A series of rare-earth metals, from element 57 (lanthanum) through element 71 (lutetium). They have very similar chemistry, mainly forming compounds in which they are trivalent. They usually occur together in mixed oxides in nature, and are separated only with difficulty.

57 - lanthanum
58 - cerium
59 - praseodymium
60 - neodymium
61 - promethium
62 - samarium
63 - europium
64 - gadolinium
65 - terbium
66 - dysprosium
67 - holmium
68 - erbium
69 - thulium
70 - ytterbium
71 - lutetium
The Lanthanides are commonly known as rare earth metals, presumably due to their scarcity. They should not be confused with the higher-numbered (though similarly offset in the periodic table, a likely source for the confusion) actinide series, which are all radioactive; the only radioactive lanthanide is element 61, Promethium.

The "rare earth" lanthanide metals can be used to make very powerful magnets, since they have strong paramagnetic properties. When cooled to low temperatures, the rare earths have ferromagnetic properties as well.

To continue a point raised by Anark - the term ‘rare earth’, which is often used to describe the lanthanides, is rather misleading as many of the 4f elements are quite abundant. Cerium is the 26th most abundant element on the Earth, neodymium is more abundant than gold and even thulium (the least common lanthanide except for the radioactive promethium) is more abundant in the Earth’s crust than iodine. The phrase ‘rare earth’ was suggested by Johan Gadolin in 1794; "rare" because when the first of the rare earth elements were discovered they were thought to be present in the Earth's crust only in small amounts, and "earths" because as oxides they have an earthy appearance. The numerous chemical similarities between the rare earth elements meant that it took more than a century from the first discovery to complete isolation and classification. Significant production of rare earth elements began in the 1880s, with mining of the mineral monazite (a mixed lanthanide orthophosphate (LnPO4)) in Brazil. The other commercially important lanthanide containing mineral is bastnaesite, a fluorcarbonate (LnCO3F). The most common metals in both ores are (in order of decreasing abundance) cerium, lanthanum, neodymium and praseodymium, with monazite also containing up to 10% ThO2 as well as smaller quantities of the later lanthanides.

Source: "The f elements", N. Kaltsoyannis and P. Scott

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