Electron shell

From Wikipedia, the free encyclopedia

In chemistry and atomic physics, an electron shell, or a principal energy level, may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond with the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with letters used in the X-ray notation (K, L, M, …).

Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n²) electrons. Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: atoms may have two or even three incomplete outer shells. For an explanation of why electrons exist in these shells see electron configuration.

The electrons in the outermost occupied shell (or shells) determine the chemical properties of the atom; it is called the valence shell.

Each shell consists of one or more subshells, and each subshell consists of one or more atomic orbitals.

History

The shell terminology comes from Arnold Sommerfeld's modification of the Bohr model. Sommerfeld retained Bohr's planetary model, but added mildly elliptical orbits (characterized by additional quantum numbers ℓ and m) to explain the fine spectroscopic structure of some elements. The multiple electrons with the same principal quantum number (n) had close orbits that formed a "shell" of positive thickness instead of the infinitely thin circular orbit of Bohr's model.

The existence of electron shells was first observed experimentally in Charles Barkla's and Henry Moseley's X-ray absorption studies. Barkla labeled them with the letters K, L, M, N, O, P, and Q. The origin of this terminology was alphabetic. A "J" series was also suspected, though later experiments indicated that the K absorption lines are produced by the innermost electrons. These letters were later found to correspond to the n values 1, 2, 3, etc. They are used in the spectroscopic Siegbahn notation.

The physical chemist Gilbert Lewis was responsible for much of the early development of the theory of the participation of valence shell electrons in chemical bonding. Linus Pauling later generalized and extended the theory while applying insights from quantum mechanics.

Shells

The electron shells are labeled K, L, M, N, O, P, and Q; or 1, 2, 3, 4, 5, 6, and 7; going from innermost shell outwards. Electrons in outer shells have higher average energy and travel farther from the nucleus than those in inner shells. This makes them more important in determining how the atom reacts chemically and behaves as a conductor, because the pull of the atom's nucleus upon them is weaker and more easily broken. In this way, a given element's reactivity is highly dependent upon its electronic configuration.

Subshells

Each shell is composed of one or more subshells, which are themselves composed of atomic orbitals. For example, the first (K) shell has one subshell, called 1s; the second (L) shell has two subshells, called 2s and 2p; the third shell has 3s, 3p, and 3d; the fourth shell has 4s, 4p, 4d and 4f; the fifth shell has 5s, 5p, 5d, and 5f and can theoretically hold more in the 5g subshell that is not occupied in the ground-state electron configuration of any known element. The various possible subshells are shown in the following table:

Subshell label	ℓ	Max electrons	Shells containing it	Historical name
s	0	2	Every shell	sharp
p	1	6	2nd shell and higher	principal
d	2	10	3rd shell and higher	diffuse
f	3	14	4th shell and higher	fundamental
g	4	18	5th shell and higher (theoretically)	(next in alphabet after f, excluding j)

• The first column is the "subshell label", a lowercase-letter label for the type of subshell. For example, the "4s subshell" is a subshell of the fourth (N) shell, with the type (s) described in the first row.
• The second column is the azimuthal quantum number (ℓ) of the subshell. The precise definition involves quantum mechanics, but it is a number that characterizes the subshell.
• The third column is the maximum number of electrons that can be put into a subshell of that type. For example, the top row says that each s-type subshell (1s, 2s, etc.) can have at most two electrons in it. In each case the figure is 4 greater than the one above it.
• The fourth column says which shells have a subshell of that type. For example, looking at the top two rows, every shell has an s subshell, while only the second shell and higher have a p subshell (i.e., there is no "1p" subshell).
• The final column gives the historical origin of the labels s, p, d, and f. They come from early studies of atomic spectral lines. The other labels, namely g, h and i, are an alphabetic continuation following the last historically originated label of f.

Although it is commonly stated that all the electrons in a shell have the same energy, this is an approximation. However, the electrons in one subshell do have exactly the same level of energy, with later subshells having more energy per electron than earlier ones. This effect is great enough that the energy ranges associated with shells can overlap.

Number of electrons in each shell

Shells and subshells. 1 rectangular triangle (1/2 of a cell) = 1 electron on the level. Red color indicates sublevel s; orange - p; yellow - d; green - f; blue - g; indigo - h; violet - i

 

Shell name	Subshell name	Subshell max electrons	Shell max electrons
K	1s	2	2
L	2s	2	2 + 6 = 8
	2p	6
M	3s	2	2 + 6 + 10 = 18
	3p	6
	3d	10
N	4s	2	2 + 6 + 10 + 14 = 32
	4p	6
	4d	10
	4f	14
O	5s	2	2 + 6 + 10 + 14 + 18 = 50
	5p	6
	5d	10
	5f	14
	5g	18

Each subshell is constrained to hold 4ℓ + 2 electrons at most, namely:

• Each s subshell holds at most 2 electrons
• Each p subshell holds at most 6 electrons
• Each d subshell holds at most 10 electrons
• Each f subshell holds at most 14 electrons
• Each g subshell holds at most 18 electrons

Therefore, the K shell, which contains only an s subshell, can hold up to 2 electrons; the L shell, which contains an s and a p, can hold up to 2 + 6 = 8 electrons, and so forth; in general, the nth shell can hold up to 2n² electrons.

Although that formula gives the maximum in principle, in fact that maximum is only achieved (by known elements) for the first four shells (K, L, M, N). No known element has more than 32 electrons in any one shell. This is because the subshells are filled according to the Aufbau principle. The first elements to have more than 32 electrons in one shell would belong to the g-block of period 8 of the periodic table. These elements would have some electrons in their 5g subshell and thus have more than 32 electrons in the O shell (fifth principal shell).

Valence shell

The valence shell is the outermost shell of an atom. Valence electrons in non-transition metal elements reside in this shell. Such elements with complete valence shells (noble gases) are the most chemically non-reactive, while those with only one electron in their valence shells (alkali metals) or just missing one electron from having a complete shell (halogens) are the most reactive.

However, this terminology is somewhat misleading in the case of transition metals. In these elements, a valence electron can also be in an inner shell. Thus, the electrons that determine how an atom reacts chemically are those that travel farthest from the nucleus, that is, those with the highest energy, and not necessarily in the valence shell.

