pearson symbol

asdf1

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

KenMSE

I found some information in Wikipedia, yet it's in German!!

http://de.wikipedia.org/wiki/Pearson-Symbol

I think R means Rhombohedral lattice.

asdf1

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

KenMSE

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

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!
What's your opinion?

KenMSE

I asked my instructor today.
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.

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!

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?...1643363274&p=3

And we often take the following one as an unit cell for convenience.
http://www.wretch.cc/album/show.php?...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.

asdf1

ok! thanks a lot~