What is the basis in crystalline solid structures?

  • Context: Undergrad 
  • Thread starter Thread starter u_know_who
  • Start date Start date
  • Tags Tags
    Difference
Click For Summary

Discussion Overview

The discussion revolves around the concept of "basis" in crystalline solid structures, particularly in relation to the CsCl structure and its classification compared to BCC (Body Centered Cubic) and SC (Simple Cubic) lattices. Participants explore the implications of different atomic arrangements and symmetry in defining these structures.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the definition of "basis" in the context of the CsCl structure, suggesting it can be represented as SC with two basis atoms (Cs+ and Cl-), and contrasts this with the BCC structure.
  • Another participant argues that iron atoms in BCC are symmetry equivalent under translations, while Cs and Cl in CsCl are not, indicating a fundamental difference in their structural classification.
  • Some participants assert that BCC can be viewed as a simple cubic structure with two atoms as a basis, and similarly, FCC can be seen as a simple cubic with four atoms as a basis, but emphasize that CsCl cannot be classified as BCC due to the different species occupying the lattice sites.
  • There is a mention of losing information by only considering a subgroup of the full crystallographic group when classifying structures.
  • A participant requests further elaboration on the implications of these classifications and symmetry considerations.
  • Another participant notes that a crystal must have at least two basis atoms for SCC and at least four for FCC, reinforcing the structural requirements for these classifications.
  • One participant suggests that using an enlarged unit cell for iron may overlook the symmetry equivalence of the two iron atoms in the basis.

Areas of Agreement / Disagreement

Participants express differing views on the classification of CsCl and the interpretation of BCC and SC structures. There is no consensus on whether BCC can be considered as a simple cubic structure with two atoms as a basis, and the discussion remains unresolved regarding the implications of symmetry and species occupancy in these classifications.

Contextual Notes

Participants highlight the importance of symmetry and species occupancy in defining crystalline structures, indicating that assumptions about these factors may influence the classification of lattices. There is also a suggestion that limiting the analysis to subgroups of crystallographic groups may lead to incomplete interpretations.

u_know_who
Messages
19
Reaction score
0
Hello, while studying crystalline solid structure one thing i don't understand. What does the "basis" means. Lattice seems clear but the basis comes along with problem. The problem arise in this case :

CsCl structure is not BCC (Body Centered Cubic). It is SC (Simple Cubic) with two basis.

That what says in the book.

My question is, if i consider CsCl is not BCC and it can be represented by SC with two basis (CS+ and Cl-) then why can't we imagine or consider original BCC structure as a combination of SC with two basis (two Fe atoms). But it is clearly declared that BCC is an unique Bravis lattice.

Can anyone clear me out?
 
Physics news on Phys.org
Because the iron atoms are symmetry equivalent with respect to translations while a Cs and a Cl atom are clearly not. The same holds already in molecular physics Fe_2 molecule has symmetry group \text{D}_{\infty h} while CsCl has only \text{C}_{\infty v}.
 
There is nothing wrong at all in considering BCC as simple cubic with two atoms as a basis. Similarly, FCC is a simple cubic with four atoms as a basis.

However, CsCl CANNOT be BCC because BCC sites are not occupied by the same species.

Chapter 4 in Solid State Physics by Ashcroft and Mermin gives a crystal clear explanation for these details.
 
Useful nucleus said:
There is nothing wrong at all in considering BCC as simple cubic with two atoms as a basis. Similarly, FCC is a simple cubic with four atoms as a basis.

However, CsCl CANNOT be BCC because BCC sites are not occupied by the same species.

Chapter 4 in Solid State Physics by Ashcroft and Mermin gives a crystal clear explanation for these details.
Yes, but you are considering then only a sub-group of the full crystallographic group and thus loose information.
 
Can you elaborate more on this, please?
 
The crystal must at least two basis if they are SCC. Similarly, FCC at least four basis.
 
If you treat e.g. iron using an enlarged unit cell, you resign to make use of the fact that the two iron atoms in your basis are symmetry equivalent.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
31K
Replies
3
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 19 ·
Replies
19
Views
5K
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
2
Views
2K