The crystal structure for Ba2TiO explained with symmetries

Click For Summary

Discussion Overview

The discussion focuses on the crystallization of barium titanate (Ba2TiO) and the role of symmetries in achieving its crystal structure. Participants explore the implications of translation and reflection symmetries in the context of crystallization, without providing specific equations or definitive conclusions.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses difficulty in understanding how barium titanate can crystallize in a specific structure and suggests using translation and reflection symmetries to address the problem.
  • Another participant proposes labeling the species in the provided picture and considering the effects of moving the center ion out of its position.
  • A different participant suggests that the species may have undergone translation due to temperature changes, affecting the position of the Ti-ion and resulting in a hexagon-shaped face, while noting the initial unit cell is a perovskite structure, which is typically face-centered cubic.
  • Further clarification is sought regarding the term "translation," specifically whether it refers to the movement of the Ti4+ ion to the center of an octahedron and the consequences of such a movement on the cubic crystal structure.

Areas of Agreement / Disagreement

Participants express varying interpretations of the crystallization process and the role of symmetries, indicating that multiple competing views remain without a consensus on the specifics of the mechanisms involved.

Contextual Notes

Participants do not provide specific equations or detailed definitions of the symmetries involved, leaving some assumptions and mathematical steps unresolved.

Beyar
Messages
7
Reaction score
0
Member has been warned not to delete the template.
Hello!

I would love to get help on this particular question that I find extremely difficult to answer.

-"Bariumtitanate can under a certain set of conditions crystallize in the given structure. With the help of the compounds symmetries, explain how it is possible for it to achieve such a crystallization structure.

No equations are given for the specific problem so I am leaning towards that one has to use translation/reflection symmetries etc. to be able to solve this specific problem.

The given crystallized structure (transparent octahedron shape) can be seen in the picture.
 

Attachments

  • bariumtitanate.jpg
    bariumtitanate.jpg
    15 KB · Views: 563
Physics news on Phys.org
It might help to label the species in the picture and then think about what happens if you try to move the center ion out of its place.
 
I believe that this species has undergone translation from either heat or cooling, which in turn has moved the Ti-ion (center ion) and caused the hexagon-shaped face to appear. Because from the start, the Ba2Tio species has a unit cell of a perovskite, which in turn is ideally face-centered cubic I believe. But I don't know how to translate this into "symmetry words", so to say..
 
Beyar said:
I believe that this species has undergone translation from either heat or cooling,
What do you mean by translation? Do you mean the Ti4+ has moved to the center of an octahedron?

If you start with the cubic crystal structure in the picture you attached, what happens when you move the Ti4+ away from the center?
 

Similar threads

Undergrad Time rondeau crystals, experimental observations
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Bravais lattices in 2 dimensions (and 3 dimensions)
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad The general structure of relativistic QFTs
  • · Replies 87 ·
3
Replies
87
Views
8K
Crystal phase transition, Diffraction peak splitting problem
  • · Replies 7 ·
Replies
7
Views
6K
Graduate Structure of Matter in Quantum Field Theory
  • · Replies 75 ·
3
Replies
75
Views
10K
Symmetry in crystal structures-
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Group Theory to Understand Band Gap Structure of Semiconductor Oxides
  • · Replies 1 ·
Replies
1
Views
5K
Admissions Could I please get critique on my SOP? (Experimental Biophysics)
  • · Replies 9 ·
Replies
9
Views
2K
Admissions Statement of purpose critique request (high-energy theory PhD application)
  • · Replies 7 ·
Replies
7
Views
4K
Admissions Can someone critique my statement of purpose? (Master's Degree in Quantum Engineering)
  • · Replies 8 ·
Replies
8
Views
5K