Question

"Describe the layers, the way the layers fit together, and the repetition of layers in hexagonal close packed versus cubic close packed. Make sure to answer ALL parts of the question."

I have no idea what type of description they are looking for or terms I should use, I would greatly appreciate an answer!

Answer 1

Cubic Close Packed (CCP- commonly called FCC crystal also) and Hexagonal Close Packed (HCP) are two common examples of close packed crystals.The term close packed crystal implies closest packed crystal (having a packing fraction of 0.74).

• Starting Point ----> Hexagonal layer
• Three positions A (the first layer atomic positions), B & C (Valleys) are shown
• The second layer (of hexagonal packing of atoms) can be positioned in valley B (or equivalently in valley C)

• The third layer can be positioned with atoms directly above the A layer (Option-1) or with atoms above the C layer (Option-2)

• ABCABC… & ABAB… are just but two amongst the infinite possibilities
• At each stage of construction we have a choice of putting an atomic layer at A, B or C position
• Possibilites include:
  • ABCAB.ABCAB.ABCAB…
  • ABCABCAB.ABCABCAB.ABCABCAB…
• Hence we can construct crystals with larger and larger unit cells.
• If we randomly put the layers we will not get a crystal in the ‘true sense’. (We can think of these as 2D crystals, which are not periodic in 3rd dimension).
• Few stages in the infinite choice tree is shown below.

• In the ABCABC… packing we start with a layer having 6-fold symmetry. Interestingly, this packing leads to a 4-fold axis at an angle of 54.74° to the original 6-fold axis and to the familiar Cubic Close Packed crystal (‘FCC’ unit cell)

• Rigid sphere-like atoms without long range interactions can arrange in any of the infinite possibilities shown before.
• Not only can we have ordered sequences, but also disordered close packed sequences (the diorder is in the way ‘A’, ‘B’ & ‘C’ appear and not within a given plane (say ‘A’)
• If Cobalt is annealed above and below 450°C a disordered sequence of ABC packing is obtained (T >450°C Co → ABCABC… packing, T <450°C Co → ABAB… packing).