The crystal structure for Ba2TiO explained with symmetries

In summary, the conversation discusses the crystallization structure of Bariumtitanate and how it can achieve such a structure. The participants also mention the use of translation and reflection symmetries to solve this problem and try to understand the structure by labeling species and considering the movement of the Ti-ion. They also raise the question of what happens when the Ti4+ is moved away from the center in a cubic crystal structure.
  • #1
Beyar
7
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: 497
Physics news on Phys.org
  • #2
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.
 
  • #3
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..
 
  • #4
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?
 

1. What is the crystal structure for Ba2TiO?

The crystal structure for Ba2TiO is a perovskite structure, which is a type of structure commonly found in many ceramic materials. It is a three-dimensional lattice made up of alternating layers of barium, titanium, and oxygen atoms.

2. How is the crystal structure for Ba2TiO explained with symmetries?

The crystal structure for Ba2TiO can be explained using the concept of crystal symmetries. This refers to the repeating patterns of atoms within the lattice, which can be described using mathematical operations called symmetry operations. These symmetries help to understand the arrangement of atoms and how they interact with each other.

3. What are the symmetries present in the crystal structure for Ba2TiO?

The crystal structure for Ba2TiO has several types of symmetries, including rotational, translational, and mirror symmetries. These symmetries are responsible for the repeating patterns and organization of atoms within the lattice.

4. How does the crystal structure for Ba2TiO affect its properties?

The crystal structure for Ba2TiO plays a significant role in determining the properties of the material. The symmetries within the structure affect factors such as density, thermal expansion, and electrical properties. Furthermore, changes in the structure, such as defects or distortions, can also alter the material's properties.

5. Why is understanding the crystal structure for Ba2TiO important?

Understanding the crystal structure for Ba2TiO is crucial for several reasons. Firstly, it allows us to predict and control the material's properties, making it useful for various applications. Additionally, knowing the symmetries in the structure can help identify any defects or impurities, which can affect the material's performance. Finally, understanding the crystal structure can also provide insight into the synthesis and processing of the material.

Similar threads

Can the volume of primitive unit cell and unit cell be different?
    • Materials and Chemical Engineering
Replies
4
Views
5K
Crystal structure/lattice resources (with examples)?
    • Science and Math Textbooks
Replies
1
Views
2K
Bravais lattices in 2 dimensions (and 3 dimensions)
    • Atomic and Condensed Matter
Replies
3
Views
4K
I The general structure of relativistic QFTs
    • Quantum Physics
3
Replies
87
Views
5K
I "Unexpected" Symmetry in Elliptical Orbit
    • Other Physics Topics
Replies
11
Views
2K
A Structure of modulo-integer matrix group GL(r,Z(n))?
    • Linear and Abstract Algebra
Replies
17
Views
4K
A Structure of Matter in Quantum Field Theory
    • Quantum Physics
3
Replies
75
Views
7K
Crystal phase transition, Diffraction peak splitting problem
    • Advanced Physics Homework Help
Replies
7
Views
5K
Admissions Can someone critique my statement of purpose? (Master's Degree in Quantum Engineering)
    • STEM Academic Advising
Replies
8
Views
2K
Group Theory to Understand Band Gap Structure of Semiconductor Oxides
    • Atomic and Condensed Matter
Replies
2
Views
4K

Hot Threads

Recent Insights

Back
Top