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I have a feeling that if my stovetop was made out of regular glass, it would have cracked from rapid cooling/heating a long time ago – especially if you consider accidental water spills. What kind of glass is able to withstand such abuse?

(I am just looking for terms to google for further reading.)

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Stovetops are made of glass-ceramic which has extremely low thermal expansion, hence no cracking from temperature change. In fact, the coefficient is with $0.1 \cdot 10^{-6} \ 1/K$ even lower than that of Borosolicate glass at $3.3 \cdot 10^{-6} \ 1/K$. Since glass-ceramic can reach a negative coefficient of thermal expansion, getting even closer to zero is just a matter of engineering (thanks to @Volker Siegel for this interesting fact).

The brand name for one kind of glass-ceramic, Ceran (by German company Schott) is in German often used to generally describe glass-ceramic stovetops. Borosilicate glass is, to my knowledge, used only for heat-resistant cookware, but not the stovetops themselves.

OpticalResonator
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Borosilicate glasses (e.g. "Pyrex") have small coefficients of expansion (about $3.3\times 10^{-6}$/°C compared with $10\times 10^{-6}$/°C for steel) and can tolerate temperature differentials of about 180 °C or 330 °F.

alephzero
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It doesn’t crack because it is the so-called Pyrex glass. It is not the same glass as common window glass which is still silica, but blended with sodium and calcium. Pyrex is silica blended with boron, making it way more thermally stable because of a smaller thermal expansion.

It also exists as pure silica glass, used mostly in high end optical applications (microscopes, lab instruments, etc.) which is even more stable and can withstand temperature variations up to a thousand degrees.