Editing Rare-earth element (section)

==Geochemistry==
The REE geochemical classification is usually done on the basis of their [[atomic weight]]. One of the most common classifications divides REE into 3 groups: light rare earths (LREE - from <sub>57</sub>La to <sub>60</sub>Nd), intermediate (MREE - from <sub>62</sub>Sm to <sub>67</sub>Ho) and heavy (HREE - from <sub>68</sub>Er to <sub>71</sub>Lu). REE usually appear as trivalent ions, except for Ce and Eu which can take the form of Ce<sup>4+</sup> and Eu<sup>2+</sup> depending on the redox conditions of the system. Consequentially, REE are characterized by a substantial identity in their chemical reactivity, which results in a serial behaviour during geochemical processes rather than being characteristic of a single element of the series. Sc, Y, and Lu can be electronically distinguished from the other rare earths because they do not have ''f'' valence electrons, whereas the others do, but the chemical behaviour is almost the same.

A distinguishing factor in the geochemical behaviour of the REE is linked to the so-called "[[lanthanide contraction]]" which represents a higher-than-expected decrease in the atomic/ionic radius of the elements along the series. This is determined by the variation of the [[shielding effect]] towards the nuclear charge due to the progressive filling of the 4''f'' orbital which acts against the electrons of the 6''s'' and 5''d'' orbitals. The lanthanide contraction has a direct effect on the geochemistry of the lanthanides, which show a different behaviour depending on the systems and processes in which they are involved.<ref name="auto1">{{cite journal |last=Bau |first=Michael |date=1996-04-01 |title=Controls on the fractionation of isovalent trace elements in magmatic and aqueous systems: evidence from Y/Ho, Zr/Hf, and lanthanide tetrad effect |journal=Contributions to Mineralogy and Petrology |language=en |volume=123 |issue=3 |pages=323–333 |doi=10.1007/s004100050159 |bibcode=1996CoMP..123..323B |s2cid=97399702 |issn=1432-0967}}</ref> 

The effect of the lanthanide contraction can be observed in the REE behaviour both in a CHARAC-type geochemical system (CHArge-and-RAdius-Controlled<ref name="auto1"/>) where elements with similar charge and radius should show coherent geochemical behaviour, and in non-CHARAC systems, such as aqueous solutions, where the electron structure is also an important parameter to consider as the lanthanide contraction affects the [[ionic potential]]. A direct consequence is that, during the formation of coordination bonds, the REE behaviour gradually changes along the series. Furthermore, the lanthanide contraction causes the ionic radius of Ho<sup>3+</sup> (0.901 Å) to be almost identical to that of Y<sup>3+</sup> (0.9 Å), justifying the inclusion of the latter among the REE.

===Applications===
The application of rare-earth elements to geology is important to understanding the petrological processes of [[igneous rock|igneous]], [[sedimentary rock|sedimentary]] and [[metamorphic rock|metamorphic]] rock formation. In [[geochemistry]], rare-earth elements can be used to infer the petrological mechanisms that have affected a rock due to the subtle [[atomic radius|atomic size]] differences between the elements, which causes preferential [[fractional crystallization (geology)|fractionation]] of some rare earths relative to others depending on the processes at work.

The geochemical study of the REE is not carried out on absolute concentrations – as it is usually done with other chemical elements – but on normalized concentrations in order to observe their serial behaviour. In geochemistry, rare-earth elements are typically presented in normalized "spider" diagrams, in which concentration of rare-earth elements are normalized to a reference standard and are then expressed as the logarithm to the base 10 of the value.

Commonly, the rare-earth elements are normalized to [[chondrite|chondritic meteorites]], as these are believed to be the closest representation of [[fractional crystallization (geology)|unfractionated]] Solar System material. However, other normalizing standards can be applied depending on the purpose of the study. Normalization to a standard reference value, especially of a material believed to be unfractionated, allows the observed abundances to be compared to the initial abundances of the element. Normalization also removes the pronounced 'zig-zag' pattern caused by the differences in abundance between even and odd [[atomic number]]s. Normalization is carried out by dividing the analytical concentrations of each element of the series by the concentration of the same element in a given standard, according to the equation:
:<math>[\text{REE}_i]_n = \frac{[\text{REE}_i]_\text{sam}}{[\text{REE}_i]_\text{std}}</math>

where '''''n''''' indicates the normalized concentration, <math>{[\text{REE}_i]_\text{sam}}</math> the analytical concentration of the element measured in the sample, and <math>{[\text{REE}_i]_\text{ref}}</math> the concentration of the same element in the reference material.<ref>{{cite journal |last1=Alibo |first1=Dia Sotto |last2=Nozaki |first2=Yoshiyuki |date=1999-02-01 |title=Rare earth elements in seawater: particle association, shale-normalization, and Ce oxidation |url=https://www.sciencedirect.com/science/article/pii/S0016703798002798 |journal=Geochimica et Cosmochimica Acta |language=en |volume=63 |issue=3 |pages=363–372 |doi=10.1016/S0016-7037(98)00279-8 |bibcode=1999GeCoA..63..363S |issn=0016-7037|url-access=subscription }}</ref>

