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Ionic radius



The ionic radius, rion, is a measure of the size of an ion in a crystal lattice. It is measured in either picometres (pm) or Angstrom (Å), with 1 Å = 100 pm. Typical values range from 30 pm (0.3 Å) to over 200 pm (2 Å).

Additional recommended knowledge

The concept of ionic radius was developed independently by Goldschmidt and Pauling in the 1920s to summarize the data being generated by the (then) new technique of X-ray crystallography: it is Pauling's approach which proved to be the more influential. X-ray crystallography can readily give the length of the side of the unit cell of a crystal, but it is much more difficult (in most cases impossible, even with more modern techniques) to distinguish a boundary between two ions. For example, it can be readily determined that each side of the unit cell of sodium chloride is 564.02 pm in length, and that this length is twice the distance between the centre of a sodium ion and the centre of a chloride ion:

2[rion(Na+) + rion(Cl)] = 564.02 pm

However, it is not apparent what proportion of this distance is due to the size of the sodium ion and what proportion is due to the size of the chloride ion. By comparing many different compounds, and with a certain amount of chemical intuition, Pauling decided to assign a radius of 140 pm to the oxide ion O2−, at which point he was able to calculate the radii of the other ions by subtraction.[1]

A major review of crystallographic data led to the publication of a revised set of ionic radii in 1976,[2] and these are preferred to Pauling's original values. Some sources have retained Pauling's reference of rion(O2−) = 140 pm, while other sources prefer to list "effective" ionic radii based on rion(O2−) = 126 pm. The latter values are thought to be a more accurate approximation to the "true" relative sizes of anions and cations in ionic crystals.

The ionic radius is not a fixed property of a given ion, but varies with coordination number, spin state and other parameters. Nevertheless, ionic radius values are sufficiently transferable to allow periodic trends to be recognized. As with other types of atomic radius, ionic radii increase on descending a group. Ionic size (for the same ion) also increases with increasing coordination number, and an ion in a high-spin state will be larger than the same ion in a low-spin state. Anions (negatively charged) are almost invariable larger than cations (positively charged), although the fluorides of some alkali metals are rare exceptions. In general, ionic radius decreases with increasing positive charge and increases with increasing negative charge.

X NaX AgX
F 464 492
Cl 564 555
Br 598 577
Unit cell parameters (in pm, equal to two M–X bond lengths) for sodium and silver halides. All compounds crystallize in the NaCl structure.

An "anomalous" ionic radius in a crystal is often a sign of significant covalent character in the bonding. No bond is completely ionic, and some supposedly "ionic" compounds, especially of the transition metals, are particularly covalent in character. This is illustrated by the unit cell parameters for sodium and silver halides in the table. On the basis of the fluorides, one would say that Ag+ is larger than Na+, but on the basis of the chlorides and bromides the opposite appears to be true.[3] This is because the greater covalent character of the bonds in AgCl and AgBr reduces the bond length and hence the apparent ionic radius of Ag+, an effect which is not present in the halides of the more electropositive sodium, nor in silver fluoride in which the fluoride ion is relatively unpolarizable.

