A Ionic Radii

Fig Data for formation ofM2+ ions of groups 2 and 12, showing (a) ionic radii, (h) sublimation enthalpies of the elements, (c) sum of the first two ionisation energies and (d) standard electrode potentials. 

Atomic number Electron configuration Atomic radius (A) Ionic radii (A)... 

A. Ionic Radii, Bond Valence, and Related Quantities... 

Figure 6-38. The variation of octahedral ionic radii according to Ref [6-21] (curve A ionic radii from Ref [6-22]) and of the bond lengths of difluorides (curve B), dichlorides (curve C), and dibromides (curve D) in the first transition metal series.

The are essentially adjustable parameters and, clearly, unless some of the parameters in A2.4.70 are fixed by physical argument, then calculations using this model will show an improved fit for purely algebraic reasons. In principle, the radii can be fixed by using tables of ionic radii calculations of this type, in which just the A are adjustable, have been carried out by Friedman and co-workers using the HNC approach [12]. Further rermements were also discussed by Friedman [F3], who pointed out that an additional temi is required to account for the fact that each ion is actually m a cavity of low dielectric constant, e, compared to that of the bulk solvent, e. A real difficulty discussed by Friedman is that of making the potential continuous, since the discontinuous potentials above may lead to artefacts. Friedman [F3] addressed this issue and derived... 

This fomuila does not include the charge-dipole interaction between reactants A and B. The correlation between measured rate constants in different solvents and their dielectric parameters in general is of a similar quality as illustrated for neutral reactants. This is not, however, due to the approximate nature of the Bom model itself which, in spite of its simplicity, leads to remarkably accurate values of ion solvation energies, if the ionic radii can be reliably estimated [15],... 

In the geochemistry of fluorine, the close match in the ionic radii of fluoride (0.136 nm), hydroxide (0.140 nm), and oxide ion (0.140 nm) allows a sequential replacement of oxygen by fluorine in a wide variety of minerals. This accounts for the wide dissemination of the element in nature. The ready formation of volatile silicon tetrafluoride, the pyrohydrolysis of fluorides to hydrogen fluoride, and the low solubility of calcium fluoride and of calcium fluorophosphates, have provided a geochemical cycle in which fluorine may be stripped from solution by limestone and by apatite to form the deposits of fluorspar and of phosphate rock (fluoroapatite [1306-01 -0]) approximately CaF2 3Ca2(P0 2 which ate the world s main resources of fluorine (1). 

Fig. 7. Ionic arrangements on different (a) < 100 >, (b) < 110 >, and (c) < 111 > crystallographic surfaces. The interionic separations are given in nanometers for AgBr and in parentheses for AgCl. Values are larger for AgBr because of the relative ionic radii of bromide and chloride.

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. 

A contraction resulting from the filling of the 4f electron shell is of course not exceptional. Similar contractions occur in each row of the periodic table and, in the d block for instance, the ionic radii decrease by 20.5 pm from Sc to Cu , and by 15 pm from Y to Ag . The importance of the lanthanide contraction arises from its consequences ... 

A number of trends connected with ionic radii are noticeable across the series. In keeping with Fajans rules, salts become somewhat less ionic as the Ln " radius decreases reduced ionic character in the hydroxide implies a reduction in basic properties and, at the end of the series, Yb(OH)3 and Lu(OH)3, though undoubtedly mainly basic, can with difficulty be made to dissolve in hot cone NaOH. Paralleling this change, the [Ln(H20)j ] + ions are subject to an increasing tendency to hydrolyse, and hydrolysis can only be prevented by use of increasingly acidic solutions. 

The redox behaviour of Th, Pa and U is of the kind expected for d-transition elements which is why, prior to the 1940s, these elements were commonly placed respectively in groups 4, 5 and 6 of the periodic table. Behaviour obviously like that of the lanthanides is not evident until the second half of the series. However, even the early actinides resemble the lanthanides in showing close similarities with each other and gradual variations in properties, providing comparisons are restricted to those properties which do not entail a change in oxidation state. The smooth variation with atomic number found for stability constants, for instance, is like that of the lanthanides rather than the d-transition elements, as is the smooth variation in ionic radii noted in Fig. 31.4. This last factor is responsible for the close similarity in the structures of many actinide and lanthanide compounds especially noticeable in the 4-3 oxidation state for which... 

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