Ionic Radius
Ionic Radius, rion, is a measure of the size of an atoms 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 Victor Goldschmidt and Linus Pauling in the 1920s to summarize the data being generated by the (at the time) 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 invariably 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. 1464 for N−3 with 4 coordinates). .[2] Atomic↓ Element↓ ↓ ionic radius pm↓
Number Charge, ls = low spin, hs= high spin
↓ ↓ ↓ −3↓ −2↓ −1↓ +1↓ +2↓ +3↓ +4↓ +5↓ +6↓ +7↓ +8↓
3 Lithium Li 76
4 Beryllium Be 45
5 Boron B 27
6 Carbon C 16
7 Nitrogen N 1464 16 13
8 Oxygen O 140
9 Fluorine F 133 8
11 Sodium Na 102
12 Magnesium Mg 72
13 Aluminum Al 53.5
14 Silicon Si 40
15 Phosphorus P 44 38
16 Sulfur S 184 37 29
17 Chlorine Cl 181 12 27
19 Potassium K 138
20 Calcium Ca 100
21 Scandium Sc 74.5
22 Titanium Ti 86 67 60.5
23 Vanadium V 79 64 58 54
24 Chromium Cr 73ls 80hs 61.5 55 49 44
25 Manganese Mn 67 58ls 64.5hs 53 334 25.54 46
26 Iron Fe 61ls 78hs 55ls 64.5hs 58.5 254
27 Cobalt Co 65ls 74.5hs 54.5ls 61hs 53
28 Nickel Ni 69 56ls 60hs 48ls
29 Copper Cu 77 73 54ls
30 Zinc Zn 74
31 Gallium Ga 62
32 Germanium Ge 73 53
33 Arsenic As 58 46
34 Selenium Se 198 50 42
35 Bromine Br 196 594sq 314 39
37 Rubidium Rb 152
38 Strontium Sr 118
39 Yttrium Y 90
40 Zirconium Zr 72
41 Niobium Nb 72 68 64
42 Molybdenum Mo 69 65 61 59
43 Technetium Tc 64.5 60 56
44 Ruthenium Ru 68 62 56.5 384 364
45 Rhodium Rh 66.5 60 55
46 Palladium Pd 592 86 76 61.5
47 Silver Ag 115 94 75
48 Cadmium Cd 95
49 Indium In 80
50 Tin Sn 112 69
51 Antimony Sb 76 60
52 Tellurium Te 221 97 56
53 Iodine I 220 95 53
54 Xenon Xe 48
55 Caesium Cs 167
56 Barium Ba 135
57 Lanthanum La 103.2
58 Cerium Ce 102 87
59 Praseodymium Pr 99 85
60 Neodymium Nd 1298 98.3
61 Promethium Pm 97
62 Samarium Sm 1224 95.8
63 Europium Eu 117 94.7
64 Gadolinium Gd 93.8
65 Terbium Tb 92.3 76
66 Dysprosium Dy 107 91.2
67 Holmium Ho 90.1
68 Erbium Er 89
69 Thulium Tm 103 88
70 Ytterbium Yb 102 86.8
71 Lutetium Lu 86.1
72 Hafnium Hf 71
73 Tantalum Ta 72 68 64
74 Tungsten W 66 62 60
75 Rhenium Re 63 58 55 53
76 Osmium Os 63 57.5 54.5 52.5 394
77 Iridium Ir 68 62.5 57
78 Platinum Pt 86 62.5 57
79 Gold Au 137 85 57
80 Mercury Hg 119 102
81 Thallium Tl 150 88.5
82 Lead Pb 119 77.5
83 Bismuth Bi 103 76
84 Polonium Po 94 67
85 Astatine At 62
87 Francium Fr 180
88 Radium Ra 1488
89 Actinium Ac 112
90 Thorium Th 94
91 Protactinium Pa 104 90 78
92 Uranium U 102.5 89 78 73
93 Neptunium Np 110 101 87 75 72 71
94 Plutonium Pu 100 86 74 71
95 Americium Am 1268 97.5 85
96 Curium Cm 97 85
97 Berkelium Bk 96 83
98 Californium Cf 95 82.1
Generalization
The concept of ionic radii is based on the assumption of a spherical ion shape. However, from a group-theoretical 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[4], which are the cubic groups O6 and Td 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, C1h, Cn or Cnv, n = 2, 3, 4 or 6[5]. A thorough analysis of the bonding geometry was recently carried out for pyrite-type disulfides, where monovalent sulfur ions reside on C3 lattice sites. It was found that the sulfur ions have to be modeled by ellipsoids with different radii in direction of the symmetry axis and perpendicular to it[6]. Remarkably, it turned out in this case that it is not the ionic radius, but the ionic volume that remains constant in different crystalline compounds.
