离子晶体 Ionic crystal — 定义、原理与由来

定义Definition

离子晶体是由阳离子和阴离子通过离子键（静电作用）按一定方式周期性排列而成的晶体，如 NaCl、CsCl、CaF₂、MgO。离子晶体一般熔点较高、硬而脆，固态不导电，熔融或溶于水后能导电。

An ionic crystal is a crystal of cations and anions held in a periodic arrangement by ionic (electrostatic) bonding, such as NaCl, CsCl, CaF₂ and MgO. Ionic crystals generally have high melting points, are hard and brittle, and conduct electricity only when molten or dissolved.

原理Principle

离子键没有方向性和饱和性，每个离子尽可能多地吸引异号离子，配位数由半径比决定。晶格能 U 衡量离子键强弱，按玻恩-朗德方程 U ∝ z⁺z⁻/(r⁺ + r⁻)，离子电荷越高、半径越小，晶格能越大，熔点越高：MgO（2852 °C）远高于 NaCl（801 °C）。受外力时离子层错位会使同号离子相对，斥力导致晶体沿解理面断裂，所以离子晶体脆。

Ionic bonding is non-directional and unsaturated, so each ion surrounds itself with as many counter-ions as the radius ratio allows. Lattice energy U measures bond strength; by the Born–Landé equation U ∝ z⁺z⁻/(r⁺ + r⁻), so higher charges and smaller radii give larger lattice energy and higher melting point: MgO (2852 °C) far above NaCl (801 °C). Under stress, a slip of one layer brings like charges face to face, and the repulsion splits the crystal along cleavage planes, which is why ionic crystals are brittle.

典型结构Typical structures

氯化钠型（6:6，八面体）、氯化铯型（8:8，立方体）、闪锌矿和纤锌矿型（4:4，四面体）、萤石型 CaF₂（8:4）、反萤石型 Na₂O（4:8）、金红石型 TiO₂（6:3）、尖晶石型 MgAl₂O₄ 和钙钛矿型 CaTiO₃ 是最常见的离子晶体结构类型。

The commonest types are rock salt (6:6, octahedral), caesium chloride (8:8, cubic), zinc blende and wurtzite (4:4, tetrahedral), fluorite CaF₂ (8:4), antifluorite Na₂O (4:8), rutile TiO₂ (6:3), spinel MgAl₂O₄ and perovskite CaTiO₃.

认识史与应用History and uses

1913 年布拉格父子测定 NaCl 结构，证明晶体中不存在独立的 NaCl 分子。1918 年玻恩和朗德、1919 年玻恩和哈伯建立了晶格能的理论计算和热力学循环。离子晶体用作光学窗口材料（NaCl、KBr、CaF₂ 红外窗片）、固体电解质（钇稳定氧化锆、β-氧化铝）、耐火材料（MgO）和闪烁晶体（NaI:Tl）。

The Braggs' 1913 NaCl structure showed that the crystal contains no separate NaCl molecules. Born and Landé (1918) and Born and Haber (1919) established the theoretical calculation of lattice energy and the thermodynamic cycle. Ionic crystals are used as optical windows (NaCl, KBr and CaF₂ for infrared), solid electrolytes (yttria-stabilised zirconia, β-alumina), refractories (MgO) and scintillators (NaI:Tl).

反应Reactions

U = −(N_A·M·z⁺z⁻·e²)/(4πε₀·r₀)·(1 − 1/n)

玻恩-朗德方程；M 为马德隆常数（NaCl 型 1.748），n 为玻恩指数。

The Born–Landé equation; M is the Madelung constant (1.748 for rock salt) and n the Born exponent.

Na(s) + ½Cl₂(g) ⟶ NaCl(s)　ΔfH° = −411 kJ/mol

离子晶体的生成

Formation of an ionic crystal

年表Timeline

1913
NaCl 晶体结构测定
The NaCl structure is determined
1918
玻恩-朗德晶格能方程
The Born–Landé lattice-energy equation
1919
玻恩-哈伯循环
The Born–Haber cycle

离子晶体Ionic crystal