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MATERIALS SCIENCE & ENGINEERING

MATERIALS SCIENCE & ENGINEERING. Part of. A Learner’s Guide. AN INTRODUCTORY E-BOOK. Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh.

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MATERIALS SCIENCE & ENGINEERING

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  1. MATERIALS SCIENCE & ENGINEERING Part of A Learner’s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email:anandh@iitk.ac.in, URL:home.iitk.ac.in/~anandh http://home.iitk.ac.in/~anandh/E-book.htm

  2. Hexagonal Close Packed Crystal • While SC, FCC, BCC are Lattices; HCP, DC (Diamond Cubic) are Crystals • HCP Crystal = Hexagonal Lattice+two identical spheresas 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’. IDEAL c/a

  3. Hexagonal Lattice HCP crystal = The atoms at c = ½ [e.g. (2/3, 1/3, 1/2)] are part of the motif and isnotlocated 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

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