## 1 Introduction
LREEs are light rare earth elements, also known as the cerium group: scandium (Sc), lanthanum (La), cerium (Ce), praseodymium (Pr), neodymium (Nd), promethium (Pm), samarium (Sm), europium (Eu), and gadolinium (Gd). 2. HREEs are heavy rare earth elements, also known as the yttrium group: yttrium (Y), terbium (Tb), dysprosium (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb), and lutetium (Lu). Occasionally, some of the heavier LREEs and lighter HREEs are placed in a separate group named MREEs (middle rare earth elements) [30; 31]. In mature markets, lanthanum and cerium represent 80% of the REEs. In the case of new markets, dysprosium, neodymium, and praseodymium make up 85% of the rare earths consumed [13; 18]. Despite the name, which may suggest that rare earths are rare and scarce, the abundance of REE in the Earth's crust is high, with the exception of promethium (Pm), which is only found as a by-product of the nuclear fission of uranium. The remaining elements are found in nature, although they can also be obtained synthetically in a laboratory. The abundance of REEs in the Earth's crust can be considered to be about 220 ppm, which is higher than the abundance, for example, of carbon (200 ppm) [32]. Table 1 shows the concentration in ppm of rare earths in the Earth's crust according to the most representative works [33; 34; 35; 36; 37; 38; 39]. For comparison, some of the REEs, such as cerium, neodymium, and yttrium, are much more abundant than lead. Thulium, which is the scarcest element of this group, is up to 200 times more abundant (\(\sim\)0.5 ppm) than platinum or gold [40; 41]. Although their presence in the crust is high, their concentration in the form of deposits is low and less common than most minerals [42], jthus it is rare to find large enough mineral deposits to make their extraction by conventional mining methods financially feasible [43; 44]. Rare earths do not occur in nature in an elemental form but are present in four geological environments: carbonates and alluvial deposits, which are the main source of production of LREEs, and alkaline igneous systems and deposits of ionic absorption clay, the main source of production of HREEs [42]. Their affinity for oxygen makes them appear as oxides, although other combinations are also possible [33]. The main minerals are monazite, bastasasite, xenotime, gadolinite, apatite, and zircon. Approximately 95% of REEs are found in the first three minerals [32]. Bastnasite, (La,Ce)CO\({}_{3}\)F, is a fluorocarbon rich in cerium and low in heavy REEs. It is found in metamorphic zones and pegmatites. Monazite, (Ce,La, Nd,Y,Th)PO\({}_{4}\), is an orthophosphate of REEs and thorium. Approximately 70% of its composition comprises oxides--between 20% and 30% of them are Ce\({}_{2}\)O\({}_{3}\), between 10% and 40% are La\({}_{2}\)O\({}_{3}\), and 5% are Y\({}_{2}\)O\({}_{3}\). The remaining elements comprise a significant presence of Nd, Pr, and Sm, as well as Dy, Er, and Ho in lower amounts. The thorium content ranges from 4% to 12%, and there is often some uranium present. Its deposits are acidic igneous and metamorphic rocks found as detrital mineral deposits in coastal and beach sands. Xenotime, YPO\({}_{4}\), is an yttrium orthophosphate with a concentration between 54% and 65% of HREE oxides, 1% LREEs, 3% ThO\({}_{2}\), 3% U\({}_{3}\)O\({}_{8}\), and between 2% and 3% ZrO\({}_{2}\). It is present in the same type of deposits as monazite, but it is much less abundant, with mixed deposits in which the content of xenotime between 0.5% and 5%. Table 2 displays the reserves according to the most reliable sources [32; 42; 45; 46]. It can be seen that there are differences between sources on similar dates; for example, in data corresponding to China, India, and Russia reserves. These deviations arise since there is no global system of classification of reserves; on the contrary, each country has its own definitions to determine the difference between reserves and contingent reserves, which makes them difficult to compare.