Problem: What type of two-dimensional lattice describes the structure of a single layer of close-packed atoms?Close packing of equal-sized spheres. Close packing of equal-sized spheres. Hexagonal (left) close packing and cubic (right) close packing are equally efficient ways of packing spheres. The red and yellow dots indicate the positions of depressions between atoms.

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What type of two-dimensional lattice describes the structure of a single layer of close-packed atoms?

For hcp and ccp, the first 2 layers are the same. Top view of first layer shows spheres arranged in 5 rows with first third and fifth rows containing 4 spheres and second and fourth rows containing 5 spheres. In the second layer for both hcp and ccp all spheres sit in the depressions marked by yellow dots in the first layer. This results in a layer with 3 spheres in the first and third rows and 4 spheres in the second and fourth rows. For the third layer there are 2 options. In hcp spheres sit in depressions that lie directly over spheres of the first layer. In ccp spheres sit in depressions in the second layer. The centers of third layer spheres are offset from centers of spheres in the first 2 layers. Side view of the 3 layers of stacking shows that in hcp the centers of spheres in first and third layer are aligned and fit into the depressions of spheres in the second layer. In ccp, spheres in the first layer are offset from spheres in both the B and C layers above.

Close packing of equal-sized spheres. Close packing of equal-sized spheres. Hexagonal (left) close packing and cubic (right) close packing are equally efficient ways of packing spheres. The red and yellow dots indicate the positions of depressions between atoms.

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