No. Of Atoms in Zinc Unit Cell

I have been going through the question papers again. I found a rather interesting question viz "Calculate the no. of atoms in zinc unit cell?"

First some basics about Calculation of Number of Particles per Unit Cell of a Cubic Crystal System.

Keeping the following points in mind we can calculate the number of atoms in a unit cell.

• An atom at the corner is shared by eight unit cells. Hence an atom at the corner contributes 1/8 to the unit cell

• An atom at the face is a shared by two unit cells

Contribution of each atom on the face is 1/2 to the unit cell.

• An atom within the body of the unit cell is shared by no other unit cell

Contribution of each atom within the body is 1 to the unit cell.

• An atom present on the edge is shared by four unit cells

Contribution of each atom on the edge is 1/4 to the unit cell.

By applying these rules, we can calculate the number of atoms in the different cubic unit cells of monoatomic substances.

(The above concepts are taken from tutorvista.com. Please refer to them from more info)

Now I intend to answer this question in this post as I find it little cool. Zinc is having HCP structure as per Material Science and Engineering by Raghavan. A cool image showing the HCP structure is here:

    It is clear from the image that 3 atoms are inside the body of the HCP unit structure. So the count of atoms is 3 as of now.  

    It is clear from the image that the hexagonal faces have one atom each. But each such atom is shared by two HCP units equally. Hence the count of atoms comes to "4" here.

   Now, the atoms at the twelve points ( hexagonal edges on top and bottom ) make another two atoms. Hence count is 6 totally. 

    A simple explaination of the same given at answers.com is given below. Please do refer to the same.

   

    There are 6 atoms in the hcp unit cell. The hex shape has six atoms at the points that are direct translations of each other making 1 atom for the top hex and one atom for the bottom hex. That's 2. The atom in the center of the top and center of the bottom are translations giving 1 more. That's 3. Then there are 3 atoms in the middle region of each cell bringing the total to 6