Ionic radii 6 coordinate unless marked
(e.g +34). ls = low spin, hs= high spin. [2]
Atomic No Element charge ionic radius pm
3 Lithium Li
+1 76
4 Beryllium Be
+2 45
5 Boron B
+3 27
6 Carbon C
+4 16
7 Nitrogen N
−34146
+3 16
+5 13
8 Oxygen O
−2 140
9 Fluorine F
−1 133
+7 8
11 Sodium Na
+1 102
12 Magnesium Mg
+2 72
13 Aluminum Al
+3 53.5
14 Silicon Si
+440
15 Phosphorus P
+344
+538
16 Sulfur S
−2184
+437
+629
17 Chlorine Cl
−1184
+512
+7 27
19 Potassium K
+1 138
20 Calcium Ca
+2 100
21 Scandium Sc
+3 74.5
22 Titanium Ti
+286
+367
+460.5
23 Vanadium V
+264
+458
+554
24 Chromium Cr
+273 ls
+280 hs
+361.5
+455
+549
+644
25 Manganese Mn
+267
+3 58 ls
+3 64.5 hs
+4 53
+54 33
+64 25.5
+7 46
26 Iron Fe
+2 61 ls
+2 78 hs
+3 55 ls
+3 64.5 hs
+458.5
+64 25
27 Cobalt Co
+265 ls
+2 74.5 hs
+354.5ls
+361hs
+453
28 Nickel Ni
+2 69
+3 56 ls
+3 60 hs
+4 48 ls
29 Copper Cu
+1 77
+2 73
+354 ls
30 Zinc Zn
+2 74
31 Gallium Ga
+3 62
32 Germanium Ge
+2 73
+4 53
33 Arsenic As
+3 58
+5 46
34 Selenium Se
−2 198
+4 50
+6 42
35 Bromine Br
−1 196
+34sq59
+5431
+739
37 Rubidium Rb
+1 152
38 Strontium Sr
+2 118
39 Yttrium Y
+3 90
40 Zirconium Zr
+4 72
41 Niobium Nb
+3 72
+4 68
+5 64
42 Molybdenum Mo
+3 69
+4 65
+561
+6 59
43 Technetium Tc
+4 64.5
+5 60
+7 56
44 Ruthenium Ru
+3 68
+462
+5 56.5
+74 38
+84 36
45 Rhodium Rh
+3 66.5
+4 60
+5 55
46 Palladium Pd
+12 59
+2 86
+3 76
+4 61.5
47 Silver Ag
+1 115
+2 94
+3 75
48 Cadmium Cd
+2 95
49 Indium In
+3 80
50 Tin Sn
+2118
+4 69
51 Antimony Sb
+3 76
+5 60
52 Tellurium Te
−2 221
+4 97
+6 56
53 Iodine I
−1220
+595
+7 53
54 Xenon Xe
+8 48
55 Caesium Cs
+1 167
56 Barium Ba
+2 135
57 Lanthanum La
+3 103.2
58 Cerium Ce
+3 102
+4 87
59 Praseodymium Pr
+3 99
+4 85
60 Neodymium Nd
+28 129
+3 98.3
61 Promethium Pm
+3 97
62 Samarium Sm
+24 122
+3 95.8
63 Europium Eu
+2 117
+3 94.7
64 Gadolinium Gd
+3 93.8
65 Terbium Tb
+3 92.3
+4 76
66 Dysprosium Dy
+2 107
+3 91.2
67 Holmium Ho
+390.1
68 Erbium Er
+3 89
69 Thulium Tm
+2 103
+3 88
70 Ytterbium Yb
+2 102
+3 86.8
71 Lutetium Lu
+3 86.1
72 Hafnium Hf
+3 71
73 Tantalum Ta
+3 72
+468
+564
74 Tungsten W
+4 66
+5 62
+660
75 Rhenium Re
+463
+5 58
+6 55
+7 53
76 Osmium Os
+4 63
+5 57.5
+6 54.5
+7 52.5
+84 39
77 Iridium Ir
+3 68
+4 62.5
+5 57
78 Platinum Pt
+2 86
+4 62.5
+5 57
79 Gold Au
+1 137
+3 85
+5 57
80 Mercury Hg
+1 119
+2 102
81 Thallium Tl
+1 150
+3 88.5
82 Lead Pb
+2 119
+4 77.5
83 Bismuth Bi
+3 103
+5 76
84 Polonium Po
+4 94
+6 67
85 Astatine At
+7 62
87 Francium Fr
+1 180
88 Radium Ra
+28 148
89 Actinium Ac
+3 112
90 Thorium Th
+4 94
91 Protactinium Pa
+3 104
+4 90
+5 78
92 Uranium U
+3 102.5
+4 89
+5 78
+673
93 Neptunium Np
+2110
+3 101
+4 87
+5 75
+6 72
+771
94 Plutonium Pu
+3100
+486
+574
+671
95 Americium Am
+28126
+3 97.5
+4 85
96 Curium Cm
+3 97
+4 85
97 Berkelium Bk
+3 96
+4 83
98 Californium Cf
+3 95
+4 82.1

See also

References

  1. ^ Pauling, L. (1960). The Nature of the Chemical Bond (3rd Edn.). Ithaca, NY: Cornell University Press.
  2. ^ a b Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides Shannon R.D. Acta Cryst. A32 751-767 (1976) doi:10.1107/S0567739476001551
  3. ^ On the basis of conventional ionic radii, Ag+ (129 pm) is indeed larger than Na+ (116 pm)
 
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Ionic_radius". A list of authors is available in Wikipedia.
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