Question

The shortest distance between the 1st and 4th layer in hcp arrangement is what?

Answer 1

Dear student
The hcp structure has three layers of atoms. In both the top and bottom layers, there are six atoms that arrange themselves in the shape of a hexagon and a seventh atom that sits in the middle of the hexagon. The middle layer has three atoms nestled in the triangular grooves of the top and bottom plane.
The hexagonal structure of alternating layers is shifted so its atoms are aligned to the gaps of the preceding layer. The atoms from one layer nest themselves in the empty space between the atoms of the adjacent layer, just like in the fcc structure. However, instead of being a cubic structure, the pattern is hexagonal.

The packing factor is 0.74, which is the same as the fcc unit cell. The atoms in a hexagonal close packed structure efficiently occupy 74% of space while 26% is empty space. Hexagonal closest packed has a coordination number of 12 and contains 6 atoms per unit cell.
Slip in hcp metals is much more limited than in body-centered cubic and face-centered cubic crystal structures. Usually, hcp crystal structures allow slip on the densely packed basal planes. The activation of other slip planes depends on various parameters, such as the c/a ratio. Since there are only three independent slip systems on the basal planes, for arbitrary plastic deformation additional slip or twin systems need to be activated. This typically requires much higher resolved shear stress and results in the brittle behavior of hcp polycrystals.
Hcp metals like cobalt and zinc are not as ductile as fcc metals. Some hcp metals are very brittle (such as magnesium) and some are very ductile (such as titanium)