Graphite is the most common allotrope of pure carbon. It takes the form of a black, soft solid. The structure is a comparatively weak one (compared to diamond), it is bonded in layers. This is one of the reasons for it being so soft. These layers can slide past each other with great ease, which makes it very useful as a solid state lubricant. The most well known use for graphite is to make "Leads" in pencils. In pencils the graphite is mixed with clay to change the hardness of the "Lead". 

As mentioned above graphite has a layered structure, the approximate distance between layers is 3.35
Angstroms. Because the separation of the layers is approximately the Van Der Vaal's radii of C, then the layers should be weakly bonded to each other. This accounts for its low hardness. This is because the layers can slide over each other easily. Each carbon is bonded to three others, this is by Pi and Sigma bonds. It is these Pi bonds which account for its high electrical conductivity. 

As mentioned above graphite is used as a solid state lubricant, also mentioned above it is a major constituent of pencil "leads". Because of its good electrical conductivity, and relatively low reactivity it is useful to use as an electrode. A more serious use for it is that it slows down neutrons in a nuclear reactor.

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