A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
Amorphous solids lack the long-range periodic order of crystals but retain short-range order — local bonding geometries are similar to the crystalline phase, but the pattern does not repeat over long distances. Glasses are the most important class of amorphous materials, formed when a liquid is cooled fast enough to bypass crystallization. The glass transition temperature (T_g) marks the reversible transformation between the liquid-like supercooled state and the rigid glassy state. Zachariasen's rules predict which oxide compositions form glasses: network formers (SiO2, B2O3, P2O5) build continuous random networks; network modifiers (Na2O, CaO) break bridging oxygen bonds and lower T_g and viscosity; intermediates (Al2O3) can act as either.
Crystallography provides a beautiful framework for understanding ordered solids, but many technologically important materials are amorphous — they lack long-range periodic order. Glass, the most familiar amorphous material, is so ubiquitous (windows, bottles, optical fibers, smartphone screens) that it is easy to forget how unusual its structure is. An amorphous solid has the local bonding environment of its crystalline counterpart (silicon is still tetrahedrally coordinated by oxygen in both quartz and silica glass) but lacks any repeating unit cell. The X-ray diffraction pattern of an amorphous material shows broad humps instead of sharp Bragg peaks.
Glass formation requires cooling a liquid fast enough that atoms cannot arrange themselves into a crystal before the viscosity becomes too high for rearrangement. The critical cooling rate depends on the material: SiO2 and B2O3 vitrify at almost any cooling rate (they are excellent glass formers), while most metals require cooling rates above 105 K/s. Zachariasen's rules explain why some oxides form glasses easily: the cation must be small and highly charged (forming strong covalent bonds), each oxygen should be linked to no more than two cations, and the coordination polyhedra should share corners rather than edges or faces. These rules favor open, flexible networks that can accommodate the disorder of the liquid state.
The glass transition (T_g) is not a thermodynamic phase transition like melting — it is a kinetic phenomenon. As a glass-forming liquid cools, its viscosity increases continuously. At T_g, the relaxation time exceeds the experimental timescale, and the liquid falls out of equilibrium, becoming a glass. The exact T_g depends on the cooling rate: faster cooling produces a higher T_g and a less dense, higher-energy glass. Below T_g, the material is mechanically a solid but structurally a frozen liquid. This distinction matters: a glass can slowly relax toward a denser, more stable state (physical aging), and this aging changes properties over time.
The practical chemistry of glass formulation balances network integrity against processability. Network formers (SiO2, B2O3, P2O5) provide the continuous bonded framework. Network modifiers (alkali and alkaline earth oxides) disrupt this framework by creating non-bridging oxygens, lowering viscosity and T_g. Intermediate oxides (Al2O3, TiO2) can enter the network as formers in some compositions and act as modifiers in others. Soda-lime glass (72% SiO2, 14% Na2O, 10% CaO) is the composition optimized over centuries for low cost and good working properties. Borosilicate glass (Pyrex), aluminosilicate glass (Gorilla Glass), and lead crystal each represent different compositional strategies tailored to specific performance requirements.