the melting point
The melting point is the temperature at which a crystalline solid gives up its ordered structure and turns to liquid. It is the headline number behind the ceramic superpower: ceramics melt far hotter than metals, which is why they work where metals would soften and flow. Iron melts at 1538 degrees C and aluminium at a mere 660, but magnesia melts near 2850, alumina near 2050, zirconia near 2700, and hafnium carbide near 3900 degrees C — among the highest melting points of any material known.
Why so high? A crystal melts when thermal jiggling finally overpowers the bonds holding atoms in their sites, so the melting point is a direct readout of bond strength — of the lattice energy stored in the strong ionic-covalent bonds that define a ceramic. Deeper, stronger bonds need more heat to shake apart. The same bonding that makes a ceramic hard and heatproof also makes it high-melting; they are two faces of the same rigidity. Small, highly charged ions packed tightly (a large Madelung sum, a big lattice energy) give the highest melting points.
Two honest complications matter in practice. First, many ceramics do not melt cleanly. Some decompose before they melt (SiC sublimes and breaks down above about 2700 degrees C rather than forming a tidy liquid), and some melt incongruently, dumping a solid of one composition and a liquid of another — mullite is the classic case. Second, glasses have no melting point at all: with no crystal to break down, a glass merely softens over a wide temperature range as its viscosity falls. The very high melting point that makes ceramics refractory is also the reason they are hard to make: you cannot cast most of them like a metal, which is exactly why they are built by sintering powders below the melting point instead.
Hafnium carbide and tantalum carbide, near 3900 degrees C, are among the highest-melting solids known and are studied for hypersonic vehicle leading edges and rocket-nozzle throats, where the surface glows white-hot and no metal could survive. That extreme refractoriness is a direct consequence of very strong, short covalent bonds.
The highest melting points belong to strongly covalent carbides and borides — the basis of the ultra-high-temperature ceramics.
A high melting point does not guarantee usefulness at high temperature: oxidation, decomposition, or a low-melting grain-boundary phase can end a ceramic's service far below its melting point, so refractoriness, not the melting point alone, decides real limits.