The simplest answer is no, diamonds (pure carbon) under normal circumstances do not have a liquid phase. Apply enough heat, maybe some extra oxygen, and yes, you will see a diamond burn. Now, change the environment, put it in a vacuum, stick some gases in with it, etc, throw some heat in, and it’ll turn into graphite with different properties. A good place to research further woukd be the outer Gas Giants where it can actually rain diamonds in the thicker atmospheric areas, but what do they turn into as they approach the heat and pressure of the planets core?
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