the coefficient of thermal expansion
Almost everything grows a little when you heat it and shrinks when you cool it — a railway track lengthens on a hot day, a jar lid loosens under hot water. The coefficient of thermal expansion, written alpha (or CTE), is simply how much a material grows per degree, as a fraction of its length: alpha = (1/L)(dL/dT), where L is length and T is temperature. A typical value like 8 x 10^-6 per kelvin means a one-metre bar grows 8 micrometres for every degree of warming. Ceramics, as a class, expand very little compared with metals and plastics.
Why do they expand at all, and why so little? Picture the bond between two atoms as a spring, but a lopsided one: it is harder to push the atoms together than to pull them apart, so the bottom of the energy well is asymmetric (this asymmetry is called anharmonicity). As heat makes the atoms vibrate with bigger swings, the average spacing creeps outward because the well is shallower on the far side. A strong, deep, symmetric bond expands little; a weak, floppy, lopsided bond expands a lot. That is why strongly bonded ceramics have low alpha: fused silica about 0.5 x 10^-6 /K, alumina about 8 x 10^-6, MgO about 13 x 10^-6, while aluminium metal is around 23 x 10^-6. The volumetric expansion is roughly three times the linear value for an isotropic solid.
Thermal expansion is one of the most consequential numbers in ceramic engineering. Match it and you can seal a ceramic to a metal, glaze a pot without crazing, or bond a coating that stays put through temperature cycles; mismatch it and you build in stress that cracks the part. Low expansion is engineered on purpose: cordierite and lithium-aluminosilicate glass-ceramics have near-zero alpha, which is why glass-ceramic cooktops and cordierite catalytic-converter substrates shrug off flame-to-ice temperature swings. Above all, alpha is the first term in the thermal-stress and thermal-shock equations — a low alpha is the single most powerful lever for surviving sudden temperature change.
A borosilicate (Pyrex) beaker has alpha near 3.3 x 10^-6 /K, versus about 9 x 10^-6 for ordinary soda-lime glass. Pour boiling water in and the low-expansion borosilicate develops less than half the internal stress, so it survives the same temperature jump that shatters the cheaper glass.
Halving the expansion coefficient roughly halves the thermal stress for the same temperature change — the core reason low-CTE ceramics resist thermal shock.
CTE is not one fixed number: it usually rises with temperature, and quoted values are averages over a stated temperature range, so always check the range before comparing two materials.