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X-ray diffraction crystallography for powder samples is a well-established and widely used method. It is applied to materials characterization to reveal the atomic scale structure of various substances in a variety of states. The book deals with fundamental properties of X-rays, geometry analysis of crystals, X-ray scattering and diffraction in polycrystalline samples and its application to the determination of the crystal structure. The reciprocal lattice and integrated diffraction intensity from crystals and symmetry analysis of crystals are explained. To learn the method of X-ray diffraction crystallography well and to be able to cope with the given subject, a certain number of exercises is presented in the book to calculate specific values for typical examples. This is particularly important for beginners in X-ray diffraction crystallography. One aim of this book is to offer guidance to solving the problems of 90 typical substances. For further convenience, 100 supplementary exercises are also provided with solutions. Some essential points with basic equations are summarized in each chapter, together with some relevant physical constants and the atomic scattering factors of the elements.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Fundamental Properties of X-rays

Abstract
X-rays with energies ranging from about 100eV to 10MeV are classified as electromagnetic waves, which are only different from the radio waves, light, and gamma rays in wavelength and energy. X-rays show wave nature with wavelength ranging from about 10 to 10−3nm. According to the quantum theory, the electromagnetic wave can be treated as particles called photons or light quanta. The essential characteristics of photons such as energy, momentum, etc., are summarized as follows.
Yoshio Waseda, Eiichiro Matsubara, Kozo Shinoda

Chapter 2. Geometry of Crystals

Abstract
The origin of crystallography can be traced to the study for the external appearance of natural minerals, such as quartz, fluorite, pyrite, and corundum, which are regular in shape and clearly exhibit a good deal of symmetry. A large amount of data for such minerals have been systematized by applying geometry and group theory. “Crystallography” involves the general consideration of how crystals can be built from small units. This corresponds to the infinite repetition of identical structural units (frequently referred to as a unit cell) in space. In other words, the structure of all crystals can be described by a lattice, with a group of atoms allocated to every lattice point.
Yoshio Waseda, Eiichiro Matsubara, Kozo Shinoda

Chapter 3. Scattering and Diffraction

Abstract
An X-ray beam is an electromagnetic wave characterized by an electric field vibrating at constant frequency, perpendicular to the direction of movement. This variation of the electric field gives electrons (charged particles) a sinusoidal change with time at the same frequency. As a result of periodic acceleration and deceleration of the electron, a new electromagnetic wave, i.e., X-rays are generated. In this sense,X-rays are scattered by electrons. This phenomenon is called Thomson scattering. On the other hand, the physical phenomenon called “diffraction as a function of atomic position” is also found when an X-ray beam encounters a crystal whose atomic arrangement shows the long range periodicity. The intensity of diffracted X-rays depends on not only the atomic arrangement but also the atomic species. When considering diffraction of X-rays from a crystal, one needs information about “atomic scattering factors” which provide a measure of the scattering ability of X-rays per atom. Since the nucleus of an atom is relatively heavy compared with an X-ray photon, it does not scatter X-rays. The scattering ability of an atom depends only on electrons, their number, and distribution.
Yoshio Waseda, Eiichiro Matsubara, Kozo Shinoda

Chapter 4. Diffraction from Polycrystalline Samples and Determination of Crystal Structure

Abstract
There are various methods for measuring the intensity of a scattered X-ray beam (hereafter referred to as diffracted X-ray beam in this chapter) from crystalline materials, and each method has the respective advantage. The most common method is to measure the X-ray diffraction intensity from a powder sample as a function of scattering angle (it is also called diffraction angle) by using a diffractometer. For this reason, several key points of structural analysis will be given with some selected examples on how to obtain structural information of powder samples of interest from measured intensity data using a diffractometer.
Yoshio Waseda, Eiichiro Matsubara, Kozo Shinoda

Chapter 5. Reciprocal Lattice and Integrated Intensities of Crystals

Abstract
The Bragg law enables us to explain all the diffraction phenomena of X-rays by a crystal described in the previous chapters. However, there are some diffraction phenomena that may not be explained by the Bragg law. The diffuse scattering at non-Bragg angles is a particular example. For this purpose, we need a more generalized theory of diffraction using the vector representation. Particularly, the concept “reciprocal lattice” is extremely effective for handling all the diffraction phenomena. In other words, the reciprocal-lattice theory of diffraction, being general, is applicable to all diffraction phenomena of X-rays by a crystal from the simplest one to the most complex case. It may be added that the usual set of three-dimensional atomic coordinates is called the crystal lattice or real-space lattice, as opposed to the reciprocal lattice.
Yoshio Waseda, Eiichiro Matsubara, Kozo Shinoda

Chapter 6. Symmetry Analysis for Crystals and the Use of the International Tables

Abstract
A crystal may be defined as a solid composed of atoms arranged on a regular threedimensional lattice and such periodicity in the atomic distribution features their structure. The geometry of atomic distributions in crystals is known to be characterized by the repetition, such as lattice translation (see Chap. 2). In addition to lattice translations, we find reflection and rotation. In these cases, an object is brought into coincidence with itself by reflection in a certain plane; rotation upon around a certain axis; or reflection in a certain plane. The repetition of a pattern by specific rules characterizes all symmetry operations and their fundamental points are given below.
Yoshio Waseda, Eiichiro Matsubara, Kozo Shinoda

Chapter 7. Supplementary Problems (100 Exercises)

Abstract
Exercise 1.1 When accelerating an electron by 1 kV, compute the values of energy, momentum and wavelength using the de Broglie relation.
Yoshio Waseda, Eiichiro Matsubara, Kozo Shinoda

Chapter 8. Solutions to Supplementary Problems

Abstract
Exercise 1.1
$$E = 1.602 \times 1{0}^{-16}\,\mathrm{J},p = 1.708 \times 1{0}^{-23}\,\mathrm{kg} \cdot \mathrm{m/s},\lambda = 3.879 \times 1{0}^{-11}\,\mathrm{m}$$
Yoshio Waseda, Eiichiro Matsubara, Kozo Shinoda

Chapter 9. Appendix A

Abstract
SI: LeSystèmac Internation d’Unitès
Yoshio Waseda, Eiichiro Matsubara, Kozo Shinoda

Backmatter

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