a ternary phase diagram
Real ceramics rarely have just two ingredients. A porcelain, a slag, a glass, a cement is a stew of three or more oxides, and to map it you need one more dimension. A ternary phase diagram handles three components by plotting composition on an equilateral triangle: each corner is one pure component, each edge is a binary between two of them, and any point inside is a unique three-way mixture. It is a clever bit of geometry — the three fractions always add to 100 percent, so a triangle captures every possible blend on one flat sheet.
Reading composition takes a moment's practice. For a point inside the triangle, the amount of each component is read from how far the point sits from the edge opposite that component's corner: the closer you are to a corner, the richer in that component. But we also need temperature. The full picture is a three-dimensional prism — the triangle on the floor, temperature rising vertically — with liquidus surfaces like hills and valleys overhead. Because a solid 3D model is hard to use, ceramists flatten it two ways: a liquidus projection draws contour lines (isotherms) of the liquidus surface onto the base triangle, like a topographic map, and an isothermal section slices the prism horizontally at one chosen temperature to show which phases are stable at that temperature across all compositions.
The phase rule scales up: with C = 3 and pressure fixed, F = C - P + 1 = 4 - P, so at fixed temperature and pressure a ternary can show up to three phases in equilibrium, and an invariant ternary eutectic has four phases meeting at once. The systems that matter are famous: CaO-Al2O3-SiO2 is the master diagram of cements, glasses, and blast-furnace slags; MgO-Al2O3-SiO2 governs cordierite and steatite bodies and many refractories; Na2O-CaO-SiO2 is the map of ordinary window and container glass. A ceramist uses these to design a batch, predict the first liquid on firing, and read the crystallization path a cooling melt will follow across the triangle.
Design a soda-lime glass on the Na2O-CaO-SiO2 triangle. Plot the batch as a point, read its three oxide fractions off the distances to the three edges, and find the liquidus valley it sits in. That location tells you the melting temperature and warns whether the glass sits dangerously close to a field where cristobalite or devitrite would crystallize on cooling.
Three components on a triangle, temperature into the third dimension; read via liquidus projections and isothermal sections.
A composition triangle alone carries no temperature — do not read a plain ternary triangle as if it showed melting behaviour. You need the liquidus projection (isotherms) or an isothermal section, and beware that flat 2D printouts hide the vertical temperature axis.