**离子半径**（*r*ion）是对晶格中离子的大小的一种量度。离子半径通常以皮米（pm）或埃（Å，1Å=100pm）作为单位，具体数值一般在30pm（0.3Å）到200pm（2Å）之间。

历史
--

离子半径的概念是由Goldschmidt和Linus Pauling在20世纪20年代分别独立提出，以总结由当时的新技术——X射线晶体学所产生的数据。Pauling所提出的方法更有影响力。X射线晶体学可以迅速给出一个晶胞的各边长度，但这一技术在大多数情况下并不能够分别两个不同的离子。例如，我们可以通过X射线晶体学得知氯化钠晶体晶胞的边长是564.02 pm，这一距离便是一个钠离子与一个氯离子中心间距离的两倍：

2[*r*ion(Na+) + *r*ion(Cl−)] = 564.02 pm
然而，我们无法看出这一长度中钠离子半径和氯离子半径各自所占的比例。通过平衡距离决定每个离子各贡献多少便成了定出离子半径的主要障碍。

Wasastjerna在1923年根据离子的摩尔折射度与体积成正比的方法，定出了八个离子的半径，包括 F−（1.33Å）和 O2−（1.32Å）。1927年Goldschmidt采用Wasastjerna的数据，从离子晶体得出的平衡距离数据，推出了八十多种离子的半径。

1927年Pauling用五个晶体核间距离的数据（Li2O、NaF、KCl、RbBr、CsI），将 O2− 的半径定为140 pm，用半经验的方法推出了大量的离子半径数据。他所用的方法是：离子的大小由它最外层的电子排布所决定，而最外层电子排布与有效核电荷成反比，而有效核电荷等于核电荷（Z）减去屏蔽常数（σ），即：

\rm r =\frac{C\_n}{Z-\sigma}，\ \ \ C\_n 为由量子数决定的常数。
经过1976年对晶体数据的校对，Shannon等人公布了一份修订版的离子半径数据，而这份新数据比Pauling的原始数据更好。部分数据保留了Pauling所采用的 *r*ion(O2−) = 140 pm 作为其他离子半径的基础，而另一部分数据则以 *r*ion(O2−) = 126 pm 作为其他离子半径的基础。后者被认为更加接近离子晶体中准确的正负离子相对大小。

性质
--

离子晶体中，正负离子存在静电吸引作用，外层电子云之间也有排斥作用。可以认为在以上两者达到平衡时，两个互相接触的球形离子的半径之和等于核间的平衡距离。

对于某一个给定的离子来说，它的离子半径并不是一定的，而是随配位数、自旋态和其它因素而发生变化。尽管如此，离子半径仍体现一定的周期性。与原子半径的变化情况相反，在同一週期中，离子半径通常随原子序数的增大而减小。离子的大小（对某个确定的离子）随配位数的增多而增大。另外，一个高自旋态的离子要比该离子在低自旋态时的半径要大。一个原子负离子态通常要比其对应的正离子态的半径要大，但某些碱金属的氟化物并不遵从如此规律。总体来说，离子半径随正电荷的增多而减小，随负电荷的增多而增大。

| X− | NaX | AgX |
| --- | --- | --- |
| F | 464 | 492 |
| Cl | 564 | 555 |
| Br | 598 | 577 |
| 钠、银卤化物的晶胞边长(以pm为单位，相当于两个M–X键长)。所有晶体均为NaCl晶型。 |
|

一个晶体中的"异常的"离子半径常常是晶体中键的较强共价性的标志。化学键中不存在彻底的离子键，而某些"离子"化合物中，特别是过渡金属的离子化合物中，具有较强的共价性。这可以利用图表中钠和银的卤化物的晶胞参数来说明。如果以氟为参照，我们可以得出 Ag+ 的离子半径比 Na+ 的大；但如果以氯或溴为参照，我们会得到相反的结论。这是因为较强的共价性缩短了 AgCl、AgBr 的键长，所以 Ag+ 的离子半径受到了一个在钠的卤化物（钠的电负性更强）和氟化银（氟离子不可极化）中均无法体现的作用的影响。

