# Hexagonal unit cell vs crystal system

Is the hexagonal unit cell (resulting from hexagonal closed packing) same as the unit cell of hexagonal crystal system?

The unit cell of hexagonal crystal system is described by the following sides and angles: $a=b\neq c$, $\alpha=\beta=90^\circ$, $\gamma=120^\circ$, where $a,b,c$ are the sides of unit cell and $\alpha,\beta,\gamma$ are the angles. This is the unit cell of hcp In the unit cell of hcp there are 17 atoms whereas in unit cell of hexagonal crystal system there are 8. Is this true?

I this, you are totally confuse with meaning hexagonal unit cell and hexagonal crystal system. First of all, I make you to clear about these two terms.

Hexagonal unit cell is single entity of hexagonal crystal system. It means there are a no. of repetitive hexagonal unit cells inside a hexagonal crystal system.

Yes, the diagram given in the question is of hcp i.e. hexagonal unit cell.

But, your next statement : In the unit cell of hcp there are 17 atoms whereas in unit cell of hexagonal crystal system there are 8.Is this true?

is incorrect. One thing I want to clear you that as per saying there are 17 atoms in unit cell of hcp is wrong. We can make the statement after correction is : To make a unit cell of hcp, we need 17 atoms. It means that there are 17 atoms present in unit cell hcp but to make a unit cell of hcp we require 17 atoms.

Now, we calculate the no. of atoms present inside the unit cell of hcp or we can say this as no. of effective atoms of unit cell of hcp.

Calculation of no. of effective atoms of unit cell of hcp :

No. of effective atoms of unit cell of hcp = 3 (there are a total of three atoms present inside the unit cell of hcp) * 1 (as all three atoms are in main unit cell of hcp, no part of atom is outside the unit cell of hcp) + 2 (there are two atoms present a centre of each base of hexagonal unit cell) * 1/2 ( half part of each atom is inside the main hexagonal unit cell) + 12 (there are a total of 12 atoms present at 12 corners of each base of hexagonal unit cell) * 1/6 ( one-sixth part of each atom is inside the main hexagonal unit cell) = 6 (not 8)

• Ohkay i got your point i meant 17 atoms are used to make a hcp unit cell whereas we use 8 atoms to make a hexagonal crystal unit cell.I thought that hexagonal crystal unit cell is used to make hcp but after seeing the difference in their unit cells I am not sure whether hexagonal crystal system unit cell and hcp unit cell are linked or not. – Raksh23 Jan 3 '16 at 13:44
• So basically I want to know the difference and similarities between hcp unit cell amd hexagonal crystal system unit cell amd how they are interlinked or different. – Raksh23 Jan 3 '16 at 13:46
• "we use 8 atoms to make a hexagonal crystal unit cell". This is again wrong. It is 6 not 8. Yes, both are interlinked with each other. Let's I clear u by simple example. There is a big cube in which a no. of small but of same sizes cubes are placed inside the given big cube with no vacant spaces between the small cubes. Now, a single small cube is called hexagonal unit cell and big cube is called hexagonal crystal system. I think u got my point. – solanki... Jan 3 '16 at 13:55
• I am not talking about effective atoms in a unit cell,I am just talking about number of atoms present in a unit cell.And I know the difference between hexagonal crystal system lattice and hexagonal crystal system unit cell.I want to know the difference between hexagonal closed packing unit cell and hexagonal crystal system unit cell.There are 8 atoms in hexagonal crystal unit cell and 17 in hexagonal closed packing unit cell,by saying the 8 and 17 atoms I am not mentioning the effective atoms present but the number of atoms present in each unit cell.I think you have misunderstood my question. – Raksh23 Jan 3 '16 at 14:12
• First can u tell where is written "There are 8 atoms in hexagonal crystal unit cell and 17 in hexagonal closed packing unit cell". Now, I already provide u the difference between the two. If u did not get my point, u tell me what is your thinking or opinion about their difference. So, on that I tell u my opinion. – solanki... Jan 3 '16 at 14:22

Only pink portion of blue hexagonal prism is the hexagonal unit cell that is 1/3 rd of the hexagonal prism is the unit cell. This picture probably clears your doubt.