Ionic radius

 ( Properties Of Chemical Elements ) 

Ionic radius, r_ion, 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 (pm) or (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.

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Trends

492

555

577

Unit cell parameters (in picometre, 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 bond character in the bonding. No bond is completely ionic, and some supposedly "ionic" compounds, especially of the , are particularly covalent in character. This is illustrated by the unit cell parameters for sodium and in the table. On the basis of the fluorides, one would say that Ag⁺ is larger than Na⁺, but on the basis of the and 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 Polarizability.

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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.Linus Pauling (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 to the publication of revised ionic radii by Shannon. 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 r_ion(O²⁻) = 140 pm; data using that value are referred to as "effective" ionic radii. However, Shannon also includes data based on r_ion(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.

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Tables

+ Crystal ionic radii in picometer 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−).
1	Hydrogen	H
3	Lithium	Li
4	Beryllium	Be
5	Boron	B
6	Carbon	C
7	Nitrogen	N	132 (4)||||||||||30||||27|||||
8	Oxygen	O
9	Fluorine	F
11	Sodium	Na
12	Magnesium	Mg
13	Aluminium	Al
14	Silicon	Si
15	Phosphorus	P
16	Sulfur	S
17	Chlorine	Cl
19	Potassium	K
20	Calcium	Ca
21	Scandium	Sc
22	Titanium	Ti
23	Vanadium	V
24	Chromium ls	Cr
24	Chromium hs	Cr
25	Manganese ls	Mn
25	Manganese hs	Mn
26	Iron ls	Fe
26	Iron hs	Fe
27	Cobalt ls	Co
27	Cobalt hs	Co
28	Nickel ls	Ni
28	Nickel hs	Ni
29	Copper	Cu
30	Zinc	Zn
31	Gallium	Ga
32	Germanium	Ge
33	Arsenic	As
34	Selenium	Se
35	Bromine	Br
37	Rubidium	Rb
38	Strontium	Sr
39	Yttrium	Y
40	Zirconium	Zr
41	Niobium	Nb
42	Molybdenum	Mo
43	Technetium	Tc
44	Ruthenium	Ru		50 (4)
45	Rhodium	Rh
46	Palladium	Pd
47	Silver	Ag
48	Cadmium	Cd
49	Indium	In
50	Tin	Sn
51	Antimony	Sb
52	Tellurium	Te
53	Iodine	I
54	Xenon	Xe		62
55	Caesium	Cs
56	Barium	Ba
57	Lanthanum	La
58	Cerium	Ce
59	Praseodymium	Pr
60	Neodymium	Nd
61	Promethium	Pm
62	Samarium	Sm
63	Europium	Eu
64	Gadolinium	Gd
65	Terbium	Tb
66	Dysprosium	Dy
67	Holmium	Ho
68	Erbium	Er
69	Thulium	Tm
70	Ytterbium	Yb
71	Lutetium	Lu
72	Hafnium	Hf
73	Tantalum	Ta
74	Tungsten	W
75	Rhenium	Re
76	Osmium	Os		53 (4)
77	Iridium	Ir
78	Platinum	Pt
79	Gold	Au
80	Mercury	Hg
81	Thallium	Tl
82	Lead	Pb
83	Bismuth	Bi
84	Polonium	Po
85	Astatine	At
87	Francium	Fr
88	Radium	Ra
89	Actinium	Ac
90	Thorium	Th
91	Protactinium	Pa
92	Uranium	U
93	Neptunium	Np
94	Plutonium	Pu
95	Americium	Am
96	Curium	Cm
97	Berkelium	Bk
98	Californium	Cf
99	Einsteinium	Es

