Ionic Radii Are

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The chemical, metallurgical, and physical behaviours of the rare earths are governed by the electron configuration of these elements. In general, these elements are trivalent, R3+, but several of them have other valences. The number of 4felectrons of each lanthanide is given in the table of the number of 4f electrons and ionic radii for the R3+ ion. The 4f electrons have lower energies than and radially lie inside the outer three valence electrons (i.e., 4f electrons are “localized” and part of the ion core), and thus they do not directly participate in the bonding with other elements when a compound is formed. This is why the lanthanides are chemically similar and difficult to separate and why they occur together in various minerals. The outer or valence electrons for the 14 lanthanides and lanthanum are the same, 5d6s2; for scandium, 3d4s2; and for yttrium, 4d5s2. There is some variation in the chemical properties of the lanthanides because of the lanthanide contraction and the hybridization, or mixing, of the 4f electrons with the valence electrons.

The systematic and smooth decrease from lanthanum to lutetium is known as the lanthanide contraction. It is due to the increase in the nuclear charge, which is not completely screened by the additional 4f electron as one goes from one lanthanide to the next. This increased effective charge draws the electrons (both the core and outer valence electrons) closer to the nucleus, thus accounting for the smaller radius of the higher-atomic-number lanthanides. The lanthanide contraction also accounts for the decreased basicity from lanthanum to lutetium and is the basis of various separation techniques.

As the 4f electrons are added when one moves across the lanthanide series from lanthanum to cerium to praseodymium and so on, the electrons, which have a magnetic moment due to the electron’s spin, maintain the same spin direction and the moments are aligned parallel with one another until the 4f level is half-filled—i.e., at seven 4f electrons in gadolinium. The next electron must align antiparallel in accordance with the Pauli exclusion principle, and thus two 4f electrons are paired. This continues until the 14th electron is added at lutetium, where all the 4f electron spins are paired up, and lutetium has no 4fmagnetic moment.

The ionic radius for an atom is measured in a crystal lattice, requiring a solid form for the compound. These radii will differ somewhat depending upon the technique used. Usually X-ray crystallography is employed to determine the radius for an ion. An ionic radius is the radius of a cation or an anion defined by the distance between ions in an ionic compound. Cations are smaller than the parent atom, whereas anions are larger. Similar to atomic radii, ionic radii are determined by the number of electrons, the. Atomic and ionic radii are found by measuring the distances between atoms and ions in chemical compounds. On the periodic table, atomic radius generally decreases as you move from left to right across a period (due to increasing nuclear charge) and increases as you move down a group (due to the increasing number of electron shells). Ionic radii are difficult to measure with any degree of certainty, and vary according to the environment of the ion. For example, it matters what the co-ordination of the ion is (how many oppositely charged ions are touching it), and what those ions are.

The 4f electron configuration is extremely important and determines the magnetic and optical behaviours for the lanthanide elements; e.g., the peculiar properties of strong Nd2Fe14B permanent magnets are due to the three 4f electrons in neodymium, and the red colour in optical displays that use cathode-ray tubes is provided by the europiumion in a host compound, while the green colour is provided by terbium.

Ionic Radius Rank

Database of Ionic Radii: Welcome to the database of ionic radii. The following web interface allows listing and comparison of ionic and crystal radii with different coordination and charge states. Suggestions as to how the scope and content of the database can be extended are gratefully received.

As noted above, several lanthanides may exhibit another valence state, R4+ for R = cerium, praseodymium, and terbium and R2+ for R = samarium, europium, and ytterbium. These additional valence states are a striking example of Hund’s rule, which states that empty, half-filled, and completely filled electronic levels tend to be more stable states: Ce4+ and Tb4+ give up an f electron to have an empty and half-filled 4f level, respectively, and Eu2+ and Yb2+ gain an f electron to have a half-filled or completely filled 4f level, respectively. Pr4+ and Sm2+ can, by giving up or gaining an f electron, respectively, in rare instances gain extra stability. In these two cases they tend toward but do not reach the respective empty or half-filled level. By giving up a 4f electron to become an R4+ ion, the radii of cerium, praseodymium, and terbium become smaller, 0.80, 0.78, and 0.76 Å, respectively. Conversely, samarium, europium, and ytterbium gain a 4f electron from the valence electrons to become an R2+ ion, and their radii increase to 1.19, 1.17, and 1.00 Å, respectively. Chemists have made use of these valence changes to separate Ce4+, Eu2+, and Yb2+ from the other trivalent R3 ions by relatively cheap chemical methods. CeO2 (where Ce is tetravalent) is the normal stable oxide form, while the oxides of praseodymium and terbium have the Pr6O11 and Tb4O7stoichiometries containing both the tetra- and the trivalent states—i.e., 4PrO2∙Pr2O3 and 2TbO2∙Tb2O3, respectively. The divalent ions Sm2+, Eu2+, and Tb2+ form dihalides—e.g., SmCl2, EuCl2, and YbCl2. Several europium oxide stoichiometries are known: EuO (Eu2+), Eu2O3 (Eu3+), and Eu3O4 (i.e., EuO∙Eu2O3).

The ionic radius of scandium is much smaller than that of the smallest lanthanide, lutetium: 0.745 Å versus 0.861 Å. Scandium’s radius is slightly larger than those of the common metal ions—e.g., Fe3+, Nb5+, U5+, and W5+. This is the main reason why scandium is essentially absent from any of the normal rare-earth minerals, generally less than 0.01 percent by weight. However, scandium is obtained as a by-product of processing other ores (e.g, wolframite) and from mining tailings (e.g., uranium). On the other hand, the radius of yttrium, 0.9 Å, is nearly the same as that of holmium, 0.901 Å, and this accounts for the presence of yttrium in the heavy lanthanide minerals.

Most rare-earth metals have a valence of three; however, that of cerium is 3.2, and europium and ytterbium are divalent. This is quite evident when the metallic radii are plotted versus atomic number. The metallic radii of the trivalent metals exhibit the normal lanthanide contraction, but a noticeable deviation occurs for cerium, where its radius falls below the line established by the trivalent metals, and also for europium and ytterbium, where their radii lie well above this line.

The melting points for europium and ytterbium are significantly lower than those of the neighbouring trivalent lanthanides when they are plotted versus atomic number, and this is also consistent with the divalent nature of these two metals. Anomalies are also evident in other physical properties of europium and ytterbium compared with the trivalent lanthanide metals (see belowProperties of the metals).

The table presents the number of 4f electrons and the radius of the R3+ ion for the rare-earth elements.

IonicIonic Radii Are

Ionic Radius Ratio

Number of 4f electrons and
ionic radii for the R3+ ion
rare-earth
element
number of
4f electrons
number of
unpaired
4f electrons
ionic
radius
(Å)
La00 1.045
Ce11 1.01
Pr22 0.997
Nd33 0.983
Pm44 0.97
Sm55 0.958
Eu66 0.947
Gd77 0.938
Tb86 0.923
Dy95 0.912
Ho104 0.901
Er113 0.890
Tm122 0.880
Yb131 0.868
Lu140 0.861
Sc00 0.745
Y00 0.900