Lanthanide radii

In sample calculations, we estimated the radii for alkaline-earth dichlorides, which are compared in Table 54 with the smoothed data from Shannon (1976). The calculation method was similar to that described above for finding bivalent lanthanide radii. These calculations were performed with the goal of elucidating the weaknesses of the... 

In Table 20.7 are listed radii of trivalent actinide ions (coordination number CN 6) derived from measurements on trichlorides by the method of Bums, Peterson, and Baybarz [288]. Determinations of M-Cl distances have been made for M = U, Pu, Am, Cm, and Cf the other values were estimated by use of unitcell data and curve fitting. All these radii are relative to the trivalent lanthanide radii of Templeton and Dauben [396], who employed data from cubic sesquioxides and assumed atomic positions to establish M-O distances. Also included in Table 20.7 are radii of tetravalent actinide ions obtained from the M-O distances calculated from unit-cell parameters of the dioxides [1] by subtracting 1.38 A for oxygen (the value used [396] for the sesquioxides). For comparison. Shannon s ionic radii, derived from oxides and fluorides, and Peterson s tetravalent radii, derived from dioxides, are shown [537,538]. As... 

Group lA Radius (A) Group IIA Radius (A) Group IIIA Radius (A) Lanthanides Radius (A)... 

The peak in the X-ray RDF at 5 A (fig. 4) was assigned to Ln-O distances for water molecules in the second (outer) hydration sphere. Curve B in fig. 6 shows the dependency of the position of this peak on the lanthanide radius. Both ion pair interactions [Ln(H20) (] -Cl and secondary solvation [Ln(H20) ] -H20 are expected to be responsive to differences in ionic radii of the lanthanide ions as well as to changes in the inner-sphere hydration. The decrease in the Ln H2O distance between La " and Lu " " (including the hydration change offset) is 0.24 A (fig. 6, curve A), in good agreement with the difference of 0.22 A for the peak at ca. 5 A. 

In conclusion, many questions remain about the mechanism of water exchange. While activation volume data support an association mechanism (I ), the ultrasound and kinetic data are interpreted in terms of an overall dissociative mechanism. Kinetic results show a discontinuity in plots of log k values versus lanthanide radius in the region of Sm -Tb which would seem to be good evidence for a change in hydration number in this region. 

Another observation that can be made from fig. 22 is that the hexagonal structure appears to persist to a smaller molecular volume in the actinide series than in the lanthanide series (e.g., curium sesquioxide should be the highest member to form a hexagonal phase based on the lanthanide radius relationship). The hexagonal form of californium sesquioxide has a very narrow phase field and it is very difficult experimentally to retain this structural form of the sesquioxide at room temperature (e.g., to quench-in this form). This latter factor may have some bearing on this volume discrepancy (e.g., the volumes may be affected by the preparation). Finally, the volume data for the cubic forms of both series, the hexagonal forms of the actinides and the monoclinic forms of the lanthanides, all show a cusp at elements with half-filled shells. 

The reason why lanthanides of high atomic number emerge first is that the stability of a lanthanide ion-citrate ion complex increases with the atomic number. Since these complexes are formed by ions, this must mean that the ion-ligand attraction also increases with atomic number, i.e. that the ionic radius decreases (inverse square law). It is a characteristic of the lanthanides that the ionic radius... 

The atom radius of an element is the shortest distance between like atoms. It is the distance of the centers of the atoms from one another in metallic crystals and for these materials the atom radius is often called the metal radius. Except for the lanthanides (CN = 6), CN = 12 for the elements. The atom radii listed in Table 4.6 are taken mostly from A. Kelly and G. W. Groves, Crystallography and Crystal Defects, Addison-Wesley, Reading, Mass., 1970. 

Chemical Properties. Although the chemical properties of the trivalent lanthanides are quite similar, some differences occur as a consequence of the lanthanide contraction (see Table 3). The chemical properties of yttrium are very similar too, on account of its external electronic stmcture and ionic radius. Yttrium and the lanthanides are typical hard acids, and bind preferably with hard bases such as oxygen-based ligands. Nevertheless they also bind with soft bases, typicaUy sulfur and nitrogen-based ligands in the absence of hard base ligands. 

A full discussion of thorium electrochemistry is available (3). Thorium is generally more acidic than the lanthanides but less acidic than other light actinides, such as U, Np, and Pu, as expected from the larger Th" " ionic radius (108 pm). 

The radius of the 24-coordinate metal site in MBs is too large (215-225 pm) to be comfortably occupied by the later (smaller) lanthanide elements Ho, Er, Tm and Lu, and these form MB4 instead, where the metal site has a radius of 185-200 pm. The structure of MB4 (also formed by Ca, Y, Mo and W) consists of a tetragonal lattice formed by chains of Bs octahedra linked along the c-axis and joined laterally by pairs of B2 atoms in the xy plane so as to form a 3D skeleton with tunnels along the c-axis that are filled by metal atoms (Fig. 6.11). The pairs of boron atoms are thus surrounded by trigonal prisms of... 

