Post on 30-Aug-2014
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
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HCPHCPNumber of Atoms per unit cellNumber of Atoms per unit cell
• 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
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HCPHCPNumber of Atoms per unit cellNumber of Atoms per unit cell
• For the HCP crystal structure, total of 6 whole atoms are assigned to a given structure.
6322112
61
=+×+×
1/61/2
1
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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.
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HCPHCPAtomic Radius and Lattice ParameterAtomic Radius and Lattice Parameter
• The hexagon edge length a and the atomic radius R are related through
a=2R
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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
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HCPHCPAtomic packing factorAtomic packing factor
1.Calculate the height C of the hexagonal structure with the aid of this regular tetrahedron.
a
b
h
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HCPHCPAtomic packing factorAtomic packing factor
aaabah36
3
2222 =−=−=
ahc3
622 ==
aab33
32
23
=×=
a
b
h
a b
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HCPHCPAtomic packing factorAtomic packing factor
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 =××××==
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HCPHCPAtomic packing factorAtomic packing factor
4. The atomic packing factor for the HCP
74.06
223 3
3
====ππ
aa
VVAPF
c
aHCP
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