离子半径数据  
（除注明外均为六配位，非六配位时以上标标注，  
如**+34**。*ls* =低自旋，*hs*=高自旋。）  
　| 原子序数 | 元素名称 | 元素符号 | 离子半径pm |
| --- | --- | --- | --- |
| 1 | 氢 | H | 

|  |  |
| --- | --- |
| **-1** | 146 |

 |
| 3 | 锂 | Li | 

|  |  |
| --- | --- |
| **+1** | 76 |

 |
| 4 | 铍 | Be | 

|  |  |
| --- | --- |
| **+2** | 45 |

 |
| 5 | 硼 | B | 

|  |  |
| --- | --- |
| **+3** | 27 |

 |
| 6 | 碳 | C | 

|  |  |
| --- | --- |
| **+4** | 16 |

 |
| 7 | 氮 | N | 

|  |  |
| --- | --- |
| **−3**4 | 146 |
| **+3** | 16 |
| **+5** | 13 |

 |
| 8 | 氧 | O | 

|  |  |
| --- | --- |
| **−2** | 140 |

 |
| 9 | 氟 | F | 

|  |  |
| --- | --- |
| **−1** | 133 |
| **+7** | 8 |

 |
| 11 | 钠 | Na | 

|  |  |
| --- | --- |
| **+1** | 102 |

 |
| 12 | 镁 | Mg | 

|  |  |
| --- | --- |
| **+2** | 72 |

 |
| 13 | 铝 | Al | 

|  |  |
| --- | --- |
| **+3** | 53.5 |

 |
| 14 | 硅 | Si | 

|  |  |
| --- | --- |
| **+4** | 40 |

 |
| 15 | 磷 | P | 

|  |  |
| --- | --- |
| **+3** | 44 |
| **+5** | 38 |

 |
| 16 | 硫 | S | 

|  |  |
| --- | --- |
| **−2** | 184 |
| **+4** | 37 |
| **+6** | 29 |

 |
| 17 | 氯 | Cl | 

|  |  |
| --- | --- |
| **−1** | 181 |
| **+5** | 12 |
| **+7** | 27 |

 |
| 19 | 钾 | K | 

|  |  |
| --- | --- |
| **+1** | 138 |

 |
| 20 | 钙 | Ca | 

|  |  |
| --- | --- |
| **+2** | 100 |

 |
| 21 | 钪 | Sc | 

|  |  |
| --- | --- |
| **+3** | 74.5 |

 |
| 22 | 钛 | Ti | 

|  |  |
| --- | --- |
| **+2** | 86 |
| **+3** | 67 |
| **+4** | 60.5 |

 |
| 23 | 钒 | V | 

|  |  |
| --- | --- |
| **+2** | 64 |
| **+4** | 58 |
| **+5** | 54 |

 |
| 24 | 铬 | Cr | 

|  |  |  |
| --- | --- | --- |
| **+2** | 73 | *ls* |
| **+2** | 80 | *hs* |
| **+3** | 61.5 |
| **+4** | 55 |
| **+5** | 49 |
| **+6** | 44 |

 |
| 25 | 锰 | Mn | 

|  |  |
| --- | --- |
| **+2** | 67 |
| **+3** | 58 | *ls* |
| **+3** | 64.5 | *hs* |
| **+4** | 53 |
| **+5**4 | 33 |
| **+6**4 | 25.5 |
| **+7** | 46 |

 |
| 26 | 铁 | Fe | 

|  |  |  |
| --- | --- | --- |
| **+2** | 61 | *ls* |
| **+2** | 78 | *hs* |
| **+3** | 55 | *ls* |
| **+3** | 64.5 | *hs* |
| **+4** | 58.5 |
| **+6**4 | 25 |

 |
| 27 | 钴 | Co | 

|  |  |  |
| --- | --- | --- |
| **+2** | 65 | *ls* |
| **+2** | 74.5 | *hs* |
| **+3** | 54.5 | *ls* |
| **+3** | 61 | *hs* |
| **+4** | 53 |

 |
| 28 | 镍 | Ni | 

|  |  |
| --- | --- |
| **+2** | 69 |
| **+3** | 56 | *ls* |
| **+3** | 60 | *hs* |
| **+4** | 48 | *ls* |

 |
| 29 | 铜 | Cu | 

|  |  |
| --- | --- |
| **+1** | 77 |
| **+2** | 73 |
| **+3** | 54 | *ls* |

 |
| 30 | 锌 | Zn | 

|  |  |
| --- | --- |
| **+2** | 74 |

 |
| 31 | 镓 | Ga | 

|  |  |
| --- | --- |
| **+3** | 62 |

 |
| 32 | 锗 | Ge | 

|  |  |
| --- | --- |
| **+2** | 73 |
| **+4** | 53 |

 |
| 33 | 砷 | As | 

|  |  |
| --- | --- |
| **+3** | 58 |
| **+5** | 46 |

 |
| 34 | 硒 | Se | 

|  |  |
| --- | --- |
| **−2** | 198 |
| **+4** | 50 |
| **+6** | 42 |

 |
| 35 | 溴 | Br | 

|  |  |
| --- | --- |
| **−1** | 196 |
| **+3**4sq | 59 |
| **+5**4 | 31 |
| **+7** | 39 |