+ Effective ionic radii in picometer 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−).
1	Hydrogen	H
3	Lithium	Li
4	Beryllium	Be
5	Boron	B
6	Carbon	C
7	Nitrogen	N	146 (4)||||||||||16||||13|||||
8	Oxygen	O
9	Fluorine	F
11	Sodium	Na
12	Magnesium	Mg
13	Aluminium	Al
14	Silicon	Si
15	Phosphorus	P
16	Sulfur	S
17	Chlorine	Cl
19	Potassium	K
20	Calcium	Ca
21	Scandium	Sc
22	Titanium	Ti
23	Vanadium	V
24	Chromium ls	Cr
24	Chromium hs	Cr
25	Manganese ls	Mn
25	Manganese hs	Mn
26	Iron ls	Fe
26	Iron hs	Fe
27	Cobalt ls	Co
27	Cobalt hs	Co
28	Nickel ls	Ni
28	Nickel hs	Ni
29	Copper	Cu
30	Zinc	Zn
31	Gallium	Ga
32	Germanium	Ge
33	Arsenic	As
34	Selenium	Se
35	Bromine	Br
37	Rubidium	Rb
38	Strontium	Sr
39	Yttrium	Y
40	Zirconium	Zr
41	Niobium	Nb
42	Molybdenum	Mo
43	Technetium	Tc
44	Ruthenium	Ru		36 (4)
45	Rhodium	Rh
46	Palladium	Pd
47	Silver	Ag
48	Cadmium	Cd
49	Indium	In
50	Tin	Sn
51	Antimony	Sb
52	Tellurium	Te
53	Iodine	I
54	Xenon	Xe		48
55	Caesium	Cs
56	Barium	Ba
57	Lanthanum	La
58	Cerium	Ce
59	Praseodymium	Pr
60	Neodymium	Nd
61	Promethium	Pm
62	Samarium	Sm
63	Europium	Eu
64	Gadolinium	Gd
65	Terbium	Tb
66	Dysprosium	Dy
67	Holmium	Ho
68	Erbium	Er
69	Thulium	Tm
70	Ytterbium	Yb
71	Lutetium	Lu
72	Hafnium	Hf
73	Tantalum	Ta
74	Tungsten	W
75	Rhenium	Re
76	Osmium	Os		39 (4)
77	Iridium	Ir
78	Platinum	Pt
79	Gold	Au
80	Mercury	Hg
81	Thallium	Tl
82	Lead	Pb
83	Bismuth	Bi
84	Polonium	Po
85	Astatine	At
87	Francium	Fr
88	Radium	Ra
89	Actinium	Ac
90	Thorium	Th
91	Protactinium	Pa
92	Uranium	U
93	Neptunium	Np
94	Plutonium	Pu
95	Americium	Am
96	Curium	Cm
97	Berkelium	Bk
98	Californium	Cf
99	Einsteinium	Es

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Soft-sphere model

+Soft-sphere ionic radii (in pm) of some ions

For many compounds, the model of ions as hard spheres does not reproduce the distance between ions, $\{d\_\{mx\}\}$, 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, $\{r\_m\}$ and $\{r\_x\}$, and $\{d\_\{mx\}\}$, is given by

$\{d\_\{mx\}\}^k\; =\; \{r\_m\}^k\; +\; \{r\_x\}^k$,

where $k$ is an exponent that varies with the type of crystal structure. In the hard-sphere model, $k$ would be 1, giving $\{d\_\{mx\}\}\; =\; \{r\_m\}\; +\; \{r\_x\}$.

+Comparison between observed and calculated ion separations (in pm)

In the soft-sphere model, $k$ 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 $k$ has been given.

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Non-spherical ions The concept of ionic radii is based on the assumption of a spherical ion shape. However, from a group theory point of view the assumption is only justified for ions that reside on high-symmetry crystal lattice sites like Na and Cl in halite or Zn and S in sphalerite. A clear distinction can be made, when the point symmetry group of the respective lattice site is considered, which are the cubic groups O _h and T _d in NaCl and ZnS. For ions on lower-symmetry sites significant deviations of their electron density from a spherical shape may occur. This holds in particular for ions on lattice sites of polar symmetry, which are the crystallographic point groups C₁, C_{1 h}, C _n or C _nv, n = 2, 3, 4 or 6. A thorough analysis of the bonding geometry was recently carried out for pyrite compounds, where monovalent chalcogen ions reside on C₃ lattice sites. It was found that chalcogen ions have to be modeled by charge distributions with different radii along the symmetry axis and perpendicular to it.

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See also

• Atomic orbital
• Atomic radii of the elements
• Born equation
• Covalent radius
• Electride
• Ionic potential
• Ionic radius ratio
• Pauling's rules
• Stokes radius
• Van der Waals radius

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External links

• Aqueous Simple Electrolytes Solutions, H. L. Friedman, Felix Franks

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