Lanthanide

From Wikipedia, the free encyclopedia

The lanthanide (/ˈlænθənaɪd/) or lanthanoid (/ˈlænθənɔɪd/) series of chemical elements comprises the 15 metallic chemical elements with atomic numbers 57 through 71, from lanthanum through lutetium. These elements, along with the chemically similar elements scandium and yttrium, are often collectively known as the rare earth elements.

The informal chemical symbol Ln is used in general discussions of lanthanide chemistry to refer to any lanthanide. All but one of the lanthanides are f-block elements, corresponding to the filling of the 4f electron shell; depending on the source, either lanthanum or lutetium is considered a d-block element, but is included due to its chemical similarities with the other 14. All lanthanide elements form trivalent cations, Ln³⁺, whose chemistry is largely determined by the ionic radius, which decreases steadily from lanthanum to lutetium.

They are called lanthanides because the elements in the series are chemically similar to lanthanum. Both lanthanum and lutetium have been labeled as group 3 elements, because they have a single valence electron in the 5d shell. However, both elements are often included in discussions of the chemistry of lanthanide elements. Lanthanum is the more often omitted of the two, because its placement as a group 3 element is somewhat more common in texts and for semantic reasons: since "lanthanide" means "like lanthanum", it has been argued that lanthanum cannot logically be a lanthanide, but IUPAC acknowledges its inclusion based on common usage.

In presentations of the periodic table, the lanthanides and the actinides are customarily shown as two additional rows below the main body of the table, with placeholders or else a selected single element of each series (either lanthanum and actinium, or lutetium and lawrencium) shown in a single cell of the main table, between barium and hafnium, and radium and rutherfordium, respectively. This convention is entirely a matter of aesthetics and formatting practicality; a rarely used wide-formatted periodic table inserts the lanthanide and actinide series in their proper places, as parts of the table's sixth and seventh rows (periods).

The 1985 International Union of Pure and Applied Chemistry “Red Book” (p. 45) recommends that "lanthanoid" is used rather than "lanthanide". The ending “-ide” normally indicates a negative ion. However, owing to wide current use, “lanthanide” is still allowed.

Etymology

Together with the two elements at the top of group 3, scandium and yttrium, the trivial name "rare earths" is sometimes used to describe all the lanthanides; a definition of rare earths including the group 3, lanthanide, and actinide elements is also occasionally seen, and rarely Sc + Y + lanthanides + thorium. The "earth" in the name "rare earths" arises from the minerals from which they were isolated, which were uncommon oxide-type minerals. However, the use of the name is deprecated by IUPAC, as the elements are neither rare in abundance nor "earths" (an obsolete term for water-insoluble strongly basic oxides of electropositive metals incapable of being smelted into metal using late 18th century technology). Group 2 is known as the alkaline earth elements for much the same reason. 

The "rare" in the "rare earths" name has much more to do with the difficulty of separating out each of the individual lanthanide elements than scarcity of any of them. By way of the Greek "dysprositos" for "hard to get at," element 66, dysprosium was similarly named; lanthanum itself is named after a word for "hidden." The elements 57 (La) to 71 (Lu) are very similar chemically to one another and frequently occur together in nature, often anywhere from three to all 15 of the lanthanides (along with yttrium as a 16th) occur in minerals such as samarskite, monazite and many others which can also contain the other two group 3 elements as well as thorium and occasionally other actinides as well. A majority of the rare earths were discovered at the same mine in Ytterby, Sweden and four of them are named (yttrium, ytterbium, erbium, terbium) after the city and a fifth *(holmium) after Stockholm; scandium is named after Scandinavia, thulium after the old name Thule, and the immediately-following group 4 element (number 72) hafnium is named for the Latin name of the city of Copenhagen.

Samarskite (a mineral which is the source of the name of the element samarium) and other similar minerals in particular also have these elements in association with the nearby metals tantalum, niobium, hafnium, zirconium, vanadium, and titanium, from group 4 and group 5 often in similar oxidation states. Monazite is a phosphate of numerous group 3 + lanthanide + actinide metals and mined especially for the thorium content and specific rare earths especially lanthanum, yttrium and cerium. Cerium and lanthanum as well as other members of the rare earth series are often produced as a metal called mischmetal containing a variable mixture of the these elements with cerium and lanthanum predominating; it has direct uses such as lighter flints and other spark sources which do not require extensive purification of one of these metals. There are also rare earth-bearing minerals based on group 2 elements such as yttrocalcite, yttrocerite, yttrofluorite which vary in content of yttrium, cerium, and lanthanum in a particular as well as varying amounts of the others. Other lanthanide/rare earth minerals include bastnäsite, florencite, chernovite, perovskite, xenotime, cerite, gadolinite, lanthanite, fergusonite, polycrase, blomstrandine, håleniusite, miserite, loparite, lepersonnite, euxenite, all of which have a range of relative element concentration and may have the symbol of a predominating one such as monazite-ce; group 3 elements do not occur as native element minerals in the fashion of gold, silver, tantalum and many others on earth but may in lunar regolith. Very rare cerium, lanthanum, and presumably other lanthanide/group 3 halides, feldspars and garnets are also known to exist.

All of this is the result of the order in which the electron shells of these elements are filled -- the outermost has the same configuration for all of them, and a deeper shell is progressively filled with electrons as the atomic number increases from 57 towards 71. For many years, mixtures of more than one rare earth were considered to be single elements, such as neodymium and praseodymium being thought to be the single element didymium and so on. Very small differences in solubility are used in solvent and ion-exchange purification methods for these elements which require a great deal of repeating to get a purified metal. The refined metals and their compounds have subtle and stark differences amongst themselves in electronic, electrical, optical, and magnetic properties which account for their many niche uses.