 |
| 37 | 铷 | Rb | 

|  |  |
| --- | --- |
| **+1** | 152 |

 |
| 38 | 锶 | Sr | 

|  |  |
| --- | --- |
| **+2** | 118 |

 |
| 39 | 钇 | Y | 

|  |  |
| --- | --- |
| **+3** | 90 |

 |
| 40 | 锆 | Zr | 

|  |  |
| --- | --- |
| **+4** | 72 |

 |
| 41 | 铌 | Nb | 

|  |  |
| --- | --- |
| **+3** | 72 |
| **+4** | 68 |
| **+5** | 64 |

 |
| 42 | 钼 | Mo | 

|  |  |
| --- | --- |
| **+3** | 69 |
| **+4** | 65 |
| **+5** | 61 |
| **+6** | 59 |

 |
| 43 | 锝 | Tc | 

|  |  |
| --- | --- |
| **+4** | 64.5 |
| **+5** | 60 |
| **+7** | 56 |

 |
| 44 | 钌 | Ru | 

|  |  |
| --- | --- |
| **+3** | 68 |
| **+4** | 62 |
| **+5** | 56.5 |
| **+7**4 | 38 |
| **+8**4 | 36 |

 |
| 45 | 铑 | Rh | 

|  |  |
| --- | --- |
| **+3** | 66.5 |
| **+4** | 60 |
| **+5** | 55 |

 |
| 46 | 钯 | Pd | 

|  |  |
| --- | --- |
| **+1**2 | 59 |
| **+2** | 86 |
| **+3** | 76 |
| **+4** | 61.5 |

