Ionic radius

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Atomic radius:

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WEINER 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).

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 recognised. 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.

Table of Elements Sorted by Ionic Radius
Ionic Radius Name Sym #
0.012 Å 1.2 pm Hydrogen H 1
0.13 Å 13 pm Nitrogen N 7
0.23 Å 23 pm Boron B 5
0.35 Å 35 pm Beryllium Be 4
0.38 Å 38 pm Phosphorus P 15
0.4 Å 40 pm Silicon Si 14
0.46 Å 46 pm Manganese Mn 25
0.5 Å 50 pm Selenium Se 34
0.52 Å 52 pm Uranium U 92
0.52 Å 52 pm Chromium Cr 24
0.53 Å 53 pm Germanium Ge 32
0.535 Å 53.5 pm Aluminum Al 13
0.56 Å 56 pm Rhenium Re 75
0.56 Å 56 pm Technetium Tc 43
0.58 Å 58 pm Arsenic As 33
0.59 Å 59 pm Vanadium V 23
0.605 Å 60.5 pm Titanium Ti 22
0.62 Å 62 pm Tungsten W 74
0.62 Å 62 pm Gallium Ga 31
0.625 Å 62.5 pm Platinum Pt 78
0.625 Å 62.5 pm Iridium Ir 77
0.63 Å 73 pm Osmium Os 76
0.64 Å 64 pm Tantalum Ta 73
0.645 Å 64.5 pm Iron Fe 26
0.65 Å 65 pm Molybdenum Mo 42
0.68 Å 68 pm Rhodium Rh 45
0.68 Å 68 pm Ruthenium Ru 44
0.69 Å 69 pm Nickel Ni 28
0.69 Å 69 pm Niobium Nb 41
0.69 Å 69 pm Tin Sn 50
0.71 Å 71 pm Hafnium Hf 72
0.72 Å 72 pm Zirconium Zr 40
0.72 Å 72 pm Magnesium Mg 12
0.73 Å 73 pm Copper Cu 29
0.74 Å 74 pm Zinc Zn 30
0.745 Å 74.5 pm Cobalt Co 27
0.745 Å 74.5 pm Scandium Sc 21
0.75 Å 75 pm Neptunium Np 93
0.76 Å 76 pm Lithium Li 3
0.76 Å 76 pm Antimony Sb 51
0.78 Å 78 pm Protactinium Pa 91
0.8 Å 80 pm Indium In 49
0.848 Å 84.8 pm Lutetium Lu 71
0.85 Å 85 pm Gold Au 79
0.858 Å 85.8 pm Ytterbium Yb 70
0.86 Å 86 pm Palladium Pd 46
0.869 Å 86.9 pm Thulium Tm 69
0.881 Å 88.1 pm Erbium Er 68
0.887 Å 88.7 pm Plutonium Pu 94
0.9 Å 90 pm Yttrium Y 39
0.901 Å 90.1 pm Holmium Ho 67
0.912 Å 91.2 pm Dysprosium Dy 66
0.923 Å 92.3 pm Terbium Tb 65
0.925 Å 92.5 pm Einsteinium Es 99
0.934 Å 93.4 pm Californium Cf 98
0.938 Å 93.8 pm Gadolinium Gd 64
0.947 Å 94.7 pm Europium Eu 63
0.949 Å 94.9 pm Berkelium Bk 97
0.964 Å 96.4 pm Samarium Sm 62
0.97 Å 97 pm Curium Cm 96
0.97 Å 97 pm Tellurium Te 52
0.97 Å 97 pm Cadmium Cd 48
0.972 Å 97.2 pm Thorium Th 90
0.979 Å 97.9 pm Promethium Pm 61
0.982 Å 98.2 pm Americium Am 95
0.99 Å 99 pm Calcium Ca 20
0.995 Å 99.5 pm Neodymium Nd 60
1.013 Å 101.3 pm Praseodymium Pr 59
1.02 Å 102 pm Mercury Hg 80
1.02 Å 102 pm Sodium Na 11
1.03 Å 103 pm Bismuth Bi 83
1.034 Å 103.4 pm Cerium Ce 58
1.061 Å 106.1 pm Lanthanum La 57
1.1 Å 110 pm Nobelium No 102
1.119 Å 111.9 pm Actinium Ac 89
1.12 Å 112 pm Strontium Sr 38
1.19 Å 119 pm Lead Pb 82
1.26 Å 126 pm Silver Ag 47
1.33 Å 133 pm Fluorine F 9
1.35 Å 135 pm Barium Ba 56
1.38 Å 138 pm Potassium K 19
1.4 Å 140 pm Oxygen O 8
1.43 Å 143 pm Radium Ra 88
1.5 Å 150 pm Thallium Tl 81
1.52 Å 152 pm Rubidium Rb 37
1.67 Å 167 pm Cesium Cs 55
