晶体缺陷Crystallographic defect

由于形成缺陷使熵增大，任何温度高于 0 K 的晶体都存在一定浓度的平衡点缺陷，浓度 n/N ≈ exp(−E_f/kT)。离子晶体中有两类本征缺陷：肖特基缺陷（等量的阳离子空位和阴离子空位，如 NaCl）和弗仑克尔缺陷（离子离开格位进入间隙，如 AgCl 中的 Ag⁺）。点缺陷使离子能在固体中扩散和导电，是固体电解质和离子电池的基础。碱金属卤化物中电子占据阴离子空位形成 F 色心，使晶体着色。

Because defects raise entropy, every crystal above 0 K contains an equilibrium concentration of point defects, n/N ≈ exp(−E_f/kT). Ionic crystals have two intrinsic kinds: Schottky defects (equal numbers of cation and anion vacancies, as in NaCl) and Frenkel defects (an ion moved from its site to an interstice, as for Ag⁺ in AgCl). Point defects let ions diffuse and conduct through solids, the basis of solid electrolytes and ion batteries. An electron trapped in an anion vacancy in an alkali halide forms an F-centre that colours the crystal.

1934 年泰勒、奥罗万和波拉尼分别提出位错理论，解释了金属实际屈服强度比理论值低几个数量级的原因：位错的滑移只需逐步断开少量键。1956 年赫什等用透射电镜首次直接观察到位错。多晶材料由许多取向不同的晶粒组成，晶界阻碍位错运动，晶粒越细，强度越高（霍尔-佩奇关系）。

In 1934 Taylor, Orowan and Polanyi independently proposed dislocations to explain why metals yield at stresses orders of magnitude below the theoretical strength: a dislocation moves by breaking only a few bonds at a time. Hirsch and colleagues first observed dislocations directly by transmission electron microscopy in 1956. Polycrystals consist of many grains of different orientation, and grain boundaries hinder dislocations, so finer grains give higher strength (the Hall–Petch relation).

缺陷并非总是有害：硅中掺入磷或硼形成取代杂质，产生 n 型或 p 型半导体；钇稳定氧化锆中的氧空位使其成为氧离子导体，用于氧传感器和燃料电池；红宝石的红色来自 Al₂O₃ 中取代的 Cr³⁺；金刚石中的氮-空位色心可用作量子传感器。非化学计量化合物（如 Fe₁₋ₓO）也是点缺陷的结果。

Defects are not always harmful: phosphorus or boron substituted into silicon make n- or p-type semiconductors; oxygen vacancies make yttria-stabilised zirconia an oxide-ion conductor for oxygen sensors and fuel cells; ruby's red comes from Cr³⁺ substituted in Al₂O₃; nitrogen–vacancy centres in diamond serve as quantum sensors. Non-stoichiometric compounds such as Fe₁₋ₓO also result from point defects.