The limiting sphere in crystallography

  • Context: Graduate 
  • Thread starter Thread starter Imperatore
  • Start date Start date
  • Tags Tags
    Crystallography Sphere
Click For Summary

Discussion Overview

The discussion revolves around the concept of the limiting sphere in crystallography, particularly in relation to Ewald's sphere. Participants explore the implications of rotating a single crystal and how these rotations relate to the observable diffraction patterns. The conversation touches on theoretical aspects and interpretations of the geometry involved in these constructs.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the meaning of "some" rotations required to obtain the limiting sphere and seeks clarification on its dependence on the number of rotations.
  • Another participant suggests that all possible rotations around all orientations of the axis will trace out the limiting sphere.
  • A different participant expresses confusion regarding the concept of rotating around a single axis versus multiple axes, referencing a source that describes the outcome of a single rotation as a toroid.
  • It is noted that a single rotation around one axis results in a toroid, while multiple rotations are necessary to achieve the limiting sphere.
  • Questions are raised about the limitations on the number of reflections based on the volume of the toroid and whether two rotations about perpendicular axes are sufficient to trace out the limiting sphere.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the number of rotations and the formation of the limiting sphere, indicating that the discussion remains unresolved with multiple competing interpretations.

Contextual Notes

There are unresolved questions regarding the assumptions about the axes of rotation and the geometric implications of these rotations on the observable diffraction patterns.

Imperatore
Messages
25
Reaction score
0
Hello there !

I am writing here, because I could not find any good explanation in the literature and on the web Going straightaway to the point, my question is connected to Ewald's sphere and so called the limiting sphere. I red that limiting sphere is such a construction that appoints the detectable reflects by rotating the single crystal (Ewald's sphere) about rotating axis, it means rotation about tangent to the Ewald's sphere. As a result of this rotation we should obtain toroid, but for more( it is said- "some") rotations about several tangent we get limiting sphere with diameter two times greater than Ewald's one. I don't see it. What does " some" mean and what does it depend on how many rotations we have to do to obtain a limiting sphere ?
 
Physics news on Phys.org
You can rotate a crystal around an arbitrary axis. If you consider all possible rotations around all possible orientations of the axis, the Ewald sphere will trace out the limiting sphere.
 
I don't understand what do you mean by "all possible rotations around all possible orientations of the axis" ? Could you describe it in more details, please ?
 
You are assuming that the crystal is rotated around only one axis. But in the construction of the limiting sphere, one considers all possible orientations of the crystal, not only the ones which arise by rotating around one fixed axis.
Consider diffraction from a powder consisting of numerous crystals with random orientation. The possible reflexes observed will be given by the ones inside the limiting sphere.
 
So a rotation about 1 axis trace out the limiting sphere ? I am asking because in one book it is written that by one rotation about the tangent to the Ewald Sphere we get toroid. I am confused now.
 
Rotation around only one axis gives you in deed only a toroid. You have to rotate around multiple axes to get the sphere.
 
here is the point,the number of possible reflection is limited to the volume of toroid after 1 rotation ?
and second question, 2 rotations about 2 perpendicular axes is enough to trace out the limiting sphere ?
 

Similar threads

Undergrad Understanding Ewald's sphere in the context of X-Ray diffraction
  • · Replies 3 ·
Replies
3
Views
6K
High School Electric Field Inside a Hollow Sphere
  • · Replies 5 ·
Replies
5
Views
1K
High School Hopf fibration, Bloch sphere and quantum rotations - interactive site
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Help with determination of crystal orientation
  • · Replies 5 ·
Replies
5
Views
2K
Which Pump Can Safely Circulate Fluid with Glass Spheres?
  • · Replies 24 ·
Replies
24
Views
4K
Undergrad What Are the Limits of the Universe According to Cosmologists?
  • · Replies 47 ·
2
Replies
47
Views
3K
Undergrad Miller indices and periodic boundary conditions
  • · Replies 0 ·
Replies
0
Views
3K
Undergrad The Einstein Clock aka Light Clock
  • · Replies 34 ·
2
Replies
34
Views
3K
Wooden sphere rolling on a double metal track
  • · Replies 97 ·
4
Replies
97
Views
6K
Undergrad Can Future Civilizations Use Dyson Spheres to Survive a Red Giant Sun?
  • · Replies 20 ·
Replies
20
Views
3K