Electron microscopy
 
Three-Dimensional (3-D) Lattice
- Practical Electron Microscopy and Database -
- An Online Book -
Microanalysis | EM 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.
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As shown in Figure 3073a, 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). The basis vectors define the “shape” of the crystal. The smallest repeating unit formed by combining the three basis vectors is called a unit cell.
        ii) All points can be determined by a series of vectors:
                Three-Dimensional (3-D) Lattice ---------------------------------- [3073a]

Part of a lattice with a unit cell indicated

Figure 3073a. Three-dimensional (3-D) lattice.

On the other hand, the number of the lattice points per unit cell in 3-D lattices can be given by,
        number of the lattice points per unit cell in 2-D lattices ---------------------------- [3073b]
where,
          NInterior and NCorner - The numbers of the lattice points inside the unit cell and at the corners, respectively, as shown in Figure 3073b.
          NFace - The number of the lattice points at the faces.

Lattice points inside the unit cell and at the corners in 2-D lattices

Figure 3073b. Lattice points inside the unit cell and at the corners in 3-D lattices.

In three-dimensional (3-D) lattice, there are only seven crystal systems:
        i) Triclinic (anorthic).
        ii) Monoclinic.
        iii) Hexagonal.
        iv) Rhombohedral (trigonal).
        v) Orthorhombic.
        vi) Tetragonal.
        vii) Cubic.
        

 

 

 

 

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