Abstract
Classical considerations of the stability of amorphous networks have sensibly concluded that a network should weaken when mechanical constraints are removed. In covalently-bonded glass networks, this weakening is evidenced by the "fragility" and, in many cases, the fragility increases as the density of covalent bonds decreases. However, covalent glasses that possess substantial intermediate range order (IRO) exhibit an increase of fragility with increasing bond density - a paradoxical weakening in spite of the addition of reinforcing constraints. Here we resolve this paradox by suggesting that such IRO-containing networks require a renormalization. A coarse-graining of IRO structural units is proposed that permits a network to effectively weaken despite increases in the overall density of bonds. Through this coarse-graining approach, we demonstrate the emergence of a universal dependence of fragility on network connectivity that is well obeyed by more than 75 distinct network-forming glasses including chalcogenides, borates, germanates, phosphates and aluminophosphates.