1.8 Å 180 pm Francium Fr 87
1.81 Å 181 pm Chlorine Cl 17
1.84 Å 184 pm Sulfur S 16
1.96 Å 196 pm Bromine Br 35
2.2 Å 220 pm Iodine I 53
2.3 Å 230 pm Polonium Po 84
Table of Ionic Radii Sorted by Atomic Number
Ionic Radius Name Sym #
0.012 Å 1.2 pm Hydrogen H 1
0.76 Å 76 pm Lithium Li 3
0.35 Å 35 pm Beryllium Be 4
0.23 Å 23 pm Boron B 5
0.13 Å 13 pm Nitrogen N 7
1.4 Å 140 pm Oxygen O 8
1.33 Å 133 pm Fluorine F 9
1.02 Å 102 pm Sodium Na 11
0.72 Å 72 pm Magnesium Mg 12
0.535 Å 53.5 pm Aluminum Al 13
0.4 Å 40 pm Silicon Si 14
0.38 Å 38 pm Phosphorus P 15
1.84 Å 184 pm Sulfur S 16
1.81 Å 181 pm Chlorine Cl 17
1.38 Å 138 pm Potassium K 19
0.99 Å 99 pm Calcium Ca 20
0.745 Å 74.5 pm Scandium Sc 21
0.605 Å 60.5 pm Titanium Ti 22
0.59 Å 59 pm Vanadium V 23
0.52 Å 52 pm Chromium Cr 24
0.46 Å 46 pm Manganese Mn 25
0.645 Å 64.5 pm Iron Fe 26
0.745 Å 74.5 pm Cobalt Co 27
0.69 Å 69 pm Nickel Ni 28
0.73 Å 73 pm Copper Cu 29
0.74 Å 74 pm Zinc Zn 30
0.62 Å 62 pm Gallium Ga 31
0.53 Å 53 pm Germanium Ge 32
0.58 Å 58 pm Arsenic As 33
0.5 Å 50 pm Selenium Se 34
1.96 Å 196 pm Bromine Br 35
1.52 Å 152 pm Rubidium Rb 37
1.12 Å 112 pm Strontium Sr 38
0.9 Å 90 pm Yttrium Y 39
0.72 Å 72 pm Zirconium Zr 40
0.69 Å 69 pm Niobium Nb 41
0.65 Å 65 pm Molybdenum Mo 42
0.56 Å 56 pm Technetium Tc 43
0.68 Å 68 pm Ruthenium Ru 44
0.68 Å 68 pm Rhodium Rh 45
0.86 Å 86 pm Palladium Pd 46
1.26 Å 126 pm Silver Ag 47
0.97 Å 97 pm Cadmium Cd 48
0.8 Å 80 pm Indium In 49
0.69 Å 69 pm Tin Sn 50
0.76 Å 76 pm Antimony Sb 51
0.97 Å 97 pm Tellurium Te 52
2.2 Å 220 pm Iodine I 53
1.67 Å 167 pm Cesium Cs 55
1.35 Å 135 pm Barium Ba 56
1.061 Å 106.1 pm Lanthanum La 57
1.034 Å 103.4 pm Cerium Ce 58
1.013 Å 101.3 pm Praseodymium Pr 59
0.995 Å 99.5 pm Neodymium Nd 60
0.979 Å 97.9 pm Promethium Pm 61
0.964 Å 96.4 pm Samarium Sm 62
0.947 Å 94.7 pm Europium Eu 63
0.938 Å 93.8 pm Gadolinium Gd 64
0.923 Å 92.3 pm Terbium Tb 65
0.912 Å 91.2 pm Dysprosium Dy 66
0.901 Å 90.1 pm Holmium Ho 67
0.881 Å 88.1 pm Erbium Er 68
0.869 Å 86.9 pm Thulium Tm 69
0.858 Å 85.8 pm Ytterbium Yb 70
0.848 Å 84.8 pm Lutetium Lu 71
0.71 Å 71 pm Hafnium Hf 72
0.64 Å 64 pm Tantalum Ta 73
0.62 Å 62 pm Tungsten W 74
0.56 Å 56 pm Rhenium Re 75
0.63 Å 73 pm Osmium Os 76
0.625 Å 62.5 pm Iridium Ir 77
0.625 Å 62.5 pm Platinum Pt 78
0.85 Å 85 pm Gold Au 79
1.02 Å 102 pm Mercury Hg 80
1.5 Å 150 pm Thallium Tl 81
1.19 Å 119 pm Lead Pb 82
1.03 Å 103 pm Bismuth Bi 83
2.3 Å 230 pm Polonium Po 84
1.8 Å 180 pm Francium Fr 87
1.43 Å 143 pm Radium Ra 88
1.119 Å 111.9 pm Actinium Ac 89
0.972 Å 97.2 pm Thorium Th 90
0.78 Å 78 pm Protactinium Pa 91
0.52 Å 52 pm Uranium U 92
0.75 Å 75 pm Neptunium Np 93
0.887 Å 88.7 pm Plutonium Pu 94
0.982 Å 98.2 pm Americium Am 95
0.97 Å 97 pm Curium Cm 96
0.949 Å 94.9 pm Berkelium Bk 97
0.934 Å 93.4 pm Californium Cf 98
0.925 Å 92.5 pm Einsteinium Es 99
1.1 Å 110 pm Nobelium No 102