Rare earth metals (REMs) are one of the most frequently discussed topics in renewable energy today, with articles appearing in major media outlets such as the New York Times practically every day.  While these elements, defined by IUPAC to include scandium, yttrium, and the fifteen lanthanides, are extremely important to a variety of technologies, they are crucial to some of alternative energy's hottest technologies, such as hybrid cars and wind turbines.  For the purpose of this work, I will restrict my discussion to neodymium (Nd), one of the most important rare earth metals. However, the general conclusions obtained in this work should shed light on the importance of these elements to our energy future.
Neodymium-containing compounds are commonly used in green energy devices such as hybrid cars and wind turbines due to their strong permanent magnetism. "Neodymium magnets" are commonly an alloy of neodymium, iron and boron that forms a tetragonal crystal structure with the molecular formula Nd2Fe14B.  This alloy has many attractive properties, such as a Curie temperature of 585 K (meaning that it will retain its ferromagnetism even at high temperatures) and an energy product as high as 440 kJ/m3, nearly ten times that of ceramic ferrite magnets.  Brushless electric motors, such as those used in the Toyota Prius, require strong permanent magnets to form the rotor; in fact, each Prius engine requires nearly 1 kg of neodymium (although as reported, it is likely that this number refers to the amount of neodymium magnet needed rather than the amount of elemental neodymium).  Neodymium is also utilized in many designs for wind turbine generators.  While the amount of neodymium needed for commercial scale wind turbines is likely a trade secret, a how-to guide for building a small-scale "homebrew" wind turbine recommends using 24 1" × 2" × 1/2" NdFeB magnets for a 5 to 10-foot diameter wind turbine.  At a density of 7500 kg / m3, this amounts to nearly 3 kg of NdFeB for each turbine; the amount of NdFeB would be expected to be much greater for multi-megawatt turbines, which can have diameters of up to 120 m.  While there are countless other uses of neodymium in the electronics industry, it is clear that its importance in renewable energy devices will be increasingly relevant as implementation of these technologies increases.
While the moniker "rare earths" is somewhat misleading, as even the rarest REMs are 200 times more prevalent in the Earth's crust than gold, the difficulty with mining these elements is that they are very rarely concentrated in deposits sizable enough to be profitably mined, and when they are, the mines often contain too much radioactive thorium to be mined safely.  Due to its even atomic number and its light atomic mass compared to the other REMs, neodymium is one of the especially abundant "light rare earth metals", along with lanthanum, cerium, and praseodymium; these four elements typically comprise 80 to 99% of the total mass in a rare earth deposit.  As a result, the price per kg of neodymium is substantially lower than that of the rarer REMs. For example, the price of neodymium oxide was $60/kg in 2008, compared to $3,500/kg for lutetium.  Thus, any concerns about the scarcity of neodymium will be even greater for the rarer REMs; in this sense, neodymium serves as an important limiting case to obtain "best estimate" trends.
The production of rare earth elements has become a source of tension in the American political and economic sectors, due to the fact that China is responsible for over 95% of the world's REM production and the US does not currently mine REMs.  When extracted from rock deposits, rare earths are not found in elemental form but typically as trivalent cations in carbonates, oxides, phosphates, and silicates. The two most important Nd-containing ores are bastnäsite, which typically contains 12-19% neodymium carbonates by weight, and monazite, which contains 17-18% neodymium phosphates.  While monazite contains thorium, making it difficult to mine due to the high radiation levels, bastnäsite is free of thorium and is thus much more commonly mined. 
China's domination of REM production is not reflective of the global distribution of REM reserves. While China is responsible for 97% of current REM production with 120 kt/yr, it contains 36 Mt of REM reserves, which represent only 36% of the estimated global total.  Also promising is the fact that the United States possesses considerable rare earth reserves (13 Mt, or 13% of the global total), and Austrialia, Russia, and Canada possess significant reserves as well.  Perhaps the most important American REM deposit is the Mountain Pass mine in California. From the 1960s until 1995, Mountain Pass was actually the primary producer of REMs globally, but production declined and eventually stopped in subsequent years due to competition from China.  While the Mountain Pass mine is currently used solely for the processing of rare-earth ores, the American company Molycorp, which bought the mine in 2000, is working hard to reopen the mine and provide competition for the Chinese producers. 
