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Comparing with other crystal structures, bodycentered 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 bodycentered cubic at low temperatures and facecentered 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.
Figure 2873. The effects of structural symmetry on XRD patterns: (a) bodycenteredcubic (bcc), (b) bodycenteredtetragonal (bct), and (c) bodycenteredorthorhombic (bco).
Table 2873a. Example of compounds with similar structures to BCC.

BCC 



Space group 
Im3m 
P42/mnm 
Pm3m 
Pn3m 
Compounds 
αFe, W, Nb, Ta, Na, K, Mo, V 
GeO_{2}, SnO_{2}, PbO_{2} 
CsI, CsBr, CsCl 
Pb_{2}O, Ag_{2}O 
Table 2873b. Some normalized surface energies of lowindex surfaces of bcc.
Solid 
(100)

(110)

(111) 
(211) 





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, V_{atom}/V_{cell}) 

1 
1 

When the adjacent atoms touch each other along the edge
of the cube 
52.4% 
BCC 
2 
2 

When the adjacent atoms touch each other along
the body diagonal of the cubic cell 
68.0% 

4 
4 

When the adjacent atoms touch each other along
the face diagonal of the cubic cell 
74.0% 

4 
8 


34 % 
For FCC and BCC structures, the lattice constants are given by, (For BCC, you can download the excel file for your own calculations)
 [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 
Im3m (229) 
dspacing 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 