By way of examples of the term meaning the above considerations rather than their scarcity, cerium is the 26th most abundant element in the Earth's crust and more abundant than copper, neodymium is more abundant than gold; thulium (the second least common naturally occurring lanthanide) is more abundant than iodine, which is itself common enough for biology to have evolved critical usages thereof, and even the lone radioactive element in the series, promethium, is more common than the two rarest naturally occurring elements, francium and astatine, combined. Despite their abundance, even the technical term "lanthanides" could be interpreted to reflect a sense of elusiveness on the part of these elements, as it comes from the Greek λανθανειν (lanthanein), "to lie hidden". However, if not referring to their natural abundance, but rather to their property of "hiding" behind each other in minerals, this interpretation is in fact appropriate. The etymology of the term must be sought in the first discovery of lanthanum, at that time a so-called new rare earth element "lying hidden" in a cerium mineral, and it is an irony that lanthanum was later identified as the first in an entire series of chemically similar elements and could give name to the whole series. The term "lanthanide" was introduced by Victor Goldschmidt in 1925.

Physical properties of the elements

Gschneider and Daane (1988) attribute the trend in melting point which increases across the series, (lanthanum (920 °C) – lutetium (1622 °C)) to the extent of hybridization of the 6s, 5d, and 4f orbitals. The hybridization is believed to be at its greatest for cerium, which has the lowest melting point of all, 795 °C. The lanthanide metals are soft; their hardness increases across the series. Europium stands out, as it has the lowest density in the series at 5.24 g/cm³ and the largest metallic radius in the series at 208.4 pm. It can be compared to barium, which has a metallic radius of 222 pm. It is believed that the metal contains the larger Eu²⁺ ion and that there are only two electrons in the conduction band. Ytterbium also has a large metallic radius, and a similar explanation is suggested. The resistivities of the lanthanide metals are relatively high, ranging from 29 to 134 μΩ·cm. These values can be compared to a good conductor such as aluminium, which has a resistivity of 2.655 μΩ·cm. With the exceptions of La, Yb, and Lu (which have no unpaired f electrons), the lanthanides are strongly paramagnetic, and this is reflected in their magnetic susceptibilities. Gadolinium becomes ferromagnetic at below 16 °C (Curie point). The other heavier lanthanides – terbium, dysprosium, holmium, erbium, thulium, and ytterbium – become ferromagnetic at much lower temperatures.

Chemistry and compounds

The colors of lanthanide complexes originate almost entirely from charge transfer interactions between the metal and the ligand. f → f transitions are symmetry forbidden (or Laporte-forbidden), which is also true of transition metals. However, transition metals are able to use vibronic coupling to break this rule. The valence orbitals in lanthanides are almost entirely non-bonding and as such little effective vibronic coupling takes, hence the spectra from f → f transitions are much weaker and narrower than those from d → d transitions. In general this makes the colors of lanthanide complexes far fainter than those of transition metal complexes. f→f transitions are not possible for the f¹ and f¹³ configurations of Ce³⁺ and Yb³⁺ and thus these ions are colorless in aqueous solution.

Effect of 4f orbitals

Going across the lanthanides in the periodic table, the 4f orbitals are usually being filled. The effect of the 4f orbitals on the chemistry of the lanthanides is profound and is the factor that distinguishes them from the transition metals. There are seven 4f orbitals, and there are two different ways in which they are depicted: as a "cubic set" or as a general set. The cubic set is f_z³, f_xz², f_yz², f_xyz, f_z(x²−y²), f_{x(x²−3y²)} and f_{y(3x²−y²)}. The 4f orbitals penetrate the [Xe] core and are isolated, and thus they do not participate in bonding. This explains why crystal field effects are small and why they do not form π bonds. As there are seven 4f orbitals, the number of unpaired electrons can be as high as 7, which gives rise to the large magnetic moments observed for lanthanide compounds. Measuring the magnetic moment can be used to investigate the 4f electron configuration, and this is a useful tool in providing an insight into the chemical bonding. The lanthanide contraction, i.e. the reduction in size of the Ln³⁺ ion from La³⁺ (103 pm) to Lu³⁺ (86.1 pm), is often explained by the poor shielding of the 5s and 5p electrons by the 4f electrons.

Lanthanide oxides: clockwise from top center: praseodymium, cerium, lanthanum, neodymium, samarium and gadolinium.

 

The electronic structure of the lanthanide elements, with minor exceptions, is [Xe]6s²4fⁿ. The chemistry of the lanthanides is dominated by the +3 oxidation state, and in Ln^III compounds the 6s electrons and (usually) one 4f electron are lost and the ions have the configuration [Xe]4f^m. All the lanthanide elements exhibit the oxidation state +3. In addition, Ce³⁺ can lose its single f electron to form Ce⁴⁺ with the stable electronic configuration of xenon. Also, Eu³⁺ can gain an electron to form Eu²⁺ with the f⁷ configuration that has the extra stability of a half-filled shell. Other than Ce(IV) and Eu(II), none of the lanthanides are stable in oxidation states other than +3 in aqueous solution. Promethium is effectively a man-made element, as all its isotopes are radioactive with half-lives shorter than 20 years.

In terms of reduction potentials, the Ln^0/3+ couples are nearly the same for all lanthanides, ranging from −1.99 (for Eu) to −2.35 V (for Pr). Thus these metals are highly reducing, with reducing power similar to alkaline earth metals such as Mg (−2.36 V).

Lanthanide oxidation states

All of the lanthanide elements are commonly known to have the +3 oxidation state and it was thought that only samarium, europium, and ytterbium had the +2 oxidation readily accessible in solution. Now, it is known that all of the lanthanides can form +2 complexes in solution.

 

The ionization energies for the lanthanides can be compared with aluminium. In aluminium the sum of the first three ionization energies is 5139 kJ·mol⁻¹, whereas the lanthanides fall in the range 3455 – 4186 kJ·mol⁻¹. This correlates with the highly reactive nature of the lanthanides.

The sum of the first two ionization energies for europium, 1632 kJ·mol⁻¹ can be compared with that of barium 1468.1 kJ·mol⁻¹ and europium's third ionization energy is the highest of the lanthanides. The sum of the first two ionization energies for ytterbium are the second lowest in the series and its third ionization energy is the second highest. The high third ionization energy for Eu and Yb correlate with the half filling 4f⁷ and complete filling 4f¹⁴ of the 4f subshell, and the stability afforded by such configurations due to exchange energy. Europium and ytterbium form salt like compounds with Eu²⁺ and Yb²⁺, for example the salt like dihydrides. Both europium and ytterbium dissolve in liquid ammonia forming solutions of Ln²⁺(NH₃)_x again demonstrating their similarities to the alkaline earth metals.

