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Chapter: 3 Chemistry
    Section: 3.7 Properties of chemical bonds
        SubSection: 3.7.6 Ionic radii

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3.7.6 Ionic radii

Empirical values for ionic radii are used for predicting interatomic distances and packing in crystals, even when the forces are far from being purely ionic. The ions are regarded as hard spheres, whose size is, to a first approximation, constant in all environments. To a second approximation, it has long been recognized that there is a dependence on coordination number, and, more recently, for transition-metal ions, a dependence also on spin state. Separate values are listed accordingly in the table.

The coordination number of an atom is the number of its first-nearest neighbours of opposite sign. It may sometimes be ambiguous when the neighbours are not all at exactly the same distance; judgement and experience, rather than formal rules, must then decide which of them are to be counted as first-nearest. Different decisions on this point will lead to small differences in estimates of the mean cation–anion distance within the polyhedron (the figure whose vertices are the first-nearest neighbour anions around the cation).

The spin state of a transition-metal ion refers to its spin angular momentum. Normally this depends on the ground state of the free atom, and is given by Hund's rule; this is the high-spin state. In a particular crystal structure, however, ions may be situated in strong ligand fields which reduce the spin angular momentum; this is the low-spin state2.

In using the table, no a priori knowledge of the ionic character of the bonds, i.e. of the degree of polarization or covalent character, is needed. An estimate of the degree of polarization is given by the Pauling electrostatic valence, whose value is the valency of the cation divided by its coordination number Z. The radii tabulated for the different coordination numbers have been so derived as to allow for this, and will predict the mean cation–anion distance within a polyhedron to an accuracy, generally, of about ±3 pm. Individual distances may, however, show a rather larger scatter. The tabulated values also predict the shortest anion–anion polyhedron edges and packing distances for polyhedra where the Pauling valence is not greater than 1; for greater Pauling valences, the polyhedron edges are considerably shorter than the anion diameter.

The radii r tabulated are taken, with some simplification, from those listed by R. D. Shannon and C. T. Prewitt, Acta Cryst., 1969, B25, 925, with corrections ibid., 1970, B26, 1046. Methods of derivation and references to earlier work will be found there. For the sort of corrections to be made for more precise work, see, for example, W. H. Baur, Trans. Am. Cryst. Assoc., 1970, 6, 129.




Ionic radii

Z
Cation

4

6  

8

12

 Z
 Cation

4

    6    

    8

12

 Z
Cation

4

6

8

     12

r/pm

r/pm

r/pm

  Li+

59

74 

 

 

  Pb2+

  94

118  

129  

149  

  Si4+

26

40

 

 

  Na+

 

102 

 116

 

   

   

 

 

 

  Ge4+

40

54

 

 

  K+

 

138 

 151

160

  B3+

  12

 

 

 

  Sn4+

 

69

 

 

  Rb+

 

149 

 160

173

  Al3+

  39

53  

 

 

  Pb4+

 

78

94

 

  Cs+

 

170 

 182

188

  Ga3+

  47

62  

 

 

   

 

 

 

 

 

 

 

 

 

  In3+

   

79  

92  

 

  Ti4+

 

60

 

 

  Ag+

 

115 

 130

 

  Tl3+

   

88  

100  

 

  Zr4+

 

72

84

 

  Tl+

 

150 

 160

176

   

   

 

 

 

  Hf 4+

 

71

83

 

 

 

 

 

 

  Sc3+

   

73  

87  

 

  Th4+

 

100

106

 

  Be2+

27

 

 

 

  Y3+

   

90  

101  

 

  U4+

 

97

100

 

  Mg2+

58

72 

 

 

  La3+

   

106  

118  

132  

    

 

 

 

 

  Ca2+

 

100 

 112

135

   

   

 

 

 

  P5+

17

35

 

 

  Sr2+

 

116 

 125

144

  Cr3+

   

61  

 

 

  As5+

34

50

 

 

  Ba2+

 

136 

 142

160

  Mn3+

LS

   

58  

 

 

  Sb5+

 

61

 

 

 

 

 

 

 

  Mn3+

HS

   

65  

 

 

  Bi5+

 

74

 

 

  Zn2+

60

75 

 

 

  Fe3+

LS

   

55  

 

 

  V5+

36

54

 

 

  Cd2+

80

95 

107

131

  Fe3+

HS

  49

65  

 

 

  Nb5+

32 

64

 

 

 

 

 

 

 

  Co3+

LS

   

53  

 

 

  Ta5+

 

64

69

 

  Mn2+   LS

 

67 

 

 

  Co3+

HS

   

61  

 

 

   

 

 

 

 

  Mn2+   HS

 

82 

 

 

   

   

 

 

 

  S6+

12

 

 

 

  Fe2+   LS

 

61 

 

 

  Bi3+

   

102  

111  

 

   

 

 

 

 

  Fe2+   HS

63

78 

 

 

   

   

 

 

 

  Cr6+

30

52

 

 

  Co2+   LS

 

57 

 

 

  Pu3+

   

100  

 

 

  Mo6+

42

60

 

 

  Co2+   HS

 

74 

 

 

   

   

 

 

 

  W6+

41

58

 

 

  Ni2+

 

70 

 

 

   

   

 

 

 

  U6+

48

75

 

 

  Cu2+

 

73 

 

 

   

   

 

 

 

    

 

 

 

 

Z
Anion

2

4  

6

  

 

Z
Anion

2

4   

6   

 

    

 

 

 

 

r/pm

   r/pm

    

 

 

 

 

  F

128  

131  

133

 

  O2−

  135

138  

140  

 

    

 

 

 

 

  Cl

 

181† 

 

 

  S2−

   

184† 

 

 

   

 

 

 

 

  Br

 

196† 

 

 

   

   

 

 

 

   

 

 

 

 

  I

 

220† 

 

 

   

   

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LS, low-spin state; HS, high-spin state.
Independent of coordination number.




M.L.McGlashan

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