# Pearson symbol

1. Oct 14, 2006

### asdf1

what does the R in hR10 mean for the pearson symbol?

2. Oct 23, 2006

### KenMSE

3. Oct 23, 2006

### asdf1

but doesn't the h means hexagonal system? hexagonal system only has a simple lattice...

4. Oct 23, 2006

### KenMSE

http://cst-www.nrl.navy.mil/lattice/struk/d5_1.html [Broken]

We take αAl2O3 (corundum) as an example.

In the link I posted, it says corundum has a rhombohedral primitive unit cell. And we often use the equivalent hexagonal lattice, which contains 3 primitive cells.
So I think h means hexagonal and R means rhombohedral, also the number 10 means the number of atoms in the hexagonal lattice.

Since I'm a beginner in crystallography, the former is pure my supposition!

Last edited by a moderator: May 2, 2017
5. Oct 23, 2006

### KenMSE

He said the first alphabet stands for crystal system, the second one stands for lattice type, and the number stands for the total number of atoms in a lattice.
The crystal system of αAl2O3 is hexagonal which contains 3 rhombohedral lattices.

6. Oct 24, 2006

### asdf1

But on pg. 44 in the book, "Elements of x-ray diffraction" by B.D. Cullity and S.R. Stock, the table shows that the hexagonal system can only have the simple bravais lattice type!

7. Oct 26, 2006

### KenMSE

Sorry for the late response. I was quite busy these days....

Lattice is the smallest arrangement of lattice points which is periodically repeating in 3-D space.

The unit cell of hR10 should be rhombohedral lattice. And the unit cell of hR10 is sometimes drawn to be hexagonal lattice(consist of 3 rhombohedral lattices) for convenience to represent the whole structure.

Just like hexagonal, the unit cell of hexagonal should be
http://www.wretch.cc/album/show.php?i=KenMSE&b=13&f=1643363274&p=3

And we often take the following one as an unit cell for convenience.
http://www.wretch.cc/album/show.php?i=KenMSE&b=13&f=1643363275&p=4

I just wanna express that we are not talking about dividing hexagonal into smaller lattices.
We focus on 3 rhombohedral lattices make up one hexagonal lattice.

Last edited: Oct 26, 2006
8. Oct 27, 2006

### asdf1

ok! thanks a lot~