1. Anandh Subramaniam & Kantesh Balani
MATERIALS SCIENCE
&
ENGINEERING
Anandh Subramaniam & Kantesh Balani
Materials Science and Engineering (MSE)
Indian Institute of Technology, Kanpur
URL: home.iitk.ac.in/~anandh
AN INTRODUCTORY E-BOOK
Part of
A Learner’s Guide

2. Hexagonal Close Packed Crystal
While SC, FCC, BCC are Lattices; HCP, DC (Diamond Cubic) are Crystals
HCP Crystal = Hexagonal Lattice + two identical spheres as motif {at (0,0,0) and (2/3, 1/3, 1/2)}  Note: there is only one type of Hexagonal Lattice  (Simple Hexagonal Lattice) (If the spheres are of different size then the crystal is not HCP)
Like CCP Crystal (CCP Crystal = FCC lattice + single sphere motif) HCP is not just close packed but is closest packed! (Packing fraction of 0.74  74% of space is filled with spheres)
Points to be noted:
HCP has a packing fraction of 74% assuming a hard sphere packing.
This packing also implies an ideal c/a ratio (see below).
As real crystals do not have an ideal c/a ratio (table below), this also implies that they are not closest packed in the ‘strictest sense’.
Metal
c/a Cd
1.886 Zn
1.856 Mg
1.624 Zr
1.590 Ti
1.588 Be
1.586
IDEAL c/a

3. = + Hexagonal Lattice HCP crystal Motif Two atom Motif
The atoms at c = ½ [e.g. (2/3, 1/3, 1/2)] are part of the motif and is not located at a lattice point +
Motif
As we have seen that HCP crystal is constructed starting with a hexgonal close packed layer, with ABABAB.. packing.
The 6-fold axis (present in a single layer) is lost on ABABAB.. packing and only a 3-fold remains.
Though 3 unit cells are often shown in diagrams- the rhombic prism (blue outline) is the unit cell.
Two atom Motif

4. Spheres at: (0,0,0), (⅔, ⅓,½)
Note: Atoms are coloured differently but are the same

5. Q: If the HCP crystal has only a 3-fold axis why does it come under the ‘Hexagonal class*’ of crystals?
A: The HCP crystal has ABAB.. packing. The C site is vacant! A 63 Screw axis passes through the C-sites (along [0001] direction). This six (6) is responsible for the crystal coming under the hexagonal crystal system (even though there is no usual 6-fold axis)
* As hexagonal word would imply 6-fold