晶格Crystal structure

点阵由三个不共面的基矢 a、b、c 定义，任意阵点位置为 r = ua + vb + wc（u、v、w 为整数）。晶格参数包括三条棱长 a、b、c 和三个夹角 α、β、γ。晶面用米勒指数 (hkl) 表示，晶向用 [uvw] 表示，晶面间距 d 与 X 射线衍射角满足布拉格方程 2d sinθ = nλ。

A lattice is defined by three non-coplanar basis vectors a, b and c, so every point is at r = ua + vb + wc with integers u, v, w. Lattice parameters are the edge lengths a, b, c and the angles α, β, γ. Planes are labelled by Miller indices (hkl) and directions by [uvw], and the interplanar spacing d relates to the X-ray diffraction angle by Bragg's law, 2d sinθ = nλ.

1784 年阿维观察方解石沿解理面碎裂成相似的小菱面体，推想晶体由相同的单元堆砌而成。1848 年布拉维把这一思想数学化，提出空间点阵理论。1913 年布拉格父子用 X 射线测定了 NaCl、KCl、金刚石等晶体的结构，晶体结构学由此诞生，父子二人共获 1915 年诺贝尔物理学奖。

In 1784 Haüy watched calcite cleave into ever-smaller similar rhombohedra and inferred that crystals are stacks of identical units. Bravais put this into mathematical form in 1848 with his theory of space lattices. In 1913 William Henry and Lawrence Bragg used X-rays to determine the structures of NaCl, KCl, diamond and others, founding structural crystallography; they shared the 1915 Nobel Prize in Physics.

“晶格”一词也用于晶格能（把 1 mol 离子晶体拆散为气态离子所需的能量）和晶格振动（声子）。晶格能越大，离子晶体熔点越高、硬度越大；声子决定了固体的热容和热导率，也参与传统超导体中的电子配对。

'Lattice' also appears in lattice energy, the energy needed to separate one mole of an ionic crystal into gaseous ions, and lattice vibrations, or phonons. The larger the lattice energy, the higher an ionic crystal's melting point and hardness; phonons govern a solid's heat capacity and thermal conductivity and mediate electron pairing in conventional superconductors.