Rings in Network Glasses: The \mathrm{B_2O_3} Case

There has been a considerable debate, in particular since the emergence of atomistic simulations, about the structure of glassy B2O3, a prototypical network-forming system based on trigonal units. Some intermediate-range order in the form of threefold rings, present in the glass but not in the crystalline phases, has remained so far very difficult to reproduce in atomistic simulations. After a brief summary of the evidences accumulated regarding the boroxol rings, a review of the numerical studies of liquid and glassy B2O3 is provided. The reasons for the failure of the quench-from-the-melt techniques are stressed and a methodology, based on first-principles calculations of experimental observables (diffraction, NMR, Raman, IR, heat capacity) from various glassy models is devised to provide incontrovertible answers to the debate. This allows assessing not only the content of boroxol rings but also the sensitivity of each observable to this quantity. The presence of threefold rings in the glass is then showed to have ramifications for the understanding of the crystalline and liquid phases. This includes the prediction of yet unknown B2O3 polymorphs structurally close to the glass, the understanding of the so-called crystallisation anomaly and the evidencing of structural transitions in the liquid. Finally, the discussion is extended to parent systems such as B2S3.