BCC (Body-Centered-Cubic) Structure
- Practical Electron Microscopy and Database -
- An Online Book -

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Comparing with other crystal structures, body-centered cubic (bcc) packings of atoms tend to be most stable near the melting point of materials because the atoms have room to vibrate (important at high temperatures). Steels are body-centered cubic at low temperatures and face-centered cubic at high temperatures. For FCC and HCP systems, the coordination numbers are 12, while for BCC it’s 8. Assuming a hard sphere model, atomic packing factor is defined as the ratio of atomic sphere volume to unit cell volume, which is 74% for both FCC and HCP and 68% for BCC. In general, ~90% elemental metals crystallize into three crystal structures which are BCC, FCC, and HCP.

Figure 2873 shows the effects of structural symmetry on XRD patterns. These effects include the difference of the reflection numbers and the peak splitting for the tetragonal and orthorhombic structures, for instance, shown in the red dotted box.

effects of structural symmetry on XRD patterns

Figure 2873. The effects of structural symmetry on XRD patterns: (a) body-centered-cubic (bcc), (b) body-centered-tetragonal (bct), and (c) body-centered-orthorhombic (bco).

Table 2873a. Example of compounds with similar structures to BCC.

 
BCC
TiO2 (Rutile)
Cu2O (Cuprite)
Space group Im-3m P42/mnm Pm-3m Pn-3m
Compounds α-Fe, W, Nb, Ta, Na, K, Mo, V GeO2, SnO2, PbO2 CsI, CsBr, CsCl Pb2O, Ag2O

Table 2873b. Some normalized surface energies of low-index surfaces of bcc.

Solid
(100)
(110)
(111)
(211)
bcc
1.00
0.71
0.87
0.80

Table 2873c. Some symmetrical diffraction patterns of cubic crystals.

Zone axis
[100]
[110]
[111]
Symmetry
Square
Rectangular
Hexagonal
Aspect Ratio
1:1 1: for BCC, SC (almost hexagonal for FCC) Equilateral

Table 2873d lists the characteristics of the three cubic Bravais lattices.

Table 2873d. The only three cubic Bravais lattices.

Lattice
Number of
lattice points
per unit cell
Number of
atoms per unit cell
Nearest distance
between lattice points
Maximum packing
Maximum packing condition
Density (or fraction of packing, Vatom/Vcell)
1 1 Nearest distance When the adjacent atoms touch each other along the edge
of the cube
52.4%
BCC
2 2 Nearest distance When the adjacent atoms touch each other along the body diagonal of the cubic cell 68.0%
4 4 Nearest distance When the adjacent atoms touch each other along the face diagonal of the cubic cell 74.0%
4 8 Nearest distance 34 %

For FCC and BCC structures, the lattice constants are given by, (For BCC, you can download the excel file for your own calculations)

         Phase Identification with XRD and its Procedure ----------------- [2873]

Table 2873e. Other characteristics of BCC structures.

Contents
Page
Close packed planes and directions page3029
Atomic packing factor page3030
Number of lattice points (atoms) per unit cell page3032
Coordination number of atoms page3031
Space groups Im-3m (229)
d-spacing ratios of allowed Bragg reflections 1, √2, √4, √6, √8, √10, √12, √14, √16, √18, √20, ...
Tables of Burgers vectors of dislocations and g·b page1995
Dominating slip planes, slip directions and stable Burgers vector for common crystal structures page3557
Digital Micrograph script to compute reflection angle Script link

 

 

 

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