a binary phase diagram

Now let two ingredients mix. A binary phase diagram is the workhorse map of ceramics: composition runs along the bottom axis, from 100 percent of one component on the left to 100 percent of the other on the right, and temperature runs up the side. Pressure is held at one atmosphere and quietly forgotten. Every point on the map is a recipe (a mix) at a temperature, and the region it falls in tells you which phase or phases are stable there and what their compositions are.

Reading one is a simple two-step habit. Find your point from its overall composition and temperature. If it lands in a single-labelled field, you have that one phase, full stop. If it lands in a two-phase field, draw a horizontal line — a tie line — across the field at that temperature; where it hits the two bounding curves gives the compositions of the two coexisting phases, and the lever rule then tells you how much of each. The upper boundary of the all-solid region, above which liquid appears, is the solidus; the boundary above which everything is molten is the liquidus; between them solid and liquid live together.

These maps carry the whole vocabulary a ceramist reads off daily: a eutectic dip where liquid first appears at the lowest temperature, regions of solid solution where one crystal dissolves the other, intermediate compounds like mullite or spinel standing as vertical lines, and peritectic ledges where a compound melts incongruently. From a single binary diagram you can predict the firing temperature at which a glassy bond will form, the safe service ceiling of a refractory, and whether a body will stay solid or slump. It is equilibrium thermodynamics drawn as a picture you can navigate with a ruler.