I believe the most expensive mineral is Painite which is valuable because it is so rare. I has been found in Mogok and in a few states in Myanmar. “Only 25 small crystals and only two faceted crystals have been discovered in the world.” The price per carat? 60,000 dollars.
In terms of rare gem stones, a flawless blue diamond was sold for £4 million at a Hong Kong auction by a British jeweller (Moussaieff Jewellers in London) in 2007. It sold for £650,000 per carat, shattering the record of a red diamond which sold for £450,000 per carat 20 years ago. Blue diamonds are mostly found in one site, the Premier Mine in South Africa.
The most expensive minerals are probably going to be the rarest ones, and I have seen painite and rhodium mentioned as the most expensive mineral. Both are very rare and very expensive. Prices are going to fluctuate based on supply of/demand for these minerals, however.
Painite is the most expensive currently because only 25 small crystals and 2 faceted crystals have been discovered. Currently, painite costs $60,000 per carat.
For this and other expensive minerals, you can check out http://www.therichest.org/mostexpensive/business/minerals/.
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