There is no substance that *absolutely* does not expand on heating. All substances expand to some degree when heated, as their molecules move faster and take up more space. However, there are a few materials that have very low thermal expansion coefficients, meaning they expand very little even with significant temperature changes.

Here are some examples:

* Invar: This nickel-iron alloy has a very low thermal expansion coefficient, making it useful for applications where dimensional stability is crucial, like precision instruments and measuring tools.

* Zerodur: This glass-ceramic material has an extremely low thermal expansion coefficient, close to zero, making it ideal for telescopes and other optical instruments.

* Carbon fiber: Though it does expand slightly, carbon fiber has a significantly lower thermal expansion coefficient compared to most metals.

It's important to note that even these materials exhibit some expansion when heated. The term "does not expand" is technically incorrect, but these materials are exceptional in their resistance to expansion.