Zachariasen's rules
/ zah-kah-REE-ah-sen /
In 1932 the Norwegian crystallographer William Zachariasen asked a deceptively simple question: why do a few oxides, like SiO2 and B2O3, form glasses easily, while most oxides, like MgO or Na2O, refuse and always crystallize? His answer, the random-network hypothesis, is one of the founding ideas of glass science. He proposed that a good glass is a three-dimensional network of the same building blocks a crystal uses, corner-linked polyhedra, but with the joints flexed to random angles so the pattern never repeats. Order in the neighbourhood, chaos in the long run.
From that picture he distilled a short list of rules an oxide must obey to build such a network. Roughly: each oxygen should link to no more than two of the network cations; the cation should sit in a small polyhedron, surrounded by only three or four oxygens; those polyhedra should share only corners, never edges or faces (edge- and face-sharing are too rigid and force crystalline order); and each polyhedron should share at least three of its corners, so the network extends in three dimensions rather than forming isolated chains or sheets. An oxide of the form A2O3 satisfies this with oxygen triangles; an oxide AO2 satisfies it with oxygen tetrahedra.
The rules are a model, not a law, and they are wonderfully predictive: they correctly single out SiO2, B2O3, P2O5, and GeO2 as classic glass-formers and explain why simple ionic oxides cannot form a network on their own. Modern diffraction and simulation have confirmed the random-network picture in remarkable detail. Be honest about the limits, though: the rules describe an idealized single-component network, and real commercial glasses deliberately break it by adding modifiers that snip the network to make it meltable and workable.
Zachariasen's rules act like a bouncer at the glass-former door. SiO2 gets in: silicon sits in an oxygen tetrahedron, each corner shared with a neighbour, building a springy random web. Na2O is turned away: sodium wants six or more oxygens around it in a dense, edge-sharing arrangement, which locks into a crystal. That is why silica glasses and window glasses are built on a silica skeleton, with the sodium added only as a guest that breaks bonds.
The rules predict who can build a glass network (SiO2) and who cannot (Na2O), and hence why oxide glasses are silica-based.
The random network is an idealized picture. It nails which pure oxides form glasses but does not by itself describe real multi-component glasses, where added modifiers deliberately depolymerize the network the rules describe.