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Starting in Chapter 3, the kinematical theory of diffraction has been developed by calculating the diffracted wave from crystals with increasing amounts of disorder. The amplitude of the diffracted wave, ψ, is the sum of phase factors of wavelets emitted from individual atoms. We have evaluated these sums analytically (as a geometric series, for example), graphically (with a phase-amplitude diagram), and numerically. These calculations of ψ(Δk) were performed for crystals having only small departures from ideality, such as crystals of small size, crystals with strain distributions, or isolated defects imaged with a TEM. In many respects these calculations were extensions of the calculation of wave interference from atoms in a perfect crystal. Recall that when accurate phase information is present in ψ(Δk), the inverse Fourier transformation, F−1ψ(Δk), gives f(r), the scattering factor distribution. Knowing f(r) is equivalent to knowing the positions of all atoms in the material. [ABSTRACT FROM AUTHOR]

This chapter begins by explaining the physical origins of three types of broadening of diffraction peaks from crystalline materials: 1) small sizes of crystallites, 2) distributions of strains in crystallites, and 3) the diffractometer. These sources of peak broadenings pertain to electron diffraction, but since x-ray and neutron diffractometry data are more amenable to lineshape analysis with kinematical diffraction theory, the concepts in this chapter are presented in the context of x-ray powder diffractometry. [ABSTRACT FROM AUTHOR]

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 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. [ABSTRACT FROM AUTHOR]