The relative ease with which the 4th electron can be removed in cerium and (to a lesser extent praseodymium) indicates why Ce(IV) and Pr(IV) compounds can be formed, for example CeO₂ is formed rather than Ce₂O₃ when cerium reacts with oxygen.

Separation of lanthanides

The similarity in ionic radius between adjacent lanthanide elements makes it difficult to separate them from each other in naturally occurring ores and other mixtures. Historically, the very laborious processes of cascading and fractional crystallization were used. Because the lanthanide ions have slightly different radii, the lattice energy of their salts and hydration energies of the ions will be slightly different, leading to a small difference in solubility. Salts of the formula Ln(NO₃)₃·2NH₄NO₃·4H₂O can be used. Industrially, the elements are separated from each other by solvent extraction. Typically an aqueous solution of nitrates is extracted into kerosene containing tri-n-butylphosphate. The strength of the complexes formed increases as the ionic radius decreases, so solubility in the organic phase increases. Complete separation can be achieved continuously by use of countercurrent exchange methods. The elements can also be separated by ion-exchange chromatography, making use of the fact that the stability constant for formation of EDTA complexes increases for log K ≈ 15.5 for [La(EDTA)]⁻ to log K ≈ 19.8 for [Lu(EDTA)]⁻.

Coordination chemistry and catalysis

When in the form of coordination complexes, lanthanides exist overwhelmingly in their +3 oxidation state, although particularly stable 4f configurations can also give +4 (Ce, Tb) or +2 (Eu, Yb) ions. All of these forms are strongly electropositive and thus lanthanide ions are hard Lewis acids. The oxidation states are also very stable; with the exceptions of SmI₂ and cerium(IV) salts, lanthanides are not used for redox chemistry. 4f electrons have a high probability of being found close to the nucleus and are thus strongly affected as the nuclear charge increases across the series; this results in a corresponding decrease in ionic radii referred to as the lanthanide contraction. 

The low probability of the 4f electrons existing at the outer region of the atom or ion permits little effective overlap between the orbitals of a lanthanide ion and any binding ligand. Thus lanthanide complexes typically have little or no covalent character and are not influenced by orbital geometries. The lack of orbital interaction also means that varying the metal typically has little effect on the complex (other than size), especially when compared to transition metals. Complexes are held together by weaker electrostatic forces which are omni-directional and thus the ligands alone dictate the symmetry and coordination of complexes. Steric factors therefore dominate, with coordinative saturation of the metal being balanced against inter-ligand repulsion. This results in a diverse range of coordination geometries, many of which are irregular, and also manifests itself in the highly fluxional nature of the complexes. As there is no energetic reason to be locked into a single geometry, rapid intramolecular and intermolecular ligand exchange will take place. This typically results in complexes that rapidly fluctuate between all possible configurations. 

Many of these features make lanthanide complexes effective catalysts. Hard Lewis acids are able to polarise bonds upon coordination and thus alter the electrophilicity of compounds, with a classic example being the Luche reduction. The large size of the ions coupled with their labile ionic bonding allows even bulky coordinating species to bind and dissociate rapidly, resulting in very high turnover rates; thus excellent yields can often be achieved with loadings of only a few mol%. The lack of orbital interactions combined with the lanthanide contraction means that the lanthanides change in size across the series but that their chemistry remains much the same. This allows for easy tuning of the steric environments and examples exist where this has been used to improve the catalytic activity of the complex and change the nuclearity of metal clusters.

Despite this, the use of lanthanide coordination complexes as homogeneous catalysts is largely restricted to the laboratory and there are currently few examples them being used on an industrial scale. It should be noted however, that lanthanides exist in many forms other that coordination complexes and many of these are industrially useful. In particular lanthanide metal oxides are used as heterogeneous catalysts in various industrial processes.

Ln(III) compounds

The trivalent lanthanides mostly form ionic salts. The trivalent ions are hard acceptors and form more stable complexes with oxygen-donor ligands than with nitrogen-donor ligands. The larger ions are 9-coordinate in aqueous solution, [Ln(H₂O)₉]³⁺ but the smaller ions are 8-coordinate, [Ln(H₂O)₈]³⁺. There is some evidence that the later lanthanides have more water molecules in the second coordination sphere. Complexation with monodentate ligands is generally weak because it is difficult to displace water molecules from the first coordination sphere. Stronger complexes are formed with chelating ligands because of the chelate effect, such as the tetra-anion derived from 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (DOTA). 

Samples of lanthanide nitrates in their hexahydrate form. From left to right: La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu.

Ln(II) and Ln(IV) compounds

The most common divalent derivatives of the lanthanides are for Eu(II), which achieves a favorable f⁷ configuration. Divalent halide derivatives are known for all of the lanthanides. They are either conventional salts or are Ln(III) "electride"-like salts. The simple salts include YbI₂, EuI₂, and SmI₂. The electride-like salts, described as Ln³⁺, 2I⁻, e⁻, include LaI₂, CeI₂ and GdI₂. Many of the iodides form soluble complexes with ethers, e.g. TmI₂(dimethoxyethane)₃. Samarium(II) iodide is a useful reducing agent. Ln(II) complexes can be synthesized by transmetalation reactions. The normal range of oxidation states can be expanded via the use of sterically bulky cyclopentadienyl ligands, in this way many lanthanides can be isolated as Ln(II) compounds.

Ce(IV) in ceric ammonium nitrate is a useful oxidizing agent. Otherwise tetravalent lanthanides are rare. The Ce(IV) is the exception owing to the tendency to form an unfilled f shell.

