Diffraction and the X-Ray Powder Diffractometer
This chapter begins with a general description of diffraction and the structure of materials, starting with Bragg’s law. It discusses how diffraction is used to determine crystal structure, but is also sensitive to disorder in the structure. The creation
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Diffraction and the X-Ray Powder Diffractometer
1.1 Diffraction 1.1.1 Introduction to Diffraction Materials are made of atoms. Knowledge of how atoms are arranged into crystal structures and microstructures is the foundation on which we build our understanding of the synthesis, structure and properties of materials. There are many techniques for measuring chemical compositions of materials, and methods based on inner-shell electron spectroscopies are covered in this book. The larger emphasis of the book is on measuring spatial arrangements of atoms in the range from 10−8 to 10−4 cm, bridging from the unit cell of the crystal to the microstructure of the material. There are many different methods for measuring structure across this wide range of distances, but the more powerful experimental techniques involve diffraction. To date, most of our knowledge about the spatial arrangements of atoms in materials has been gained from diffraction experiments. In a diffraction experiment, an incident wave is directed into a material and a detector is typically moved about to record the directions and intensities of the outgoing diffracted waves. B. Fultz, J. Howe, Transmission Electron Microscopy and Diffractometry of Materials, Graduate Texts in Physics, DOI 10.1007/978-3-642-29761-8_1, © Springer-Verlag Berlin Heidelberg 2013
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Diffraction and the X-Ray Powder Diffractometer
“Coherent scattering” preserves the precision of wave periodicity. Constructive or destructive interference then occurs along different directions as scattered waves are emitted by atoms of different types and positions. There is a profound geometrical relationship between the directions of waves that interfere constructively, which comprise the “diffraction pattern,” and the crystal structure of the material. The diffraction pattern is a spectrum of real space periodicities in a material.1 Atomic periodicities with long repeat distances cause diffraction at small angles, while short repeat distances (as from small interplanar spacings) cause diffraction at high angles. It is not hard to appreciate that diffraction experiments are useful for determining the crystal structures of materials. Much more information about a material is contained in its diffraction pattern, however. Crystals with precise periodicities over long distances have sharp and clear diffraction peaks. Crystals with defects (such as impurities, dislocations, planar faults, internal strains, or small precipitates) are less precisely periodic in their atomic arrangements, but they still have distinct diffraction peaks. Their diffraction peaks are broadened, distorted, and weakened, however, and “diffraction lineshape analysis” is an important method for studying crystal defects. Diffraction experiments are also used to study the structure of amorphous materials, even though their diffraction patterns lack sharp diffraction peaks. In a diffraction experiment, the incident waves must have wavelengths comparable to the spacings between atoms. Three types of waves have proved usef
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