The concept of ionic radius was developed independently by Victor Goldschmidt and Linus Pauling in the 1920s to summarize the data being generated by the (at the time) 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 invariably 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. 1464 for N−3 with 4 coordinates). .[2] Atomic↓ Element↓ ↓ ionic radius pm↓
Number Charge, ls = low spin, hs= high spin
↓ ↓ ↓ −3↓ −2↓ −1↓ +1↓ +2↓ +3↓ +4↓ +5↓ +6↓ +7↓ +8↓
3 Lithium Li 76
4 Beryllium Be 45
5 Boron B 27
6 Carbon C 16
7 Nitrogen N 1464 16 13
8 Oxygen O 140
9 Fluorine F 133 8
11 Sodium Na 102
12 Magnesium Mg 72
13 Aluminum Al 53.5
14 Silicon Si 40
15 Phosphorus P 44 38
16 Sulfur S 184 37 29
17 Chlorine Cl 181 12 27
19 Potassium K 138
20 Calcium Ca 100
21 Scandium Sc 74.5
22 Titanium Ti 86 67 60.5
23 Vanadium V 79 64 58 54
24 Chromium Cr 73ls 80hs 61.5 55 49 44
25 Manganese Mn 67 58ls 64.5hs 53 334 25.54 46
26 Iron Fe 61ls 78hs 55ls 64.5hs 58.5 254
27 Cobalt Co 65ls 74.5hs 54.5ls 61hs 53
28 Nickel Ni 69 56ls 60hs 48ls
29 Copper Cu 77 73 54ls
30 Zinc Zn 74
31 Gallium Ga 62
32 Germanium Ge 73 53
33 Arsenic As 58 46
34 Selenium Se 198 50 42
35 Bromine Br 196 594sq 314 39
37 Rubidium Rb 152
38 Strontium Sr 118
39 Yttrium Y 90
40 Zirconium Zr 72
41 Niobium Nb 72 68 64
42 Molybdenum Mo 69 65 61 59
43 Technetium Tc 64.5 60 56
44 Ruthenium Ru 68 62 56.5 384 364
45 Rhodium Rh 66.5 60 55
46 Palladium Pd 592 86 76 61.5
47 Silver Ag 115 94 75
48 Cadmium Cd 95
49 Indium In 80
50 Tin Sn 112 69
51 Antimony Sb 76 60
52 Tellurium Te 221 97 56
53 Iodine I 220 95 53
54 Xenon Xe 48
55 Caesium Cs 167
56 Barium Ba 135
57 Lanthanum La 103.2
58 Cerium Ce 102 87
59 Praseodymium Pr 99 85
60 Neodymium Nd 1298 98.3
61 Promethium Pm 97
62 Samarium Sm 1224 95.8
63 Europium Eu 117 94.7
64 Gadolinium Gd 93.8
65 Terbium Tb 92.3 76
66 Dysprosium Dy 107 91.2
67 Holmium Ho 90.1
68 Erbium Er 89
69 Thulium Tm 103 88
70 Ytterbium Yb 102 86.8
71 Lutetium Lu 86.1
72 Hafnium Hf 71
73 Tantalum Ta 72 68 64
74 Tungsten W 66 62 60
75 Rhenium Re 63 58 55 53
76 Osmium Os 63 57.5 54.5 52.5 394
77 Iridium Ir 68 62.5 57
78 Platinum Pt 86 62.5 57
79 Gold Au 137 85 57
80 Mercury Hg 119 102
81 Thallium Tl 150 88.5
82 Lead Pb 119 77.5
83 Bismuth Bi 103 76
84 Polonium Po 94 67
85 Astatine At 62
87 Francium Fr 180
88 Radium Ra 1488
89 Actinium Ac 112
90 Thorium Th 94
91 Protactinium Pa 104 90 78
92 Uranium U 102.5 89 78 73
93 Neptunium Np 110 101 87 75 72 71
94 Plutonium Pu 100 86 74 71
95 Americium Am 1268 97.5 85
96 Curium Cm 97 85
97 Berkelium Bk 96 83
98 Californium Cf 95 82.1
Generalization
The concept of ionic radii is based on the assumption of a spherical ion shape. However, from a group-theoretical 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[4], which are the cubic groups O6 and Td 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, C1h, Cn or Cnv, n = 2, 3, 4 or 6[5]. A thorough analysis of the bonding geometry was recently carried out for pyrite-type disulfides, where monovalent sulfur ions reside on C3 lattice sites. It was found that the sulfur ions have to be modeled by ellipsoids with different radii in direction of the symmetry axis and perpendicular to it[6]. Remarkably, it turned out in this case that it is not the ionic radius, but the ionic volume that remains constant in different crystalline compounds.
- ^ Pauling, L. (1960). The Nature of the Chemical Bond (3rd Edn.). Ithaca, NY: Cornell University Press.
- ^ 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
- ^ On the basis of conventional ionic radii, Ag+ (129 pm) is indeed larger than Na+ (116 pm)
- ^ H. Bethe (1929). "Termaufspaltung in Kristallen". Ann. Physik 3: 133–208.
- ^ M. Birkholz (1995). "Crystal-field induced dipoles in heteropolar crystals – II. Physical significance". Z. Phys. B 96: 333–340. doi:10.1007/BF01313055.
- ^ M. Birkholz, R. Rudert (2008). "Interatomic distances in pyrite-structure disulfides – a case for ellipsoidal modelling of sulphur ions". phys. stat. sol. (b) 245: 1858–1864. doi:10.1002/pssb.200879532.
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