Ionic radius, rion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice. Ionic radii are typically given in units of either picometers (pm) or angstroms (Å), with 1 Å = 100 pm. Typical values range from 31 pm (0.3 Å) to over 200 pm (2 Å).
The concept can be extended to solvated ions in liquid solutions taking into consideration the solvation shell.
Trends X−NaXAgXF464492Cl564555Br598577Unit cell parameters (in pm, equal to two M–X bond lengths) for sodium and silver halides. All compounds crystallize in the NaCl structure.
Ions may be larger or smaller than the neutral atom, depending on the ion's electric charge. When an atom loses an electron to form a cation, the other electrons are more attracted to the nucleus, and the radius of the ion gets smaller. Similarly, when an electron is added to an atom, forming an anion, the added electron increases the size of the electron cloud by interelectronic repulsion.
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. In general, ionic radius decreases with increasing positive charge and increases with increasing negative charge.
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.On the basis of conventional ionic radii, Ag+ (129 pm) is indeed larger than Na+ (116 pm) 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.
Determination
The distance between two ions in an ionic crystal can be determined by X-ray crystallography, which gives the lengths of the sides of the unit cell of a crystal. For example, the length of each edge of the unit cell of sodium chloride is found to be 564.02 pm. Each edge of the unit cell of sodium chloride may be considered to have the atoms arranged as Na+∙∙∙Cl−∙∙∙Na+, so the edge is twice the Na-Cl separation. Therefore, the distance between the Na+ and Cl− ions is half of 564.02 pm, which is 282.01 pm. However, although X-ray crystallography gives the distance between ions, it doesn't indicate where the boundary is between those ions, so it doesn't directly give ionic radii.
Landé estimated ionic radii by considering crystals in which the anion and cation have a large difference in size, such as LiI. The lithium ions are so much smaller than the iodide ions that the lithium fits into holes within the crystal lattice, allowing the iodide ions to touch. That is, the distance between two neighboring iodides in the crystal is assumed to be twice the radius of the iodide ion, which was deduced to be 214 pm. This value can be used to determine other radii. For example, the inter-ionic distance in RbI is 356 pm, giving 142 pm for the ionic radius of Rb+. In this way values for the radii of 8 ions were determined.
Wasastjerna estimated ionic radii by considering the relative volumes of ions as determined from electrical polarizability as determined by measurements of refractive index. These results were extended by Victor Goldschmidt. This is an 8 volume set of books by Goldschmidt. Both Wasastjerna and Goldschmidt used a value of 132 pm for the O2− ion.
Pauling used effective nuclear charge to proportion the distance between ions into anionic and a cationic radii.Pauling, L. (1960). The Nature of the Chemical Bond (3rd Edn.). Ithaca, NY: Cornell University Press. His data gives the O2− ion a radius of 140 pm.
A major review of crystallographic data led Shannon to publish revised ionic radii. Shannon gives different radii for different coordination numbers, and for high and low spin states of the ions. To be consistent with Pauling's radii, Shannon has used a value of rion(O2−) = 140 pm; data using that value are referred to as "effective" ionic radii. However, Shannon also includes data based on rion(O2−) = 126 pm; data using that value are referred to as "crystal" ionic radii. Shannon states that "it is felt that crystal radii correspond more closely to the physical size of ions in a solid." The two sets of data are listed in the two tables below.
