Rudiments of Crystallography
Crystallography deals basically with the question “Where are the atoms in solids?” The purpose of this section is to introduce briefly the basics of modern crystallography. The focus is on the description of periodic solids, which represent the major prop
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Rudiments of
The structure of a solid material is very important, because the physical properties are closely related to the structure. In most cases solids are crystalline: they may consist of one single crystal, or be polycrystalline, consisting of many tiny single crystals in different orientations. All periodic crystals have a perfect translational symmetry. This leads to selection rules, which are very useful for the understanding of the physical properties of solids. Therefore, most textbooks on solid-state physics begin with some chapters on symmetry and structure. Today we know that other solids, which have no translational symmetry, also exist. These are amorphous materials, which have little order (in most cases restricted to the short-range arrangement of the atoms), and aperiodic crystals, which show perfect long-range order, but no periodicity – at least in 3-D space. In this chapter of the book, the basic concepts of crystallography – how the space of a solid can be filled with atoms – are briefly discussed. Readers who want to inform themselves in more detail about crystallography are referred to the classic textbooks [3.1–5]. Many crystalline materials, especially minerals and gems, were described more than 2000 years ago. The regular form of crystals and the existence of facets, which have fixed angles between them, gave rise to
1.3.1
Crystalline Materials ........................... 1.3.1.1 Periodic Materials ................... 1.3.1.2 Aperiodic Materials..................
28 28 33
1.3.2 Disorder.............................................
38
1.3.3 Amorphous Materials ..........................
39
1.3.4 Methods for Investigating Crystallographic Structure....................
39
References ..................................................
41
local phenomena. The section is concluded by touching on the basics of diffraction methods, the most powerful tool kit used by experimentalists dealing with structure at the atomic level in the solid state.
a belief that crystals were formed by a regular repetition of tiny, identical building blocks. After the discovery of X-rays by Röntgen, Laue investigated crystals in 1912 using these X-rays and detected interference effects caused by the periodic array of atoms. One year later, Bragg determined the crystal structures of alkali halides by X-ray diffraction. Today we know that a crystal is a 3-D array of atoms or molecules, with various types of long-range order. A more modern definition is that all materials which show sharp diffraction peaks are crystalline. In this sense, aperiodic or quasicrystalline materials, as well as periodic materials, are crystals. A real crystal is never a perfect arrangement. Defects in the form of vacancies, dislocations, impurities, and other imperfections are often very important for the physical properties of a crystal. This aspect has been largely neglected in classical crystallography but is becoming more and more a topic of modern crystallographic investigations [3.6, 7]. As indicated in Table 1.3-1, conde
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