Hydrides

Lanthanide metals react exothermically with hydrogen to form LnH₂, dihydrides. With the exception of Eu and Yb which resemble the Ba and Ca hydrides (non conducting, transparent salt like compounds) they form black pyrophoric, conducting compounds where the metal sub-lattice is face centred cubic and the H atoms occupy tetrahedral sites. Further hydrogenation produces a trihydride which is non-stoichiometric, non-conducting, more salt like. The formation of trihydride is associated with and increase in 8–10% volume and this is linked to greater localization of charge on the hydrogen atoms which become more anionic (H⁻ hydride anion) in character.

Halides

The only tetrahalides known are the tetrafluorides of cerium, praseodymium, terbium, neodymium and dysprosium, the last two known only under matrix isolation conditions. All of the lanthanides form trihalides with fluorine, chlorine, bromine and iodine. They are all high melting and predominantly ionic in nature. The fluorides are only slightly soluble in water and are not sensitive to air, and this contrasts with the other halides which are air sensitive, readily soluble in water and react at high temperature to form oxohalides. The trihalides were important as pure metal can be prepared from them. In the gas phase the trihalides are planar or approximately planar, the lighter lanthanides have a lower % of dimers, the heavier lanthanides a higher proportion. The dimers have a similar structure to Al₂Cl₆.

Some of the dihalides are conducting while the rest are insulators. The conducting forms can be considered as Ln^III electride compounds where the electron is delocalised into a conduction band, Ln³⁺ (X⁻)₂(e⁻). All of the diodides have relatively short metal-metal separations. The CuTi₂ structure of the lanthanum, cerium and praseodymium diodides along with HP-NdI₂ contain 4⁴ nets of metal and iodine atoms with short metal-metal bonds (393-386 La-Pr). these compounds should be considered to be two-dimensional metals (two-dimensional in the same way that graphite is). The salt-like dihalides include those of Eu, Dy, Tm, and Yb. The formation of a relatively stable +2 oxidation state for Eu and Yb is usually explained by the stability (exchange energy) of half filled (f⁷) and fully filled f¹⁴. GdI₂ possesses the layered MoS₂ structure, is ferromagnetic and exhibits colossal magnetoresistance The sesquihalides Ln₂X₃ and the Ln₇I₁₂ compounds listed in the table contain metal clusters, discrete Ln₆I₁₂ clusters in Ln₇I₁₂ and condensed clusters forming chains in the sesquihalides. Scandium forms a similar cluster compound with chlorine, Sc₇Cl₁₂ Unlike many transition metal clusters these lanthanide clusters do not have strong metal-metal interactions and this is due to the low number of valence electrons involved, but instead are stabilised by the surrounding halogen atoms.

LaI is the only known monohalide. Prepared from the reaction of LaI₃ and La metal, it has a NiAs type structure and can be formulated La³⁺ (I⁻)(e⁻)₂.

Oxides and hydroxides

All of the lanthanides form sesquioxides, Ln₂O₃. The lighter/larger lanthanides adopt a hexagonal 7-coordinate structure while the heavier/smaller ones adopt a cubic 6-coordinate "C-M₂O₃" structure. All of the sesquioxides are basic, and absorb water and carbon dioxide from air to form carbonates, hydroxides and hydroxycarbonates. They dissolve in acids to form salts.

Cerium forms a stoichiometric dioxide, CeO₂, where cerium has an oxidation state of +4. CeO₂ is basic and dissolves with difficulty in acid to form Ce⁴⁺ solutions, from which Ce^IV salts can be isolated, for example the hydrated nitrate Ce(NO₃)₄.5H₂O. CeO₂ is used as an oxidation catalyst in catalytic converters. Praseodymium and terbium form non-stoichiometric oxides containing Ln^IV, although more extreme reaction conditions can produce stoichiometric (or near stoichiometric) PrO₂ and TbO₂.

Europium and ytterbium form salt-like monoxides, EuO and YbO, which have a rock salt structure. EuO is ferromagnetic at low temperatures, and is a semiconductor with possible applications in spintronics. A mixed Eu^II/Eu^III oxide Eu₃O₄ can be produced by reducing Eu₂O₃ in a stream of hydrogen. Neodymium and samarium also form monoxides, but these are shiny conducting solids, although the existence of samarium monoxide is considered dubious.

All of the lanthanides form hydroxides, Ln(OH)₃. With the exception of lutetium hydroxide, which has a cubic structure, they have the hexagonal UCl₃ structure. The hydroxides can be precipitated from solutions of Ln^III. They can also be formed by the reaction of the sesquioxide, Ln₂O₃, with water, but although this reaction is thermodynamically favorable it is kinetically slow for the heavier members of the series. Fajans' rules indicate that the smaller Ln³⁺ ions will be more polarizing and their salts correspondingly less ionic. The hydroxides of the heavier lanthanides become less basic, for example Yb(OH)₃ and Lu(OH)₃ are still basic hydroxides but will dissolve in hot concentrated NaOH.

Chalcogenides (S, Se, Te)

All of the lanthanides form Ln₂Q₃ (Q= S, Se, Te). The sesquisulfides can be produced by reaction of the elements or (with the exception of Eu₂S₃) sulfidizing the oxide (Ln₂O₃) with H₂S. The sesquisulfides, Ln₂S₃ generally lose sulfur when heated and can form a range of compositions between Ln₂S₃ and Ln₃S₄. The sesquisulfides are insulators but some of the Ln₃S₄ are metallic conductors (e.g. Ce₃S₄) formulated (Ln³⁺)₃ (S²⁻)₄ (e⁻), while others (e.g. Eu₃S₄ and Sm₃S₄) are semiconductors. Structurally the sesquisulfides adopt structures that vary according to the size of the Ln metal. The lighter and larger lanthanides favoring 7-coordinate metal atoms, the heaviest and smallest lanthanides (Yb and Lu) favoring 6 coordination and the rest structures with a mixture of 6 and 7 coordination. Polymorphism is common amongst the sesquisulfides. The colors of the sesquisulfides vary metal to metal and depend on the polymorphic form. The colors of the γ-sesquisulfides are La₂S₃, white/yellow; Ce₂S₃, dark red; Pr₂S₃, green; Nd₂S₃, light green; Gd₂S₃, sand; Tb₂S₃, light yellow and Dy₂S₃, orange. The shade of γ-Ce₂S₃ can be varied by doping with Na or Ca with hues ranging from dark red to yellow, and Ce₂S₃ based pigments are used commercially and are seen as low toxicity substitutes for cadmium based pigments.