Scandium is very widely but thinly distributed and its only rich mineral is the rare thortveitite, Sc2Si20v (p. 348), found in Norway, but since scandium has only small-scale commercial use, and can be obtained as a byproduct in the extraction of other materials, this is not a critical problem. Yttrium and lanthanum are invariably associated with lanthanide elements, the former (Y) with the heavier or Yttrium group lanthanides in minerals such as xenotime, M "P04 and gadolinite, M M SijOio (M = Fe, Be), and the latter (La) with the lighter or cerium group lanthanides in minerals such as monazite, M P04 and bastnaesite, M C03F. This association of similar metals is a reflection of their ionic radii. While La is similar in size to the early lanthanides which immediately follow it in the periodic table, Y , because of the steady fall in ionic radius along the lanthanide series (p. 1234), is more akin to the later lanthanides. 

Figure 30.2 Variation of metal radius and 3+ ionic radius for La and the lanthanides. Other data for Ln" and Ln" are in Table 30.2.

By the time Ho is reached the Ln radius has been sufficiently reduced to be almost identical with that of Y which is why this much lighter element is invariably associated with the heavier lanthanides. 

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

The coordination chemistry of the large, electropositive Ln ions is complicated, especially in solution, by ill-defined stereochemistries and uncertain coordination numbers. This is well illustrated by the aquo ions themselves.These are known for all the lanthanides, providing the solutions are moderately acidic to prevent hydrolysis, with hydration numbers probably about 8 or 9 but with reported values depending on the methods used to measure them. It is likely that the primary hydration number decreases as the cationic radius falls across the series. However, confusion arises because the polarization of the H2O molecules attached directly to the cation facilitates hydrogen bonding to other H2O molecules. As this tendency will be the greater, the smaller the cation, it is quite reasonable that the secondary hydration number increases across the series. 

Various crown ethers (p. 96) with differing cavity diameters provide a range of coordination numbers and stoichiometries, although crystallographic data are sparse. An interesting series, illustrating the dependence of coordination number on cationic radius and ligand cavity diameter, is provided by the complexes formed by the lanthanide nitrates and the 18-crown-6 ether (i.e. 1,4,7,10,13,16-... 

By contrast, the ionic radius in a given oxidation state falls steadily and, though the available data are less extensive, it is clear that an actinide contraction exists, especially for the -f3 state, which is closely similar to the lanthanide contraction (see p. 1232). 

The atomic radii of the second row of d-metals (Period 5) are typically greater than those in the first row (Period 4). The atomic radii in the third row (Period 6), however, are about the same as those in the second row and smaller than expected. This effect is due to the lanthanide contraction, the decrease in radius along the first row of the / block (Fig. 16.4). This decrease is due to the increasing nuclear charge along the period coupled with the poor shielding ability of /-electrons. When the d block resumes (at lutetium), the atomic radius has fallen from 217 pm for barium to 173 pm for lutetium. 

Hg is much more dense than Cd, because the decrease in atomic radius that occurs between Z = 58 and Z = 71 (the lanthanide contraction) causes the atoms following the rare earths to he smaller than might have been expected for their atomic masses and atomic numbers. Zn and Cd have densities that are not too dissimilar because the radius of Cd is subject only to a smaller d-block contraction. 

Actinium is similarly easy to find a proxy for. It forms large trivalent cations with an ionic radius of 1.12 A in Vl-fold coordination. This is somewhat larger than La (1.032 A), which we will adopt as a proxy. The partitioning behavior of the lanthanides (denoted collectively Ln) is sufficiently well understood to make this a prudent choice. In some minerals, however, the larger size of Ac, may place it onto a larger lattice site than the lanthanides. This possibility should be considered for minerals with very large cation sites, such as amphiboles and micas. 

Water exchange on [Ln(H20)8]3+ for the heavier lanthanides Gd3+-Yb3+ is characterized by a systematic decrease in /feHa0 and an increase in AH as the ionic radius decreases from Tb3+ to Yb3+, and both A Si and AV-t are negative (311-313). The AV are significantly less than either the value of -12.9 cm3 mol-1 calculated for water... 

At the first step, the insertion of MMA to the lanthanide-alkyl bond gave the enolate complex. The Michael addition of MMA to the enolate complex via the 8-membered transition state results in stereoselective C-C bond formation, giving a new chelating enolate complex with two MMA units one of them is enolate and the other is coordinated to Sm via its carbonyl group. The successive insertion of MMA afforded a syndiotactic polymer. The activity of the polymerization increased with an increase in the ionic radius of the metal (Sm > Y > Yb > Lu). Furthermore, these complexes become precursors for the block co-polymerization of ethylene with polar monomers such as MMA and lactones [215, 217]. 

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