It is possible to observe the serial trend of the REE by reporting their normalized concentrations against the atomic number. The trends that are observed in "spider" diagrams are typically referred to as "patterns", which may be diagnostic of petrological processes that have affected the material of interest.<ref name="Rollinson"/>

According to the general shape of the patterns or thanks to the presence (or absence) of so-called "anomalies", information regarding the system under examination and the occurring geochemical processes can be obtained. The anomalies represent enrichment (positive anomalies) or depletion (negative anomalies) of specific elements along the series and are graphically recognizable as positive or negative "peaks" along the REE patterns. The anomalies can be numerically quantified as the ratio between the normalized concentration of the element showing the anomaly and the predictable one based on the average of the normalized concentrations of the two elements in the previous and next position in the series, according to the equation:
:<math>\frac{\text{REE}_i}{\text{REE}_i^*} = \frac{[\text{REE}_i]_n \times 2}{[\text{REE}_{i-1}]_n + [\text{REE}_{i+1}]_n}</math>

where <math>[\text{REE}_i]_n</math> is the normalized concentration of the element whose anomaly has to be calculated, <math>[\text{REE}_{i-1}]_n</math> and <math>[\text{REE}_{i+1}]_n</math> the normalized concentrations of the respectively previous and next elements along the series.

The rare-earth elements patterns observed in igneous rocks are primarily a function of the chemistry of the source where the rock came from, as well as the fractionation history the rock has undergone.<ref name=Rollinson/> Fractionation is in turn a function of the [[partition coefficient]]s of each element. Partition coefficients are responsible for the fractionation of trace elements (including rare-earth elements) into the liquid phase (the melt/magma) into the solid phase (the mineral). If an element preferentially remains in the solid phase it is termed 'compatible', and if it preferentially partitions into the melt phase it is described as 'incompatible'.<ref name=Rollinson/> Each element has a different partition coefficient, and therefore fractionates into solid and liquid phases distinctly. These concepts are also applicable to metamorphic and sedimentary petrology.

In igneous rocks, particularly in [[felsic]] melts, the following observations apply: anomalies in europium are dominated by the crystallization of [[feldspar]]s. [[Hornblende]], controls the enrichment of MREE compared to LREE and HREE. Depletion of LREE relative to HREE may be due to the crystallization of [[olivine]], [[pyroxene|orthopyroxene]], and [[pyroxene|clinopyroxene]]. On the other hand, the depletion of HREE relative to LREE may be due to the presence of [[garnet]], as garnet preferentially incorporates HREE into its crystal structure. The presence of [[zircon]] may also cause a similar effect.<ref name=Rollinson/>

In sedimentary rocks, rare-earth elements in [[clastic rock|clastic sediments]] are a representation of provenance. The rare-earth element concentrations are not typically affected by sea and river waters, as rare-earth elements are insoluble and thus have very low concentrations in these fluids. As a result, when sediment is transported, rare-earth element concentrations are unaffected by the fluid and instead the rock retains the rare-earth element concentration from its source.<ref name=Rollinson/>

Sea and river waters typically have low rare-earth element concentrations. However, aqueous geochemistry is still very important. In oceans, rare-earth elements reflect input from rivers, [[hydrothermal vent]]s, and [[aeolian processes|aeolian]] sources;<ref name=Rollinson/> this is important in the investigation of ocean mixing and circulation.<ref name=gsl>{{cite web |author=Working Group |url=https://www.geolsoc.org.uk/~/media/shared/documents/policy/Rare%20Earth%20Elements%20briefing%20note%20final%20%20%20new%20format.pdf |title=Rare Earth Elements |date=December 2011 |publisher=Geological Society of London |access-date=18 May 2018 |archive-date=February 9, 2022 |archive-url=https://web.archive.org/web/20220209233309/https://www.geolsoc.org.uk/~/media/shared/documents/policy/Rare%20Earth%20Elements%20briefing%20note%20final%20%20%20new%20format.pdf |url-status=live}}</ref>

Rare-earth elements are also useful for dating rocks, as some [[radioactive isotope]]s display long half-lives. Of particular interest are the {{sup|138}}La-{{sup|138}}Ce, [[samarium-147|{{sup|147}}Sm]]-{{sup|143}}Nd, and {{sup|176}}Lu-{{sup|176}}Hf systems.<ref name=gsl/>