All of the lanthanides form monochalcogenides, LnQ, (Q= S, Se, Te). The majority of the monochalcogenides are conducting, indicating a formulation Ln^IIIQ²⁻(e-) where the electron is in conduction bands. The exceptions are SmQ, EuQ and YbQ which are semiconductors or insulators but exhibit a pressure induced transition to a conducting state. Compounds LnQ₂ are known but these do not contain Ln^IV but are Ln^III compounds containing polychalcogenide anions.

Oxysulfides Ln₂O₂S are well known, they all have the same structure with 7-coordinate Ln atoms, and 3 sulfur and 4 oxygen atoms as near neighbours. Doping these with other lanthanide elements produces phosphors. As an example, gadolinium oxysulfide, Gd₂O₂S doped with Tb³⁺ produces visible photons when irradiated with high energy X-rays and is used as a scintillator in flat panel detectors. When mischmetal, an alloy of lanthanide metals, is added to molten steel to remove oxygen and sulfur, stable oxysulfides are produced that form an immiscible solid.

Pnictides (group 15)

All of the lanthanides form a mononitride, LnN, with the rock salt structure. The mononitrides have attracted interest because of their unusual physical properties. SmN and EuN are reported as being "half metals". NdN, GdN, TbN and DyN are ferromagnetic, SmN is antiferromagnetic. Applications in the field of spintronics are being investigated. CeN is unusual as it is a metallic conductor, contrasting with the other nitrides also with the other cerium pnictides. A simple description is Ce⁴⁺N³⁻ (e–) but the interatomic distances are a better match for the trivalent state rather than for the tetravalent state. A number of different explanations have been offered. The nitrides can be prepared by the reaction of lanthanum metals with nitrogen. Some nitride is produced along with the oxide, when lanthanum metals are ignited in air. Alternative methods of synthesis are a high temperature reaction of lanthanide metals with ammonia or the decomposition of lanthanide amides, Ln(NH₂)₃. Achieving pure stoichiometric compounds, and crystals with low defect density has proved difficult. The lanthanide nitrides are sensitive to air and hydrolyse producing ammonia.

The other pnictides phosphorus, arsenic, antimony and bismuth also react with the lanthanide metals to form monopnictides, LnQ. Additionally a range of other compounds can be produced with varying stoichiometries, such as LnP₂, LnP₅, LnP₇, Ln₃As, Ln₅As₃ and LnAs₂.

Carbides

Carbides of varying stoichiometries are known for the lanthanides. Non-stoichiometry is common. All of the lanthanides form LnC₂ and Ln₂C₃ which both contain C₂ units. The dicarbides with exception of EuC₂, are metallic conductors with the calcium carbide structure and can be formulated as Ln³⁺C₂²⁻(e–). The C-C bond length is longer than that in CaC₂, which contains the C₂²⁻ anion, indicating that the antibonding orbitals of the C₂²⁻ anion are involved in the conduction band. These dicarbides hydrolyse to form hydrogen and a mixture of hydrocarbons. EuC₂ and to a lesser extent YbC₂ hydrolyse differently producing a higher percentage of acetylene (ethyne). The sesquicarbides, Ln₂C₃ can be formulated as Ln₄(C₂)₃. These compounds adopt the Pu₂C₃ structure which has been described as having C₂²⁻ anions in bisphenoid holes formed by eight near Ln neighbours. The lengthening of the C-C bond is less marked in the sesquicarbides than in the dicarbides, with the exception of Ce₂C₃. Other carbon rich stoichiometries are known for some lanthanides. Ln₃C₄ (Ho-Lu) containing C, C₂ and C₃ units; Ln₄C₇ (Ho-Lu) contain C atoms and C₃ units and Ln₄C₅ (Gd-Ho) containing C and C₂ units. Metal rich carbides contain interstitial C atoms and no C₂ or C₃ units. These are Ln₄C₃ (Tb and Lu); Ln₂C (Dy, Ho, Tm) and Ln₃C (Sm-Lu).

Borides

All of the lanthanides form a number of borides. The "higher" borides (LnB_x where x > 12) are insulators/semiconductors whereas the lower borides are typically conducting. The lower borides have stoichiometries of LnB₂, LnB₄, LnB₆ and LnB₁₂. Applications in the field of spintronics are being investigated. The range of borides formed by the lanthanides can be compared to those formed by the transition metals. The boron rich borides are typical of the lanthanides (and groups 1–3) whereas for the transition metals tend to form metal rich, "lower" borides. The lanthanide borides are typically grouped together with the group 3 metals with which they share many similarities of reactivity, stoichiometry and structure. Collectively these are then termed the rare earth borides.

Many methods of producing lanthanide borides have been used, amongst them are direct reaction of the elements; the reduction of Ln₂O₃ with boron; reduction of boron oxide, B₂O₃, and Ln₂O₃ together with carbon; reduction of metal oxide with boron carbide, B₄C. Producing high purity samples has proved to be difficult. Single crystals of the higher borides have been grown in a low melting metal (e.g. Sn, Cu, Al).

Diborides, LnB₂, have been reported for Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu. All have the same, AlB₂, structure containing a graphitic layer of boron atoms. Low temperature ferromagnetic transitions for Tb, Dy, Ho and Er. TmB₂ is ferromagnetic at 7.2 K.

Tetraborides, LnB₄ have been reported for all of the lanthanides except EuB₄, all have the same UB₄ structure. The structure has a boron sub-lattice consists of chains of octahedral B₆ clusters linked by boron atoms. The unit cell decreases in size successively from LaB₄ to LuB₄. The tetraborides of the lighter lanthanides melt with decomposition to LnB₆. Attempts to make EuB₄ have failed. The LnB₄ are good conductors and typically antiferromagnetic.

