Diffraction Physics
Diffraction Physics
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DOI：
10.1107/s0108767398011271
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
A. Authier;C. Malgrange
中科院分区：
文献类型：
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作者：
A. Authier;C. Malgrange
对主要的衍射理论作了布里简要的介绍，并对它们的重要结果作了比较。几何理论的局限性进行了讨论，并介绍了消光的概念。本文简要地评述了完整晶体衍射的主要特征：与布喇格隙有关的全反射和达尔文宽度，驻波，反常吸收，光线追迹，平面波和球面波的彭德洛衍射，偏振特性。真实的水晶很少是完美的。它们可以是几乎完美的，具有小应变和/或单个晶格缺陷，或者它们可以是高度变形的，具有大应变和高密度缺陷。由前者的衍射处理使用扩展的动态理论的衍射完美的晶体使用射线追踪。结果分析的情况下，一个恒定的应变梯度，否则描述的模拟，可以与实验结果进行比较。后一种情况更困难，但可以通过更复杂的理论来处理，如Takagi和Taupin的理论。1.介绍衍射波晶体已允许晶体学的发展在世纪。这一切都始于埃瓦尔德的论文和他的反射和折射理论，该理论将晶体中色散和折射的宏观性质与传播波与谐振器的微观分布（即原子结构）的相互作用联系起来。推导并不取决于波长，这是这句话，他在1912年1月回答一个问题的劳厄开始劳厄的推理，并导致弗里德里希和Frepping的决定性实验。随后是劳厄的几何理论和达尔文的几何和动力学理论（达尔文，1914年a，B）。埃瓦尔德将他的理论扩展到X射线的情况（埃瓦尔德，1916年，1917年）表明，光波的折射和反射以及X射线衍射本质上是相同的物理现象。衍射物理学的范围非常广泛，从波与物质的相互作用到完美和不完美晶体、粉末、调制结构、准晶体等的衍射理论，消光理论，X射线光学，干涉测量，缺陷成像，。. .并且在本文中将仅涉及有限的方面。2.衍射理论2.1.几何理论劳厄的X射线衍射的“几何理论”的基础是在两篇论文的第一篇中给出的，这两篇论文描述了X射线衍射的发现（Friedrich等人，（1912年）：通过简单地考虑每个原子衍射的波的振幅，但忽略传播波与物质的相互作用，将它们之间的光程差相加，得到由原子的三维周期性组件衍射的振幅。这可以简单地使用傅里叶变换来表示。三重周期性Inite介质的电子密度（或更一般地说衍射中心）分布的表达式1 r，可以由在巴黎大学和巴黎高等师范学院研究的三重周期性Andre奥蒂耶写成一个单元中电子密度的卷积0 r。他于1961年获得巴黎大学的博士学位，并担任巴黎大学（现为巴黎P. 1965年至1996年。他于1997年成为名誉教授。1972年至1975年，他是欧洲晶体学委员会（现为欧洲晶体学协会）的第一任主席。1990年至1993年，他担任国际晶体学联合会主席。他是《Acta Crystallographica》A部分和《International Tables for Crystal》D卷的编辑，
The main theories of diffraction are brie ̄y described and their more important results compared. The limitations of the geometrical theory are discussed and the concept of extinction introduced. The main features of the diffraction by a perfect crystal are brie ̄y reviewed: total re ̄ection and Darwin width associated with the Bragg gap, standing waves, anomalous absorption, ray tracing, plane-wave and spherical-wave PendelloÈsung, polarization properties. Real crystals are seldom perfect. They may be nearly perfect with small strains and/or individual lattice defects faults or they may be highly deformed with large strains and a high density of defects. The diffraction by the former is handled using extensions of the dynamical theory of diffraction by perfect crystals using ray tracing. The results are analytical in the case of a constant strain gradient and are otherwise described by simulations which can be compared to the experimental results. The latter case is more dif®cult but can be approached by more sophisticated theories such as that of Takagi and Taupin. 1. Introduction Diffraction of waves by crystals has permitted the development of crystallography in the 20th century. It all started with Ewald's thesis and his theory of re ̄ection and refraction, which relates the macroscopic properties of dispersion and refraction in a crystal to the interaction of the propagating waves with a microscopic distribution of resonators, that is with its atomic structure. The derivation does not depend on the wavelength and it is this remark by him in January 1912 in answer to a question by Laue that started off Laue's reasoning and led to Friedrich & Knipping's decisive experiment. It was promptly followed by Laue's geometrical theory and Darwin's geometrical and dynamical theories (Darwin, 1914a,b). Ewald's extension of his theory to the case of X-rays (Ewald, 1916, 1917) shows that refraction and re ̄ection of light waves and X-ray diffraction are essentially the same physical phenomenon. The scope of diffraction physics is very wide, ranging from the interaction of waves with matter to diffraction theory for perfect and imperfect crystals, powders, modulated structures, paracrystals etc., extinction theory, X-ray optics, interferometry, imaging of defects, . . . and only limited aspects will be broached upon in this paper. 2. The theories of diffraction 2.1. Geometrical theory The basis of Laue's `geometrical theory' of X-ray diffraction is given in the very ®rst of the two papers that gave the account of the discovery of X-ray diffraction (Friedrich et al., 1912): the amplitude diffracted by a three-dimensional periodic assembly of atoms is derived by adding the amplitudes of the waves diffracted by each atom, simply taking into account the optical path differences between them, but neglecting the interaction of the propagating waves and matter. This can be expressed simply using Fourier transforms. The expression of the distribution of electronic density (or more generally of diffracting centres) of a triply periodic in®nite medium, 1 r, can be written as the convolution of the electron density in one cell, 0 r, by a triply Andre Authier studied at the University of Paris and at the Ecole Normale SupeÂrieure. He obtained a DSci from the University of Paris in 1961 and was Professor at the University of Paris (now Universite P. et M. Curie) from 1965 to 1996. He became Professor Emeritus in 1997. He was the ®rst President of the European Crystallographic Committee (now European Crystallographic Association) from 1972 to 1975. He was President of the International Union of Crystallography from 1990 to 1993. He is Editor of Section A of Acta Crystallographica and of Volume D of International Tables for Crystal-