Ionic radius

Template:Atomic radius The ionic radius, r_ion, 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[r_ion(Na⁺) + r_ion(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.

A major review of crystallographic data led to the publication of a revised set of ionic radii in 1976, and these are preferred to Pauling's original values. Some sources have retained Pauling's reference of r_ion(O²⁻) = 140 pm, while other sources prefer to list "effective" ionic radii based on r_ion(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. 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

See also

• Atomic radii of the elements

External links

• WebElements