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Excellent thought... Actually I had planned this article to be longer but it would have been too long.
So when my students give me a break, I will write a second part to it where I will discuss an idea not too far from what you are saying.
Silicon under HPHT conditions converts to a Diamond structure, but if specific impurities are present it can crystallise under clathrate form, a cousin structure of the buckyball, for example Na8Si46. This was my PhD thesis.
I will discuss this possibility for Carbon (same valence electronic structure than Si), leading to a potentially carbon whitedwarf crust exhibiting a clathrate structure, for example He8C46 or He8O16Si136.
Stay tuned!

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