HCP

The Hexagonal ClosedThe Hexagonal Closed--packed packed Crystal Structure (HCP)Crystal Structure (HCP)

Adapted from Figure 3.30, W. Callister, Fundamentals of Materials Science and Engineering: An Integrated Approach, 2e, P. 71, Copyright (c ) 2005 by John Wiley & Sons, New York.

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HCPHCPNumber of Atoms per unit cellNumber of Atoms per unit cell

• First, each corner atom is shared among six unit cells.

• Second, the atoms located in the center of the top and bottom planes belong to only two unit cells.

1/61/2




• Third, there are three independent atoms in the center of this structure.

• So, a total of 6 whole atoms are assigned to such a unit cell.

1




• For the HCP crystal structure, total of 6 whole atoms are assigned to a given structure.

6322112

61

=+×+×

1/61/2

1



HCPHCPCoordination numberCoordination number

• The coordination number for HCP is 12.

• For example, first, this blue atom has 6 nearest neighbors around it on this plane. Second, there are three atoms above it, and another three are beneath this atom.



HCPHCPAtomic Radius and Lattice ParameterAtomic Radius and Lattice Parameter

• The hexagon edge length a and the atomic radius R are related through

a=2R



HCPHCPAtomic packing factorAtomic packing factor

• The atomic packing factor is the fraction of solid sphere volume in cell, assuming the atomic hard sphere model.

• The APF for HCP is the same as FCC:0.74




1.Calculate the height C of the hexagonal structure with the aid of this regular tetrahedron.

a

b

h




aaabah36

3

2222 =−=−=

ahc3

622 ==

aab33

32

23

=×=

a

b

h

a b




2.Calculate the volume of atoms in a unit cell

3.Calculate the total unit cell volume

33

346 aRVa ππ

=×=

3233

62)23

216( aaaaScVc =××××==




4. The atomic packing factor for the HCP

74.06

223 3

3

====ππ

aa

VVAPF

c

aHCP



HCP

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