Hexaborides, LnB₆ have been reported for all of the lanthanides. They all have the CaB₆ structure, containing B₆ clusters. They are non-stoichiometric due to cation defects. The hexaborides of the lighter lanthanides (La – Sm) melt without decomposition, EuB₆ decomposes to boron and metal and the heavier lanthanides decompose to LnB₄ with exception of YbB₆ which decomposes forming YbB₁₂. The stability has in part been correlated to differences in volatility between the lanthanide metals. In EuB₆ and YbB₆ the metals have an oxidation state of +2 whereas in the rest of the lanthanide hexaborides it is +3. This rationalises the differences in conductivity, the extra electrons in the Ln^III hexaborides entering conduction bands. EuB₆ is a semiconductor and the rest are good conductors. LaB₆ and CeB₆ are thermionic emitters, used, for example, in scanning electron microscopes.

Dodecaborides, LnB₁₂, are formed by the heavier smaller lanthanides, but not by the lighter larger metals, La – Eu. With the exception YbB₁₂ (where Yb takes an intermediate valence and is a Kondo insulator), the dodecaborides are all metallic compounds. They all have the UB₁₂ structure containing a 3 dimensional framework of cubooctahedral B₁₂ clusters.

The higher boride LnB₆₆ is known for all lanthanide metals. The composition is approximate as the compounds are non-stoichiometric. They all have similar complex structure with over 1600 atoms in the unit cell. The boron cubic sub lattice contains super icosahedra made up of a central B₁₂ icosahedra surrounded by 12 others, B₁₂(B₁₂)₁₂. Other complex higher borides LnB₅₀ (Tb, Dy, Ho Er Tm Lu) and LnB₂₅ are known (Gd, Tb, Dy, Ho, Er) and these contain boron icosahedra in the boron framework.

Organometallic compounds

Lanthanide-carbon σ bonds are well known; however as the 4f electrons have a low probability of existing at the outer region of the atom there is little effective orbital overlap, resulting in bonds with significant ionic character. As such organo-lanthanide compounds exhibit carbanion-like behavior, unlike the behavior in transition metal organometallic compounds. Because of their large size, lanthanides tend to form more stable organometallic derivatives with bulky ligands to give compounds such as Ln[CH(SiMe₃)₃]. Analogues of uranocene are derived from dilithiocyclooctatetraene, Li₂C₈H₈. Organic lanthanide(II) compounds are also known, such as Cp*₂Eu.

Physical properties

Magnetic and spectroscopic

All the trivalent lanthanide ions, except lanthanum and lutetium, have unpaired f electrons. However, the magnetic moments deviate considerably from the spin-only values because of strong spin-orbit coupling. The maximum number of unpaired electrons is 7, in Gd³⁺, with a magnetic moment of 7.94 B.M., but the largest magnetic moments, at 10.4–10.7 B.M., are exhibited by Dy³⁺ and Ho³⁺. However, in Gd³⁺ all the electrons have parallel spin and this property is important for the use of gadolinium complexes as contrast reagent in MRI scans. 

A solution of 4% holmium oxide in 10% perchloric acid, permanently fused into a quartz cuvette as a wavelength calibration standard

 

Crystal field splitting is rather small for the lanthanide ions and is less important than spin-orbit coupling in regard to energy levels. Transitions of electrons between f orbitals are forbidden by the Laporte rule. Furthermore, because of the "buried" nature of the f orbitals, coupling with molecular vibrations is weak. Consequently, the spectra of lanthanide ions are rather weak and the absorption bands are similarly narrow. Glass containing holmium oxide and holmium oxide solutions (usually in perchloric acid) have sharp optical absorption peaks in the spectral range 200–900 nm and can be used as a wavelength calibration standard for optical spectrophotometers, and are available commercially.

As f-f transitions are Laporte-forbidden, once an electron has been excited, decay to the ground state will be slow. This makes them suitable for use in lasers as it makes the population inversion easy to achieve. The Nd:YAG laser is one that is widely used. Europium-doped yttrium vanadate was the first red phosphor to enable the development of color television screens. Lanthanide ions have notable luminescent properties due to their unique 4f orbitals. Laporte forbidden f-f transitions can be activated by excitation of a bound "antenna" ligand. This leads to sharp emission bands throughout the visible, NIR, and IR and relatively long luminescence lifetimes.

Occurrence

The lanthanide contraction is responsible for the great geochemical divide that splits the lanthanides into light and heavy-lanthanide enriched minerals, the latter being almost inevitably associated with and dominated by yttrium. This divide is reflected in the first two "rare earths" that were discovered: yttria (1794) and ceria (1803). The geochemical divide has put more of the light lanthanides in the Earth's crust, but more of the heavy members in the Earth's mantle. The result is that although large rich ore-bodies are found that are enriched in the light lanthanides, correspondingly large ore-bodies for the heavy members are few. The principal ores are monazite and bastnäsite. Monazite sands usually contain all the lanthanide elements, but the heavier elements are lacking in bastnäsite. The lanthanides obey the Oddo-Harkins rule – odd-numbered elements are less abundant than their even-numbered neighbors. 

Three of the lanthanide elements have radioactive isotopes with long half-lives (¹³⁸La, ¹⁴⁷Sm and ¹⁷⁶Lu) that can be used to date minerals and rocks from Earth, the Moon and meteorites.

Applications

Industrial

Lanthanide elements and their compounds have many uses but the quantities consumed are relatively small in comparison to other elements. About 15000 ton/year of the lanthanides are consumed as catalysts and in the production of glasses. This 15000 tons corresponds to about 85% of the lanthanide production. From the perspective of value, however, applications in phosphors and magnets are more important.

The devices lanthanide elements are used in include superconductors, samarium-cobalt and neodymium-iron-boron high-flux rare-earth magnets, magnesium alloys, electronic polishers, refining catalysts and hybrid car components (primarily batteries and magnets). Lanthanide ions are used as the active ions in luminescent materials used in optoelectronics applications, most notably the Nd:YAG laser. Erbium-doped fiber amplifiers are significant devices in optical-fiber communication systems. Phosphors with lanthanide dopants are also widely used in cathode ray tube technology such as television sets. The earliest color television CRTs had a poor-quality red; europium as a phosphor dopant made good red phosphors possible. Yttrium iron garnet (YIG) spheres can act as tunable microwave resonators. Lanthanide oxides are mixed with tungsten to improve their high temperature properties for TIG welding, replacing thorium, which was mildly hazardous to work with. Many defense-related products also use lanthanide elements such as night vision goggles and rangefinders. The SPY-1 radar used in some Aegis equipped warships, and the hybrid propulsion system of Arleigh Burke-class destroyers all use rare earth magnets in critical capacities. The price for lanthanum oxide used in fluid catalytic cracking has risen from $5 per kilogram in early 2010 to $140 per kilogram in June 2011.

