Electron microscopy
 
Number of Lattice Points (Atoms) per Unit Cell
- Practical Electron Microscopy and Database -
- An Online Book -
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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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The number of the lattice points per unit cell in 2-D lattices can be given by,
        number of the lattice points per unit cell in 2-D lattices ---------------------------- [3555a]
where,
          NInterior and NCorner - The numbers of the lattice points inside the unit cell and at the corners, respectively, as shown in Figure 3032a.

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

Figure 3032a. Lattice points inside the unit cell and at the corners in 2-D lattices.

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 ---------------------------- [3555b]
where,
          NFace - The number of the lattice points at the faces as shown in Figure 3032b.

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

Figure 3032b. Lattice points inside the unit cell and at the corners in 3-D lattices.

Table 3032a lists the number of the lattice points per unit cell of some structures.

Table 3032a. The number of the lattice points per unit cell of some structures.
Structure
Lattice points per unit cell
Simple cubic (SC)
1
Body-centered cubic (BCC)
2
Face-centered cubic (FCC)
4
Hexagonal close-packed (HCP)
2

Many simple crystals only have an atom per lattice point, for instance, listed in Table 3032b. Therefore, the number of atoms per unit cell equals the number of lattice points per unit cell.

Table 3032b. The number of the atoms per unit cell of some structures.
Structure
Atoms per unit cell
Examples
Simple cubic (SC)
1 Polonium (Po), α-Mn
Body-centered cubic (BCC)
2 Fe, Ti, W, Mo, Nb, Ta, K, Na, V, Zr, Cr
Face-centered cubic (FCC)
4 Fe, Cu, Au, Pt, Ag, Pb, Ni
Hexagonal close-packed (HCP)
2 Ti, Mg, Zn, Be, Co, Zr, Cd


 

 

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