Most of us won't have looked at a periodic table since school, but now's the time to brush up on your chemistry as mining companies go chasing ever more exotic and elusive elements.Rare earth metals are the latest craze in the mining world. China has the biggest deposits and is getting protective. It announced last year that exports would be cut in 2010-15, and if recent press reports are to be believed, will ship out 30% less in 2011. There are 17 so-called rare earth elements: Scandium, Yttrium, Lanthanum, Cerium, Praseodymium, Neodymium, Promethium, Samarium, Europium, Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium, Ytterbium and Lutetium.They are used in the US weapons industry, by electronics manufacturers, in nuclear batteries, lasers, x-ray machines, wind turbines and much more. Prices have rocketed in recent years and the companies that mine for the treasure have done equally well, despite not actually getting anything out of the ground.An index of rare earth company shares put together by researcher Kaiser Bottom-Fish Online is up 12-fold in less than two years and up 35% in a month.Those who have done best out of a boom that's fast becoming a bubble are listed overseas.America's Rare Element Resources, Canada's Quest Rare Minerals and Australia's Greenland Minerals and Energy have made canny investors a fortune. Aussie duo Lynas Corporation and Arafura Resources, and Canadians Great Western Minerals and Avalon Rare Metals are also flying high. New US listing Molycorp hopes to do the same.The pickings in London are rarer than the minerals themselves. Just a few are kicking around the dirt for rare earths. One of them is £43m AIM-quoted Red Rock Resources. It's got gold interests in Africa and iron ore projects in Australia, but investor attention has shifted to its 26% stake in Australia's Resource Star. Their Machinga license in Malawi has proved to have strong niobium and rare earths over at least 7km of strike. A note from Edison Investment Research last month suggesting the company could be worth more than 20p a share caused its value to triple.Thor Mining, never one to miss an opportunity, has resurrected its Daicos project in the Harts Range area of the Northern Territory.Executive chairman Mick Billing told ShareCast he's been talking with the Japanese who are chasing access to rare earths. Previous reconnaissance sampling at Daicos returned high values from very radioactive samples, with a best assay of 19.37% Uranium, 26.52% Niobium, 6.25% Tantalum and 2.68% Yttrium. But Billing is careful not to overplay the project."It's in its infancy," he said of the find, first made in 2007. "Our guys came across surface samples that looked tasty. The best of the assays were exciting, although they are just surface samples. But it's a very interesting sniff." Work on Daicos stopped during the financial crisis when funding dried up, but Thor plans to go back and do some trench work to intersect zones of interest and reasonable grades. Geophysics then drilling could follow."We'll do some early stage exploration and see where it takes us," said Billing. "We need approvals from the relevant authorities first."Thor wants its men to be up at the project again by the end of the year before it gets too hot.Of the quoted miners, African Consolidated Resources could also be interesting. In June it struck a joint venture deal with Rare Earths International (REI) on the Nkombwa Hill project in Zambia. The Australians have just completed due diligence and agreed to spend at least $750,000 to define an initial inferred resource in exchange for a 30% equity interest in the project. They're looking for Cerium, Lanthanum, Neodymium, Praseodymium and Gadolinium.Whether this latest 'bubble' will mirror the dotcom boom and bust remains to be seen. Billing isn't so sure."The Chinese take the attitude that metals will be in short supply in years to come, so they go and take a strategic footprint before others do," he said. "I think it's less like the dotcom boom and more part of a re-rating of a bunch of commodities over the past five or six years.""The bubble won't burst. Prices will just settle back to more sensible levels."