The Meaning of R in hR10 for Pearson Symbol

  • Thread starter asdf1
  • Start date
  • Tags
    Symbol
In summary, the R in hR10 means rhombohedral lattice, while the h represents the hexagonal crystal system. The number 10 indicates the total number of atoms in the hexagonal lattice, which is made up of 3 rhombohedral lattices. This is often used as a convenient way to represent the structure of certain crystals, such as αAl2O3 (corundum). The first alphabet in the notation stands for crystal system, the second for lattice type, and the number for total number of atoms in a lattice.
  • #1
asdf1
734
0
what does the R in hR10 mean for the pearson symbol?
 
Physics news on Phys.org
  • #2
  • #3
but doesn't the h means hexagonal system? hexagonal system only has a simple lattice...
 
  • #4
asdf1 said:
but doesn't the h means hexagonal system? hexagonal system only has a simple lattice...

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?
 
Last edited by a moderator:
  • #5
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.
 
  • #6
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
asdf1 said:
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!

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 want to 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:
  • #8
ok! thanks a lot~
 

Related to The Meaning of R in hR10 for Pearson Symbol

1. What does the "R" stand for in hR10 for Pearson Symbol?

The "R" in hR10 for Pearson Symbol stands for the radius ratio. This is a measure of the relative sizes of the cations and anions in a crystal structure.

2. How is the radius ratio (R) calculated in hR10 for Pearson Symbol?

The radius ratio (R) is calculated by dividing the radius of the cation by the radius of the anion. This ratio is then compared to a set of pre-defined ranges to determine the Pearson Symbol for the crystal structure.

3. What is the significance of the radius ratio in hR10 for Pearson Symbol?

The radius ratio is significant because it helps to predict the type of crystal structure that a compound will form. Different ranges of R correspond to different types of crystal structures, such as ionic, covalent, or metallic.

4. How does the radius ratio affect the properties of a crystal structure?

The radius ratio can affect the properties of a crystal structure in several ways. For example, a smaller radius ratio often results in a more compact and dense structure, while a larger radius ratio may lead to a more open and less dense structure. The radius ratio can also influence the strength and stability of the crystal lattice.

5. Are there any limitations to using hR10 for Pearson Symbol in crystallography?

While hR10 for Pearson Symbol is a useful tool in predicting crystal structures, it has some limitations. It does not take into account factors such as covalent bonding or molecular packing, which can also play a role in determining the crystal structure. Additionally, the radius ratio alone may not be enough to accurately predict the structure, and other factors such as electronegativity and coordination numbers may need to be considered as well.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
  • Quantum Physics
Replies
1
Views
715
  • Feedback and Announcements
Replies
3
Views
366
Replies
8
Views
659
  • Quantum Physics
Replies
5
Views
781
Replies
2
Views
990
  • Special and General Relativity
Replies
13
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
996
  • Engineering and Comp Sci Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
708
Back
Top