How does compression of carbon atoms work?

From what I understand, it's extremely difficult/ impossible to compress atoms closer together.

I'm wondering how this applies in the case of graphite and diamond, where the carbon atoms adopt a different structure under different temperatures and pressure.

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One thing: graphite is anisotropic, so all properties depend upon orientation. Compressing it in one direction Is relatively easy as compared to another. –  Manishearth Feb 7 '12 at 18:13
"extremely difficult/ impossible to compress atoms closer together". That really depends on the prior state. If the atoms are in a gas, it's quite easy to do so. –  MSalters Feb 9 '12 at 15:01