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I understand why most substances expand when heated (the particles get more kinetic or vibrational energy and tend to occupy more space). The volume of water decreases between 0 degree to 4 degree centigrade as the crystal structure breaks down and the molecules come closer. But, are their other substances which decrease in volume, when heat is applied ?

If you want to answer with something like the phase diagram, please explain why the phase diagram is so, instead of just stating that the substance behaves according to its phase diagram.

Archisman Panigrahi
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Yes, negative thermal expansion is a thing. That article mentions ice, graphene, Cu$_2$O, ZrW$_2$O$_8$, beta-quartz, and zeolites. Some do it only over a short temperature range, others over a long. It doesn't seem to be that uncommon.

My favourite example is rubber, which often shows up in intro statistical mechanics textbooks. As it gets hotter the long polymer chains get access to more and more randomly crinkled modes, and it contracts.

Scandium triflouride shrinks because the energy scales with the fourth power of the bond strain, and when heated the fluorine atoms (each shared between two scandium atoms) oscillate more wildly, dragging the lattice closer.

Anders Sandberg
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This is due to the following formula, which only applies to ideal gases.

${\displaystyle PV=nRT,}$

Where ${\displaystyle P}$ is the pressure of the gas, ${\displaystyle V}$ is the volume of the gas, ${\displaystyle n}$ is the amount of substance of gas (in moles), ${\displaystyle R}$ is the ideal gas constant and ${\displaystyle T}$ is the absolute temperature of the gas.

If you now increase the temperature of the gas, the overall value of ${\displaystyle PV}$ would have to increase since ${\displaystyle R}$ is a constant and you have not increased nor decreased the mass of the gas. Thus, the volume of the gas has increased.

Think of a hot air balloon. When you increase the temperature of the air, then the volume of the air inside the balloon increases, and so you start to go up.

Matthew
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