 |
| 47 | 银 | Ag | 

|  |  |
| --- | --- |
| **+1** | 115 |
| **+2** | 94 |
| **+3** | 75 |

 |
| 48 | 镉 | Cd | 

|  |  |
| --- | --- |
| **+2** | 95 |

 |
| 49 | 铟 | In | 

|  |  |
| --- | --- |
| **+3** | 80 |

 |
| 50 | 锡 | Sn | 

|  |  |
| --- | --- |
| **+2** | 112 |
| **+4** | 69 |

 |
| 51 | 锑 | Sb | 

|  |  |
| --- | --- |
| **+3** | 76 |
| **+5** | 60 |

 |
| 52 | 碲 | Te | 

|  |  |
| --- | --- |
| **−2** | 221 |
| **+4** | 97 |
| **+6** | 56 |

 |
| 53 | 碘 | I | 

|  |  |
| --- | --- |
| **−1** | 220 |
| **+5** | 95 |
| **+7** | 53 |

 |
| 54 | 氙 | Xe | 

|  |  |
| --- | --- |
| **+8** | 48 |

 |
| 55 | 铯 | Cs | 

|  |  |
| --- | --- |
| **+1** | 167 |

 |
| 56 | 钡 | Ba | 

|  |  |
| --- | --- |
| **+2** | 135 |

 |
| 57 | 镧 | La | 

|  |  |
| --- | --- |
| **+3** | 103.2 |
|

 |
| 58 | 铈 | Ce | 

|  |  |
| --- | --- |
| **+3** | 102 |
| **+4** | 87 |

 |
| 59 | 镨 | Pr | 

|  |  |
| --- | --- |
| **+3** | 99 |
| **+4** | 85 |

 |
| 60 | 钕 | Nd | 

|  |  |
| --- | --- |
| **+2**8 | 129 |
| **+3** | 98.3 |

 |
| 61 | 钷 | Pm | 

|  |  |
| --- | --- |
| **+3** | 97 |

 |
| 62 | 钐 | Sm | 

|  |  |
| --- | --- |
| **+2**4 | 122 |
| **+3** | 95.8 |

 |
| 63 | 铕 | Eu | 

|  |  |
| --- | --- |
| **+2** | 117 |
| **+3** | 94.7 |

 |
| 64 | 钆 | Gd | 

|  |  |
| --- | --- |
| **+3** | 93.8 |

 |
| 65 | 铽 | Tb | 

|  |  |
| --- | --- |
| **+3** | 92.3 |
| **+4** | 76 |

 |
| 66 | 镝 | Dy | 

|  |  |
| --- | --- |
| **+2** | 107 |
| **+3** | 91.2 |

 |
| 67 | 钬 | Ho | 

|  |  |
| --- | --- |
| **+3** | 90.1 |

 |
| 68 | 铒 | Er | 

|  |  |
| --- | --- |
| **+3** | 89 |

 |
| 69 | 铥 | Tm | 

|  |  |
| --- | --- |
| **+2** | 103 |
| **+3** | 88 |

 |
| 70 | 镱 | Yb | 

|  |  |
| --- | --- |
| **+2** | 102 |
| **+3** | 86.8 |

 |
| 71 | 镥 | Lu | 

|  |  |
| --- | --- |
| **+3** | 86.1 |

 |
| 72 | 铪 | Hf | 

|  |  |
| --- | --- |
| **+4** | 71 |

 |
| 73 | 钽 | Ta | 

|  |  |
| --- | --- |
| **+3** | 72 |
| **+4** | 68 |
| **+5** | 64 |

 |
| 74 | 钨 | W | 

|  |  |
| --- | --- |
| **+4** | 66 |
| **+5** | 62 |
| **+6** | 60 |

 |
| 75 | 铼 | Re | 

|  |  |
| --- | --- |
| **+4** | 63 |
| **+5** | 58 |
| **+6** | 55 |
| **+7** | 53 |

 |
| 76 | 锇 | Os | 

|  |  |
| --- | --- |
| **+4** | 63 |
| **+5** | 57.5 |
| **+6** | 54.5 |
| **+7** | 52.5 |
| **+8**4 | 39 |

 |
| 77 | 铱 | Ir | 

|  |  |
| --- | --- |
| **+3** | 68 |
| **+4** | 62.5 |
| **+5** | 57 |

 |
| 78 | 铂 | Pt | 

|  |  |
| --- | --- |
| **+2** | 86 |
| **+4** | 62.5 |
| **+5** | 57 |

 |
| 79 | 金 | Au | 

|  |  |
| --- | --- |
| **+1** | 137 |
| **+3** | 85 |
| **+5** | 57 |

 |
| 80 | 汞 | Hg | 

|  |  |
| --- | --- |
| **+1** | 119 |
| **+2** | 102 |

 |
| 81 | 铊 | Tl | 

|  |  |
| --- | --- |
| **+1** | 150 |
| **+3** | 88.5 |

 |
| 82 | 铅 | Pb | 

|  |  |
| --- | --- |
| **+2** | 119 |
| **+4** | 77.5 |

 |
| 83 | 铋 | Bi | 

|  |  |
| --- | --- |
| **+3** | 103 |
| **+5** | 76 |

 |
| 84 | 钋 | Po | 

|  |  |
| --- | --- |
| **+4** | 94 |
| **+6** | 67 |

 |
| 85 | 砹 | At | 

|  |  |
| --- | --- |
| **+7** | 62 |

 |
| 87 | 钫 | Fr | 

|  |  |
| --- | --- |
| **+1** | 180 |

 |
| 88 | 镭 | Ra | 

|  |  |
| --- | --- |
| **+2**8 | 148 |

 |
| 89 | 锕 | Ac | 

|  |  |
| --- | --- |
| **+3** | 112 |

 |
| 90 | 钍 | Th | 

|  |  |
| --- | --- |
| **+4** | 94 |

 |
| 91 | 镤 | Pa | 

|  |  |
| --- | --- |
| **+3** | 104 |
| **+4** | 90 |
| **+5** | 78 |

 |
| 92 | 铀 | U | 

|  |  |
| --- | --- |
| **+3** | 102.5 |
| **+4** | 89 |
| **+5** | 78 |
| **+6** | 73 |

 |
| 93 | 镎 | Np | 

|  |  |
| --- | --- |
| **+2** | 110 |
| **+3** | 101 |
| **+4** | 87 |
| **+5** | 75 |
| **+6** | 72 |
| **+7** | 71 |

 |
| 94 | 钚 | Pu | 

|  |  |
| --- | --- |
| **+3** | 100 |
| **+4** | 86 |
| **+5** | 74 |
| **+6** | 71 |

 |
| 95 | 镅 | Am | 

|  |  |
| --- | --- |
| **+2**8 | 126 |
| **+3** | 97.5 |
| **+4** | 85 |

 |
| 96 | 锔 | Cm | 

|  |  |
| --- | --- |
| **+3** | 97 |
| **+4** | 85 |

 |
| 97 | 锫 | Bk | 

|  |  |
| --- | --- |
| **+3** | 96 |
| **+4** | 83 |

 |
| 98 | 锎 | Cf | 

|  |  |
| --- | --- |
| **+3** | 95 |
| **+4** | 82.1 |

 |

参见
--

* 原子半径

参考文献
----

1. ↑  Pauling, L. (1960). *The Nature of the Chemical Bond* (3rd Edn.). Ithaca, NY: Cornell University Press.
2. 1 2  Shannon, R.D.. Acta. Cryst. A. 1976, **32**: 751–767. doi:10.1107/S0567739476001551.
3. ↑  通常来讲，Ag+(129 pm)的离子半径事实上比Na+(116 pm)的大。