Why is diamond so hard even though it is basically graphite?

The hardness of minerals is measured on a scale of 1-10 which was devised in 1822 by an Austrian named Friedrich Mohs. Number 1 on Mohs’ scale is talc, an extremely soft mineral. Number 10 is diamond, the hardest natural substance. When cut and polished, diamond is prized in jewellery, but the only thing that can be used to cut and polish a diamond is diamond itself.
Diamond, which is 40 times as hard as talc, is made of pure carbon. Chemically, it is exactly the same as graphite, the substance used to make pencil lead. Graphite has hardness of between 1 and 2 on Mohs’ scale. The difference between hard carbon and soft graphite is caused by the arrangement of carbon atoms. In graphite, the atoms are linked in flat planes which readily slide over each other. In diamond, which is formed in great heat and under intense pressure, the atoms are bound in a rigid structure.

Additional reading:
Diamond (Wikipedia)
Mohs scale of mineral hardness (Wikipedia)

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