The Meaning of R in hR10 for Pearson Symbol

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Discussion Overview

The discussion revolves around the meaning of the letter "R" in the Pearson symbol hR10, particularly in the context of crystallography and the classification of crystal structures. Participants explore the implications of the notation related to crystal systems and lattice types, using examples such as αAl2O3 (corundum).

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that "R" stands for Rhombohedral lattice, while others question this interpretation, suggesting that "h" indicates a hexagonal system.
  • One participant mentions that the hexagonal system typically has a simple lattice, which raises questions about the classification of hR10.
  • A participant provides a link to a source that describes corundum as having a rhombohedral primitive unit cell and discusses the use of an equivalent hexagonal lattice containing three primitive cells.
  • Another participant cites their instructor, who states that the first letter denotes the crystal system, the second letter indicates the lattice type, and the number represents the total number of atoms in the lattice.
  • Concerns are raised regarding a textbook reference that claims the hexagonal system can only have a simple Bravais lattice type, which contradicts some interpretations of hR10.
  • One participant elaborates that the unit cell of hR10 is often represented as a hexagonal lattice for convenience, despite being fundamentally based on rhombohedral lattices.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the Pearson symbol hR10, with no consensus reached regarding the meanings of "R" and "h" or the implications for lattice types. The discussion remains unresolved with multiple competing interpretations.

Contextual Notes

There are limitations in the discussion, including potential misunderstandings of the definitions of crystal systems and lattice types, as well as unresolved references to textbooks that may conflict with participants' interpretations.

asdf1
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what does the R in hR10 mean for the pearson symbol?
 
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but doesn't the h means hexagonal system? hexagonal system only has a simple lattice...
 
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:
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.
 
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!
 
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:
ok! thanks a lot~
 

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