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A rare-earth element (REE) or rare-earth metal (REM), as defined by the International Union of Pure and Applied Chemistry, is one of a set of seventeen chemical elements in the periodic table, specifically the fifteen lanthanides, as well as scandium and yttrium. Scandium and yttrium are considered rare-earth elements because they tend to occur in the same ore deposits as the lanthanides and exhibit similar chemical properties, but have different electronic and magnetic properties. Rarely, a broader definition that includes actinides may be used, since the actinides share some mineralogical, chemical, and physical (especially electron shell configuration) characteristics.

The 17 rare-earth elements are cerium (Ce), dysprosium (Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho), lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr), promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium (Tm), ytterbium (Yb), and yttrium (Y). They are often found in minerals with thorium (Th), and less commonly uranium (U). Despite their name, rare-earth elements are – with the exception of the radioactive promethium – relatively plentiful in Earth's crust, with cerium being the 25th most abundant element at 68 parts per million, more abundant than copper. However, because of their geochemical properties, rare-earth elements are typically dispersed and not often found concentrated in rare-earth minerals; as a result economically exploitable ore deposits are less common. The first rare-earth mineral discovered (1787) was gadolinite, a mineral composed of cerium, yttrium, iron, silicon, and other elements. This mineral was extracted from a mine in the village of Ytterby in Sweden; four of the rare-earth elements bear names derived from this single location.

A table listing the 17 rare-earth elements, their atomic number and symbol, the etymology of their names, and their main usages (see also Applications of lanthanides) is provided here. Some of the rare-earth elements are named after the scientists who discovered or elucidated their elemental properties, and some after their geographical discovery. The first rare-earth element discovered was the black mineral "ytterbite" (renamed to gadolinite in 1800). It was discovered by Lieutenant Carl Axel Arrhenius in 1787 at a quarry in the village of Ytterby, Sweden.

Arrhenius's "ytterbite" reached Johan Gadolin, a Royal Academy of Turku professor, and his analysis yielded an unknown oxide (earth) that he called yttria. Anders Gustav Ekeberg isolated beryllium from the gadolinite but failed to recognize other elements ore contained. After this discovery in 1794 a mineral from Bastnäs near Riddarhyttan, Sweden, which was believed to be an iron–tungsten mineral, was re-examined by Jöns Jacob Berzelius and Wilhelm Hisinger. In 1803 they obtained a white oxide and called it ceria. Martin Heinrich Klaproth independently discovered the same oxide and called it ochroia. Thus by 1803 there were two known rare-earth elements, yttrium and cerium, although it took another 30 years for researchers to determine that other elements were contained in the two ores ceria and yttria (the similarity of the rare-earth metals' chemical properties made their separation difficult).

In 1839 Carl Gustav Mosander, an assistant of Berzelius, separated ceria by heating the nitrate and dissolving the product in nitric acid. He called the oxide of the soluble salt lanthana. It took him three more years to separate the lanthana further into didymia and pure lanthana. Didymia, although not further separable by Mosander's techniques, was in fact still a mixture of oxides.

In 1842 Mosander also separated the yttria into three oxides: pure yttria, terbia and erbia (all the names are derived from the town name "Ytterby"). The earth giving pink salts he called terbium; the one that yielded yellow peroxide he called erbium. So in 1842 the number of known rare-earth elements had reached six: yttrium, cerium, lanthanum, didymium, erbium and terbium.

Nils Johan Berlin and Marc Delafontaine tried also to separate the crude yttria and found the same substances that Mosander obtained, but Berlin named (1860) the substance giving pink salts erbium, and Delafontaine named the substance with the yellow peroxide terbium. This confusion led to several false claims of new elements, such as the mosandrium of J. Lawrence Smith, or the philippium and decipium of Delafontaine. Due to the difficulty in separating the metals (and determining the separation is complete), the total number of false discoveries was dozens,[12][13] with some putting the total number of discoveries at over a hundred.

There were no further discoveries for 30 years, and the element didymium was listed in the periodic table of elements with a molecular mass of 138. In 1879 Delafontaine used the new physical process of optical flame spectroscopy and found several new spectral lines in didymia. Also in 1879, the new element samarium was isolated by Paul Émile Lecoq de Boisbaudran from the mineral samarskite. The samaria earth was further separated by Lecoq de Boisbaudran in 1886, and a similar result was obtained by Jean Charles Galissard de Marignac by direct isolation from samarskite. They named the element gadolinium after Johan Gadolin, and its oxide was named "gadolinia".

Further spectroscopic analysis between 1886 and 1901 of samaria, yttria, and samarskite by William Crookes, Lecoq de Boisbaudran and Eugène-Anatole Demarçay yielded several new spectroscopic lines that indicated the existence of an unknown element. The fractional crystallization of the oxides then yielded europium in 1901. In 1839 the third source for rare earths became available. This is a mineral similar to gadolinite, uranotantalum (now called "samarskite"). This mineral from Miass in the southern Ural Mountains was documented by Gustav Rose. The Russian chemist R. Harmann proposed that a new element he called "ilmenium" should be present in this mineral, but later, Christian Wilhelm Blomstrand, Galissard de Marignac, and Heinrich Rose found only tantalum and niobium (columbium) in it.

The exact number of rare-earth elements that existed was highly unclear, and a maximum number of 25 was estimated. The use of X-ray spectra (obtained by X-ray crystallography) by Henry Gwyn Jeffreys Moseley made it possible to assign atomic numbers to the elements. Moseley found that the exact number of lanthanides had to be 15, and that element 61 had yet to be discovered. Using these facts about atomic numbers from X-ray crystallography, Moseley also showed that hafnium (element 72) would not be a rare-earth element. Moseley was killed in World War I in 1915, years before hafnium was discovered. Hence, the claim of Georges Urbain that he had discovered element 72 was untrue. Hafnium is an element that lies in the periodic table immediately below zirconium, and hafnium and zirconium are very similar in their chemical and physical properties.

During the 1940s, Frank Spedding and others in the United States (during the Manhattan Project) developed the chemical ion-exchange procedures for separating and purifying the rare-earth elements. This method was first applied to the actinides for separating plutonium-239 and neptunium from uranium, thorium, actinium, and the other actinides in the materials produced in nuclear reactors. The plutonium-239 was very desirable because it is a fissile material.

The principal sources of rare-earth elements are the minerals bastnäsite, monazite, and loparite and the lateritic ion-adsorption clays. Despite their high relative abundance, rare-earth minerals are more difficult to mine and extract than equivalent sources of transition metals (due in part to their similar chemical properties), making the rare-earth elements relatively expensive. Their industrial use was very limited until efficient separation techniques were developed, such as ion exchange, fractional crystallization and liquid–liquid extraction during the late 1950s and early 1960s. Some ilmenite concentrates contain small amounts scandium and other rare-earth elements, which could be analysed by XRF.

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