There are two main factors that will determine the success of future American REM mining endeavors: abundance and cost competitiveness. The question of abundance is somewhat easier to discuss quantitatively. While there are many uses for many different REMs, our discussion will focus on the use of neodymium in alternative energy technologies. Thus, let us assume that each hybrid car uses 1 kg of NdFeB and each 120 m turbine uses 30 kg of NdFeB based on our earlier discussion. Let us also assume that each 120 m turbine generates 2 MW, a typical to high generating capacity.  A conservative goal would be to replace 20% of existing cars and 5% of existing energy generation capacity with these greener technologies. Since there are approximately 2.5 × 108 cars in the United States, this would require the construction of 5 × 107 hybrid cars, and would thus require 5 × 107 kg of Nd.  Furthermore, since the US consumes approximately 4 × 1012 kWh annually, this would require 2 × 1011 kWh, or 7.2 × 1014 kW, which would require the construction of 3.6 × 108 wind turbines, thus requiring 1.1 × 1010 kg of Nd.  This would require 1.105 × 1010 kg of NdFeB overall, or 2.9 × 109 kg of elemental Nd. Current estimates suggest that the Mountain Pass reserve contains 1.8 Mt of REM ores, of which 11.16% is neodymium oxide, Nd2O3, giving 1.7 × 108 kg of Nd. This is less than the potential demand, even before non renewable-energy uses of neodymium are factored in. Thus, from these rough calculations, it appears that the Mountain Pass reserves are insufficient to achieve America's renewable energy goals. If the United States wants to reduce its dependence on Chines REMs, it will need to develop more mines in addition to Mountain pass.
Even if the United States is able to develop its other REM reserves, it will be incredibly difficult to do so economically. As mentioned earlier, the very reason that Mountain Pass shut down was due to economic competition from China. Due to weaker safety and ecological impact restrictions, China is able to produce REMs at significantly lower prices. However, Molycorp officials are confident that carmakers and other clean-energy users will pay a higher premium for locally mined REMs, both as a commitment to environmental quality and national security.  However, if the United States want to mine a significant fraction of their REM demand locally, more extensive mining efforts are clearly necessary.
© Andrew Moir. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 K. Bradsher, "China Still Bans Rare Earth to Japan," New York Times, 10 Nov 10.
 N. G. Connelly et al., eds., Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005, (Royal Society of Chemistry,2005).
 M. Drak and L. A. Dobrzanski, "Corrosion of Nd-Fe-B Permanent Magnets," Journal of Achievements in Materials and Manufacturing Engineering, 20 239 (2007).
 J. F. Herbst, "Neodymium-Iron-Boron Permanent Magnets," Journal of Magnetism and Magnetic Materials 100, 57 (1991).
 W. D. Jones, "The Rare-Earth Bottleneck," IEEE Spectrum 47, 80 (2010).
 T. F. Chan and L. L. Lai, "An Axial-Flux Permanent-Magnet Synchronous Generator for a Direct Coupled Wind-Turbine System," IEEE Transactions on Energy Conversion 22, 86 (2007).
 D. Bartmann and D. Fink, Homebrew Wind Power: A Hands-on Guide to Harnessing the Wind, (Buckville Publications, 2009).
 E. Hau, Wind Turbines: Fundamentals, Technologies, Applications, Economics (Birkhauser, 2006).
 G. B. Haxel, J. B. Hedrick, G. J. Orris, "Rare Earth Elements-Critical Resources for High Technology," U.S. Geological Survey Fact Sheet 087-02, 20 Nov 02.
 D. J. Cordier, J. B. Hedrick, "2008 Minerals Yearbook: Rare Earths," US Geological Survey, October 2010.
 J. F. Papp et al., "Factors that influence the price of Al, Cd, Co, Cu, Fe, Ni, Pb, Rare Earth Elements, and Zn," U.S. Geological Survey Open-File Report 1356 (2008).
 M. Humphries, "Rare Earth Elements: The Global Supply Chain," Congressional Research Service Report R41347, 30 Sep 10.
 S. B. Castor, "Rare Earth Deposits of North America," Resource Geology 58, 337 (2008).
 L. Margonelli, "Clean Energy's Dirty Little Secret," The Atlantic, May 2009.
 V. Nelson, Wind Energy: Renewable Energy and the Environment, (CRC Press, 2009).
 M. Weissenbacher, Sources of Power: How Energy Forges Human History (ABC-CLIO, Inc., 2009).
 "Annual Energy Review 2009," U.S. Energy Information Agency.