Question

Please identify the cubic close-packed layers and hexagonal close-packed layers and give a brief explaination.

Answer 1

Simple cubic close packing consists of placing spheres centered on integer coordinates in Cartesian space. Arranging layers of close-packed spheres such that the spheres of every third layer overlying one another gives cubic close packing. See the example for the origin of the name, consider packing six spheres together in the shape of an equilateral triangle and place another sphere on top to create a triangular pyramid. Now create another such group of seven spheres and place the two pyramids together facing in opposite directions. A cube emerges

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 other spheres.

The hexagonal close-packed (hcp) structure has an ABABAB--- repeating arrangement and the cubic close packed (ccp) structure has an ABCABC repeting pattern, the latter is identical to fcc lattice . The hcp and ccp arrangements fill 74 % of the available space and have a coordination number 12 for each of the atom in the lattice, the number of nearest neighbours.