Even a diamond eventually melts, but under very particular conditions.
Diamond is a crystalline form of carbon. Its atoms are arranged in an especially strong lattice. At ordinary pressure, heating it is not enough to produce a pool of liquid diamond. Experiments under extremely high pressure therefore make it possible to explore behavior that cannot be observed in our everyday environment.

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Researchers at Lawrence Livermore National Laboratory used powerful laser pulses. They created shock waves that passed through tiny diamond samples for a few billionths of a second. The pressure then approached 1 terapascal, or nearly ten million times the atmospheric pressure at sea level.
The researchers simultaneously tracked the temperature, the speed of the shock wave and the structure of the material using X-rays. Around 7,300 K, or slightly above 7,000 °C, several measurements changed together. In particular, the signal produced by the crystal structure decreased, indicating that the diamond was beginning to lose its solid organization.
Calculations predicted that under extremely high pressure, carbon could adopt another crystal structure called BC8. However, the measurements did not show this transformation under the conditions tested. The diamond structure persisted up to approximately 1 terapascal.
These measurements are of particular interest for studying the interiors of planets. Some planets that are very rich in carbon could reach pressures at which it changes structure or becomes liquid. Precisely determining the limits of diamond therefore helps calculate the possible composition and evolution of their deep layers.
Inertial confinement fusion is also concerned. Some experiments use diamond around a small fuel capsule compressed by lasers.
The experiments now provide a direct reference near 1 terapascal. However, they do not determine the entire carbon phase diagram at even higher pressures. Further measurements will need to establish how long diamond can remain temporarily solid before other structures or the liquid state definitively take over.