stiffness
Stiffness answers a simple question: when you push or pull on something, how far does it give before you let go and it springs back? A steel ruler bends a little and snaps straight again; a rubber band stretches a long way under the same pull. The steel is stiffer. Ceramics are among the stiffest solids we have. A fired ceramic is earth whose atoms are locked by strong ionic and covalent bonds into a rigid cage, and stretching such a solid means stretching those short, strong bonds directly, which they resist fiercely. That is why an alumina rod barely flexes where an aluminium one of the same size would visibly bow.
The number that measures stiffness is Young's modulus, written E. In the elastic range, where the material springs back completely, stress and strain grow in step: sigma = E times epsilon, where sigma is the stress (force per area) and epsilon is the strain (fractional stretch). E is the slope of that straight line, and a steep slope means a stiff material. Ceramics have very high E: alumina (Al2O3) is about 380 to 400 GPa, silicon carbide (SiC) about 450 GPa, and diamond over 1000 GPa, compared with roughly 200 GPa for steel and 70 GPa for aluminium. Because E comes from the stiffness of the atomic bonds themselves, it is a bulk bond property that changes little from part to part; it drops only when the solid is diluted, for example by porosity, since empty pores carry no load.
Stiffness matters wherever a shape must hold its dimensions under load: precision machine-tool bases, semiconductor wafer stages, telescope mirror blanks, and cutting-tool inserts all exploit the high E of ceramics to stay rigid and vibration-free. But stiffness runs right up to a sudden, warning-free brittle fracture, because a ceramic cannot yield and relieve the load the way a metal does. The crucial honest point is that stiffness is not strength: a very stiff ceramic can still break at a low stress if it hides a bad flaw. E tells you how hard it is to bend the material elastically, not how much stress it can survive before it shatters.
A silicon-carbide mirror for a space telescope is chosen largely for its stiffness: at about 450 GPa its E is more than twice that of steel while it is far lighter, so the mirror face holds its optical shape against gravity and vibration and barely sags.
High Young's modulus keeps a shape rigid under load, but says nothing about the stress at which it will finally break.
The commonest mistake is to read a high Young's modulus as high strength. Stiffness (E) is set by the bonds and is almost the same for every sample; strength is set by the worst flaw and scatters wildly. A stiff ceramic can still fail at a modest stress.