X射线衍射X-ray crystallography

X 射线波长（约 0.05–0.25 nm，常用 Cu Kα 0.154 nm、Mo Kα 0.071 nm）与原子间距相当。X 射线主要被电子散射，相邻晶面的散射波程差等于波长整数倍时相互加强，满足布拉格方程 2d sinθ = nλ。衍射点的位置给出晶胞参数和空间群，强度给出电子密度分布；由于只能测到强度而丢失相位（“相位问题”），需用直接法、帕特森法等求解。

X-ray wavelengths (about 0.05–0.25 nm; Cu Kα 0.154 nm and Mo Kα 0.071 nm are common) match interatomic spacings. X-rays scatter mainly from electrons, and waves from adjacent planes reinforce when their path difference is a whole number of wavelengths, satisfying Bragg's law 2d sinθ = nλ. Spot positions give the unit cell and space group, and intensities give the electron density; because only intensities are measured and the phases are lost (the phase problem), direct methods, Patterson methods and others are used to solve structures.

1895 年伦琴发现 X 射线。1912 年劳厄用硫酸铜晶体首次观察到 X 射线衍射（1914 年诺贝尔物理学奖），1913 年布拉格父子提出布拉格方程并测定 NaCl 结构（1915 年诺贝尔物理学奖）。此后霍奇金测定青霉素、维生素 B₁₂（1964 年诺贝尔化学奖）；佩鲁茨和肯德鲁测定血红蛋白和肌红蛋白；富兰克林的 DNA 衍射照片促成双螺旋模型；豪普特曼和卡尔勒发展直接法（1985 年诺贝尔化学奖）。与晶体学相关的诺贝尔奖超过 20 项。

Röntgen discovered X-rays in 1895. In 1912 Laue first saw X-ray diffraction from a copper sulfate crystal (Nobel Prize in Physics 1914), and in 1913 the Braggs derived Bragg's law and solved NaCl (Nobel Prize in Physics 1915). Hodgkin went on to solve penicillin and vitamin B₁₂ (Nobel Prize in Chemistry 1964); Perutz and Kendrew solved haemoglobin and myoglobin; Franklin's DNA photographs led to the double helix; and Hauptman and Karle developed direct methods (Nobel Prize in Chemistry 1985). More than twenty Nobel Prizes are linked to crystallography.

单晶衍射需要约 0.1–0.3 mm 的单晶，可得到完整的三维结构；粉末衍射（PXRD）用于物相鉴定、晶型分析、结晶度和晶粒尺寸测定（谢乐公式）；同步辐射和 X 射线自由电子激光使微小晶体和超快过程研究成为可能。应用于新化合物结构确认、药物晶型专利、矿物鉴定、蛋白质结构与药物设计、材料相变研究。

Single-crystal diffraction needs a crystal about 0.1–0.3 mm across and gives a complete three-dimensional structure; powder diffraction (PXRD) identifies phases and polymorphs and measures crystallinity and crystallite size (the Scherrer equation); synchrotrons and X-ray free-electron lasers allow tiny crystals and ultrafast processes to be studied. Applications include confirming new structures, patenting drug polymorphs, identifying minerals, protein structures for drug design and studying phase transitions.