定义Definition
晶格能（晶格焓）是 1 mol 离子化合物由气态离子形成晶体时的焓变，为负值，如 Na⁺(g) + Cl⁻(g) → NaCl(s)，ΔH = −787 kJ mol⁻¹。也有教材定义为拆散晶体成气态离子的焓变，数值相同而符号相反，使用时需注意定义。
Lattice energy (lattice enthalpy) is the enthalpy change when one mole of an ionic compound forms from its gaseous ions, a negative quantity: Na⁺(g) + Cl⁻(g) → NaCl(s), ΔH = −787 kJ mol⁻¹. Some texts define it for breaking the lattice into gaseous ions, with the same size but opposite sign, so check the definition in use.
影响因素What affects it
离子电荷越高、半径越小，离子间静电吸引越强，晶格能越负。例如 MgO（Mg²⁺、O²⁻）约 −3791 kJ mol⁻¹，远大于 NaCl；同族卤化物中 LiF 的晶格能最负。晶格能越大，离子化合物熔点越高、越硬。
Higher ionic charges and smaller ions give stronger attraction and a more negative lattice energy. MgO (Mg²⁺, O²⁻) is about −3791 kJ mol⁻¹, far larger than NaCl, and LiF has the most negative value of the alkali-metal halides. Larger lattice energies mean higher melting points and harder crystals.
测定：玻恩–哈伯循环Finding it: the Born–Haber cycle
晶格能无法直接测量，可根据盖斯定律由玻恩–哈伯循环求出：生成焓 = 原子化焓 + 电离能 + 电子亲和能 + 晶格能。把实验值与按纯离子模型计算的理论值比较，差别越大说明化合物的共价性越强。
Lattice energy cannot be measured directly; it is found from the Born–Haber cycle by Hess's law: enthalpy of formation = atomisation enthalpies + ionisation energies + electron affinities + lattice energy. Comparing this experimental value with one calculated for a purely ionic model shows how much covalent character the compound has.
年表Timeline
- 1918
玻恩与朗德给出计算晶格能的玻恩–朗德方程
Born and Landé give the Born–Landé equation for lattice energy
- 1919
玻恩与哈伯提出玻恩–哈伯循环
Born and Haber introduce the Born–Haber cycle
- 1956
卡普斯京斯基提出估算晶格能的简化公式
Kapustinskii proposes a simplified equation for estimating lattice energy
相关公式Formulas
例题Worked example
NaCl：−411 = 107 + 496 + 122 − 349 + U_L → U_L = −787 kJ/mol。
NaCl: −411 = 107 + 496 + 122 − 349 + U_L → U_L = −787 kJ/mol.
例题Worked example
NaCl：M = 1.74756，r₀ = 2.814 Å，n = 8：U_L = −755 kJ/mol（玻恩–哈伯实验值 −787 kJ/mol）。
NaCl: M = 1.74756, r₀ = 2.814 Å, n = 8: U_L = −755 kJ/mol (Born–Haber −787).
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).