Tables + Crystal ionic radii in pm of elements as a function of ionic charge and spin (ls = low spin, hs = high spin). Ions are 6-coordinate unless indicated differently in parentheses (e.g. "146 (4)" for 4-coordinate N3−).NumberNameSymbol3−2−1−1+2+3+4+5+6+7+8+1HydrogenH 208−4 (2) 3LithiumLi 90 4BerylliumBe595BoronB416CarbonC307NitrogenN132 (4)30278OxygenO1269FluorineF1192211SodiumNa 116 12MagnesiumMg 86 13AluminiumAl67.514SiliconSi5415PhosphorusP58 52 16SulfurS1705143 17ChlorineCl167 26 (3py)41 19PotassiumK152 20CalciumCa114 21ScandiumSc88.5 22TitaniumTi1008174.5 23VanadiumV93787268 24Chromium lsCr8775.5696358 24Chromium hsCr94 25Manganese lsMn81726747 (4)39.5 (4)60 25Manganese hsMn9778.5 26Iron lsFe756972.539 (4) 26 Iron hsFe9278.5 27Cobalt lsCo7968.5 27Cobalt hsCo88.57567 28Nickel lsNi837062 28Nickel hsNi74 29CopperCu918768 ls 30ZincZn88 31GalliumGa76 32GermaniumGe8767 33ArsenicAs726034SeleniumSe1846456 35 BromineBr18273 (4sq)45 (3py)53 37RubidiumRb166 38StrontiumSr132 39YttriumY104 40ZirconiumZr86 41NiobiumNb868278 42MolybdenumMo83797573 43TechnetiumTc78.57470 44RutheniumRu827670.552 (4)50 (4)45Rhodium Rh80.57469 46 Palladium Pd73 (2)1009075.5 47 Silver Ag12910889 48 Cadmium Cd109 49 Indium In94 50 Tin Sn 83 51 Antimony Sb 9074 52 Tellurium Te 20711170 53 Iodine I20610967 54 Xenon Xe 62 55 Caesium Cs 181 56 Barium Ba149 57 Lanthanum La 117.2 58 Cerium Ce 115101 59 Praseodymium Pr11399 60 Neodymium Nd143 (8)112.3 61 Promethium Pm 111 62 Samarium Sm 136 (7)109.8 63 Europium Eu 131108.7 64 Gadolinium Gd107.8 65 Terbium Tb 106.390 66 Dysprosium Dy 121105.2 67 Holmium Ho104.1 68 Erbium Er 103 69 Thulium Tm117102 70 Ytterbium Yb116100.8 71 Lutetium Lu 100.1 72 Hafnium Hf 85 73 Tantalum Ta 868278 74 Tungsten W807674 75 Rhenium Re77726967 76 Osmium Os7771.568.566.553 (4) 77 Iridium Ir8276.571 78 Platinum Pt9476.571 79 Gold Au1519971 80 Mercury Hg133116 81 Thallium Tl 164102.5 82 Lead Pb13391.5 83 Bismuth Bi 11790 84 Polonium Po10881 85 Astatine At76 87 Francium Fr 194 88 Radium Ra162 (8) 89Actinium Ac126 90 Thorium Th 108 91 Protactinium Pa11610492 92 Uranium U 116.51039087 93 Neptunium Np 124115101898685 94 Plutonium Pu 1141008885 95 Americium Am 140 (8)111.599 96 Curium Cm 11199 97 Berkelium Bk 11097 98 Californium Cf 10996.1 99 Einsteinium Es92.8R. G. Haire, R. D. Baybarz: "Identification and Analysis of Einsteinium Sesquioxide by Electron Diffraction", in: Journal of Inorganic and Nuclear Chemistry, 1973, 35 (2), S. 489–496; .
