Why is diamond hard and graphite soft?

Each carbon in diamonds is bound to four other carbons with a tetrahedral bond structure. This creates a cubic lattice with tremendous strength in all directions. Hence, diamonds are very hard.

Graphite, on the other hand, forms bonds with three other carbons in a single plane. This results in a sheet-like lattice that is analogous to the pages in a book, with one sheet on top of the other. These sheets may bend or shear easily, resulting in a much softer substance.

I haven't had the opportunity to research it fully, but some fullerites are even harder than diamonds. I don't know why; this seems counter intuitive to me (unless there is some kind of bonding between adjacent fullerine structures that I don't know about.)

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