双语化学辞典Chem Lexicon
概念 · 无机化学 · 周期性 Inorganic chemistry · Periodicity

离子半径Ionic radius

高中High school
拼音Pinyin lí zǐ bàn jìng 

定义Definition

离子半径是离子晶体中离子的有效半径,由晶体中相邻阴阳离子的核间距按一定规则分配得到。离子半径与配位数有关,常用 Shannon 的数据表。

Ionic radius is the effective radius of an ion in an ionic crystal, obtained by sharing out the distance between neighbouring cation and anion nuclei by an agreed rule. It depends on coordination number; Shannon's tables are the usual source.

规律Trends

阳离子比相应原子小,因为失去了最外层电子,剩余电子受到更强的核吸引,如 Na 原子 186 pm,Na⁺ 102 pm。阴离子比相应原子大,因为增加的电子之间相互排斥,如 Cl⁻ 181 pm。同族离子从上到下半径增大。

Cations are smaller than their atoms because the outer shell is lost and the remaining electrons are held more tightly: Na 186 pm, Na⁺ 102 pm. Anions are larger than their atoms because the extra electrons repel each other: Cl⁻ 181 pm. Down a group ionic radii increase.

等电子离子Isoelectronic ions

电子数相同的离子,核电荷越大,半径越小:O²⁻(140 pm)> F⁻(133 pm)> Na⁺(102 pm)> Mg²⁺(72 pm)> Al³⁺(54 pm),它们都有 10 个电子。

For ions with the same number of electrons, the larger the nuclear charge the smaller the ion: O²⁻ (140 pm) > F⁻ (133 pm) > Na⁺ (102 pm) > Mg²⁺ (72 pm) > Al³⁺ (54 pm), all with ten electrons.

影响Consequences

离子越小、电荷越高,晶格能越大,离子化合物熔点越高;小而高电荷的阳离子极化能力强,使相邻阴离子电子云变形,化合物带有共价性,并影响水合离子的酸性和碳酸盐的热稳定性。

Smaller, more highly charged ions give larger lattice energies and higher melting points; small, highly charged cations are strongly polarising, distorting neighbouring anions and giving compounds covalent character, which also affects the acidity of hydrated ions and the thermal stability of carbonates.

年表Timeline

  • 1926

    戈尔德施密特发表系统的离子半径表

    Goldschmidt publishes a systematic table of ionic radii

  • 1927

    鲍林提出计算离子半径的方法

    Pauling proposes a method for calculating ionic radii

  • 1976

    香农发表修订的有效离子半径表

    Shannon publishes his revised table of effective ionic radii

相关公式Formulas

卡普斯京斯基方程 Kapustinskii equation→
\[U_L \approx -\frac{1.2025\times10^{-4}\,\nu\,|z_+z_-|}{r_+ + r_-}\left(1 - \frac{3.45\times10^{-11}}{r_+ + r_-}\right)\ \mathrm{J\,mol^{-1}\,m}\]
例题Worked example

NaCl:ν = 2,d = 102 + 181 = 283 pm:U ≈ −1.2025×10⁵×2/283×(1 − 34.5/283) ≈ −746 kJ/mol(玻恩–哈伯值 −787)。

NaCl: ν = 2, d = 283 pm → U ≈ −746 kJ/mol (Born–Haber −787).

半径比规则 Radius ratio rule→
\[\frac{r_+}{r_-}:\ \ 0.225\ (\mathrm{CN\,4})\ \ 0.414\ (\mathrm{CN\,6})\ \ 0.732\ (\mathrm{CN\,8})\ \ 1\ (\mathrm{CN\,12})\]
戈尔德施密特容忍因子 Goldschmidt tolerance factor→
\[t = \frac{r_\mathrm{A} + r_\mathrm{X}}{\sqrt2\,(r_\mathrm{B} + r_\mathrm{X})}\]
例题Worked example

SrTiO₃:r(Sr²⁺) = 144,r(Ti⁴⁺) = 60.5,r(O²⁻) = 140 pm → t = 1.00,立方钙钛矿。

SrTiO₃: t = 1.00, cubic perovskite.