+ Effective ionic radii in pm of elements as a function of ionic charge and spin (ls = low spin, hs = high spin). Ions are 6-coordinate unless indicated differently in parentheses (e.g. "146 (4)" for 4-coordinate N3−). NumberNameSymbol3−2−1−1+2+3+4+5+6+7+8+1HydrogenH 139.9−18 (2) 3LithiumLi764BerylliumBe455BoronB276CarbonC167NitrogenN146 (4)16138OxygenO1409FluorineF133811SodiumNa10212MagnesiumMg7213AluminiumAl53.514SiliconSi4015PhosphorusP21244 38 16SulfurS1843729 17ChlorineCl18112 (3py)27 19PotassiumK138 20CalciumCa100 21ScandiumSc74.5 22TitaniumTi866760.5 23VanadiumV79645854 24Chromium lsCr7361.5554944 24Chromium hsCr80 25Manganese lsMn67585333 (4)25.5 (4)46 25Manganese hsMn8364.5 26Iron lsFe615558.525 (4) 26Iron hsFe7864.5 27Cobalt lsCo6554.5 27Cobalt hsCo74.56153 28Nickel lsNi695648 28Nickel hsNi60 29CopperCu777354 ls 30ZincZn74 31GalliumGa62 32GermaniumGe7353 33ArsenicAs584634SeleniumSe1985042 35 BromineBr19659 (4sq)31 (3py)39 37RubidiumRb152 38StrontiumSr118 39YttriumY90 40ZirconiumZr72 41NiobiumNb726864 42MolybdenumMo69656159 43TechnetiumTc64.56056 44RutheniumRu686256.538 (4)36 (4)45Rhodium Rh66.56055 46 Palladium Pd59 (2)867661.5 47 Silver Ag1159475 48 Cadmium Cd95 49 Indium In80 50 Tin Sn 10269 51 Antimony Sb 7660 52 Tellurium Te 2219756 53 Iodine I2209553 54 Xenon Xe 48 55 Caesium Cs 167 56 Barium Ba135 57 Lanthanum La 103.2 58 Cerium Ce 10187 59 Praseodymium Pr9985 60 Neodymium Nd129 (8)98.3 61 Promethium Pm 97 62 Samarium Sm 122 (7)95.8 63 Europium Eu 11794.7 64 Gadolinium Gd93.5 65 Terbium Tb 92.376 66 Dysprosium Dy 10791.2 67 Holmium Ho90.1 68 Erbium Er 89 69 Thulium Tm10388 70 Ytterbium Yb 10286.8 71 Lutetium Lu 86.1 72 Hafnium Hf 71 73 Tantalum Ta 726864 74 Tungsten W666260 75 Rhenium Re 63585553 76 Osmium Os 6357.554.552.539 (4) 77 Iridium Ir6862.557 78 Platinum Pt 8062.557 79 Gold Au 1378557 80 Mercury Hg 119102 81 Thallium Tl 15088.5 82 Lead Pb 11977.5 83 Bismuth Bi 10376 84 Polonium Po223. 9467 85 Astatine At62 87 Francium Fr 180 88 Radium Ra148 (8) 89Actinium Ac106.5 (6)122.0 (9) 90 Thorium Th 94 91 Protactinium Pa1049078 92 Uranium U 102.5897673 93 Neptunium Np 11010187757271 94 Plutonium Pu 100867471 95 Americium Am 126 (8)97.585 96 Curium Cm 9785 97 Berkelium Bk 9683 98 Californium Cf 9582.1 99 Einsteinium Es83.5
Soft-sphere model +Soft-sphere ionic radii (in pm) of some ionsCation, MRMAnion, XRX Li+ 109.4 Cl− 218.1 Na+ 149.7 Br− 237.2For many compounds, the model of ions as hard spheres does not reproduce the distance between ions, , to the accuracy with which it can be measured in crystals. One approach to improving the calculated accuracy is to model ions as "soft spheres" that overlap in the crystal. Because the ions overlap, their separation in the crystal will be less than the sum of their soft-sphere radii. The relation between soft-sphere ionic radii, and , and , is given by
,
where is an exponent that varies with the type of crystal structure. In the hard-sphere model, would be 1, giving . +Comparison between observed and calculated ion separations (in pm) MX Observed Soft-sphere model LiCl 257.0 257.2 LiBr 275.1 274.4 NaCl 282.0 281.9 NaBr 298.7 298.2 In the soft-sphere model, has a value between 1 and 2. For example, for crystals of group 1 halides with the sodium chloride structure, a value of 1.6667 gives good agreement with experiment. Some soft-sphere ionic radii are in the table. These radii are larger than the crystal radii given above (Li+, 90 pm; Cl−, 167 pm). Inter-ionic separations calculated with these radii give remarkably good agreement with experimental values. Some data are given in the table. Curiously, no theoretical justification for the equation containing has been given.
Non-spherical ions