Lattice Systems
- Practical Electron Microscopy and Database -
- An Online Book -

http://www.globalsino.com/EM/

 This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers. ================================================================================= A lattice symmetry has the following basic characteristics:          i) Each lattice point must have identical surroundings, i.e., have the same environment.          ii) In a given direction, all lattice points must be separated by an identical distance, so-called lattice parameter. As shown in Figure 4545a, for an one-dimensional (1-D) lattice, a translation of l from one lattice point to another will present an “identical” lattice:          ----------------------------- [4545] where,         n -- An integer.         l and a -- Vectors. Figure 4545a. One-dimensional (1-D) lattice. As shown in Figure 4545b, a two-dimensional (2-D) lattice has the following characteristics:         i) It has two non-collinear basis vectors (a and b). The interaxial angle γ determines the relationship between the two basis vectors.         ii) A translation of na + pb (e.g. 1a + 3b in Figure 4545b) from one lattice point to another must form an “identical” lattice structure. Here, n and p are  integers. Figure 4545b. Two-dimensional (2-D) lattice. As shown in Figure 4545c, a three-dimensional (3-D) lattice has the following characteristics:         i) It has 3 non-collinear basis vectors (a, b, and c) and 3 interaxial angles (α, β, and γ).         ii) All points can be determined by a series of vectors:                  ---------------------------------- [3073] Figure 4545c. Three-dimensional (3-D) lattice. Note that crystal lattices must exhibit a specific minimal amount of symmetry, and each crystal system has a certain symmetry. Table 4545 lists the relationship between three-dimensional crystal families, crystal systems, and lattice systems. Table 4545. Relationship between three-dimensional crystal families, crystal systems, and lattice systems.
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