the lime-silica system
The lime-silica system is the chemistry that literally holds up the built world: it is the heart of Portland cement, of metallurgical slags, and of glass. Its two components are lime (CaO) at one end and silica (SiO2) at the other, and along the way it forms a family of calcium silicate compounds. Cement chemists compress the names with a shorthand where C means CaO and S means SiO2, so the key compounds read as C3S, C2S, C3S2, and CS.
The important compounds, from lime-rich to silica-rich, are tricalcium silicate C3S (the mineral alite, 3CaO to SiO2), dicalcium silicate C2S (belite, 2CaO to SiO2), rankinite C3S2, and wollastonite CS (CaSiO3). Several of these do not behave simply. Tricalcium silicate C3S — the single most important strength-giving phase in cement — is only stable over a high-temperature window and melts (or decomposes) incongruently, and on slow cooling it tends to break down; it must be quenched to survive to room temperature. That is a phase-diagram fact with billion-tonne consequences: cement clinker is fired hot and cooled fast precisely to trap metastable C3S, because the equilibrium diagram would rather it not exist at room temperature at all.
For a ceramist and a cement maker the CaO-SiO2 diagram is a working tool. It sets the firing temperature of clinker, tells you which silicate phases will crystallize from a slag as it cools, and explains why lime content is tuned so carefully. It is also the honest illustration of the gap between equilibrium and practice: the phase you most want (C3S) is a kinetically trapped, metastable one, kept alive only by fast cooling. Extend to the three-component CaO-Al2O3-SiO2 system and you have essentially the entire map of cements, glasses, and blast-furnace slags.
Fire cement clinker in a rotary kiln to about 1450 degrees C, then cool it fast. The rapid cooling traps tricalcium silicate (C3S, alite) — the phase that gives concrete its early strength — even though the equilibrium CaO-SiO2 diagram says it should decompose on slow cooling. The whole cement industry runs on deliberately dodging equilibrium.
CaO-SiO2: the calcium silicates (C3S, C2S, ...) of cement and slag, with C3S kept metastable by fast cooling.
The strongest cement phase, C3S (alite), is metastable at room temperature — the equilibrium diagram would have it decompose, and it survives only because clinker is quenched. This is a vivid case where practice deliberately defies the equilibrium map.