Most lanthanides are widely used in lasers, and as (co-)dopants in doped-fiber optical amplifiers; for example, in Er-doped fiber amplifiers, which are used as repeaters in the terrestrial and submarine fiber-optic transmission links that carry internet traffic. These elements deflect ultraviolet and infrared radiation and are commonly used in the production of sunglass lenses. Other applications are summarized in the following table:

Application	Percentage
Catalytic converters	45
Petroleum refining catalysts	25
Permanent magnets	12
Glass polishing and ceramics	7
Metallurgical	7
Phosphors	3
Other	1

The complex Gd(DOTA) is used in magnetic resonance imaging.

Life science

As mentioned in the industrial applications section above, lanthanide metals are particularly useful in technologies that take advantage of their reactivity to specific wavelengths of light. Certain life science applications take advantage of the unique luminescence properties of lanthanide ion complexes (Ln(III) chelates or cryptates). These are well-suited for this application due to their large Stokes shifts and extremely long emission lifetimes (from microseconds to milliseconds) compared to more traditional fluorophores (e.g., fluorescein, allophycocyanin, phycoerythrin, and rhodamine). The biological fluids or serum commonly used in these research applications contain many compounds and proteins which are naturally fluorescent. Therefore, the use of conventional, steady-state fluorescence measurement presents serious limitations in assay sensitivity. Long-lived fluorophores, such as lanthanides, combined with time-resolved detection (a delay between excitation and emission detection) minimizes prompt fluorescence interference.

Time-resolved fluorometry (TRF) combined with fluorescence resonance energy transfer (FRET) offers a powerful tool for drug discovery researchers: Time-Resolved Fluorescence Resonance Energy Transfer or TR-FRET. TR-FRET combines the low background aspect of TRF with the homogeneous assay format of FRET. The resulting assay provides an increase in flexibility, reliability and sensitivity in addition to higher throughput and fewer false positive/false negative results.

This method involves two fluorophores: a donor and an acceptor. Excitation of the donor fluorophore (in this case, the lanthanide ion complex) by an energy source (e.g. flash lamp or laser) produces an energy transfer to the acceptor fluorophore if they are within a given proximity to each other (known as the Förster’s radius). The acceptor fluorophore in turn emits light at its characteristic wavelength.

The two most commonly used lanthanides in life science assays are shown below along with their corresponding acceptor dye as well as their excitation and emission wavelengths and resultant Stokes shift (separation of excitation and emission wavelengths). 

Donor	Excitation⇒Emission λ (nm)	Acceptor	Excitation⇒Emission λ (nm)	Stoke's Shift (nm)
Eu3+	340⇒615	Allophycocyanin	615⇒660	320
Tb3+	340⇒545	Phycoerythrin	545⇒575	235

Upcoming Medical Uses

Currently there is research showing that lanthanides elements can be used as anticancer agents. The main role of the lanthanides in these studies is to inhibit proliferation of the cancer cells. Specifically cerium and lanthanum have been studied for their role as anti-cancer agents. 

One of the specific elements from the lanthanide group that has been tested and used is cerium (Ce). There have been studies that use a protein-cerium complex to observe the effect of cerium on the cancer cells. The hope was to inhibit cell proliferation and promote cytotoxicity. Transferrin receptors in cancer cells, such as those in breast cancer cells and epithelial cervical cells, promote the cell proliferation and malignancy of the cancer. Transferrin is a protein used to transport iron into the cells and is needed to aid the cancer cells in DNA replication. Transferrin acts as a growth factor for the cancerous cells and is dependent on iron. Cancer cells have much higher levels of transferrin receptors than normal cells and are very dependent on iron for their proliferation. Cerium has shown results as an anti-cancer agent due to its similarities in structure and biochemistry to iron. Cerium may bind in the place of iron on to the transferrin and then be brought into the cancer cells by transferrin-receptor mediated endocytosis. The cerium binding to the transferrin in place of the iron inhibits the transferrin activity in the cell. This creates a toxic environment for the cancer cells and causes a decrease in cell growth. This is the proposed mechanism for cerium’s effect on cancer cells, though the real mechanism may be more complex in how cerium inhibits cancer cell proliferation. Specifically in HeLa cancer cells studied in vitro, cell viability was decreased after 48 to 72 hours of cerium treatments. Cells treated with just cerium had decreases in cell viability, but cells treated with both cerium and transferrin had more significant inhibition for cellular activity.

Another specific element that has been tested and used as an anti-cancer agent is lanthanum, more specifically lanthanum chloride (LaCl3 ). The lanthanum ion is used to affect the levels of let-7a and microRNAs miR-34a in a cell throughout the cell cycle. When the lanthanum ion was introduced to the cell in vivo or in vitro, it inhibited the rapid growth and induced apoptosis of the cancer cells (specifically cervical cancer cells). This effect was caused by the regulation of the let-7a and microRNAs by the lanthanum ions. The mechanism for this effect is still unclear but it is possible that the lanthanum is acting in a similar way as the cerium and binding to a ligand necessary for cancer cell proliferation.

Biological effects

Due to their sparse distribution in the earth's crust and low aqueous solubility, the lanthanides have a low availability in the biosphere, and for a long time were not known to naturally form part of any biological molecules. In 2007 a novel methanol dehydrogenase that strictly uses lanthanides as enzymatic cofactors was discovered in a bacterium from the phylum Verrucomicrobia, Methylacidiphilum fumariolicum. This bacterium was found to survive only if there are lanthanides present in the environment. Compared to most other nondietary elements, non-radioactive lanthanides are classified as having low toxicity.