alkali germanate glasses and has been studied with various spectroscopy techniques. However, it has been difficult to understand its atomic scale origin, especially since the germanium nucleus is not easily observed by nuclear magnetic resonance. To gain insights into the mechanisms of the germanate anomaly, we have constructed a structural model using statistical mechanics and topological constraint theory to provide an accurate prediction of alkali germanate glass properties. The temperature onsets for the rigid bond constraints are deduced from in situ Brillouin light scattering, and the number of constraints is shown to be accurately calculable using statistical methods. The alkali germanate model accurately captures the effect of the germanate anomaly on glass transition temperature, liquid fragility, and Young's modulus. We also reveal that compositional variations in the glass transition temperature and Young's modulus are governed by the O–Ge–O angular constraints, whereas the variations in fragility are governed by the Ge–O radial constraints.